Results 1  10
of
16
Simple tests for models of dependence between multiple financial time series: with applications to U.S. equity returns and exchange rates
 Mimeo. (Financial Markets Group, London School of Economics, Discussion paper 483
, 2004
"... Evidence that asset returns are more highly correlated during volatile markets and during market downturns (see Longin and Solnik, 2001, and Ang and Chen, 2002) has lead some researchers to propose alternative models of dependence. In this paper we develop two simple goodnessoffit tests for such m ..."
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Cited by 56 (0 self)
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Evidence that asset returns are more highly correlated during volatile markets and during market downturns (see Longin and Solnik, 2001, and Ang and Chen, 2002) has lead some researchers to propose alternative models of dependence. In this paper we develop two simple goodnessoffit tests for such models. We use these tests to determine whether the multivariate Normal or the Student’s t copula models are compatible with U.S. equity return and exchange rate data. Both tests are robust to specifications of marginal distributions, and are based on the multivariate probability integral transform and kernel density estimation. The firsttestis consistent but requires the estimation of a multivariate density function and is recommended for testing the dependence structure between a small number of assets. The second test may not be consistent against all alternatives but it requires kernel estimation of only a univariate density function, and hence is useful for testing the dependence structure between a large number of assets. We justify our tests for both observable multivariate strictly stationary time series and for standardized innovations of GARCH models. A simulation study demonstrates the efficacy of both tests. When applied to equity return data and exchange rate return data, we find strong
Asymptotic normality of the quasimaximum likelihood estimator for multidimensional causal processes
 Ann. Statist
, 2009
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Time series properties of ARCH processes with persistent covariates," RMI working paper 06/11
, 2006
"... We consider ARCH processes with persistent covariates and provide asymptotic theories that explain how such covariates affect various characteristics of volatility. Specifically, we propose and study a volatility model, named ARCHNNH model, that is an ARCH(1) process with a nonlinear function of a ..."
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Cited by 6 (4 self)
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We consider ARCH processes with persistent covariates and provide asymptotic theories that explain how such covariates affect various characteristics of volatility. Specifically, we propose and study a volatility model, named ARCHNNH model, that is an ARCH(1) process with a nonlinear function of a persistent, integrated or nearly integrated, explanatory variable. Statistical properties of time series given by this model are investigated for various volatility functions. It is shown that our model generates time series that have two prominent characteristics: high degree of volatility persistence and leptokurtosis. Due to persistent covariates, the time series generated by our model has the long memory property in volatility that is commonly observed in high frequency speculative returns. On the other hand, the sample kurtosis of the time series generated by our model either diverges or has a welldefined limiting distribution with support truncated on the left by the kurtosis of the innovation, which successfully explains the empirical finding of leptokurtosis in financial time series. We present two empirical applications of our model. It is shown that the default premium (the yield spread between Baa and Aaa corporate bonds) predicts stock return volatility, and the interest rate differential between two countries accounts for exchange rate return volatility. The forecast evaluation shows that our model generally performs better than GARCH(1,1) and FIGARCH at relatively lower frequencies.
Weak dependence for infinite ARCHtype bilinear models. Statistics: A
 Journal of Theoretical and Applied Statistics
, 2007
"... (September 29, 2006) Giraitis and Surgailis (2002) introduced ARCHtype bilinear models for their specific long range dependence properties. We rather consider weak dependence properties of these models. The computation of mixing coefficients for such models does not look as an accessible objective ..."
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Cited by 4 (2 self)
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(September 29, 2006) Giraitis and Surgailis (2002) introduced ARCHtype bilinear models for their specific long range dependence properties. We rather consider weak dependence properties of these models. The computation of mixing coefficients for such models does not look as an accessible objective. So, we resort to the notion of weak dependence introduced by Doukhan and Louhichi (1999), whose use seems more relevant here. The decay rate of the weak dependence coefficients sequence is established under different specifications of the model coefficients. This implies various limit theorems and asymptotics for statistical procedures. We also derive bounds for the joint densities of this model in the case of regular inputs.
WHITTLE ESTIMATION OF EXPONENTIAL VOLATILITY MODELS
, 2007
"... The strong consistency and asymptotic normality of the Whittle estimate of the parameters in a class of exponential volatility processes are established. Among many models of interest, this class includes oneshock models, such as the EGARCH model of Nelson (1991), and twoshock models, such as the ..."
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Cited by 4 (0 self)
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The strong consistency and asymptotic normality of the Whittle estimate of the parameters in a class of exponential volatility processes are established. Among many models of interest, this class includes oneshock models, such as the EGARCH model of Nelson (1991), and twoshock models, such as the SV model of Taylor (1986). The variable of interest might not have finite fractional moment of any order and so, in particular, finite variance is not imposed. We allow for a wide range of degrees of persistence of shocks to conditional variance, allowing for both short and long memory. A detailed MonteCarlo exercise shows the smallsample properties of the estimator. We present an empirical application using the Standard & Poor’s 500 composite stock index.
