Research Reports

On the Computation of Autocovariances for Generalized Gegenbauer Processes

Tucker S. McElroy and Scott H. Holan

KEY WORDS:

ARFIMA; Exponential model; FEXP model; GARMA; k-factor GARMA; k-factor

ABSTRACT

Gegenbauer processes and their generalizations represent an extremely general way of modeling long memory and seasonal long memory; they include ARFIMA, seasonal ARFIMA, and GARMA processes as special cases. Models from this class of processes have been used extensively in economics, finance and in the physical sciences and are thus of widespread interest. Nonetheless, one obstacle to using this class of models is finding explicit formulas for the autocovariances that are valid for all lags. We provide a computationally effcient method of computing these autocovariances by determining the moving average representation of these processes, and also give an asymptotic formula for the determinant of the covariance matrix. The techniques are then illustrated using maximum likelihood estimation to model atmospheric CO2 data.

CITATION:

Tucker S. McElroy and Scott H. Holan. (2011). On the Computation of Autocovariances for Generalized Gegenbauer Processes. Center for Statistical Research & Methodology, Research and Methodology Directorate Research Report Series (Statistics #2011-06). U.S. Census Bureau. Available online at <http://www.census.gov/srd/papers/pdf/rrs2011-06.pdf>.

Source: U.S. Census Bureau, Center for Statistical Research & Methodology, Research and Methodology Directorate

Published online: April 20, 2011
Last revised: April 20, 2011