Further results on the finite-sample distribution of Monti's portmanteau test for the adequacy of an ARMA (p,q) model

Kwan, Connie; Wu, Yangru

doi:10.1093/biomet/84.3.733

Cited by 12 publications

(6 citation statements)

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“…Monti (1994) showed by simulations that the estimated size of the test is adequate with moderate sample sizes and the test is more powerful than the Ljung-Box test when the fitted model underestimates the order of the moving average component. Kwan and Wu (1997) examined the finite-sample properties of both tests, (1) and (2), via Monte Carlo simulation. They computed the empirical powers of QMT and QLB when the data were generated with monthly seasonality, finding only slight differences between Q MT and…”

mentioning

confidence: 99%

A Powerful Portmanteau Test of Lack of Fit for Time Series

Peña

Rodríguez

2002

Journal of the American Statistical Association

111

105

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A new portmanteau test for time series more powerful than the tests ofLjung and Box (1978) and Monti (1994} is proposed. The test is based on the pth root of the determinant of the pth autocorrelation matrix. It is shown that this statistic can be interpreted as the geometric mean of the squared multiple correlation coefficients with m lag values when m goes from 1 to p. It can also be interpreted as a geometric mean of the partial autocorrelation coefficients. The asymptotic distribution of the test statistic is obtained. This distribution is a linear combination of chi-squared distributions and it is shown that it can be approximated by a gamma distribution. The power of the test is compared with that of the Ljung and Box and Monti tests and it is shown that the proposed test can be up to 50% more powerful depending upon the model and sample size.The test is applied to the detection of nonlinearity by using the same matrix but with coefficients that are now the autocorrelations of the squared residuals. The new test is more powerful than the test of McLeod and Li (1983) (1978) and Monti (1994) is proposed. The test is based on the pth root of the determinant of the pth autocorrelation matrix. It is shown that this statistic can be interpreted as the geometric mean of the squared multiple correlation coefficients with m lag values when m goes from 1 to p. It can also be interpreted as a geometric mean of the partial autocorrelation coefficients. The asymptotic distribution of the test statistic is obtained. This distribution is a linear combination of chi-squared distributions and it is shown that it can be approximated by a gamma distribution. The power of the test is compared with that of the Ljung and Box and Monti tests and it is shown that the proposed test can be up to 50% more powerful depending upon the model and sample size.The test is applied to the detection of nonlinearity by using the same matrix but with coefficients that are now the autocorrelations of the squared residuals. The new test is more powerful than the test of McLeod and Li (1983) for nonlinearity. An example is presented in which this test detects nonlinearity in the residuals of the sunpot series.

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confidence: 99%

A Powerful Portmanteau Test of Lack of Fit for Time Series

Peña

Rodríguez

2002

Journal of the American Statistical Association

111

105

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“…The result shows that this model is also correct. Although both the models are correct, a basic difference exists between the models in (4) and (5). Our model indicates that not only the data have a seasonal variation but also that within each year, the beer productions in the spring and summer seasons are correlated with those in the fall and winter seasons, respectively, whereas Wei's model exhibits only a pure seasonal variation.…”

Section: Real Data Analysismentioning

confidence: 73%

“…Davies et al [2] and Ljung and Box [3] demonstrated that a modified statistic yields a small sample approximation that is closer to the chi-square distribution. Recently, Monti [4] suggested a diagnostic test based on residual partial autocorrelations, and Kwan and Wu [5] investigated the 182 S. Lee et al finite sample performance of Monti's test. Peña and Rodríguez [6] proposed a new portmanteau test based on the mth root of the determinant of an mth autocorrelation matrix.…”

Section: Introductionmentioning

confidence: 99%

Diagnostic test for unstable autoregressive models

Lee

Kim

2007

Statistics

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In this article, we investigate the limiting distribution of the Ljung and Box test statistic based on squared residuals in unstable autoregressive models [Chan, N.H. and Wei, C.Z., 1988, Limiting distribution of least squares estimates of unstable autoregressive processes. Annals of Statistics, 16, 367-401.]. We show that the limiting distribution is a chi-square distribution in which the degrees of freedom depends only on the number of lags of the residual autocorrelations. Further, we investigate the limiting distribution of Hong's [Hong, Y., 1996, Consistent testing for serial correlation of unknown form. Econometrica, 64, 837-864.] test statistic based on the original and squared residuals. It is shown that their limiting distributions are independent of the unit roots of the characteristic polynomial of the unstable model. The simulation results are listed and an application to quarterly US beer production data has been provided for illustration.

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“…The results from Table VII, however, present rather a mixed picture. The powers of Q LB and Q MT depend greatly on the value of m (as pointed out by Kwan and Wu, 1997) and the estimator.…”

Section: Monte Carlo Experiments and Simulation Resultsmentioning

confidence: 99%

“…Monti's simulation results indicated that the empirical sizes of Q MT are adequate in moderate sample sizes and the test is more powerful than Q LB when the fitted model understates the order of the moving-average component. However, Kwan and Wu (1997) found that the size of Q MT can be affected considerably by m and the empirical power of Q MT is similar to that of Q LB if m is properly chosen. In this paper we analyze, by means of simulation, the effect of the choice of estimation procedures on the finite-sample behaviors of Q LB and Q MT tests.…”

Section: Introductionmentioning

confidence: 97%

The Effect of the Estimation on Goodness‐of‐Fit Tests in Time Series Models

Fang

2005

Journal Time Series Analysis

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We analyze, by simulation, the finite-sample properties of goodness-of-fit tests based on residual autocorrelation coefficients (simple and partial) obtained using different estimators frequently used in the analysis of autoregressive moving-average timeseries models. The estimators considered are unconditional least squares, maximum likelihood and conditional least squares. The results suggest that although the tests based on these estimators are asymptotically equivalent for particular models and parameter values, their sampling properties for samples of the size commonly found in economic applications can differ substantially, because of differences in both finite-sample estimation efficiencies and residual regeneration methods.

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Further results on the finite-sample distribution of Monti's portmanteau test for the adequacy of an ARMA (p,q) model

Cited by 12 publications

References 0 publications

A Powerful Portmanteau Test of Lack of Fit for Time Series

A Powerful Portmanteau Test of Lack of Fit for Time Series

Diagnostic test for unstable autoregressive models

The Effect of the Estimation on Goodness‐of‐Fit Tests in Time Series Models

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