Modelling long-memory volatilities with leverage effect A-LMSV versus FIEGARCH

Computational Statistics &Data Analysis 52(2008)2846–2862

https://www.sodocs.net/doc/518703423.html,/locate/csda

Modelling long-memory volatilities with leverage effect:

A-LMSV versus FIEGARCH

Esther Ruiz ?,Helena Veiga

Departamento de Estadística,Universidad Carlos III de Madrid,28903Getafe (Madrid),Spain

Available online 7October 2007

Abstract

A new stochastic volatility model,called A-LMSV ,is proposed to cope simultaneously with leverage effect and long-memory in volatility.Its statistical properties are derived and compared with the properties of the FIEGARCH model.It is shown that the dependence of the autocorrelations of squares on the parameters measuring the asymmetry and the persistence is different in both models.The kurtosis and autocorrelations of squares do not depend on the asymmetry in the A-LMSV model while they increase with the asymmetry in the FIEGARCH model.Furthermore,the autocorrelations of squares increase with the persistence in the A-LMSV model and decrease in the FIEGARCH model.On the other hand,if the correlation between returns and future volatilities is negative,the autocorrelations of absolute returns increase with the magnitude of the asymmetry in the FIEGARCH model while they decrease in the A-LMSV model.Finally,the cross-correlations between squares and original observations are,in general,larger in absolute value in the FIEGARCH model than in the A-LMSV model.The results are illustrated by ?tting both models to represent the dynamic evolution of volatilities of daily returns of the S&P500and DAX indexes.?2007Elsevier B.V .All rights reserved.

Keywords:Autocorrelations of squares and of absolute values;Conditional heteroscedasticity;Kurtosis;EMM estimator

1.Introduction

One of the main empirical characteristics of ?nancial returns is the dynamic evolution of their volatilities.There are two important properties that characterized this evolution.First of all,power transformations of absolute returns have signi?cant autocorrelations which decay toward zero slower than in a short-memory process.Many authors have argued that this pattern of the sample autocorrelations suggests that the volatilities of ?nancial returns can be represented by long-memory processes;see Ding et al.(1993)and Lobato and Savin (1998)among many others.The second property that characterizes volatilities is their asymmetric response to positive and negative returns.This property,known as leverage effect,was ?rst described by Black (1976).

There are two main families of econometric models proposed to represent the dynamic evolution of volatilities.The ARCH-type models are mainly characterized by specifying the volatility as a function of powers of past absolute returns and,consequently,the volatility can be observed one-step ahead.On the other hand,stochastic volatility (SV)models specify the volatility as a latent variable that is not directly observable.There have been several proposals of ARCH-type models that represent simultaneously leverage effect and long-memory.For example,Hwang (2001)generalizes the

?Corresponding author.Tel.:+34916249851;fax:+34916249849.

E-mail address:ortega@est-econ.uc3m.es (E.Ruiz).

0167-9473/$-see front matter ?2007Elsevier B.V .All rights reserved.doi:10.1016/j.csda.2007.09.031

E.Ruiz,H.Veiga /Computational Statistics &Data Analysis 52(2008)2846–28622847

long-memory FIGARCH model of Baillie et al.(1996)to represent the leverage effect.However,Davidson (2004)shows that the FIGARCH model has the unpleasant property that the persistence of shocks to volatility decreases as the long-memory parameter increases.A similar conclusion appears in Zaffaroni (2004)who shows that the FIGARCH model cannot generate autocorrelations of squares with long-memory.Finally,Ruiz and Pérez (2003)showed that the model proposed by Hwang (2001)has identi?cation problems.Consequently,in this paper,we focus on the fractionally integrated EGARCH (FIEGARCH)model proposed by Bollerslev and Mikkelsen (1996)which extends the asymmetric EGARCH model of Nelson (1991)to long-memory.Following the arguments of He et al.(2002)for the short-memory EGARCH model,we derive the kurtosis,autocorrelations of squares and absolute observations and the cross-correlations between returns and powers of absolute returns of the FIEGARCH (1,d,0)model with Gaussian errors.

Alternatively,in the context of SV models,Harvey (1998)and Breidt et al.(1998)have independently proposed long-memory stochastic volatility (LMSV)models in which the underlying log-volatility is modelled as an ARFIMA process.On the other hand,Harvey and Shephard (1996)propose to model the leverage effect of the short-memory SV model by introducing correlation between the noises of the level and volatility equations.Recently,Yu et al.(2006)have also proposed an extension of this asymmetric SV model in which a Box–Cox transformation of the volatility follows an AR(1)process.This model encompasses several popular SV models as special cases.However,the statistical properties of the new model are still unknown.So et al.(2002)have proposed a threshold SV model which is also able to represent the leverage effect.In this paper,we focus on the proposal of Harvey and Shephard (1996)and propose the Asymmetric LMSV (A-LMSV)model that generalizes the LMSV model to cope with leverage effect.Assuming that the log-volatility is an ARFIMA (1,d,0)model and Gaussianity of the errors,we derive the statistical properties of the new model and compare them with the properties of the FIEGARCH model.We show that both models explain in different ways the kurtosis and correlations of absolute and squared returns.However,the cross-correlations between returns and powers of absolute returns behave in a similar fashion.

The rest of the paper is organized as follows.The description of the statistical properties of the A-LMSV (1,d,0)model is done in Section 2.In Section 3,we derive the properties of the FIEGARCH (1,d,0)model and compare them with the properties of the A-LMSV model.Section 4contains an empirical illustration by ?tting both models to daily ?nancial returns of the S&P500and the DAX indexes.Section 5concludes the paper.2.Asymmetric LMSV models

The LMSV model,proposed independently by Harvey (1998)and Breidt et al.(1998),extends the stochastic volatility model of Taylor (1982)by assuming that the volatility follows a weakly stationary fractional integrated process.Therefore,the LMSV model captures the long-memory property often observed in the powers of absolute returns.In this section,we extend the LMSV model to represent the asymmetric response of volatility to positive and negative returns.Following Taylor (1994)and Harvey and Shephard (1996),this asymmetry is introduced by allowing the disturbances of the level and volatility equations to be correlated.In this paper,we consider that the log-volatility is speci?ed as an ARFIMA (1,d,0)process.In this case,the A-LMSV model is given by

y t = ? t t ,

(1? L)(1?L)d log 2t = t ,(1)where y t is the return at time t and t is its volatility.The parameter ?is a scale parameter and L is the lag operator such that Lx t =x t ?1.The disturbances ( t , t +1) are assumed to have the following bivariate normal distribution:

t t +1 ～NID 00 , 1

2 ,(2)where ,the correlation between t and t +1,induces correlation between the returns,y t ,and the variations of the

volatility one period ahead, t +1? t .The dynamic properties of the symmetric LMSV model are described by Ghysels et al.(1996).In particular,the stationarity of y t depends on the stationarity of the log-volatility,h t =log 2t .Therefore,if | |<1and d <0.5,y t is stationary.In this case,they show that the variance and kurtosis of y t are given by

Var (y t )= 2

?exp 2h 2

(3)

2848 E.Ruiz,H.Veiga/Computational Statistics&Data Analysis52(2008)2846–2862 and

y=E(y 4 t )

E(y2t)2

=3exp( 2h),(4)

respectively,where 2h= 2 (1?2d)

[ (1?d)]2F(1,1+d;1?d; )

(1+ )

, (·)is the gamma function and F(·,·;·;·)is the hypergeometric

function;see Hosking(1981)for the expressions of the variance and autocorrelation function(acf)of an ARFIMA process.From(4),it can be shown that,given 2 and ,the kurtosis of returns, y,increases with d,the parameter of fractional integration.On the other hand,introducing correlation between t and t+1does not change the marginal moments of y t with respect to the symmetric model with =0;see Harvey and Shephard(1996)for the model with d=0.Therefore,expressions(3)and(4)are also the variance and kurtosis of y t in the A-LMSV model.

