A Unified Approach to Validating Univariate and Multivariate Conditional Distribution Models in Time Series
Bin Chen, Yongmiao Hong
Journal of Econometrics 178 (2014) 22–44
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Modeling conditional distributions in time series has attracted increasing attention in economics and
finance.Wedevelop a new class of generalized Cramer–von Mises (GCM) specification tests for time series
conditional distribution models using a novel approach, which embeds the empirical distribution function
in a spectral framework. Our tests check a large number of lags and are therefore expected to be powerful
against neglected dynamics at higher order lags, which is particularly useful for non-Markovian processes.
Despite using a large number of lags, our tests do not suffer much from loss of a large number of degrees
of freedom, because our approach naturally downweights higher order lags, which is consistent with the
stylized fact that economic or financial markets are more affected by recent past events than by remote
past events. Unlike the existing methods in the literature, the proposed GCM tests cover both univariate
and multivariate conditional distribution models in a unified framework. They exploit the information
in the joint conditional distribution of underlying economic processes. Moreover, a class of easy-tointerpret
diagnostic procedures are supplemented to gauge possible sources of model misspecifications.
Distinct from conventionalCMand Kolmogorov–Smirnov (KS) tests, which are also based on the empirical
distribution function, our GCM test statistics follow a convenient asymptotic N(0, 1) distribution and
enjoy the appealing ‘‘nuisance parameter free’’ property that parameter estimation uncertainty has no
impact on the asymptotic distribution of the test statistics. Simulation studies show that the tests provide
reliable inference for sample sizes often encountered in economics and finance.
JEL-Codes: C4 G0
Keywords: Diagnostic procedure Empirical distribution function Frequency domain Generalized Cramer–von Mises test Kernel method Non-Markovian process Time series conditional distribution model