A <i>k</i>‐Factor GARMA Long‐memory Model

Woodward, Wayne A.; Cheng, Qinglu; Gray, Helen

doi:10.1111/j.1467-9892.1998.00105.x

Cited by 131 publications

(94 citation statements)

References 11 publications

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“…These processes were introduced by Giraitis and Leipus (1995), Woodward, Cheng, andRay (1998), Ferrara andGuegan (2001), and Sadek and Khotanzad (2004) among others. One special case here is the seasonal I(d) model that, using a very simple specification may be expressed as…”

Section: Other Cases A) the Case Of A Cyclical I(d) Modelmentioning

confidence: 99%

Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials

Cuestas

Gil-Alana

2016

Studies in Nonlinear Dynamics &Amp; Econometrics

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This paper examines the interaction between non-linear deterministic trends and long run dependence by means of employing Chebyshev time polynomials and assuming that the detrended series displays long memory with the pole or singularity in the spectrum occurring at one or more possibly non-zero frequencies. The combination of the non-linear structure with the long memory framework produces a model which is linear in parameters and therefore it permits the estimation of the deterministic terms by standard OLS-GLS methods. Moreover, the orthogonality property of Chebyshev's polynomials makes them especially attractive to approximate non-linear structures of data. We present a procedure which allows us to test (possibly fractional) orders of integration at various frequencies in the presence of the Chebyshev trends with no effect on the standard limit distribution of the method. Several Monte Carlo experiments are conducted and the results indicate that the method performs well. An empirical application, using data of real exchange rates is also carried out at the end of the article.

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Section: Other Cases A) the Case Of A Cyclical I(d) Modelmentioning

confidence: 99%

Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials

Cuestas

Gil-Alana

2016

Studies in Nonlinear Dynamics &Amp; Econometrics

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“…This section introduces some of the main definitions of the Gegenbauer random fields given in Espejo et al (2014) (see also, Chung (1996a,b), Gray et al (1989), and Woodward et al (1998), for the temporal case).…”

Section: Gegenbauer Random Fieldsmentioning

confidence: 99%

“…Parameter estimation of stationary Gegenbauer random processes was considered by numerous authors, see, for example, Gray et al (1989), Chung (1996a, Woodward et al (1998), Collet and Fadili (2006), McElroy and Holan (2012). Gray et al (1989) used the generating function of the Gegenbauer polynomials to develop long memory Gegenbauer autoregressive moving-average (GARMA) models that generalize the FARIMA process.…”

Section: Introductionmentioning

confidence: 99%

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On a class of minimum contrast estimators for Gegenbauer random fields

Espejo

Leonenko

Olenko

et al. 2015

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The article introduces spatial long-range dependent models based on the fractional difference operators associated with the Gegenbauer polynomials. The results on consistency and asymptotic normality of a class of minimum contrast estimators of long-range dependence parameters of the models are obtained. A methodology to verify assumptions for consistency and asymptotic normality of minimum contrast estimators is developed. Numerical results are presented to confirm the theoretical findings.Keywords Gegenbauer random field · long-range dependence · minimum contrast estimator · consistency · asymptotic normality

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“…As suggested in Woofward, Cheng, and Gray (1998), general (or multifactor) Gegenbauer process has multiple (unbounded) peaks. The general Gegenbauer process encompasses seasonal long memory as a special case.…”

Section: Introductionmentioning

confidence: 99%

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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A k‐Factor GARMA Long‐memory Model

Cited by 131 publications

References 11 publications

Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials

Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials

On a class of minimum contrast estimators for Gegenbauer random fields

Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

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