Furthermore,although the series of returns,y t,is a martingale difference and,consequently a serially uncorrelated sequence,it is not an independent sequence.Note that if the asymmetry is introduced as in Jacquier et al.(2004)by a correlation between t and t,the series y t is not a martingale difference;see Harvey and Shephard(1996)and Yu(2004).There are nonlinear transformations of returns,as for example,powers of absolute returns,which are correlated.After some very tedious algebra,and assuming that t and t are Gaussian and mutually independent,we derive the following expression of the acf of|y t|c for c=1and2:

c(k)=exp

c2

4

2h h(k)

1+( )c

4

c

(c?2)/2

c k

?1

c exp

c2

4

2h

?1

,k 1,(5)

where h(k)is the acf of the log-volatility given by

h(k)=

k?1

i=0

d+i

1?d+i

F(1,d+k;1?d+k; )+F(1,d?k;1?d?k; )?1

(1? )F(1,1+d;1?d; )

,

c=E(| t|2c)

{E| t|c}2= (c+0.5) (0.5)

[ (0.5(c+1)]2

which takes values 1= /2and 2=3,respectively.Finally,if d>0, k=

k?1

i=0

(i+d)

(i+1) (d)

k?i?1.Note that when =0,expression(5)becomes the acf of|y t|c derived by Harvey(1998)

for symmetric LMSV models.The expression of the autocorrelations of|y t|c in(5)is also valid for non-Normal dis-tributions of the errors t as far as =0;see Ghysels et al.(1996).The only difference is that the value of c depends on this distribution.On the other hand,when d=0, k= k?1and expression(5)becomes the acf of a short-memory SV model with leverage effect.Taylor(1994)have obtained this expression for c=2.

The acf in expression(5)depends on the parameters d, and 2 that affect both the variance and the acf of the underlying log-volatility process, 2h and h(k),respectively.The autocorrelations also depend on the correlation between t and t+1, ,and on the power parameter,c.For?xed values of the parameters d, 2 and ,the effect of the asymmetry, ,on the autocorrelation of order k of y2t is measured by( k)2.First of all note that this effect is the same regardless of the sign of .Furthermore,in empirical applications,the variance of the log-volatility process and the constant k are typically very small and consequently,this effect is also rather small.Therefore,the autocorrelations of squared returns generated by symmetric and asymmetric LMSV processes are very similar;see Carnero et al.(2004) for a similar result in the context of short-memory ARSV models.As an illustration,the right column of Fig.1plots the acfs of squared returns,for the following four A-LMSV models:{ =0,d=0.49, 2 =0.05},{ =0,d=0.49, 2 =0.1},{ =0.5,d=0.49, 2 =0.1}and{ =0.98,d=0, 2 =0.05}.For each of these models,we consider =0,?0.2,?0.5and?0.8.These models have been chosen to resemble the parameter values often estimated when the LMSV model is?tted to time series of?nancial returns;see,for example,Pérez and Ruiz(2001).Fig.1shows that,for the four models considered,the acfs of squares are nearly the same regardless of the value of the asymmetry parameter .

E.Ruiz,H.Veiga /Computational Statistics &Data Analysis 52(2008)2846–28622849

0.00

0.050.100.150.200.250.300.350.00

0.050.100.150.200.250.300.350.00

0.050.100.150.200.250.300.3510

20

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(phi=0, d=0.49, vareta=0.05)

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0.050.100.150.200.250.300.3510203040

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(phi=0, d=0.49, vareta=0.1)0.000.050.100.150.200.250.300.3510203040

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0.00

0.050.100.150.200.250.300.3510

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(phi=0.98, d=0, vareta=0.05)0.00

0.050.100.150.200.250.300.3510203040

50

(phi=0.98, d=0, vareta=0.05)

Fig.1.Autocorrelations of |y t |(left column)and y 2t (right column)in four A-LMSV models with different values of the asymmetric parameter:continuous ( =0),dotted ( =?0.2),dashed ( =?0.5)and dotted–dashed ( =?0.8).

We consider now the effect of on the autocorrelation of order k of absolute observations which is measured by 0.627 k .Note that,in this case,a negative correlation between t and t +1decreases the autocorrelations.Depending on the parameters that govern the dynamic evolution of the volatility,the autocorrelations of absolute returns can even be

2850 E.Ruiz,H.Veiga /Computational Statistics &Data Analysis 52(2008)2846–2862

-0.1

-0.1

-0.1

-0.1

0.00.10.20.3-0.8-0.6-0.4-0.20.0

0.20.40.6

0.8

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0.60.8

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0.20.40.6

0.8

-0.8-0.6-0.4-0.20.00.20.4

0.6

0.8

delta

r h o 1(1)-r h o 2(1)

(phi=0, d=0.49, vareta=0.05)

0.00.10.2

0.3delta

r h o 1(1)-r h o 2(1)

(phi=0, d=0.49, v areta=0.1)

0.00.10.2

0.3delta

r h o 1(1)-r h o 2(1)

(phi=0.5, d=0.49, vareta=0.1)

0.00.10.2

0.3delta

r h o 1(1)-r h o 2(1)

(phi=0.98, d=0, v areta=0.05)

Fig.2.Differences between the ?rst order autocorrelations of absolute and squared returns as a function of the correlation between t and t +1in four A-LMSV models.

negative if is large enough.The magnitude of this effect is larger than the corresponding effect on the autocorrelations of squared returns if | k |<0.627.Even more,the combination of negative correlations between t and t +1and long-memory generates the possibility of negative autocorrelations in absolute observations.As an illustration,the left column of Fig.1plots the acf of absolute returns for the same models considered above.We observe that,in general,the autocorrelations decay toward zero monotonically.However,in the ?rst model,the autocorrelations increase for the ?rst few lags and then decay toward zero.

A property that has often interested researches dealing with models for second order moments,is the so-called Taylor effect that states that the autocorrelations of absolute returns are larger than the autocorrelations of squares.In the context of symmetric and stationary ARSV models,Mora-Galán et al.(2004)show that,if the persistence,measured by ,is large,the autocorrelations of powers of absolute observations are maximized when the power is close to one.They also show that the Taylor effect is reinforced when t has a leptokurtic distribution.The results previously described suggest that,if the correlation between the errors is negative,the Taylor effect may disappear.This result is illustrated in Fig.2which plots the differences 1(1)? 2(1)as a function of for the same four models considered before.The ?rst result that emerges from Fig.2is that there is an approximately linear positive relationship between and 1(1)? 2(1).When is negative and large enough in magnitude,the autocorrelations of squares could be larger than the autocorrelations of absolute returns.

As we mentioned in the Introduction,real time series of ?nancial returns are often characterized by signi?cant autocorrelations of powers of absolute returns that decay very slowly toward zero and by the asymmetric response of volatility to positive and negative returns.On top of this,these series usually have excess kurtosis and the autocorre-lations of squares are rather small in magnitude.We now analyze whether the proposed A-LMSV is able to explain simultaneously the excess kurtosis and small autocorrelations of squares.We have seen before that the presence of leverage effect does not have any effect on the kurtosis and only very marginal effects on the autocorrelations of squares.Therefore,whether the parameter is zero or not is not going to change the ability of the A-LMSV model to

E.Ruiz,H.Veiga /Computational Statistics &Data Analysis 52(2008)2846–28622851

00.10.20.30.4ρ2(1)

Fig.3.Relationship between kurtosis,?rst order autocorrelation of squared observations, 2(1)and the ?rst order autocorrelation of the underlying volatility h (1),for A-LMSV models with =0.

represent simultaneously both effects.However,we want to analyze how the presence of long-memory may change the relationship between kurtosis, y ,and 2(1)which is given by

2(1)= k y

3

h (1)(1+( )2)?1

k y ?1.(6)

Fig.3plots the relationship between y and 2(1)as a function of the autocorrelation of order 1of the underlying log-volatility, h (1),when =0.Given that neither the kurtosis nor the autocorrelations of squares depend on the asymmetry parameter,the results for other values of are similar to the ones plotted in Fig.3.Note that h (1)depends on and d .For ?xed d , h (1)is a non-monotonous function of .On the other hand,when is ?xed,the autocorrelations of the log-volatility increase with the long-memory parameter,d .Therefore,when interpreting Fig.3,if we assume that is ?xed,larger values of h (1)are identi?ed with larger values of d .We can observe that for a given kurtosis, y ,the autocorrelation of order one of squares increases with the long-memory parameter,d .However,the rate of growth of 2(1)is very small for low values of the kurtosis and increases with it.On the other hand,given 2(1),the kurtosis decreases as d increases.Fig.3also illustrates that there is a wide range of combinations of the parameters that govern the dynamic evolution of the underlying volatilities, and d able to generate series with large kurtosis and small autocorrelations of squares as the ones usually observed in real time series.

