scholarly journals Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes

2017 ◽  
Vol 6 (6) ◽  
pp. 13
Author(s):  
Manabu Asai ◽  
Michael McAleer
Keyword(s):  
Asymptotic Theory ◽  
Asymptotic Properties ◽  
Autoregressive Process ◽  
Multivariate Garch ◽  
Regularity Conditions ◽  
Conditional Volatility ◽  
Empirical Estimation ◽  
Equivalent Representation ◽  
Volatility Model ◽  
Quasi Maximum Likelihood

The paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive asymptotic theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated asymptotic properties.

scholarly journals Asymptotic Theory for Regressions with Smoothly Changing Parameters

2013 ◽  
Vol 5 (2) ◽  
pp. 133-162 ◽  
Author(s):  
Eric Hillebrand ◽  
Marcelo C. Medeiros ◽  
Junyue Xu
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Theory ◽  
Asymptotic Properties ◽  
Smooth Transition ◽  
Finite Sample ◽  
Likelihood Estimator ◽  
Output Data ◽  
Asymptotically Normal ◽  
Finite Sample Properties ◽  
Quasi Maximum Likelihood

Abstract: We derive asymptotic properties of the quasi-maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual -rate and has an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data.

scholarly journals A New Volatility Model: GQARCH-Ito Model

2020 ◽  
Author(s):  
Huiling Yuan ◽  
Yong Zhou ◽  
Lu Xu ◽  
Yulei Sun ◽  
Xiangyu Cui
Keyword(s):  
High Frequency ◽  
Historical Data ◽  
Asymptotic Properties ◽  
Low Frequency ◽  
Simulation Studies ◽  
Finite Sample ◽  
Volatility Model ◽  
Forecasting Performance ◽  
Volatility Asymmetry ◽  
Quasi Maximum Likelihood

Volatility asymmetry is a hot topic in high-frequency financial market. In this paper, we propose a new econometric model, which could describe volatility asymmetry based on high-frequency historical data and low-frequency historical data. After providing the quasi-maximum likelihood estimators for the parameters, we establish their asymptotic properties. We also conduct a series of simulation studies to check the finite sample performance and volatility forecasting performance of the proposed methodologies. And an empirical application is demonstrated that the new model has stronger volatility prediction power than GARCH-It\^{o} model in the literature.

STRONG CONSISTENCY OF ESTIMATORS FOR MULTIVARIATE ARCH MODELS

1998 ◽  
Vol 14 (1) ◽  
pp. 70-86 ◽  
Author(s):  
Thierry Jeantheau
Keyword(s):  
Maximum Likelihood ◽  
Error Term ◽  
Strong Consistency ◽  
Asymptotic Properties ◽  
Maximum Likelihood Estimators ◽  
Multivariate Garch ◽  
Arch Models ◽  
Multivariate Garch Model ◽  
Quasi Maximum Likelihood ◽  
Derivatives Of

This paper deals with the asymptotic properties of quasi-maximum likelihood estimators for multivariate heteroskedastic models. For a general model, we give conditions under which strong consistency can be obtained; unlike in the current literature, the assumptions on the existence of moments of the error term are weak, and no study of the various derivatives of the likelihood is required. Then, for a particular model, the multivariate GARCH model with constant correlation, we describe the set of parameters where these conditions hold.

Standard Asymptotic Theory

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Asymptotic Theory ◽  
Asymptotic Variance ◽  
Statistical Significance ◽  
Regularity Conditions ◽  
Parameter Estimates ◽  
Asymptotic Results ◽  
Ml Estimation ◽  
True Parameter ◽  
Log Likelihood ◽  
Ml Estimator

This book relies on maximum likelihood (ML) estimation of parameters. Asymptotic theory assumes regularity conditions hold when the ML estimator is consistent. Typically an additional third derivative condition is assumed to ensure that the ML estimator is also asymptotically normally distributed. Standard asymptotic results that then hold are summarized in this chapter; for example, the asymptotic variance of the ML estimator is then given by the Fisher information formula, and the log-likelihood ratio, the Wald and the score statistics for testing the statistical significance of parameter estimates are all asymptotically equivalent. Also, the useful profile log-likelihood then behaves exactly as a standard log-likelihood only in a parameter space of just one dimension. Further, the model can be reparametrized to make it locally orthogonal in the neighbourhood of the true parameter value. The large exponential family of models is briefly reviewed where a unified set of regular conditions can be obtained.

