324 – Modeling and Seasonal Adjustment of Economic Time Series
Gaussianity versus Correlation in Time Series Residual Diagnostics
James Livsey
U.S. Census Bureau
Tucker Sprague McElroy
U.S. Census Bureau
Anindya Roy
U.S. Census Bureau
The time series model selection problem is strongly rooted in residual analysis. Due to increased data collection, computing power and public interest, more-and-more important time series models are fit using iterative computer aided methods. These iterative methods usually fit competing models and compare residuals or likelihood based criteria to select then best models. The basis of this work is to improve the iterative methodology. This proceedings paper will discuss current methods used during iterative model fitting; then, introduce a measure for model residuals that weighs whiteness and marginal distribution concurrently. For example, if residuals are assumed normal then perfect residuals are Gaussian noise. We seek a single score that is minimized at uncorrelated Gaussian and grows as residuals deviate from either property. Distributional theory of such a measure will be described. Finally, empirical studies will be presented supporting ideas and illustrating the practical uses of such a measure.