The asymmetric response of volatility to positive and negative returns is re?ected in the cross-correlations between y t and |y t +k |c for c =1and 2.If the distribution of y t is symmetric,the main difference between heteroscedastic series with and without leverage effect is that,in the latter case the correlations between returns and future powers of absolute returns is zero while in the former they are different from zero.Consequently,another instrument for the identi?cation of the leverage effect is the correlation between returns and future absolute returns to the power c .We consider the more interesting cases from the empirical point of view of c =1and 2.In these cases,the covariances are given by

Cov (y t ,|y t +k |c )=?????????0.5 2? 2

k exp 2h 4( h (k)+1) ,c =1, 3? k exp 2h 8(4 h (k)+5) ,c =2.(7)Note that the expression of the covariance between returns and squared returns has been derived by Taylor (2005)

in the short-memory case.However,his value of Cov (y t ,|y t +k |2)is twice the value obtained from (7)with c =2and

2852 E.Ruiz,H.Veiga /Computational Statistics &Data Analysis 52(2008)2846–2862

d =0.On th

e other hand,the variance o

f |y t |c ,derived by Harvey (1998)for the symmetric LMSV model with Gaussian errors,is given by

Var (|y t |c )= 2c ?2c exp c 2 2h 2 ????

? c +12 12 ????? c 2+12

12 ????2?

????.(8)Given that the asymmetry does not change the marginal moments of y t and given the expression of the variance of y t

in (3),it is possible to derive the following expression for the correlation between y t and |y t +k |c

Corr (y t ,|y t +k |c )=

???????????????????0.5 k exp {0.25 2h h (k)}

exp 2h 8 2

exp {0.25 2h }?1,c =1, k exp {0.5 2h h (k)}exp 2h 8 3exp { 2h }?1,c =2.(9)From (9),it is clear that the correlations between y t and |y t +k |c have the same sign as and that their absolute values

increase with the absolute value of .As an illustration,Fig.4plots these correlations for the same models considered above.It is possible to observe that the correlations are only slightly larger in absolute value between observations and future squares than between observations and future absolute values in the model with =0.5,d =0.49and 2 =0.1.In all the other models,they are very similar.It is also interesting to observe that the cross-correlations plotted in Fig.4show the same pattern as the corresponding autocorrelations in the sense that they decay toward zero hyperbolically when the volatility has long-memory while the decay is exponential in the short-memory model.3.Properties of the FIEGARCH model

The FIEGARCH model was proposed by Bollerslev and Mikkelsen (1996).In its simplest form,the FIEGARCH (1,d,0)model is given by

y t = t t ,

(1? L)(1?L)d log 2t = +g( t ?1),

(10)where g( t )= (| t |? 2

)+ t and t is a Gaussian white noise with variance 1.The parameter measures the leverage effect while,as before,d is the long-memory parameter.When d =0,the short-memory EGARCH model of Nelson (1991)is obtained.Note that the main difference between the A-LMSV model and the FIEGARCH model is the way the noise is de?ned in the log-volatility equation;see Zaffaroni (2005)who proposes an exponential speci?-cation of the volatility that encompasses both models.The FIEGARCH model is stationary if | |<1and |d |<0.5.He et al.(2002)have derived the kurtosis and autocorrelations of absolute and squared observations for the short-memory EGARCH model,i.e.model (10)with d =0.Following their arguments,we have obtained the kurtosis and acf of |y t |c for c =1and 2in the long-memory FIEGARCH model.In particular,if the stationarity conditions are satis?ed,the kurtosis is given by

k y =3 ∞

j =1E {exp [2 j g ]}

∞

j =1E( j g) 2,(11)where for notational simplicity g =g( t )and j is de?ned as in (5).Furthermore,if the errors are normally distributed,the expectations involved in equation (11)can be evaluated using the following result due to Nelson (1991):

E [exp (bg)]={ (bc 1)exp {0.5b 2c 21

}+ (bc 2)exp {0.5b 2c 22}}exp {?b (2/ )1/2},

E.Ruiz,H.Veiga /Computational Statistics &Data Analysis 52(2008)2846–28622853

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0.0010

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30

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1020304050

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40

50

(phi=0.98, d=0, vareta=0.05)1020304050

(phi=0.98, d=0, vareta=0.05)

Fig.4.Correlations between y t and |y t +k |(left column)and y t and y 2t +k (right column)in four A-LMSV models with different values of :continuous ( =?0.2),dotted ( =?0.5)and dashed ( =?0.8).

where c 1= + and c 2= ? .Although it is not evident from expression (11),given the parameters , and d ,the kurtosis of y t increases as the magnitude of the asymmetry parameter increases.This is an important difference with respect to the A-LMSV model in which we have seen that the kurtosis does not depend on the leverage effect.

2854 E.Ruiz,H.Veiga/Computational Statistics&Data Analysis52(2008)2846–2862 On the other hand,the acf of|y t|c in the FIEGARCH model is given by

c(k)=E[| t |c exp(0.5c k g)]

c ∞

j=1

E[exp(c j g)]?P3

2

(2?c)/2

P1P2?P3

,(12)

where P1= k

j=1

E[exp(0.5c j g)],P2=

∞

j=1

E[exp(0.5c( j+1+k+ j))g]and P3=

∞

j=1

(E[exp(0.5c j g)])2

and k is de?ned as in A-LMSV model.Furthermore,He et al.(2002)show that

E[| t|c exp(bg)]=(2 )?1/2 (c+1)exp{?b (2 )1/2}D(?(c+1))(?b( + ))

+exp{?b2 }D(?(c+1))(?b( ? )),

where D(q)is the parabolic cylinder function and (·)is the standard normal cumulative function.Nelson(1991) derived this expression for squares,i.e.c=2.First,note that the autocorrelations of squares and absolute returns are symmetric with respect to the asymmetry parameter, .

As an illustration,Fig.5plots the acf of absolute and squared returns for the following FIEGARCH models: { =0,d=0.49, =0.2},{ =0.5,d=0.49, =0.1},{ =0.5,d=0.49, =0.2}and{ =0.5,d=0, =0.2}with the asymmetry parameter =0,?0.1,?0.2,and?0.3.These models have been chosen to resemble the parameter values often estimated when the FIEGARCH model is?tted to real time series;see,for example,Bollerslev and Mikkelsen (1996,1999).Comparing the autocorrelations of the FIEGARCH model with the corresponding autocorrelations of the A-LMSV model plotted in Fig.1,we can observe that while in the latter model,the autocorrelations of squares are nearly the same regardless of the asymmetry parameter,they may be different in the FIEGARCH model.In general, the?rst order autocorrelations of squares increase with the magnitude of .Furthermore,note that,in the considered models,the autocorrelations of squares and absolute observations are rather similar between them when the asymmetry parameter is small.However,the Taylor effect is reinforced by the leverage effect in the models with both parameters and d different from zero while it seems that it is not a property of the short-memory model and of the model with =0.To have a clearer picture of this phenomena,Fig.6plots the differences between the?rst order autocorrelations of absolute and squared returns for the same four FIEGARCH models described above.This?gure con?rms the suspicion that when =0or d=0there is not Taylor effect.On the other hand,in the models with both and d different from zero,it is present if is relatively large in absolute https://www.sodocs.net/doc/518703423.html,paring Figs.6and2,we can observe that there are clear differences with respect to the Taylor effect in the A-LMSV and FIEGARCH models.When looking at FIEGARCH models,the differences between the?rst order autocorrelations of absolute values and those of squares are not an increasing function of the asymmetry parameter.On the other hand,there are particular speci?cations of the FIEGARCH model in which the Taylor effect is not a property unless the magnitude of the asymmetry parameter is very large.

