Análise de variância em séries temporais: uma abordagem usando ondaletas

Abstract

The analysis of variance (ANAVA) is widely used to check for significant di erences among treatments. However, for the results to be reliable, it is necessary to check the assumptions of ANAVA, which are additivity of e ects in the model and independence, normality and homoscedasticity of errors. However, quite frequently it turns out that one or more of these assumptions does not occur. And that’s what happens when working with time series data, which leads to problems such as non-independence between consecutive observations. Thus, this study was conducted with the objective to propose a methodology for conducting the ANAVA in time series data. As the traditional analysis is not adequate, the proposal is “ transform ” the data, eliminating the dependency between them, in order to meet the required assumptions. The transformation occurs by means of the discrete wavelet transform decimated for non-stational temporal series and the discrete wavelet transform not decimated for non-stational temporal series, using, in both cases, the Haar and Daubechies bases. Thus, a simulation study was conducted considering stational and non-stational temporal series. We also conducted a study with real data. We concluded that the analysis of variance using wavelets could be successfully used when working with temporal series data. For the temporal series considered non-stational categorical, we must prioritize the use of not decimated discrete wavelet transform on the Daubechies basis.