The replacement of the Neumann trend test and the Durbin-Watson test on residuals by one-way ANOVA with resampling and an extension of the tests to different time lags

摘要

In our investigation we focused on the replacement and on the extension of two traditional parametric tests used for detecting trend and autocorrelation in time series. We found that the Neumann test of gradual trend and the Durbin-Watson test of residuals can be replaced by one-way analysis of variance (ANOVA) with resampling. Resampling meant a proper choice of numerous pairs of data, where each pair consisted of two successive data points. We extended the Neumann test, the Durbin-Watson test and our ANOVA method with the introduction of time lag. If the resampled data consisted of pairs with a time lag of h, we obtained a set of tests with different answers on the hypothesis at the h-values. The time lag extended tests with resampling seemed to be efficient in the detection of hidden autocorrelation, trend and relevant time scales for data modelling. The methods were compared on simple model data and on data of air pollutants recorded in Hungary. The Neumann(h) and the ANOVA(h) curves were specific for the different pollutant and helped to detect and explain local peculiarities.