Given that it is rather dif?cult to?nd an analytical expression relating the kurtosis and the autocorrelation of order one of squared observations,Fig.7plots this relationship for different FIEGARCH models.This?gure illustrates that as the kurtosis increases(the asymmetry increases),the autocorrelation of order one of squares also increases.On the other hand,given , and ,larger values of the long-memory parameter,d,imply smaller autocorrelations of squares except when the kurtosis(the asymmetry)is very large.Carnero et al.(2004)have also shown for the short-memory EGARCH model that,given the kurtosis,the autocorrelation of order one of squared observations decreases with the persistence parameter, .On the other hand,for?xed ,d and ,the autocorrelations of squares are larger the larger is the ARCH effect,i.e. .Once more,this relationship can be reverse for large values of .In any case,it is important to point out that the effect of d and on 2(1)is relatively weak while the effect of the asymmetry parameter, ,is rather strong.

Comparing now the results illustrated in Fig.7with the corresponding results for the A-LMSV model illustrated in Fig.3,we can observe that in both models,the autocorrelations of order1of squares increase with the kurtosis. However,while in the A-LMSV model,the kurtosis is the same regardless the asymmetry parameter,in the FIEGARCH model,the kurtosis depends on the asymmetry.Therefore,given the parameters that measure the evolution of volatility, in the FIEGARCH model and 2 in the A-LMSV models,respectively,its persistence, ,and its memory,d,the kurtosis and the autocorrelations of squares increase with the leverage effect in the FIEGARCH model while they are approximately constant in the A-LMSV model.On the other hand,for?xed and 2 ,the autocorrelations of squares

E.Ruiz,H.Veiga /Computational Statistics &Data Analysis 52(2008)2846–28622855

0.00

0.050.100.150.200.250.300.350.00

0.050.100.150.200.250.300.350.00

0.050.100.150.200.250.300.3510

20

30

40

50

(phi=0, d=0.49, alpha=0.2)

0.00

0.050.100.150.200.250.300.351020304050

(phi=0, d=0.49, alpha=0.2)

10

20

30

40

50

(phi=0.5, d=0.49, alpha=0.1)

0.00

0.050.100.150.200.250.300.351020304050

(phi=0.5, d=0.49, alpha=0.1)

0.00

0.050.100.150.200.250.300.3510

20

30

40

50

(phi=0.5, d=0.49, alpha=0.2)

1020304050

(phi=0.5, d=0.49, alpha=0.2)

0.00

0.050.100.150.200.250.300.3510

20

30

40

50

(phi=0.5, d=0, alpha=0.2)

0.00

0.050.100.150.200.250.300.351020304050

(phi=0.5, d=0, alpha=0.2)

Fig.5.Auto correlations of |y t |(left column)and y 2t (right column)in four FIEGARCH models with different values of :continuous ( =0),dotted ( =?0.1),dashed ( =?0.2)and dotted–dashed ( =?0.3).

increase with and d in the A-LMSV model while they decrease in the FIEGARCH model.In both models it is possible to observe that the variations in the values of 2(1)are small for moderate values of the kurtosis while they are large when the kurtosis is large.

2856 E.Ruiz,H.Veiga /Computational Statistics &Data Analysis 52(2008)2846–2862

-0.04

-0.020.000.020.04-0.04

-0.020.000.020.04-0.04

-0.020.000.020.04-0.04

-0.020.000.020.04-0.4-0.3-0.2-0.4-0.3-0.2-0.10.00.10.20.3

0.4

delta

r h o 1(1)-r h o 2(1)

(phi=0, d=0.49, alpha=0.2)

-0.10.00.10.20.3

0.4

-0.4-0.3-0.2-0.4-0.3-0.2-0.10.00.10.20.3

0.4

-0.10.00.10.20.3

0.4

delta

r h o 1(1)-r h o 2(1)

(phi=0.5, d=0.49, alpha=0.1)

delta

r h o 1(1)-r h o 2(1)

(phi=0.5, d=0.49, alpha=0.2)

delta

r h o 1(1)-r h o 2(1)

(phi=0.5, d=0, alpha=0.2)

Fig.6.Differences between the ?rst order autocorrelations of absolute and squared returns as a function of in FIEGARCH models.

2

4

6

81012

00.1

0.2

0.30.4

0.5

k y

ρ2(1)

Fig.7.Relationship between kurtosis and ?rst order autocorrelation of squared observations for different values of the persistence for FIEGARCH (1,d,0)models.

As in the A-LMSV model,we have also derived the cross-correlations between returns and powers of absolute returns.In particular,

Corr (y t ,|y t +k |c )

=E [exp (0.5c k g( t )) t ] k ?1j =1exp [E [0.5c j g ]] ∞

j =1E [exp (0.5(c j +k + j ))g ] c ∞j =1E [exp (c j g)]? ∞j =1E [exp (0.5c j g)] c 1/2 ∞

j =1E [exp ( j g)]

1/2.(13)

E.Ruiz,H.Veiga /Computational Statistics &Data Analysis 52(2008)2846–28622857

-0.25

-0.20-0.15-0.10-0.050.00-0.25

-0.20-0.15-0.10-0.050.00-0.25

-0.20-0.15-0.10-0.050.00-0.25

-0.20-0.15-0.10-0.050.00-0.25

-0.20-0.15-0.10-0.050.00-0.25-0.20-0.15-0.10-0.050.00-0.25

-0.20-0.15-0.10-0.050.00-0.25

-0.20-0.15-0.10-0.050.0010

20

30

40

50

(phi=0, d=0.49, alpha=0.2)

1020304050

(phi=0, d=0.49, alpha=0.1)

10

20

30

40

50

(phi=0.5, d=0.49, alpha=0.1)1020304050

(phi=0.5, d=0.49, alpha=0.1)

10

20

30

40

50

(phi=0.5, d=0.49, alpha=0.2)1020304050

(phi=0.5, d=0.49, alpha=0.2)

10

20

30

40

50

(phi=0.5, d=0, alpha=0.2)1020304050

(phi=0.5, d=0, alpha=0.2)

Fig.8.Correlations between y t and |y t +k |(left column)and y t and y 2t +k (right column)in four FIEGARCH models with different values of :continuous ( =?0.1),dotted ( =?0.2)and dashed ( =?0.3).

The cross-correlations in expression (13)are symmetric with respect to the parameter .Once more,we illustrate their shape by plotting them in Fig.8for the same four models considered before and c =1,2.As in the A-LMSV model,we can observe that the cross-correlations between y t and y 2t +k are larger in magnitude than between y t and |y t +k |.Furthermore,comparing these cross-correlations with the ones plotted in Fig.4for the A-LMSV models,it

2858 E.Ruiz,H.Veiga/Computational Statistics&Data Analysis52(2008)2846–2862

is possible to observe that,in general,the FIEGARCH model generates cross-correlations which are larger for small

lags and then decay toward zero very quickly.Note that we have chosen the FIEGARCH models so that the?rst

order autocorrelations of squares and absolute values are similar.Obviously,one can chose to?t the?rst order cross-

correlations in both models and,in this case,the autocorrelations of squares and absolute values of the FIEGARCH

model will be,in general,larger than those of the A-LMSV model.

