Dependent SiZer: Goodness-of-Fit Tests for Time Series Models
Vitaliana Rondonotti, Cheolwoo Park, James Stephen Marron · UNC Libraries · 2021
In this paper, we extend SiZer (SIgnificant ZERo crossing of the derivatives) to dependent data for the purpose of goodness of fit tests for time series models. Dependent SiZer compares the observed data with a specific null model being tested by adjusting the statistical inference using an assumed autocovariance function. This new approach uses a SiZer type visualization to flag statistically significant differences between the data and a given null model. The power of this approach is demonstrated through some examples of time series of Internet traffic data. It is seen that such time series can have even more burstiness than is predicted by the popular, long range dependent, Fractional Gaussian Noise model.