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.
ARFIMA-(FI)GARCH Dual long memory Volatility Fractional impulse-response Unemployment Inflation