Long memory with stochastic variance model

The time seriescharacteristics of postwar US inflation have been found to vary over time. The changes are investigated in a model-based analysis where the time seriesof inflation is specified by a long memory autoregressive fractionally integrated moving averageprocess with its variance modelled by a stochastic volatilityprocess. Estimates of the parameters are obtained by a Monte Carlo maximum likelihood method. A long sample of monthly core inflationis considered in the analysis as well as subsamples of varying length. The empirical results reveal major changes in the variance, in the orderof integration, in the short memory characteristics, and in the volatility of volatility. The findings provide further evidence that the time seriesproperties of inflation are not stable over time.