Testing against changing correlation

Abstract

A test for time-varying correlation is developed within the framework of a dynamic conditional score (DCS) model for both Gaussian and Student t-distributions. The test may be interpreted as a Lagrange multiplier test and modi…ed to allow for the estimation of models for time-varying volatility in the individual series. Unlike standard moment-based tests, the score-based test statistic includes information on the level of correlation under the null hypothesis and local power arguments indicate the bene…ts of doing so. A simulation study shows that the performance of the score-based test is strong relative to existing tests across a range of data generating processes. An application to the Hong Kong and South Korean equity markets shows that the new test reveals changes in correlation that are not detected by the standard moment-based test.

Generalized Autoregressive Score Models in R: The GAS Package

“…It does not matter whether they are real-valued, integer-valued, (0,1)-bounded or strictly positive, as long as there is a conditional density for which the score function and the Hessian are well-defined. The practical relevance of the GAS framework has been illustrated in the case of financial risk forecasting (see e.g., Harvey and Sucarrat (2014) for market risk, Oh and Patton (2013) for systematic risk, and Creal et al (2014) for credit risk analysis), dependence modelling (see e.g., Harvey and Thiele (2015) and Janus et al (2014)), and spatial econometrics (see e.g., Blasques et al (2014d) and Catania and Billé (2016)). For a more complete overview of the work on GAS models, we refer the reader to the GAS community page at http://www.gasmodel.com/.…”

Score-Driven Time Series Models

“…As a result u t is negative and so t+1jt falls unless x 1t and The scores may be computed under the null hypothesis of constant correlation tjt 1 = r; where r is the maximum likelihood estimator of ; and used in a portmanteau test. When r = 0; moment-based tests are obtained because u t = x 1t x 2t , but when r 6 = 0 the score-based tests can be much more powerful; see Harvey and Thiele (2016). The tests can be modi…ed for a bivariate t-distribution with estimated EGARCH models.…”

Modeling and Forecasting Macroeconomic Downside Risk

“…Then, using the estimated parameters we recover the time series of of the scores s γ and s δ , which we use to carry out the tests. Specifically, following Harvey and Thiele (2016), which apply this methodology to test against the time variation of correlations, we employ three different test specifications: the Portmanteau test, Q, the Ljung-Box test, Q * , and the test. For all these test, the optimal lag-length is selected following the methodology of .…”