Detecting misspecifications in autoregressive conditional duration models and non-negative time-series processes

Abstract

We develop a general theory to test correct specification of multiplicative error models of non-negative time-series processes, which include the popular autoregressive conditional duration (ACD) models. Both linear and nonlinear conditional expectation models are covered, and standardized innovations can have time-varying conditional dispersion and higher-order conditional moments of unknown form. No specific estimation method is required, and the tests have a convenient null asymptotic N(0,1) distribution. To reduce the impact of parameter estimation uncertainty in finite samples, we adopt Wooldridge's (1990a) device to our context and justify its validity. Simulation studies show that in the context of testing ACD models, finite sample correction gives better sizes in finite samples and are robust to parameter estimation uncertainty. And, it is important to take into account timevarying conditional dispersion and higher-order conditional moments in standardized innovations; failure to do so can cause strong overrejection of a correctly specified ACD model. The proposed tests have reasonable power against a variety of popular linear and nonlinear ACD alternatives.

A Goodness-of-Fit Test for a Class of Autoregressive Conditional Duration Models

“…In a simulation study, the KS and CvM tests were evaluated and compared with four tests currently available in the literature, namely the general purpose Ljung-Box Q [LBQ] test, a Lagrange multiplier [LM] test (Meitz and Teräsvirta, 2006), a generalized moment test (Chen and Hsieh, 2010) and a generalized spectral derivative test (Hong and Lee, 2011). …”

“…The generalized moment tests of Chen and Hsieh [2010] unifies several existing parametric tests for ACD models. Hong and Lee [2011] developed tests for a given parametric specification of the conditional mean E x t t−1 of an ACD model, by adapting a generalized spectral derivative approach. These tests are based on certain kernel density estimates and involves the choice of a preliminary bandwidth which is somewhat arbitrary.…”

“…A simulation study was carried out to investigate the finite sample performance of the proposed tests KS and CvM, and compare them with the Ljung-Box Q test (Ljung and Box, 1978), a Lagrange multiplier (LM) test (Meitz and Teräsvirta, 2006), a generalized moment test (Chen and Hsieh, 2010), and a generalized spectral derivative test (Hong and Lee, 2011). The use of the Ljung-Box Q test, in the context of ACD models, was first suggested by Engle and Russell [1998].…”

“…By adapting a particular generalized spectral derivative approach, Hong and Lee [2011] developed a class of tests for a given parametric specification of E x t t−1 These tests are based on certain kernel density estimates, and hence, their finite sample performances may be sensitive to the choice of the kernal and/or the bandwidth. Chen and Hsieh [2010] proposed a set of generalized moment tests, unifying several existing parametric tests for ACD models.…”

Econometric Time Series Specification Testing in a Class of Multiplicative Error Models

“…Li and Yu (2003) derive a portmanteau test that can be used to evaluate the adequacy of an estimated ACD model. On the one hand, Meitz and Teräsvirta (2006) present a framework for evaluating models of conditional duration based on Lagrange multiplier misspecification tests of the functional form of the conditional mean duration, while, on the other hand, Hong and Lee (2011) do so based on the generalized spectral derivative approach. Moreover, a number of recent studies consider explicit tests on the distribution of the error terms.…”