LONG MEMORY IN PRODUCER PRICES OF SOUTH AFRICA'S TRADING PARTNERS: ARFIMA MODEL

摘要

The fractionally integrated autoregressive moving average model, denoted by ARFIMA can be used for the analysis of a univariate time series y{sub}t with long memory. The long run behavior of a time series can be modelled in a flexible way with the ARFIMA model. Models of long-memory processes include fractional Brownian noise[1] and the ARFIMA process introduced by [2] and [3]. Long memory entails that shocks or innovations to a time series do not have a persistent or a short-run transitory effect, but that they last for a long time. The producer prices of 10 trading partner countries of South Africa are modelled as fractionally integrated processes. The countries included are USA, UK, Japan, Korea, Canada, Singapore, Sweden, Israel, South Africa, Switzerland and Euro. Three parametric estimation procedures are used in the present study; one, due to [4] is the Exact Maximum Likelihood (EML) estimator, and the others are the nonlinear least squares (NLS) estimator by [5] and the Modified Profile Likelihood (MPL). These procedures are implemented using the ARFIMA package for the Ox program [6].