Testing for seasonal means in time series data

Abstract

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.

Multiple changepoint detection with partial information on changepoint times

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Simultaneous Confidence Band Approach for Comparison of COVID-19 Case Counts

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On testing for the equality of autocovariance in time series

“…Such a test can be applied to reference series identification, inference by proxy and time series clustering. For example, reference series are commonly used in climatology to adjust or detect outlying observations, detect changepoints or differences in periodicities of series (see Liu et al, 2016;Peterson & Easterling, 1994, for examples). Lund and Li (2009) defined climatic zones in Colorado through a clustering method that incorporated the mean and autocorrelation structure of the series.…”