A Generalization of Some Classical Time Series Tools

Henrik Aalborg Nielsen, Henrik Madsen

AbstractIn classical time series analysis the sample autocorrelation function
(SACF) and the sample partial autocorrelation function
(SPACF) has gained wide application for structural identification of
linear time series models. We suggest generalizations, founded on
smoothing techniques, applicable for structural identification of
non-linear time series models. A similar generalization of the sample
cross correlation function is discussed. Furthermore, a measure of
the departure from linearity is suggested. It is shown how
bootstrapping can be applied to construct confidence intervals under
independence or linearity. The generalizations do not prescribe a
particular smoothing technique. In fact, when the smoother is
replaced by a linear regression the generalizations reduce to close
approximations of SACF and SPACF. For this reason a smooth transition
from the linear to the non-linear case can be obtained by varying the
bandwidth of a local linear smoother. By adjusting the flexibility of
the smoother the power of the tests for independence and linearity
against specific alternatives can be adjusted. The generalizations
allow for graphical presentations, very similar to those used for SACF
and SPACF. In this paper the generalizations are applied to some
simulated data sets and to the Canadian lynx data. The generalizations
seem to perform well and the measure of the departure from linearity
proves to be an important additional tool.
KeywordsLagged scatter plot; R-squared; Non-linear time series; Smoothing; Non-parametric; Independence; Bootstrap.
TypeJournal paper [With referee]
JournalComputational Statistics and Data Analysis
Year2001    Vol. 37    No. 1    pp. 13-31
PublisherElsevier Science B.V.
Electronic version(s)[pdf]
BibTeX data [bibtex]
IMM Group(s)Mathematical Statistics