Further Long Memory Properties of Inflationary Shocks

Several previous studies have found fractionally integrated, or long memory behavior, in the conditional mean of inflation. This paper notes that extremely similar phenomena are also apparent in the squared and absolute values of residuals from fractionally filtered inflation series. Hence, the inflation process appears to have a dual long memory feature in both its first and its second conditional moments. We suggest a parametric model of long memory in both the conditional mean and the conditional variance. Some Monte Carlo evidence is presented that supports estimation of the model by approximate maximum likelihood methods. We then report estimated models for the inflation series for several different industrialized countries, including the United States. For nearly all of the countries in our study, there is strong evidence of statistically significant long memory parameters in both the conditional mean and the variance. We note some of the implications for modeling inflation.