Spectral Density Based Goodness‐of‐Fit Tests for Time Series Models

Paparoditis, Efstathios

doi:10.1111/1467-9469.00184

Cited by 72 publications

(94 citation statements)

References 32 publications

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“…Box and Pierce (1970), Ljung and Box (1978), or more recently, Paparoditis (2000), Peña and Rodriguez (2001) or Delgado, Hidalgo and Velasco (2003). However, it is well-known that, in general, the serial uncorrelatedness of the errors {e t (θ 0 )} neither imply (3) nor (2), and therefore, these tests may not be able to detect some misspecifications in the conditional mean.…”

Section: Introductionmentioning

confidence: 99%

Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models

Escanciano

2006

Journal of the American Statistical Association

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In this article we study a general class of goodness-of-fit tests for the conditional mean of a linear or nonlinear time series model. Among the properties of the proposed tests are that they are suitable when the conditioning set is infinite-dimensional; are consistent against a broad class of alternatives including Pitman's local alternatives converging at the parametric rate ; and do not need to choose a lag order depending on the sample size or to smooth the data. It turns out that the asymptotic null distributions of the tests depend on the data generating process, so a new bootstrap procedure is proposed and theoretically justified. The proposed bootstrap tests are robust to higher order dependence, in particular to conditional heteroskedasticity of unknown form. A simulation study compares the finite sample performance of the proposed and competing tests and shows that our tests can play a valuable role in time series modeling. Finally, an application to an economic price series highlights the merits of our approach. GOODNESS-OF-FIT TESTS FOR LINEAR AND NON-LINEAR TIME SERIES MODELSJ. C E * January 18, 2005Abstract In this article we study a general class of goodness-of-fit tests for the conditional mean of a linear or nonlinear time series model. Among the properties of the proposed tests are that they are suitable when the conditioning set is infinite-dimensional; are consistent against a broad class of alternatives including Pitman's local alternatives converging at the parametric rate n −1/2 , with n the sample size; and do not need to choose a lag order depending on the sample size or to smooth the data. It turns out that the asymptotic null distributions of the tests depend on the data generating process, so a new bootstrap procedure is proposed and theoretically justified. The proposed bootstrap tests are robust to higher order dependence, in particular to conditional heteroskedasticity of unknown form. A simulation study compares the finite sample performance of the proposed and competing tests and shows that our tests can play a valuable role in time series modeling. Finally, an application to an economic price series highlights the merits of our approach.

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Section: Introductionmentioning

confidence: 99%

Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models

Escanciano

2006

Journal of the American Statistical Association

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“…For extensions of this basic approach see also Paparoditis (2000) and Delgado, Hidalgo and Velasco (2005), among others.…”

Section: Tests Based On a In…nite-dimensional Conditioning Setmentioning

confidence: 99%

Testing the Martingale Hypothesis

Escanciano¹,

Lobato²

2009

Palgrave Handbook of Econometrics

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This article examines testing the Martingale Di¤erence Hypothesis (MDH) and related statistical inference issues. The earlier literature on testing the MDH was based on linear measures of dependence, such as sample autocorrelations, for instance the classical Box-Pierce Portmanteau test and the Variance Ratio test. In order to account for the existing nonlinearity in economic and …nancial data, two directions have been entertained. First, to modify these classical approaches by taking into account the possible nonlinear dependence. Second, to use more sophisticated statistical tools such as those based on empirical processes theory or the use of generalized spectral analysis. This paper discusses these developments and applies them to exchange rate data.

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“…His procedure relies on a distance measure between two spectral densities of the data and the one under the null hypothesis of no serial correlation. Paparoditis (2000) proposes a test statistic based on the distance between a kernel estimator of the ratio between the true and the hypothesized spectral density and the expected value of the estimator under the null. Wavelet methods are particularly suitable in such situations where the data has jumps, kinks, seasonality and nonstationary features.…”

Section: Introductionmentioning

confidence: 99%