One of the important and widely used classes models for non-Gaussian time series is generalized autoregressive model average (GARMA), which specifies an ARMA structure conditional mean process underlying series. However, in many applications one often encounters heteroskedasticity. In this paper we propose a new class models, referred to as GARMA-GARCH that jointly specify both variance process...

Time series models are often constructed by combining nonstationary effects such as trends with stochastic processes that are believed to be stationary. Although stationarity of the underlying process is typically crucial to ensure desirable properties or even validity of statistical estimators, there are numerous time series models for which this stationarity is not yet proven. A major barrier...

2 Moving average models Definition. The moving average model of order q, or MA(q), is defined to be Xt = t + θ1 t−1 + θ2 t−2 + · · ·+ θq t−q, where t i.i.d. ∼ N(0, σ). Remarks: 1. Without loss of generality, we assume the mean of the process to be zero. 2. Here θ1, . . . , θq (θq 6= 0) are the parameters of the model. 3. Sometimes it suffices to assume that t ∼WN(0, σ). Here we assume normality...

We study the properties of an MA1-representation of an autoregressive a p p r o x-imation for a stationary, real-valued process. In doing so we g i v e an extension of Wiener's Theorem in the deterministic approximation setup. When dealing with data, we can use this new key result to obtain insight i n to the structure of MA1-representations of tted autoregressive models where the order increas...

This study compares the forecasting performance of various Autoregressive integrated moving average (ARIMA) models by using time series data. Primarily, The Box-Jenkins approach is considered here for forecasting. For empirical analysis, we used CPI as a proxy for inflation and employed quarterly data from 1970 to 2006 for Pakistan. The study classified two important models for forecasting out ...

Strong coupling between values at different times that exhibit properties of long range dependence, non-stationary, spiky signals cannot be processed by the conventional time series analysis. The autoregressive fractional integral moving average (ARFIMA) model, a fractional order signal processing technique, is the generalization of the conventional integer order models—autoregressive integral ...