Illusory Statistical Power in Time Series Analysis

Abstract

Preprocessing of time series data with moving average and autoregressive processes serves a useful purpose in time series analysis; but the further use of the preprocessed series for computing probability in hypothesis tests or for constructing confidence intervals requires a correction to the degrees of freedom imposed on the filtered series by multiplicity. Multiplicity derives from repeated use of the same data item in the source data series for the computation of multiple items in the filtered series. A procedure for estimating multiplicity and the effective degrees of freedom implied by multiplicity is proposed and its utility is demonstrated with examples. It is found that without a multiplicity correction the filtered series can show an illusory increase in statistical power.

Keywords: Applied Statistics, Spurious Correlations, Cumulative Values, Moving Averages, Moving Window, Degrees of Freedom, Information Theory, Time Series, Data Analysis, Climate Change, Global Warming, Hurricane Trends