Properties of selected garma models and their estimation procedures

Time series is an ordered sequence of random variables. In other words, a time series is a set of observations fxtg, each one being recorded at a speci¯c time t. Usually time series are modelled as Autoregressive Moving Average (ARMA), Autoregressive Integrated Moving Average (ARIMA), Autoregressive...

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Main Author:	Ramiah Pillai, Thulasyammal
Format:	Thesis
Language:	English
Published:	2012
Subjects:	Time-series analysis Mathematical models Estimation theory
Online Access:	http://psasir.upm.edu.my/id/eprint/31440/7/IPM%202012%205R.pdf
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id	my-upm-ir.31440
record_format	uketd_dc
spelling	my-upm-ir.314402015-02-25T03:22:53Z Properties of selected garma models and their estimation procedures 2012-10 Ramiah Pillai, Thulasyammal Time series is an ordered sequence of random variables. In other words, a time series is a set of observations fxtg, each one being recorded at a speci¯c time t. Usually time series are modelled as Autoregressive Moving Average (ARMA), Autoregressive Integrated Moving Average (ARIMA), Autoregressive Fractional Integrated Moving Average (ARFIMA) and etc. An extension of the class of time series models by introducing a new parameter, ± as an index includes Generalized Autoregressive (GAR(p)), Generalized Moving Average (GMA(q)) and Generalized Autoregressive Moving Average (GARMA (p; q; ±1; ±2)). The focus of this study is to investigate the properties specically the variance and autocovariance of the GARMA (p; q; ±1; ±2) models. We also study the estimation of the parameters of these models. Evaluation of the performance of two estimators based on the Hannan-Rissanen Algorithm Estimator (HRA) and the Whittle's Estimator (WE) through a series of simulation studies have been conducted in this thesis. In this research, applications illustrating the ¯tting of GARMA(1, 1; 1, ±), GARMA(1, 1; ±1, ±2) and GARMA(1, 2; ±, 1) models are presented and expounded using GDP per capita of Malaysia, the Forest Area of Malaysia and the Dow Jones Utilities Index data set. The results of our study are presented as prepositions in this study. The ¯ndings presented can contribute to the theory of the new class of time series model with index which is important in modelling certain time series data. Time-series analysis Mathematical models Estimation theory 2012-10 Thesis http://psasir.upm.edu.my/id/eprint/31440/ http://psasir.upm.edu.my/id/eprint/31440/7/IPM%202012%205R.pdf application/pdf en staffonly phd doctoral Universiti Putra Malaysia Time-series analysis Mathematical models Estimation theory Institute for Mathematical Research
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Time-series analysis Mathematical models Estimation theory
spellingShingle	Time-series analysis Mathematical models Estimation theory Ramiah Pillai, Thulasyammal Properties of selected garma models and their estimation procedures
description	Time series is an ordered sequence of random variables. In other words, a time series is a set of observations fxtg, each one being recorded at a speci¯c time t. Usually time series are modelled as Autoregressive Moving Average (ARMA), Autoregressive Integrated Moving Average (ARIMA), Autoregressive Fractional Integrated Moving Average (ARFIMA) and etc. An extension of the class of time series models by introducing a new parameter, ± as an index includes Generalized Autoregressive (GAR(p)), Generalized Moving Average (GMA(q)) and Generalized Autoregressive Moving Average (GARMA (p; q; ±1; ±2)). The focus of this study is to investigate the properties specically the variance and autocovariance of the GARMA (p; q; ±1; ±2) models. We also study the estimation of the parameters of these models. Evaluation of the performance of two estimators based on the Hannan-Rissanen Algorithm Estimator (HRA) and the Whittle's Estimator (WE) through a series of simulation studies have been conducted in this thesis. In this research, applications illustrating the ¯tting of GARMA(1, 1; 1, ±), GARMA(1, 1; ±1, ±2) and GARMA(1, 2; ±, 1) models are presented and expounded using GDP per capita of Malaysia, the Forest Area of Malaysia and the Dow Jones Utilities Index data set. The results of our study are presented as prepositions in this study. The ¯ndings presented can contribute to the theory of the new class of time series model with index which is important in modelling certain time series data.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Ramiah Pillai, Thulasyammal
author_facet	Ramiah Pillai, Thulasyammal
author_sort	Ramiah Pillai, Thulasyammal
title	Properties of selected garma models and their estimation procedures
title_short	Properties of selected garma models and their estimation procedures
title_full	Properties of selected garma models and their estimation procedures
title_fullStr	Properties of selected garma models and their estimation procedures
title_full_unstemmed	Properties of selected garma models and their estimation procedures
title_sort	properties of selected garma models and their estimation procedures
granting_institution	Universiti Putra Malaysia
granting_department	Institute for Mathematical Research
publishDate	2012
url	http://psasir.upm.edu.my/id/eprint/31440/7/IPM%202012%205R.pdf
_version_	1747811614727340032

Properties of selected garma models and their estimation procedures

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