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Testing for seasonal means in time series data
Author(s) -
Liu Gang,
Shao Qin,
Lund Robert,
Woody Jonathan
Publication year - 2016
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.2383
Subject(s) - series (stratigraphy) , statistics , independent and identically distributed random variables , statistic , mathematics , gaussian , time series , test statistic , variance (accounting) , moment (physics) , statistical hypothesis testing , computer science , random variable , paleontology , physics , accounting , classical mechanics , quantum mechanics , business , biology
The statistician often needs to test whether or not a time series has a seasonal first moment. The problem often arises in environmental series, where most time‐ordered data display some type of periodic structure. This paper reviews the problem, proposing new statistics in both the time and frequency domains. Our new time domain statistic has an analysis of variance form that is based on the one‐step‐ahead prediction errors of the series. This statistic inherits the classic traits of the F ‐distribution arising in one‐way analysis of variance tests, is easy to use, and is asymptotically equivalent to the likelihood ratio test. The statistics asymptotic distribution is quantified when time series parameters are estimated. In the frequency domain, a statistic modifying Fisher's classical test for a sinusoidal mean superimposed on independent and identically distributed Gaussian noise is devised. The performance and comparison of these statistics are studied via simulation. Implementation of the methods merely requires sample means, autocovariances, and periodograms of the series. Application to a data set of monthly temperatures from Tuscaloosa, Alabama, is given. Copyright © 2016 John Wiley & Sons, Ltd.