Asymptotic Theory of Statistical Inference for Time Series

Taniguchi, Masanobu; Kakizawa, Yoshihide

doi:10.1007/978-1-4612-1162-4

Cited by 318 publications

(269 citation statements)

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“…As shown in Theorem 3.1.3 of Taniguchi and Kakizawa (2000) in the general framework, the QLR test under known ω has the asymptotic χ 2 (2) distribution. The last entries of Table 2 report the rejection frequencies of the QLR statistic at the five percent significance level, indicating that the rejection frequency under the null model approaches the nominal size of 5% as T increases.…”

Section: Finite Sample Propertiesmentioning

confidence: 94%

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Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

McAleer

Peiris

2017

SSRN Journal

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In recent years fractionally differenced processes have received a great deal of attention due to their exibility in nancial applications with long memory. In this paper, we develop a new realized stochastic volatility (RSV) model with general Gegenbauer long memory (GGLM), which encompasses a new RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks apart from the origin in the power spectrum.Forestimating the RSV-GGLM model, we suggest estimating the location parameters for the peaks of the power spectrum in the rst step, and the remaining parameters based on the Whittle likelihood in the second step. We conduct Monte Carlo experiments for investigating the nite sample properties of the estimators, with a quasi-likelihood ratio test of RSV-SLM model against theRSV-GGLM model.We apply the RSV-GGLM and RSV-SLM model to three stock market indices. The estimation and forecasting results indicate the adequacy of considering general long memory.Keywords Stochastic Volatility; Realized Volatility Measure; Long Memory; Gegenbauer Polynomial; Seasonality; Whittle Likelihood. JEL Classification AbstractIn recent years fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, we develop a new realized stochastic volatility (RSV) model with general Gegenbauer long memory (GGLM), which encompasses a new RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks apart from the origin in the power spectrum. For estimating the RSV-GGLM model, we suggest estimating the location parameters for the peaks of the power spectrum in the first step, and the remaining parameters based on the Whittle likelihood in the second step. We conduct Monte Carlo experiments for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of RSV-SLM model against theRSV-GGLM model. We apply the RSV-GGLM and RSV-SLM model to three stock market indices. The estimation and forecasting results indicate the adequacy of considering general long memory.

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Section: Finite Sample Propertiesmentioning

confidence: 94%

“…The approximation was originally proposed by Whittle (1952) for scalar-valued stationary processes (see also Dunsmuir and Hannan (1976), and Taniguchi and Kakizawa (2000)). Define the Whittle likelihood (WL) estimator,δ T , which is obtained by minimizing −L T (δ).…”

Section: Whittle Likelihood Estimation Of Short and Long Memory Parammentioning

confidence: 99%

Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

McAleer

Peiris

2017

SSRN Journal

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“…We assume that ω(·) and h(·) satisfy the following standard assumptions: For functions satisfying (1.14)-(1.17) we refer to Taniguchi and Kakizawa (2000). Following the methods in Liu and Wu (2010) and Horváth and Reeder (2012), the following weak law of large numbers can be established under H 0 :…”

Section: Estimation Of the Long Run Variancementioning

confidence: 99%

Change Point Detection with Stable AR(1) Errors

Bazarova

Berkes

Horváth

2015

Fields Institute Communications

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In this paper we develop two types of tests to detect changes in the location parameters of dependent observations with infinite variances. We consider the case of autoregressive processes of order one with independent innovations in the domain of attraction of a stable law. If the d largest (in magnitude) observations are removed from the sample, then the standard CUSUM process developed for weakly dependent observations with finite variance can be used assuming that d = d(n) → ∞ as n, the sample size tends to ∞. We study two types of statistics. The maximally selected CUSUM process we estimate the long run variance by kernel estimators. We also propose ratio statistics which do not depend on the long run variances. Monte Carlo simulations illustrate the the limit results can be used even in case of small and moderate sample sizes.

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“…Under ergodicity assumptions and for large T it is well known that the methodology developed for nonparametric regression can be used for inference on the drift function, for an overview see Taniguchi and Kakizawa (2000) for autoregressive processes and Kutoyants (2003), Fan (2004) for diffusions. In this paper we corroborate the folklore that 'autoregression is just regression' by showing strong asymptotic equivalence of the scalar diffusion model (1.2) with a signal detection or Gaussian shift model, which can be interpreted as a regression model with random design.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic statistical equivalence for scalar ergodic diffusions

Dalalyan

Reiß

2005

Probab. Theory Relat. Fields

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Abstract. For scalar diffusion models with unknown drift function asymptotic equivalence in the sense of Le Cam's deficiency between statistical experiments is considered under long-time asymptotics. A local asymptotic equivalence result is established with an accompanying sequence of simple Gaussian shift experiments. Corresponding globally asymptotically equivalent experiments are obtained as compound experiments. The results are extended in several directions including time discretisation. An explicit transformation of decision functions from the Gaussian to the diffusion experiment is constructed.

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Asymptotic Theory of Statistical Inference for Time Series

Abstract: Asymptotic theory of statistical inference for time series/Masanobu Taniguchi, Yoshihide Kakizawa. p. cm. -(Springer series in statistics) Includes bibliographical references and index.

Cited by 318 publications

References 0 publications

Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

Change Point Detection with Stable AR(1) Errors

Asymptotic statistical equivalence for scalar ergodic diffusions

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