The use of the autocorrelation function in modeling of multivariate data

The use of the autocorrelation function ( R 1) with lag 1 in univariate and multivariate model selection is proposed. In the univariate case, a Z-value is calculated from the R 1 of the residual vector. A high positive value of Z indicates the presence of smooth, non-random variations in the data not explained by the model considered. In the multivariate case, a new procedure is proposed. A “short” path is found in the independent variable space, and the Z from the dependent variable residual vector is used to measure the smoothness of the changes in the dependent variable. Applications are shown for variable selection and determination of the number of latent variables in PLS1 models.