The Analysis of Variance of Time Series Data. Part I: One-Way Layout

摘要

The classical mean and variance estimators do not allow autocorrelation in observed data; therefore, new estimators are developed for application to this type of data. The method of maximum likelihood is used to obtain the estimators as linear and quadratic forms whose coefficients are derived from the correlation matrix of the data. They are stochastically independent and unbiased. The distributions of these estimators are found; and as a result, the new estimators are applied to the analysis of variance (AOV) of autocorrelated time series data using the one-way layout. The new AOV expressions are developed for arbitrary autocorrelation functions and presented in detail for the special cases of white noise and red noise in the data. The effect of falsely assuming white noise rather than the correct red noise is investigated, and the results indicate wrong conclusions can be expected more often than the confidence level indicates. (Author)