4.Empirical illustration

In this section we evaluate the performance of the A-LMSV(1,d,0)and FIEGARCH(1,d,0)models in capturing

the empirical features of?nancial data.For this purpose,we analyze daily close prices of the S&P500and DAX

composite indexes observed from November26,1990to September6,2006,respectively.The sample size is3980

observations in each case.The series of returns have been computed as usual,y t=100(log p t?log p t?1),where p t denotes the price at time t.

The series of S&P500prices and returns have been plotted in Fig.9.The returns have a kurtosis of4.053and

show volatility clustering.The presence of conditional heteroscedasticity can also be observed in the correlograms

of the absolute and squared observations also plotted in Fig.9.In both correlograms,the sample autocorrelations are

signi?cant and very persistent.The observed decay of the correlations is not compatible with the expected decay if

squared and absolute returns could be represented by a short-memory model.In consequence,it seems that the volatility

of the S&P500returns should be approximated by a conditional heteroscedasticity model with long-memory.Fig.9

also plots the Corr(y t,|y t+k|)and Corr(y t,y2t+k).In both cases,the cross-correlations are similar in magnitude,being negative and signi?cant.Therefore,it seems that a model with leverage effect could be adequate.We?t the A-LMSV and the FIEGARCH models to the series of S&P500returns.

The A-LMSV model has been estimated by the EMM estimator;see Gallant et al.(1997).Alternatively,Zaffaroni

(2005)has proposed a Whittle estimator of A-LMSV model.However,the parameters ?and are not identi?ed by

the Whittle estimator that is based on the linearizing transformation log(y2t).Furthermore,it is not obvious how to

obtain expressions of the asymptotic variances of the estimator using the expressions given by Zaffaroni(2005).On

the other hand,there are several estimators proposed to estimate separately asymmetric SV models or long-memory

SV models;see,for example,Omori and Watanabe(2007)and Arteche(2006),respectively,for some very recent

references.However,none of these estimators have been considered for the estimation of models with the simultaneous

presence of long-memory and leverage effect.Consequently,we implement the EMM estimator with a score generator

which is a GARCH model with fully nonlinear nonparametric error density.The estimated model is given by

(1?0.442

(0.141)L)(1?L)

0.541

(0.007)log 2t= t,(14)

where the scale parameter estimate is ?=0.801,the variance of the log-volatility noise estimate is 2 =0.048and the correlation between the level and volatility noises estimate is =?0.75.

The FIEGARCH model has been estimated by QML using the GARCH package version4.0of Laurent and Peters (2005)with the following results:

(1?0.538

(0.145)L)(1?L)

0.538

(0.053)log 2t=0.453

(0.215)

+0.143

(0.029)

| t?1|?

2

?0.108

(0.028)

t?1,(15)

where the quantities in parenthesis are estimated standard deviations.

Note that both models have estimates of the long-memory parameter larger than0.5implying that the series of S&P500returns is not stationary.Similar results have been found by other authors analyzing different sample periods; see,for example,Bollerslev and Mikkelsen(1996)and Granger and Hyung(2004).In these circumstances,the moments implied by the estimated models are not de?ned.Therefore,it is not possible to compare the sample moments of the S&P500returns with the moments implied by each of the estimated models.

The DAX prices and returns have been plotted in Fig.10.To avoid the pernicious effect of large extreme observations on the sample moments and estimates of the parameters that govern the volatility,all the observations larger than7 conditional standard deviations have been corrected by substituting them by their estimated conditional standard deviation;see Carnero et al.(2007)for the effects of outliers on the identi?cation and estimation of conditional

E.Ruiz,H.Veiga /Computational Statistics &Data Analysis 52(2008)2846–28622859

400800120016001000

2000

3000

-8

-40481000

2000

3000

-0.1

0.00.10.20.30.410

20

30

40

50

-0.1

0.00.10.20.30.410

20

30

40

50

-0.15

-0.10-0.050.000.0510

20

30

40

50

-0.15

-0.10-0.050.000.0510

20

30

40

50

Fig.9.(a)Observations of daily S&P500prices and (b)returns together with (c)sample autocorrelations of absolute returns and (d)squared returns and (e)cross-correlations between y t and |y t +k |and (f)between y t and y 2t +k .

heteroscedasticity.In particular,the unique observation corrected corresponds to 19thAugust 1991.The corrected series has a kurtosis of 6.221and also shows clear signs of conditional heteroscedasticity when looking at the correlations of squares and absolute returns plotted in Fig.10.Both correlograms show signi?cant positive correlations which decay slowly toward zero.Finally,the cross-correlations between y t and y 2t +k and between y t and |y t +k |are negative and signi?cant.Therefore,it seems that the dynamic evolution of the DAX returns can be also represented by a conditionally heteroscedastic model with long-memory and asymmetry.As before,we ?t the A-LMSV and FIGARCH models.The estimated A-LMSV model is given by

(1?0.883(0.018)

L)(1?L)0.413

(0.008)log 2t = t ,

(16)

where the scale parameter estimate is ?=0.906,the variance of the log-volatility noise estimate is 2 =0.01and the correlation between the level and volatility noises estimate is =?0.373.

2860 E.Ruiz,H.Veiga /Computational Statistics &Data Analysis 52(2008)2846–2862

2000

400060008000100001000

2000

3000

-8

-6

-4-2024681000

2000

3000

0.0

0.1

0.20.30.410

20

30

40

50

0.0

0.1

0.20.30.4

10

20

30

40

50

-0.15

-0.10-0.050.000.05

1020304050

-0.15

-0.10

-0.05

0.00

0.05

1020304050

Fig.10.(a)Observations of daily DAX prices and (b)returns together with (c)sample autocorrelations of absolute returns and (d)squared returns and (e)cross-correlations between y t and |y t |and (f)between y t and y 2t .In each case,the continuous and dashed lines represent the plug-in autocorrelations and cross-correlations implied by the A-LMSV and FIEGARCH models,respectively.

The estimated FIEGARCH (1,d,0)model is given by

(1?0.817(0.086)

L)(1?L)0.436

(0.10)

log 2t

=0.837(0.229)+0.140(0.024)

| t ?1|? 2

?0.063(0.014) t ?1.(17)

First,note that the estimated long-memory parameter,d ,is smaller than 0.5in both models.Therefore,DAX returns

are stationary and their moments are well de?ned.We now analyze which model implies moments closer to the observed moments of DAX returns.The plug-in kurtosis implied by the estimated A-LMSV and FIEGARCH models are 7.702

E.Ruiz,H.Veiga/Computational Statistics&Data Analysis52(2008)2846–28622861 and4.449,respectively.Therefore,the kurtosis of the A-LMSV is closer to the observed kurtosis.Looking at the plug-in autocorrelations of absolute and squared returns implied by each of the two models,plotted in Fig.10,it is possible to observe that they are clearly smaller than the observed autocorrelations.However,the sample autocorrelations of the standardized residuals are not signi?cant.We do not report the corresponding diagnostics to save space although they are available upon request.On the other hand,the plug-in cross-correlation between y t and|y t+1|implied by the

A-LMSV model,?0.021,is closer to the corresponding sample cross-correlation,?0.029,than the one implied by the FIEGARCH model,?0.039.The same happens with respect to the cross-correlations between y t and y2t+1.The sample ?rst order cross-correlation is?0.031while the plug-in cross-correlations implied by the A-LMSV and FIEGARCH models are?0.021and?0.049,respectively.However,for other lags,the plug-in cross-correlations implied by both models are,in general,under the sample cross-correlations.

