A Note on Interpolation of Stable Processes

Interpolation procedures tailored for gaussian processes may not be applied to infinite variance stable processes. Alternative techniques suitable for a limited set of stable case with index α∈(1,2] were initially studied by Pourahmadi (1984) for harmonizable processes. This was later extended to the ARMA stable process with index α∈(0,2] by Nassiuma (1994). In this paper, the problem of interpolation of stable processes is studied with the aim of developing an algorithm applicable to general linear and nonlinear processes by using the state space formulation. Application of this procedure to the estimation of missing values is discussed. Journal of Agriculture, Science and Technology Vol.3(1) 2001: 81-8

Gamma and Exponential Autoregressive Moving Average (ARMA) Processes

Time series data encountered in practice depict properties that deviate from those of gaussian processes. The gamma and exponentially distributed processes which are used as basic models for positive time series fall in the class of non-gaussian processes. In this paper, we develop new and simpler representations of the pth order autoregressive and the qth order moving average processes in gamma and exponential variables. The gamma autoregressive moving average (GARMA(p,q)) model of order p and q and the exponential autoregressive moving average (EARMA(p,q)) model of order p and q are consequently developed. The distributions of developed models, unlike those studied by Lawrance and Lewis (1980), can be determined given either the distribution of the innovation sequence {et} or that of the process itself. The autocorrelation structure, which is a major identification tool in time series, is discussed for each of the proposed models. Journal of Agriculture, Science and Technology Vol.3(1) 2001: 71-8