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Detection of Periodic Autocorrelation in Time Series Data via Zero‐Crossings
Author(s) -
Martin Donald E. K.
Publication year - 1999
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00148
Subject(s) - autocorrelation , mathematics , series (stratigraphy) , zero (linguistics) , statistic , autocorrelation technique , statistics , time series , statistical hypothesis testing , moving average model , test statistic , partial autocorrelation function , inverse , algorithm , autoregressive integrated moving average , geometry , paleontology , linguistics , philosophy , biology
A statistical procedure for detection of periodic autocorrelation in time series data is presented. Intuitively, the probability of a zero‐crossing at time t should be inversely related to the correlation between observations at times t and t − 1. Explicit formulas displaying this inverse relationship are given for mean‐zero periodically correlated time series with certain distributional structures. A test statistic based on this relationship is developed. This testing method provides a robust approach to detection of periodic autocorrelation. Analysis of simulated and actual data sets illustrates the usefulness of the proposed method.