On Goodness of Fit of Time Series Models: An Application of Higher Order Crossings
Benjamin Kedem, ERIC V. SLUD · Biometrika · 1981
A relation between the graphical appearance of a stationary time series and its autocorrelations is discussed. The use of counts of visual features termed higher order crossings is proposed in testing goodness of fit of hypothesized models against very general alternatives. Attention is focused on a specific example of a new type of nonparametric test statistic arising from iterative feature extraction procedures called extractors. The statistic is compared with Box & Pierce's portmanteau Q statistic on real data as well as on simulated normal autoregressive-moving average series.