5.Conclusions

We propose an extension of the LMSV to represent the asymmetric response of volatility to positive and negative returns.We consider the model in which the log-volatility is speci?ed as an ARFIMA(1,d,0)model.We compare the statistical properties of the new model with the FIEGARCH(1,d,0)model.As a byproduct,we derive expressions of the autocorrelations of squares and absolute returns as well as cross-correlations between these transformations of returns and the original returns when they are generated by the FIEGARCH model.We show that the kurtosis and autocorrelations of squares of the A-LMSV model are not affected by the presence of the leverage effect while in the FIEGARCH model,both moments increase with the asymmetry.Furthermore,we show that the autocorrelations of squares increase with the persistence in the A-LMSV model and decrease in the FIEGARCH model.On the other hand,in the empirically relevant A-LMSV models,the correlation between the volatility and the level of returns is negative.If this is the case,we show that the autocorrelations of absolute observations decrease with respect to the autocorrelations of the corresponding symmetric model.With respect to the FIEGARCH model,the autocorrelations of absolute returns increase with the magnitude of the asymmetry regardless of its sign.Finally,we show that the patterns of the cross-correlations between y t and|y t+k|c are rather similar in the two models considered.Although the moments have been derived for the A-LMSV(1,d,0)and FIEGARCH(1,d,0)models,they can be easily extended to more general speci?cations of the dynamic dependence of volatilities.In particular,if the log-volatility is assumed to be a general ARFIMA(p,d,q)process,the results in Hosking(1981)can be used to derive the corresponding moments.Similarly,the arguments in He et al.(2002)can be used to derive moments for the FIEGARCH(p,d,q) model.

In general,the A-LMSV model reproduces better the empirical features of?nancial data:volatility persistence, excess kurtosis,autocorrelations of absolute and squared returns and cross-correlations between returns and future squared returns.In fact,the FIEGARCH model needs simultaneously high values of d and ,close to the level of nonstationary,and small values of in order to capture simultaneously persistence and small?rst order autocorrelation. On the other hand,this last requirement interferes with generating large kurtosis.The Gaussian FIEGARCH model is only able to reproduce high kurtosis if is not close to zero.Therefore,it seems to exist,for this model,a trade off among different moments.Contrarily,the A-LMSV model is able to reproduce these three features of?nancial data for larger combinations of the parameters.The larger?exibility of the A-LMSV model could be expected due to the added noise in the volatility equation;see Carnero et al.(2004)for the comparison between symmetric and short-memory ARSV and GARCH(1,1)models.

In an empirical application to daily S&P500and DAX returns,we show that when both models are?tted to real data,the conclusions in terms of the stationarity of the volatility are similar.When one of the models imply sta-tionarity,the other does and the other way round.If the estimated parameters of both models satisfy the station-arity conditions,then the kurtosis and?rst order cross-autocorrelations of absolute and squared returns implied by the A-LMSV model are closer to the corresponding sample moments of the real data than the ones implied by the FIEGARCH model.However,in our empirical application to the DAX returns none of the implied autocorrelations explain completely the slow decay of the autocorrelations toward zero.Consequently,and given that,as we have seen in this paper,dealing with the statistical properties of the A-LMSV model is easier than when considering the properties of the FIEGARCH model,we think that the former is a model to be considered when modelling the dynamic evolution of the volatility of series with long-memory and asymmetric response to positive and negative returns.

2862 E.Ruiz,H.Veiga/Computational Statistics&Data Analysis52(2008)2846–2862

Acknowledgments

We are very grateful to Ana Pérez,Stephen Taylor,two anonymous referees and participants at the seminar in the Department of Economics,Universidad de Alicante,for many helpful suggestions.

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Zaffaroni,P.,2005.Whittle estimation of exponential volatility models.Manuscript.

centrifugemodelling离心模拟centrifuge离心机

centrifugemodelling离心模拟centrifuge离心机centripetalacceleration向心加速度centripetalforce向心力centripetal向心的centrode瞬心轨迹centroidaxis重心轴线centroidofarea面心centroid质心centroidalprincipalaxesofinertia重心诌性轴centrosymmetric中心对称的ceramicbearing陶瓷轴承ceramicbond陶瓷结合剂ceramiccoating陶瓷涂层ceramicengine陶瓷发动机ceramicfilter陶瓷过滤器ceramicindustry陶瓷工业ceramici ulater陶瓷绝缘子ceramictip陶瓷刀片ceramictool陶瓷车刀ceramic 陶瓷的ceramics陶瓷cermettool金属陶瓷刀具cermet金属陶瓷cesium铯cetanenumber十六烷值CF 吸顶型风机CeilingMountedTypeFancfrp碳纤维增强塑料cg ystemcgs单位制cgsunit厘米克秒单位chai eltconveyor链带输送机chai elt链带chai lock链动滑轮chai rake链闸chai ridge链桥nondime ional无量纲的nondirective非定向的nondi ersivewave非弥散波nonelasticbuckling非弹性屈曲nonelasticscattering非弹性散射nonelastic非弹性的nonequilibriumplasma非平衡等离子体nonequilibriumproce非平衡过程nonequilibriumstate非平衡态nonequilibriumstate非平衡状态nonequilibriumsurfacete ion非平衡表面张力nonequilibriumthermodynamics非平衡态热力学nonequilibrium非平衡nonevanescentwave无阻尼波nonferrousalloy非铁合金nonferrousmetal有色金属nonferrousmetallurgy非铁金属冶炼术nonflatne不平面度nonfreepoint非自由质点nongeostrophicflow非地转怜nonholonomicco traint非完整约束nonholonomicsystem非完整系统nonholonomicvelocitycoordinate非完整速度坐标nonhomogeneou oundary非齐次边界nonidealflow非理想怜noninertia无惯性noninertialsystemofcoordinates非惯性坐标系noninertialsystem非惯性系nonisentropicflow非等熵怜nonisotropicmaterial非蛤同性材料nonisotropy非蛤同性nonius游标nonlinearaerodynamics非线性空气动力学nonlineardistortion非线性失真nonlinearelectrodynamics非线性电动力学collarbearing环状止推轴承collarheadscrew带缘螺钉collarjournal有环轴颈collarnut凸缘螺collarpin凸缘销collarthrustbearing环状止推轴承collarvortex涡环collar凸边collateralmotion次级运动collectivemodeofmotion集体运动模式collectivemotion集体运动collectorefficiency集热僻率collectorring滑环collector集电器colletchuck弹簧夹头collier运煤船collimation视准collimation准直collimator视准仪Collimator准直仪collisionchain碰撞链collisioncro ection碰撞截面collisiondiameter 碰撞直径collisiondiffusion碰撞扩散collisionexcitation碰撞激发collisionfrequency碰撞频率

欧洲车联网项目 5GCAR_D3.2-Channel Modelling and Positioning for 5G V2X

Fifth Generation Communication Automotive Research and innovation Deliverable D3.2 Report on Channel Modelling and Positioning for 5G V2X Version: v1.0 2018-11-30 This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 761510. Any 5GCAR results reflects only the authors’ view and the Commission is thereby not responsible for any use that may be made of the information it contains. http://www.5g-ppp.eu

Deliverable D3.2 Report on Channel Modelling and Positioning for 5G V2X

Abstract 5GCAR has identified the most important use cases for future V2X communications together with their key performance indicators and respective requirements. One outcome of this study is that accurate positioning is important for all these use cases, however with different level of accuracy. In this deliverable we summarize existing solutions for positioning of road users and justify that they are not sufficient to achieve the required performance always and everywhere. Therefore, we propose a set of solutions for different scenarios (urban and highway) and different frequency bands (below and above 6 GHz). Furthermore, we link these new technical concepts with the ongoing standardization of 3GPP New Radio Rel-16. An important prerequisite for this work is the availability of appropriate channel models. For that reason, we place in front a discussion of existing channel models for V2X, including the sidelink between two road users, their gaps, as well as our 5GCAR contributions beyond the state of the art. This is complemented with results from related channel measurement campaigns.