Evidence of leverage effects and volatility spillover among exchange rates of selected emerging and growth leading economies

2019 ◽  
Vol 11 (2) ◽  
pp. 174-192 ◽  
Author(s):  
Ajaya Kumar Panda ◽  
Swagatika Nanda ◽  
Vipul Kumar Singh ◽  
Satish Kumar
Keyword(s):  
Exchange Rates ◽  
Asset Management ◽  
Spillover Effects ◽  
International Investment ◽  
Multivariate Garch ◽  
Conditional Volatility ◽  
Substantial Impact ◽  
Content Type ◽  
Volatility Spillovers ◽  
Strongly Connected

Purpose The purpose of this study is to examine the evidences of leverage effects on the conditional volatility of exchange rates because of asymmetric innovations and its spillover effects among the exchange rates of selected emerging and growth-leading economies. Design/methodology/approach The empirical analysis uses the sign bias test and asymmetric generalized autoregressive conditional heteroskedasticity (GARCH) models to capture the leverage effects on conditional volatility of exchange rates and also uses multivariate GARCH (MGARCH) model to address volatility spillovers among the studied exchange rates. Findings The study finds substantial impact of asymmetric innovations (news) on the conditional volatility of exchange rates, where Russian Ruble is showing significant leverage effect followed by Indian Rupee. The exchange rates depict significant mean spillover effects, where Rupee, Peso and Ruble are strongly connected; Real, Rupiah and Lira are moderately connected; and Yuan is the least connected exchange rate within the sample. The study also finds the assimilation of information in foreign exchanges and increased spillover effects in the post 2008 periods. Practical implications The results probably have the implications for international investment and asset management. Portfolio managers could use this research to optimize their international portfolio. Policymakers such as central banks may find the study useful to monitor and design interventions strategies in foreign exchange markets keeping an eye on the nature of movements among these exchange rates. Originality/value This is one of the few empirical research studies that aim to explore the leverage effects on exchange rates and their volatility spillovers among seven emerging and growth-leading economies using advanced econometric methodologies.

scholarly journals ASYMPTOTIC THEORY FOR NONLINEAR QUANTILE REGRESSION UNDER WEAK DEPENDENCE

2015 ◽  
Vol 32 (3) ◽  
pp. 686-713 ◽  
Author(s):  
Walter Oberhofer ◽  
Harry Haupt
Keyword(s):  
Quantile Regression ◽  
Asymptotic Normality ◽  
Regression Model ◽  
Asymptotic Theory ◽  
Asymptotic Properties ◽  
Covariance Estimation ◽  
First Order ◽  
Regression Quantiles ◽  
Quantile Regression Model ◽  
Consistency And Asymptotic Normality

This paper studies the asymptotic properties of the nonlinear quantile regression model under general assumptions on the error process, which is allowed to be heterogeneous and mixing. We derive the consistency and asymptotic normality of regression quantiles under mild assumptions. First-order asymptotic theory is completed by a discussion of consistent covariance estimation.

scholarly journals What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity, and (Non-) Asymptotic Properties of the Dynamic Conditional Correlation (DCC) Model

2019 ◽  
Vol 12 (2) ◽  
pp. 61 ◽  
Author(s):  
McAleer
Keyword(s):  
Financial Risk ◽  
Dynamic Models ◽  
Asymptotic Properties ◽  
Regularity Conditions ◽  
Conditional Correlation ◽  
Risky Assets ◽  
Dynamic Conditional Correlation ◽  
Volatility Models ◽  
Dynamic Time ◽  
Optimal Hedge

In order to hedge efficiently, persistently high negative covariances or, equivalently, correlations, between risky assets and the hedging instruments are intended to mitigate against financial risk and subsequent losses. If there is more than one hedging instrument, multivariate covariances and correlations have to be calculated. As optimal hedge ratios are unlikely to remain constant using high frequency data, it is essential to specify dynamic time-varying models of covariances and correlations. These values can either be determined analytically or numerically on the basis of highly advanced computer simulations. Analytical developments are occasionally promulgated for multivariate conditional volatility models. The primary purpose of this paper is to analyze purported analytical developments for the only multivariate dynamic conditional correlation model to have been developed to date, namely the widely used Dynamic Conditional Correlation (DCC) model. Dynamic models are not straightforward (or even possible) to translate in terms of the algebraic existence, underlying stochastic processes, specification, mathematical regularity conditions, and asymptotic properties of consistency and asymptotic normality, or the lack thereof. This paper presents a critical analysis, discussion, evaluation, and presentation of caveats relating to the DCC model, with an emphasis on the numerous dos and don’ts in implementing the DCC model, as well as a related model, in practice.

