Testing Dependence Among Serially Correlated Multicategory Variables

Abstract

The contingency table literature on tests for dependence among discrete multicategory variables is extensive. Standard tests assume, however, that draws are independent and only limited results exist on the effect of serial dependency-a problem that is important in areas such as economics, finance, medical trials, and meteorology. This article proposes new tests of independence based on canonical correlations from dynamically augmented reduced rank regressions. The tests allow for an arbitrary number of categories as well as multiway tables of arbitrary dimension and are robust in the presence of serial dependencies that take the form of finite-order Markov processes. For three-way or higher order tables we propose new tests of joint and marginal independence. Monte Carlo experiments show that the proposed tests have good finite sample properties. An empirical application to microeconomic survey data on firms' forecasts of changes to their production and prices demonstrates the importance of correcting for serial dependencies in predictability tests.

Asymptotic variance of Brier (skill) score in the presence of serial correlation

“…One implication of serial correlation is that the usual sampling variance of the score obtained by assuming independence is no longer valid. This phenomenon has been recognized by Lahiri and Yang (2015) and Pesaran and Timmermann (2009) in various scenarios. Wilks (2010) has shown that the failure to accommodate positive serial correlation will significantly underestimate the standard error of the Brier (skill) score and the magnitude of underestimation depends on the event probability and the quality of the forecast.…”

Forecasting Local Inflation with Global Inflation: When Economic Theory Meets the Facts

“…Tossing a fair coin on a su¢ ciently long sample already predicts the direction of change correctly about 50% of the time, so a model needs to attain a success ratio greater than 0:5 to provide an improvement in directional accuracy over pure chance. 8 The statistical signi…cance of the directional accuracy relative to pure chance (as implied by the directional accuracy of tossing a fair coin) is assessed based on our implementation of the test of Pesaran and Timmermann (2009).…”

Confidence Bands for ROC Curves With Serially Dependent Data

“…Blaskowitz and Herwartz (2011) and Pesaran and Timmermann (2009) have developed tests designed to take care of the serial correlation while testing dependence among binary variables. Wilks (2010) has shown that the failure to accommodate serial correlation will seriously underestimate the standard error of the Brier skill score.…”

“…Wilks (2010) has shown that the failure to accommodate serial correlation will seriously underestimate the standard error of the Brier skill score. Pesaran and Timmermann (2009) cite many articles that deal with the effect of serial dependence on the chi-squared tests of independence based on two-way contingency tables. Our paper parallels this literature in that we robustify the current procedures to accommodate serial dependence in the parametric binormal ROC model.…”