financial modelling training

财务模型培训

今天的议题
财务预测模型介绍 工具与数据 构建简单的财务预测模型 构建复杂的财务预测模型

财务模型可以用来做什么？ 财务模型可以用来做什么？
预算Budgeting 成本估算Cost Estimating 销售预测Sales Forecasting 销售预测 市场表现预测Market Share Forecasting 市场表现预测 投资项目的选择Project Selection & Management 投资项目的选择 业务/产品组合管理－ 业务 产品组合管理－组合方案与优化 产品组合管理 实时的市场分析Time-to-Market Analysis 战略决策的评估Real Options Valuation 并购M & A

战略规划项目中的财务预测模型是什么？用来干什么？ 战略规划项目中的财务预测模型是什么？用来干什么？
战略规划项目中的财务预测模型是 模拟各业务在不同运营策略/ 各业务在不同运营策略 模拟各业务在不同运营策略/业务模 式下及不同市场环境下各项业务的 式下及不同市场环境下各项业务的 大体财务表现及发展趋势。因此， 大体财务表现及发展趋势。因此，
在模拟业务表现时，先不考虑股权比 例、投资收益、少数股东权益等问 题；在最后并总表时，可以综合考虑 最后计数单位宜采用“千元”、“百 万元”等较大计量单位，切忌采用 元、角、分等极其精准的单位计量
财务预测模型绝对不能直接作为： 财务预测模型绝对不能直接作为： 直接作为
–
精准的预算 绩效考核的标准
–
但是，可以作为制定预算时的初步参 照，且其中部分有关运营方面的假设 项，例如产能利用率、损耗率等也可在 绩效考核中作为参照
在战略项目中， 财务预测模型将用于 在战略项目中，财务预测模型将用于 在战略项目中， 在战略项目中， 比较不同战略备选方案的经济价值 比较不同战略备选方案的经济价值 促进战略规划、行动方案的细化，并进行验证，反过来指导战略的制定 促进战略规划、行动方案的细化，并进行验证，反过来指导战略的制定 根据财务计划对未来进行资源安排提供依据 根据财务计划对未来进行资源安排提供依据

modelling_the_wireless_propagation_channel_a

Brochure More information from https://www.sodocs.net/doc/518703423.html,/reports/2171649/ Modelling the Wireless Propagation Channel. A simulation approach with Matlab. Wireless Communications and Mobile Computing Description: A practical tool for propagation channel modeling with MATLAB? simulations. Many books on wireless propagation channel provide a highly theoretical coverage, which for some interested readers, may be difficult to follow. This book takes a very practical approach by introducing the theory in each chapter first, and then carrying out simulations showing how exactly put the theory into practice. The resulting plots are analyzed and commented for clarity, and conclusions are drawn and explained from the obtained results. Key features include: A unique approach to propagation channel modeling with accompanying MATLAB? simulations to demonstrate the theory in practice Contains step by step commentary and analysis of the obtained simulation results in order to provide a comprehensive and structured learning tool Covers a wide range of topics including shadowing effects, coverage and interference, Multipath Narrowband channel, Multipath Wideband channel, propagation in micro and pico–cells, the land mobile satellite (LMS) channel, the directional Multipath channel and MIMO and propagation effects in fixed radio links (terrestrial and satellite) The book comes with an accompanying website that contains the MATLAB? simulations and allows readers to try them out themselves Well suited for lab–use, as reference and as a self–learning tool both for advanced students and professionals Modeling the Wireless Propagation Channel: A simulation approach with MATLAB? will be best suited for postgraduate (Masters and PhD) students and practicing engineers in telecommunications and electrical engineering fields, who are seeking to familiarise themselves with the topic without too many formulas. The book will also be of interest to network engineers, system engineers and researchers. Contents:Contents About the Series Editors Preface Acknowledgments 1 Introduction to Wireless Propagation 1.1 Introduction 1.2 Wireless Propagation Basics 1.3 Link Budgets 1.4 Projects 1.5 Summary References Software Supplied 2 Shadowing Effects 2.1 Introduction 2.2 Projects 2.3 Summary

AVEVA E3D Equipment Modelling TM-1811

CHAPTER 1 1Introduction AVEVA Everything3D?(AVEVA E3D?) enables designers to create a 3D model of a Plant design in a multi-discipline environment. One of these disciplines is Equipment modelling and AVEVA E3D enables designers to create 3D representations of plant equipment of all types for use within the wider context of the model. The aim of this training module is to provide basic knowledge of Equipment Modelling within AVEVA E3D. At the end of this course the Trainee will be able to: ?Explain the basics of Equipment Modelling in AVEVA E3D. ?Create equipment using primitives. ?Demonstrate the use of Standard Equipment models. ?Explain the creation of Electrical Equipment. ?Prepare equipment reports. ?Utilise Equipment Associations. ?Understand Hole Management for Equipment. Explain how to create Volume Models in AVEVA E3D. ? course. methods, and complete the set exercises. Menu pull downs and button press actions are indicated by bold dark turquoise text. Information the User has to Key-in will be bold red text. Additional information notes and references to other documentation will be indicated in the styles below. Additional information

机械CADChapter 4 Modelling of Solids

Chapter 4 Modeling of Solids 4.1 Introduction So far we have represented objects with wireframe and surface modeling. Another method of geometric modeling is to use vertices, edges and surfaces to define a solid. Solid modeling systems allow users to create, store and manipulate unambiguous models of physical solid objects, In recent years, solid modeling has become the prevalent and favorable tool for applications in design and manufacturing. Some of the major advantages of solid modeling are listed here. (1) Visualization of components in 3D space or in realistic surroundings can be made easier. (2) Solid models can be used as data input to other systems, like FE-systems, integration between solid model and FE-model provides great possibility to cut short the product development process. (3) Components can be machined straight from the files created by these systems. A solid model contains both the geometry data and topological data. Topological data describe the connectivity and associability of the object entities. Solid model generation is often not unique, that is, there are often several different ways to create a solid model. CAD users need to generate solid models which can make the computer storage small and suited for later utilize. Boundary representation (B-rep) and Constructive Solid Geometry (CSG) are two most popular schemes for solid modeling. B-reps are based on the topological notion that an object is bounded by faces. CSG is based on that an object can be divided into a set of primitives. Table 4.1 shows some widely used CAD systems. 4.2 Solid Representation Most geometric objects we see every day are solids. Solids can be very simple like a cube or very complex like a piston engine. To be processed by computers, solids must have some representations that can describe the geometry and characteristics completely. In fact, a good representation should address the following issues. ①Domain: While no representation can describe all possible solids, a representation should be able to represent a useful set of geometric objects. Domain should give a useful set of physical objects that can be represented. ②Unambiguity: A solid should be represented without any doubt. An unambiguous representation is usually referred to as a complete one. Figure 4.1 shows an example of ambiguous solids. ③Uniqueness: There is only one way to represent a particular solid. If a representation is unique, then it is easy to determine if two solids are identical since one can just compare their representations. ④Accuracy: A representation is said accurately if no approximation is required. ⑤Validity: A representation should not create any invalid or impossible solids. More precisely, a representation will not represent an object that does not correspond to a solid.