Optimal estimation for semimartingales

1986 ◽  
Vol 23 (02) ◽  
pp. 409-417 ◽  
Author(s):  
A. Thavaneswaran ◽  
M. E. Thompson
Keyword(s):  
Continuous Time ◽  
Asymptotic Properties ◽  
Optimal Estimation ◽  
Parametric Estimation ◽  
Local Martingale ◽  
Regularity Conditions ◽  
Probability Measures ◽  
Simple Process ◽  
Special Cases ◽  
Least Squares Estimates

This paper extends a result of Godambe's theory of parametric estimation for discrete-time stochastic processes to the continuous-time case. LetP={P} be a family of probability measures such that (Ω,F, P) is complete, (Ft, t≧0) is a standard filtration, andX = (XtFt, t ≧ 0)is a semimartingale for everyP ∈ P. For a parameterθ(Ρ), supposeXt=Vt,θ+Ht,θwhere theVθprocess is predictable and locally of bounded variation and theHθprocess is a local martingale. Consider estimating equations forθof the formprocess is predictable. Under regularity conditions, an optimal form forαθin the sense of Godambe (1960) is determined. WhenVt,θis linear inθthe optimal, corresponds to certain maximum likelihood or least squares estimates derived previously in special cases. Asymptotic properties of, are discussed.

scholarly journals What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity and (Non-) Asymptotic Properties of the Full BEKK Dynamic Conditional Covariance Model

2019 ◽  
Vol 12 (2) ◽  
pp. 66 ◽  
Author(s):  
Michael McAleer
Keyword(s):  
Dynamic Models ◽  
Asymptotic Properties ◽  
Regularity Conditions ◽  
Covariance Model ◽  
Conditional Covariance ◽  
Risky Assets ◽  
Volatility Models ◽  
Hedge Ratios ◽  
Covariance Models ◽  
Optimal Hedge

Persistently high negative covariances between risky assets and hedging instruments are intended to mitigate against risk and subsequent financial losses. In the event of having more than one hedging instrument, multivariate covariances need to be calculated. Optimal hedge ratios are unlikely to remain constant using high frequency data, so it is essential to specify dynamic covariance models. These values can either be determined analytically or numerically on the basis of highly advanced computer simulations. Analytical developments are occasionally promulgated for multivariate conditional volatility models. The primary purpose of the paper is to analyze purported analytical developments for the most widely-used multivariate dynamic conditional covariance model to have been developed to date, namely the Full BEKK model, named for Baba, Engle, Kraft and Kroner. Dynamic models are not straightforward (or even possible) to translate in terms of the algebraic existence, underlying stochastic processes, specification, mathematical regularity conditions, and asymptotic properties of consistency and asymptotic normality, or the lack thereof. The paper presents a critical analysis, discussion, evaluation and presentation of caveats relating to the Full BEKK model, and an emphasis on the numerous dos and don’ts in implementing the Full BEKK and related non-Diagonal BEKK models, such as Triangular BEKK and Hadamard BEKK, in practice.

An Improved Selection Test between Autoregressive and Moving Average Disturbances in Regression Models

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
Pierre Nguimkeu
Keyword(s):  
Interest Rate ◽  
Regression Models ◽  
Real Interest Rate ◽  
Moving Average ◽  
Asymptotic Properties ◽  
Autoregressive Process ◽  
Small Samples ◽  
Average Scheme ◽  
First Order ◽  
Selection Test

AbstractThis paper proposes an improved likelihood-based method to test the hypothesis that the disturbances of a linear regression model are generated by a first-order autoregressive process against the alternative that they follow a first-order moving average scheme. Compared with existing tests which usually rely on the asymptotic properties of the estimators, the proposed method has remarkable accuracy, particularly in small samples. Simulations studies are provided to show the superior accuracy of the method compared to the traditional tests. An empirical example using Canada real interest rate illustrates the implementation of the proposed method in practice.

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