A note on uniform convergence of an ARCH(∞) estimator
 Sankhya
"... We consider parameter estimation for a class of ARCH(∞) models, which do not necessarily have a parametric form. The estimation is based on a normalised least squares approach, where the normalisation is the weighted sum of past observations. The number of parameters estimated depends on the sample ..."
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Cited by 2 (2 self)
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We consider parameter estimation for a class of ARCH(∞) models, which do not necessarily have a parametric form. The estimation is based on a normalised least squares approach, where the normalisation is the weighted sum of past observations. The number of parameters estimated depends on the sample size and increases as the sample size grows. Using maximal inequalities for martingales and mixingales we derive a uniform rate of convergence for the parameter estimator. We show that the rate of convergence depends both on the number of parameters estimated and the rate that the ARCH(∞) parameters tend to zero. 1
On Approximate Pseudo Maximum Likelihood Estimation for LARCHProcesses
"... Linear ARCH (LARCH) processes have been introduced by Robinson (1991) to model longrange dependence in volatility and leverage. Basic theoretical properties of LARCH processes have been investigated in the recent literature. However, there is a lack of estimation methods and corresponding asympto ..."
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Cited by 1 (1 self)
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Linear ARCH (LARCH) processes have been introduced by Robinson (1991) to model longrange dependence in volatility and leverage. Basic theoretical properties of LARCH processes have been investigated in the recent literature. However, there is a lack of estimation methods and corresponding asymptotic theory. In this paper, we consider estimation of the dependence parameters for LARCH processes with nonsummable hyperbolically decaying coecients. Asymptotic limit theorems are derived. A central limit theorem with p nrate of convergence holds for an approximate conditional pseudolikelihood estimator. To obtain a computable version that includes observed values only, a further approximation is required. The computable estimator is again asymptotically normal, however with a rate of convergence that is slower than p n:
GARCH(1,1) Process with Persistent Covariates
, 2007
"... We consider a model called GARCHNNH, which is a GARCH(1,1) process with a nonlinear function of a persistent, integrated or nearly integrated, variable. We derive the asymptotic distribution theory of the quasimaximum likelihood estimator in the GARCHNNH model. We establish the consistency and as ..."
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We consider a model called GARCHNNH, which is a GARCH(1,1) process with a nonlinear function of a persistent, integrated or nearly integrated, variable. We derive the asymptotic distribution theory of the quasimaximum likelihood estimator in the GARCHNNH model. We establish the consistency and asymptotic mixed normality of the quasimaximum likelihood estimator in the GARCHNNH model. Next, we investigate how the GARCHNNH model explains stylized facts about volatility in …nancial return series such as the long memory property in volatility, leptokurtosis and the IGARCH behavior.
c © 2006, Indian Statistical Institute A Note on Uniform Convergence of an ARCH(∞)
"... We consider parameter estimation for a class of ARCH(∞) models, which do not necessarily have a parametric form. The estimation is based on a normalized least squares approach, where the normalization is the weighted sum of past observations. The number of parameters estimated depends on the sample ..."
Abstract
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We consider parameter estimation for a class of ARCH(∞) models, which do not necessarily have a parametric form. The estimation is based on a normalized least squares approach, where the normalization is the weighted sum of past observations. The number of parameters estimated depends on the sample size and increases as the sample size grows. Using maximal inequalities for martingales and mixingales we derive a uniform rate of convergence for the parameter estimator. We show that the rate of convergence depends both on the number of parameters estimated and the rate that the ARCH(∞) parameters tend to zero. AMS (2000) subject classification. Primary 62M09; secondary 91B84, 37B10.
Time Series Properties of ARCH Processes with Persistent Covariates 1
"... We consider ARCH processes with persistent covariates and provide asymptotic theories that explain how such covariates a¤ect various characteristics of volatility. Speci
cally, we propose and study a volatility model, named ARCHNNH model, that is an ARCH(1) process with a nonlinear function of a pe ..."
Abstract
 Add to MetaCart
We consider ARCH processes with persistent covariates and provide asymptotic theories that explain how such covariates a¤ect various characteristics of volatility. Speci
cally, we propose and study a volatility model, named ARCHNNH model, that is an ARCH(1) process with a nonlinear function of a persistent, integrated or nearly integrated, explanatory variable. Statistical properties of time series given by this model are investigated for various volatility functions. It is shown that our model generates time series that have two prominent characteristics: high degree of volatility persistence and leptokurtosis. Due to persistent covariates, the time series generated by our model has the long memory property in volatility that is commonly observed in high frequency speculative returns. On the other hand, the sample kurtosis of the time series generated by our model either diverges or has a wellde
ned limiting distribution with support truncated on the left by the kurtosis of the innovation, which successfully explains the empirical
nding of leptokurtosis in
nancial time series. We present two empirical applications of our model. It is shown that the default premium (the yield spread between Baa and Aaa corporate bonds) predicts stock return volatility, and the interest rate di¤erential between two countries accounts for exchange rate return volatility. The forecast evaluation shows that our model generally performs better than GARCH(1,1) and FIGARCH at relatively lower frequencies.