The usefulness of econometric models with stochastic volatility and long memory: Applications for macroeconomic and financial time series

Abstract

This study aims to examine the usefulness of econometric models with stochastic volatility and long memory in the application of macroeconomic and financial time series. An ARFIMA-FIAPARCH process is used to estimate the two main parameters driving the degree of persistence in the US real interest rate and its uncertainty. It provides evidence that the US real interest rates exhibit dual long memory and suggests that much more attention needs to be paid to the degree of persistence and its consequences for the economic theories which are still inconsistent with the finding of either near-unit-root or long memory mean-reverting behavior. A bivariate GARCH-type of model with/without long-memory is constructed to concern the issue of temporal ordering of inflation, output growth and their respective uncertainties as well as all the possible causal relationships among the four variables in the US/UK, allowing several lags of the conditional variances/levels used as regressors in the mean/variance equations. Notably, the findings are quite robust to changes in the specification of the model. The applicability and out-of-sample forecasting ability of a multivariate constant conditional correlation FIAPARCH model are analysed through a multi-country study of national stock market returns. This multivariate specification is generally applicable once power, leverage and long-memory effects are taken into consideration. In addition, both the optimal fractional differencing parameter and power transformation are remarkably similar across countries.