626 – Statistical Inference for Economic Time Series
Fast Estimation of Time Series with Multiple Long-Range Persistencies
Tucker Sprague McElroy
U.S. Census Bureau
Scott H. Holan
University of Missouri
Gegenbauer processes allow for flexible and convenient modeling of time series data with multiple spectral peaks, where the qualitative description of these peaks is via the concept of cyclical long-range dependence. The Gegenbauer class is extensive, including ARFIMA, seasonal ARFIMA, and GARMA processes as special cases. Model estimation is challenging for Gegenbauer processes when multiple zeroes and poles occur in the spectral density, because the autocovariance function is laborious to compute. The method of splitting -- essentially computing autocovariances by convolving long memory and short memory dynamics -- is only tractable when a single long memory pole exists. The main contribution of this paper is to propose an additive decomposition of the spectrum into a sum of spectra that each have a single singularity, so that an efficient splitting method can be applied to each term and then aggregated. This approach differs from McElroy and Holan (2012), which handles all poles in the spectral density at once through a careful analysis of truncation error. This paper's technique allows for fast estimation of time series with multiple long-range dependencies, which we illustrate numerically and through several case-studies.