Approximating long-memory DNA sequences by short-memory process

Abstract

This paper analyzes the approximation of a general long-memory ARFIMA ( p , d , q ) process by a short-memory ARMA(1, 1) process. To validate this approximation, a mean square error forecast criterion is considered, and the calculation of the mean square error between the observation X t + l of an ARFIMA process and the l -step-ahead forecast of the ARMA(1, 1) process is presented. The performance of the ARMA(1, 1) approximation to an ARFIMA model is illustrated by using an application to a DNA sequence of orf virus. This paper gives some theoretical justification on the mean square error forecast criterion based on a selected ARMA(1, 1) model when compared to the general ARFIMA( p , d , q ) process. The paper also provides a DNA sequence of orf virus analysis when the time series is originated from the tangent values of the Chaos Game Representation coordinates for each nucleotide. The conclusions of this paper work well because the estimator value of d is small ( d ˆ = 0.16 ). The paper also gives the other parameter estimate of the fitted ARFIMA (0, d , 1) model and one-step predictions using ARMA(1, 1) model.