Long Memory and Estimation of Memory Parameters: Nigerian and US Inflation Rates

Abstract

Most economic series have been analyzed on the assumption that they are integrated of order d that is I(d), where d is an integer. Such series exhibit a short memory process characterized with exponential decay in the autocorrelation function (ACF) sometimes with alternating signs after dth order of difference. However, evidence of long memory and persistent autocorrelations characterized by (fractional integration) has been documented in literature for many economic series. Thus results of analysis based on wrong assumptions of the order of integration will produce biased estimates and unreliable forecast values. This paper therefore focuses on investigating the existence or otherwise of long memory in the Nigerian and US inflation series using some standard tests. It also seeks to estimate the memory parameters if it exists using the parametric and non-parametric methods. Even though the US inflation is fractionally integrated and Nigerian inflation series has unit root, the linear model specified for them are not adequate. The residual analyses shows evidence of nonlinearity and ARCH effect implying suggesting that nonlinear models or generalized autoregressive conditional heteroscedastic models may be appropriate for the series.

Keywords: Fractional Integration, KPSS Test, Long Memory, Rescaled Statistics, Spectral Density

JEL Classification: C22, C51, C87