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 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.

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