17 Citations (Scopus)

Abstract

A bootstrap algorithm is proposed for testing Gaussianity and linearity in stationary time series, and consistency of the relevant bootstrap approximations is proven rigorously for the first time. Subba Rao and Gabr (1980) and Hinich (1982) have formulated some well-known nonparametric tests for Gaussianity and linearity based on the asymptotic distribution of the normalized bispectrum. The proposed bootstrap procedure gives an alternative way to approximate the finite-sample null distribution of such test statistics. We revisit a modified form of Hinich's test utilizing kernel smoothing, and compare its performance to the bootstrap test on several simulated data sets and two real data sets-the S&P 500 returns and the quarterly US real GNP growth rate. Interestingly, Hinich's test and the proposed bootstrapped version yield substantially different results when testing Gaussianity and linearity of the GNP data.

Original languageEnglish (US)
Pages (from-to)3841-3857
Number of pages17
JournalJournal of Statistical Planning and Inference
Volume140
Issue number12
DOIs
StatePublished - Dec 1 2010

Fingerprint

Bootstrap Test
Linearity
Bootstrap
Time series
Testing
Time Consistency
Bispectrum
Kernel Smoothing
Stationary Time Series
Non-parametric test
Null Distribution
Statistics
Asymptotic distribution
Test Statistic
Alternatives
Approximation
Bootstrap test
Gross national product

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Berg, Arthur ; Paparoditis Efstathios, E. ; Politis, Dimitris N. / A bootstrap test for time series linearity. In: Journal of Statistical Planning and Inference. 2010 ; Vol. 140, No. 12. pp. 3841-3857.
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A bootstrap test for time series linearity. / Berg, Arthur; Paparoditis Efstathios, E.; Politis, Dimitris N.

In: Journal of Statistical Planning and Inference, Vol. 140, No. 12, 01.12.2010, p. 3841-3857.

Research output: Contribution to journalArticle

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AU - Berg, Arthur

AU - Paparoditis Efstathios, E.

AU - Politis, Dimitris N.

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