Testing time series linearity: traditional and bootstrap methods

We review the notion of time series linearity and describe recent advances in linearity and Gaussianity testing via data-resampling methodologies. Many advances have been made since the first published tests of linearity and Gaussianity by Subba Rao and Gabr in 1980, including several resampling-based proposals. This article is intended to be instructive in explaining and motivating linearity testing. Recent results on the validity of the AR–sieve bootstrap for linearity testing are reviewed. In addition, a subsampling-based linearity and Gaussianity test is proposed where asymptotic consistency of the testing procedure is justified. ∗Department of Biostatistics, Penn State University, Hershey, PA 17033 email: [email protected]. †Department of Mathematics, DePaul University Chicago, IL 60614 email: [email protected]. ‡Department of Mathematics, University of California at San Diego, La Jolla, CA 92093-0112; email: [email protected].