Long Memory in UK Real GDP, 1851-2013: An ARFIMA-FIGARCH Analysis

Abstract

This paper analyses the long-memory properties of both the conditional mean and variance of UK real GDP over the period 1851-2013 by estimating a multivariate ARFIMA-FIGARCH model (with the unemployment rate and inflation as explanatory variables). The results suggest that this series is non-stationary and non-mean-reverting, the null hypotheses of I(0), I(1) and I(2) being rejected in favour of fractional integration -- shocks appear to have permanent effects, and therefore policy actions are required to restore equilibrium. The estimate of the long-memory parameter (1.37) is similar to that reported by Candelon and Gil-Alana (2004), implying that aggregate output is not an I(1) process. The presence of long memory in output volatility (d=0.80) is also confirmed.

Keywords: ARFIMA-(FI)GARCH, Dual long memory, Volatility, Fractional impulse-response, Unemployment, Inflation

JEL Classification: B23, C14, C32, C53, C54