State space modeling of Gegenbauer processes with long memory

Dissanayake, Gnanadarsha; Peiris, Shelton; Proietti, Tommaso

doi:10.1016/j.csda.2014.09.014

Cited by 21 publications

(16 citation statements)

References 30 publications

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“…This family in (5) is known as the Gegenbauer ARMA of order (p, d, q; η) or GARMA(p, d, q; η) suggested by Gray et al (1989) (see also Chung (1996aChung ( , 1996b and Dissanayake et al (2016)). The GARMA process has the following properties:…”

Section: Gegenbauer Arma (Garma) Modelmentioning

confidence: 99%

“…With that view in mind, below we report Gegenbauer polynomials and Gegenbauer ARMA (GARMA) for later reference. See Dissanayake et al (2016) for further details.…”

Section: Review Of Stochastic Volatility (Sv) Modelsmentioning

confidence: 99%

“…In the general case of (5), the corresponding stationary and invertible solutions can be obtained from: Dissanayake et al (2016) for further details). In recent papers, Peiris (2008, 2013) have considered an alternative family of generalized fractional processes given by:…”

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confidence: 99%

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Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models

Peiris

McAleer

2017

JRFM

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This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications.

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Section: Gegenbauer Arma (Garma) Modelmentioning

confidence: 99%

“…With that view in mind, below we report Gegenbauer polynomials and Gegenbauer ARMA (GARMA) for later reference. See Dissanayake et al (2016) for further details.…”

Section: Review Of Stochastic Volatility (Sv) Modelsmentioning

confidence: 99%

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Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models

Peiris

McAleer

2017

JRFM

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“…Potential applications are provided. In addition, quasi-likelihood-type ratio tests have been developed for testing unit roots, stationarity versus nonstationarity and Gegenbauer long memory versus standard long memory.The results of the thesis have been reported in a series of working papers of the School of Mathematics and Statistics of the University of Sydney and in the papers [2,3]. …”

mentioning

confidence: 99%

“…The results of the thesis have been reported in a series of working papers of the School of Mathematics and Statistics of the University of Sydney and in the papers [2,3]. …”

mentioning

confidence: 99%

Advancement of Fractionally Differenced Gegenbauer Processes With Long Memory

Dissanayake

2016

Bull. Aust. Math. Soc.

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The class of long memory time series models involving Gegenbauer processes is investigated in detail in terms of formulation, parameter estimation, prediction and testing. Corresponding truncated AR (autoregressive) and MA (moving average) approximations driven by Gaussian white noise are analysed through state-space modelling and Kalman filtering to assess the viability of estimating techniques. The optimal approximation option is employed to proceed with the estimation of model parameters. The resulting mean-square errors are validated by the predictive accuracy to establish an optimal lag order through a large-scale simulation study. It is shown that the use of this newly established lag order for a real data application provides benchmarks which are comparable to and mostly better than a number of existing results in the literature. It is followed by an execution of this technique to extract and assess seasonal models through a Monte Carlo experiment. Thereafter empirical applications are provided.The above approach has been extended to model fractionally differenced Gegenbauer processes with conditional heteroskedastic errors and models with seasonality (see [1]). This paper motivated the development of the model in the thesis. Potential applications are provided. In addition, quasi-likelihood-type ratio tests have been developed for testing unit roots, stationarity versus nonstationarity and Gegenbauer long memory versus standard long memory.The results of the thesis have been reported in a series of working papers of the School of Mathematics and Statistics of the University of Sydney and in the papers [2,3].

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An introduction to vector Gegenbauer processes with long memory

Peiris

2018

Stat

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This paper introduces a flexible new class of time series models generated by the vector Gegenbauer autoregressive moving average structure. We establish existence and uniqueness of second order solutions under certain regularity conditions. Following a simulation study, we provide evidence that supports parsimonious properties of the model building and applications.From (2), it is clear that the long memory features are characterized by the unbounded spectrum at ! D ! g D cos 1 .Á/, when jÁj < 1 and d > 0. Therefore, (1) is stationary and explains a generalized long memory behaviour when jÁj < 1 and 0 < d < 1=2. The frequency ! g is known as the Gegenbauer frequency. It is obvious that when Á D 1, ! g D 0 and then (1) reduces to a standard long memory ARFIMA with index 2d for 0 < d < 1=4. In both cases, it is clear to see that there is a hyperbolic decay of the autocorrelation function (ACF). In their recent papers, Peiris (2008, 2013) have considered an alternative family of generalized fractional processes given by

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State space modeling of Gegenbauer processes with long memory

Cited by 21 publications

References 30 publications

Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models

Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models

Advancement of Fractionally Differenced Gegenbauer Processes With Long Memory

An introduction to vector Gegenbauer processes with long memory

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