NONLINEAR EXPONENTIAL AUTOREGRESSIVE TIME-SERIES MODEL WITH MOVING AVERAGE ERRORS : AN APPLICATION

摘要

In this article, an important parametric nonlinear Exponential autoregressive (EXPAR) family of time-series model is considered for modelling and forecasting of "cyclical" data. An important feature of this model is that the parameters are able to explain various types of marginal distributions of the time-series, like heavy-tail and bimodal patterns. However, error terms of the EXPARmodel are usually not identically and independently distributed (i.i.d.) and exhibit a systematic behaviour. Accordingly, a generalization of EXPAR model, viz. EXPAR model with moving average (MA) errors is thoroughly investigated here. Specifically, procedure for estimation of parameters of EXPAR model with MA errors is developed. Relevant computer programs are writtenin SAS/IML 9.3 software package and are appended as an annexure. As an illustration, the model is applied to Indian lac production time-series data and performance of fitted model is compared by computing various measures of forecast performance. Finally, it is concluded that the EXPAR model with MA errors performs superior to EXPAR model for the data under consideration.