A Powerful Portmanteau Test of Lack of Fit for Time Series

By D. Pena, Julio Rodríguez. 2002

135 citations recorded by the source corpus.

A new portmanteau test for time series, more powerful than the tests of Ljung and Box and Monti, is proposed. The test is based on the mth root of the determinant of the mth autocorrelation matrix. It is shown that the proposed statistic is a function of all of the squared multiple correlation coefficients of the regressions of the residuals on their lags when the number of lags goes from 1 to m. It can also be written as a function of the first m partial autocorrelation coefficients. The asymptotic distribution of the test statistic is a linear combination of chi-squared distributions and can be approximated by a gamma distribution. It is shown, depending on the model and sample size, that this test can be up to 50% more powerful than the Ljung and Box and Monti tests. The test is applied to the detection of several types of nonlinearity by using the autocorrelation matrix of the squared residuals, and it is shown that, in general, the new test is more powerful than the test of McLeod and Li. An example is presented in which this test finds nonlinearity in the residuals of the sunspot series.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/45e5438bfd4f9faeafc0169a321dec034dc270cd

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Citations in the corpus

Effects of outliers on the identification and estimation of GARCH models (2007, background): “Many popular tests for conditional homoscedasticity, such as those proposed by Engle (1982), McLeod and Li (1983), Peña and Rodriguez (2002), and Rodriguez and Ruiz (2005) among others, are based on autocorrelations of squares and if these autocorrelations are biased, their properties will be…”
New Weighted Portmanteau Statistics for Time Series Goodness of Fit Testing (2012, background): “Pena and Rodriguez ( 2002 ) proposed a statistic based on the determinant of the Toeplitz matrix of sample autocorrelations”
The log of the determinant of the autocorrelation matrix for testing goodness of fit in time series (2006, methodology): “For linear models the test is shown to be more powerful than the ones proposed by Ljung and Box (1978), Monti (1994), Peña and Rodríguez (2002) and Hong (1996), whereas for detecting nonlinearity the test is shown to be also more powerful than those proposed by McLeod and Li (1983) and Peña and…”
Improved multivariate portmanteau test (2012, methodology): “Hence, one can not simply use the generalized variance of the standardized residuals as in [28].”
Discussion: Performance of Bayesian Model Averaging (2003, methodology): “…research on testing methods routinely implicitly de nes such a distribution through the parameter values chosen for the simulation studies carried out to assess the power of a test; for recent articles of this kind in this journal, see Pena and Rodríguez (2002) and Horowitz and Spokoiny(2002).”