Functional Coefficient Autoregressive Nonlinear Time-series Model for Describing Indian Lac Export Data

INTRODUCTION Box Jenkins’ linear autoregressive integrated moving average (ARIMA) methodology is widely used for analyzing time-series data. Beyond ‘linear’ domain, there are many nonlinear forms to be explored. In fact, nonlinear time-series analysis has been one of the major areas of research in Time-series analysis for more than two decades now. These models are generally more appropriate than linear models for accurately describing dynamics of the series and for making multistep-ahead forecasts. Early development of nonlinear time-series analysis focused on various parametric forms. Engle (1982), in a path breaking work, proposed Autoregressive conditional heteroscedastic (ARCH) model for modelling volatility present in a data set. However, the conditional variance of ARCH(q) model, where q indicates the order of lag, has the property that the unconditional autocorrelation function of squared residuals, if it exists, decays very rapidly, unless q is large. To overcome this limitation of ARCH model, Bollerslev (1986) proposed the Generalized ARCH (GARCH) model, in which the unconditional autocorrelation function of squared residuals has slow decay rate. Unlike ARIMA model, these models are able to capture the presence of heteroscedasticity of conditional error variances. Another important family is bilinear timeseries model, proposed by C. W. G. Granger in 1978, which is capable of modelling data sets in which outliers appear in random epochs (Ghosh et al., 2006b). A heartening feature of the third important family, viz. Self exciting threshold autoregressive (SETAR) family, proposed by H. Tong, is that it is able to describe cyclical data quite efficiently (Tong, 1995).