SiZer for time series: A new approach to the analysis of trends

Smoothing methods and SiZer are a useful statistical tool for discovering statistically significant structure in data. Based on scale space ideas originally developed in the computer vision literature, SiZer (SIgnificant ZERo crossing of the derivatives) is a graphical device to assess which observed features are `really there' and which are just spurious sampling artifacts. In this paper, we develop SiZer like ideas in time series analysis to address the important issue of significance of trends. This is not a straightforward extension, since one data set does not contain the information needed to distinguish `trend' from `dependence'. A new visualization is proposed, which shows the statistician the range of trade-offs that are available. Simulation and real data results illustrate the effectiveness of the method.Comment: Published at http://dx.doi.org/10.1214/07-EJS006 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

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

Il metodo SiZer nello studio delle serie storiche: un nuovo approccio per la stima non parametrica del trend

Dottorato di ricerca in statistica metodologica. 11. cicloConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

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

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