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Dependent SiZer: Goodness-of-Fit Tests for Time Series Models

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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.
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Keywords: Autocovariance function; Internet traffic data; SiZer; dependent SiZer; fractional Gaussian noise; goodness-of-fit test; time series

Document Type: Research Article

Affiliations: 1: Statistical and Applied Mathematical Sciences Institute, North Carolina, USA 2: Department of Statistics and Operations Research, University of North Carolina, USA 3: Monetary, Financial Institutions and Markets Statistics Division, European Central Bank, Germany

Publication date: October 1, 2004

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