Design and modelling of a fluid inerter

This article was downloaded by: [Beihang University] On: 13 March 2014, At: 23:20 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK International Journal of Control Publication details, including instructions for authors and subscription information: https://www.sodocs.net/doc/518703423.html,/loi/tcon20 Design and modelling of a fluid inerter S. J. Swift a , M. C. Smith a , A. R. Glover b , C. Papageorgiou a , B. Gartner c & N. E. Houghton a a Department of Engineering , University of Cambridge , Cambridge , CB2 1PZ , UK b McLaren Automotive , Chertsey Road, Woking, Surrey , GU21 4YH , UK c Penske Racing Shocks , 150 Franklin Street, Box 1056, Reading , PA , 19603 , USA Accepted author version posted online: 18 Sep 2013.Published online: 14 Nov 2013. PLEASE SCROLL DOWN FOR ARTICLE

Business Modelling For Decision Making

The Faculty of Business and Law Business Modelling for Decision Makers Assignment code：APC310 Student name：Lin Yu Student ID:109053367 Submission date:13 August,2012 Moderators: Rob Hall and Jeff Evans

Contents Introduction (2) Question 1 (2) Section A (2) Section B (6) Question 2 (9) Section A (9) Section B (11) Conclusion (12) Reference (13)

Introduction As a business manager, there are a numbers of factors and probabilities which are necessary to take consideration before making decisions. Mangers need to do some theoretical analysis to support decisions that he or she makes. Today, there are many analysis tools and applications that can be used to analyze data and making decisions, such as the decision trees, linear programming, discrete simulation and so on (Curwin, 2011). By using these tools, managers can make their decisions more effectively; minimize negative side of risk, facilitate business in order to achieve the maximum profits. Question 1 Section A 1.1 Analyzing the data we have collected. From data, we can know the approximate time of making each range of coffee and the probability of choosing each range of coffee; it is shown in the following table. The table shows that consumers more prefer to select the regular coffee and the probability of selection is 0.4. It only takes one minute to make one regular coffee. The most time effective type of coffee is Espresso, it is made in 0.5 minute. But the probability of selection of this type is relatively low, which is only 0.1. The most time consuming type of coffee is Cappuccino, it needs 2.3 minutes to be made. The

An Overview of the OCML Modelling Language

An Overview of the OCML Modelling Language Enrico Motta Knowledge Media Institute The Open University Walton Hall, Milton Keynes, UK E.Motta@https://www.sodocs.net/doc/518703423.html, Abstract. This paper provides an overview of the OCML modelling language: it illustrates the underlying philosophy, describes the main modelling constructs provided, and compares it to other modelling languages. 1.INTRODUCTION OCML1 was originally developed in the context of the VITAL project (Shadbolt et al., 1993) to provide operational modelling capabilities for the VITAL workbench (Domingue et al., 1993). Over the years the language has undergone a number of changes and improvements and in what follows we will provide an overview of the current version of the language (v5.1), illustrate its underlying philosophy and compare it to other knowledge modelling languages. https://www.sodocs.net/doc/518703423.html,NGUAGE TENETS A number of ideas/principles have shaped the development of the OCML language. These are discussed in the following sections. 2.1.Knowledge-level modelling support. The main goal of OCML is to support knowledge-level modelling (Newell, 1982; Fensel and Van Harmelen, 1994). In practice this role implies that OCML focuses on logical, rather than implementation-level primitives. Thus it provides mechanisms for expressing items such as relations, functions, rules, classes and instances, rather than arrays or hash tables. This approach is consistent with several other proposals for knowledge modelling (Gruber, 1993; Fensel and Van Harmelen, 1994). In the case of an operational language, such as OCML, this approach causes severe limitations in the support that the language can offer for efficient execution of application models. This problem can be (partially) addressed by providing a good compiler and by adding extra logical mechanisms for efficient reasoning - e.g. procedural attachments (Weyhrauch, 1980). Thus, while it is possible to specify and prototype knowledge models in OCML, the language does not aim to support efficient delivery of applications. 2.2.Support for the TMDA modelling framework While OCML can be used to support various modelling approaches, such as CommonKADS (Schreiber et al., 1994b) or Components of Expertise (Steels, 1990), its design has been specifically informed by the Task/Method/Domain/Application (TMDA) framework (Motta, 1997; Motta and Zdrahal, 1997), which is illustrated in the next section. 2.2.1.Overview of the TMDA framework The TMDA framework distinguishes between four generic types of components in an application model: task knowledge, problem solving knowledge, domain knowledge, and application-specific knowledge. 1The acronym "OCML" stands for Operational Conceptual Modelling Language.

Agent Modelling Language (AML) A comprehensive approach to modelling MAS

Informatica29(2005)391–400391 Agent Modeling Language(AML):A Comprehensive Approach to Modeling MAS Ivan Trencansky and Radovan Cervenka Whitestein Technologies,Panenska28,81103Bratislava,Slovakia Tel+421(2)5443-5502,Fax+421(2)5443-5512 E-mail:{itr,rce}@https://www.sodocs.net/doc/518703423.html, Keywords:agent,multi-agent system,modeling language,agent-oriented software engineering Received:May6,2005 The Agent Modeling Language(AML)is a semi-formal visual modeling language for specifying,mod- eling and documenting systems that incorporate features drawn from multi-agent systems theory.It is speci?ed as an extension to UML2.0in accordance with major OMG modeling frameworks(MDA,MOF, UML,and OCL).The ultimate objective of AML is to provide software engineers with a ready-to-use, complete and highly expressive modeling language suitable for the development of commercial software solutions based on multi-agent technologies.This paper presents an overview of AML.The scope of the language,its structure and extensibility mechanisms are discussed,and the core AML modeling constructs and mechanisms are introduced and demonstrated by examples. Povzetek:Opisana je vizualizacija agentnega jezika za modeliranje. 1Introduction The Agent Modeling Language(AML)[3,5,4]is a semi-formal1visual modeling language for specifying,modeling and documenting systems that incorporate concepts drawn from Multi-Agent Systems(MAS)theory. The most signi?cant motivation driving the development of AML was the extant need for a ready-to-use,com-prehensive,versatile and highly expressive modeling lan-guage suitable for the development of commercial software solutions based on multi-agent technologies.To qualify this more precisely,AML was intended to be a language that:(1)is built on proved technical foundations,(2)in-tegrates best practices from agent-oriented software engi-neering(AOSE)and object-oriented software engineering (OOSE)domains,(3)is well speci?ed and documented, (4)is internally consistent from the conceptual,semantic and syntactic perspectives,(6)is versatile and easy to ex-tend,(7)is independent of any particular theory,software development process or implementation environment,and (8)is supported by Computer-Aided Software Engineering (CASE)tools. Given these requirements,AML is designed to address the most signi?cant de?ciencies with current state-of-the-art and practice in the area of MAS oriented model-ing languages,which are often:(1)insuf?ciently docu-mented and/or speci?ed,or(2)using proprietary and/or non-intuitive modeling constructs,or(3)aimed at model-ing only a limited set of MAS aspects,or(4)applicable only to a speci?c theory,application domain,MAS archi-1The term“semi-formal”implies that the language offers the means to specify systems using a combination of natural language,graphical nota-tion,and formal language speci?cation.tecture,or technology,or(5)mutually incompatible,or(6) insuf?ciently supported by CASE tools. The objective of this paper is to present the approach applied to speci?cation of AML,and a brief overview of the various modeling constructs AML provides to model MASs.Due to limitations in paper length,a comprehen-sive description of AML abstract syntax,semantics,and notation is not provided. The rest of the paper is structured as follows:Section2 presents the approach applied to speci?cation of AML and the available extensibility mechanisms.Section3ex-plains the AML fundamental entities and their features, sections4,5,6,7and8present an overview of AML ap-proach to modeling different aspects of agents and MASs, like social aspects,different kinds of interactions,capabil-ities,mobility,and mental attitudes.In the end the conclu-sions are drawn. 2The AML Approach Toward achieving the stated goals and overcoming the de-?ciencies associated with many existing approaches,AML has been designed as a language,which: –incorporates and uni?es the most signi?cant concepts from the broadest set of existing multi-agent theo-ries and abstract models(e.g.DAI[24],BDI[17], SMART[9]),modeling and speci?cation languages (e.g.AUML[1,11,12],TAO[18],OPM/MAS[20], AOR[23],UML[15],OCL[14],OWL[19],UML-based ontology modeling[7],methodologies(e.g. MESSAGE[10],Gaia[25],TROPOS[2],PASSI[6],