Modeling U.S. Historical Time-Series Prices and Inflation Using Various Linear and Nonlinear Long-Memory Approaches

This paper estimates the complete historical US price data by employing a relatively new statistical methodology based on long memory. We consider, in addition to the standard case, the possibility of nonlinearities in the form of nonlinear deterministic trends as well as the possibility that persistence exists at both the zero frequency and a frequencies away from zero. We model the fractional nonlinear case using Chebyshev polynomials and model the fractional cyclical structures as a Gegenbauer process. We find in the latter case that that secular (i.e., long-run) persistence and cyclical persistence matter in the behavior of prices, producing long-memory effects that imply mean reversion at both the long-run and cyclical frequencies