New mixed portmanteau tests for time series models
Tóm tắt
This article proposes omnibus portmanteau tests for contrasting adequacy of time series models. The test statistics are based on combining the autocorrelation function of the conditional residuals, the autocorrelation function of the conditional squared residuals, and the cross-correlation function between these residuals and their squares. The maximum likelihood estimator is used to derive the asymptotic distribution of the proposed test statistics under a general class of time series models, including ARMA, GARCH, and other nonlinear structures. An extensive Monte Carlo simulation study shows that the proposed tests successfully control the type I error probability and tend to have more power than other competitor tests in many scenarios. Two applications to a set of weekly stock returns for 92 companies from the S &P 500 demonstrate the practical use of the proposed tests.
Tài liệu tham khảo
Akaike, H.: A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)
Box, G.E.P.: Some theorems on quadratic forms applied in the study of analysis of variance problems, I effect of inequality of variance in the one-way classification. Ann. Math. Stat. 25(2), 290–302 (1954)
Box, G., Jenkins, G.: Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco (1970)
Box, G.E.P., Pierce, D.A.: Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. J. Am. Stat. Assoc. 65(332), 1509–1526 (1970)
Efron, B., Tibshirani, R.: An Introduction to the Bootstrap. Monographs on Statistics & Applied Probability, Taylor & Francis (1994)
Engle, R.: Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica 50(4), 987–1007 (1982)
Fisher, T.J., Gallagher, C.M.: New weighted portmanteau statistics for time series goodness of fit testing. J. Am. Stat. Assoc. 107(498), 777–787 (2012)
Granger, C.W.J., Andersen, A.P.: An Introduction to Bilinear Time Series Models. Gottingen, Vandenhoeck and Ruprecht (1978)
Hall, P., Heyde, C.: Estimation of parameters from stochastic processes. In: Martingale Limit Theory and its Application, Probability and Mathematical Statistics: A Series of Monographs and Textbooks, pp. 155–199. Academic Press, New York (1980)
Han, N.S., Ling, S.: Goodness-of-fit test for nonlinear time series models. Ann. Financ. Econ. 12(02), 1750006 (2017)
Higgins, M.L., Bera, A.K.: A class of nonlinear arch models. Int. Econ. Rev. 33(1), 137–158 (1992)
Kapetanios, G.: Testing for strict stationarity in financial variables. J. Bank. Finance 33, 2346–2362 (2009)
Lawrance, A.J., Lewis, P.A.W.: Modelling and residual analysis of nonlinear autoregressive time series in exponential variables. J. Roy. Stat. Soc. Ser. B (Methodological) 47(2), 165–202 (1985)
Lawrance, A.J., Lewis, P.A.W.: Higher-order residual analysis for nonlinear time series with autoregressive correlation structures. Int. Stat. Rev. 55(1), 21–35 (1987)
Li, W.K., Mak, T.K.: On the squared residual autocorrelations in non-linear time series with conditional heteroskedasticity. J. Time Ser. Anal. 15(6), 627–636 (1994)
Li, D., Zhang, X., Zhu, K., Ling, S.: The ZD-GARCH model: a new way to study heteroscedasticity. J. Econ. 202(1), 1–17 (2018)
Lin, J.-W., McLeod, A.: Improved peña-rodríguez portmanteau test. Comput. Stat. Data Anal. 51(3), 1731–1738 (2006)
Ling, S., Li, W.K.: Diagnostic checking of nonlinear multivariate time series with multivariate arch errors. J. Time Ser. Anal. 18(5), 447–464 (1997)
Ling, S., McAleer, M.: Asymptotic theory for a vector ARMA-GARCH model. Economet. Theor. 19(2), 280–310 (2003)
Ling, S., McAleer, M.: A general asymptotic theory for time-series models. Stat. Neerl. 64(1), 97–111 (2010)
Ljung, G.M., Box, G.E.P.: On a measure of lack of fit in time series models. Biometrika 65(2), 297–303 (1978)
Mahdi, E., Ian McLeod, A.: Improved multivariate portmanteau test. J. Time Ser. Anal. 33(2), 211–222 (2012)
Mahdi, E.: Portmanteau test statistics for seasonal serial correlation in time series models. SpringerPlus 5, 1485 (2016)
Mahdi, E.: Kernel-based portmanteau diagnostic test for ARMA time series models. Cogent Math. 4(1), 1296327 (2017)
Mahdi, E., McLeod, A.I.: Portes: portmanteau tests for univariate and multivariate time series models. R package version 5.0 (2020)
McLeod, A.I., Li, W.K.: Diagnostic checking ARMA time series models using squared-residual autocorrelations. J. Time Ser. Anal. 4(4), 269–273 (1983)
Ng, S., Perron, P.: A note on the selection of time series models. Oxford Bull. Econ. Stat. 67(1), 115–134 (2005)
Peña, D., Rodríguez, J.: A powerful portmanteau test of lack of fit for time series. J. Am. Stat. Assoc. 97(458), 601–610 (2002)
Peña, D., Rodríguez, J.: The log of the determinant of the autocorrelation matrix for testing goodness of fit in time series. J. Stat. Plan. Inference 136(8), 2706–2718 (2006)
Psaradakis, Z., Vávra, M.: Portmanteau tests for linearity of stationary time series. Economet. Rev. 38(2), 248–262 (2019)
R Core Team.: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2020)
Rodríguez, J., Ruiz, E.: A powerful test for conditional heteroscedasticity for financial time series with highly persistent volatilities. Stat. Sin. 15(2), 505–525 (2005)
Tong, H., Lim, K.S.: Threshold autoregression, limit cycles and cyclical data. J. Roy. Stat. Soc.: Ser. B (Methodol.) 42(3), 245–268 (1980)
Velasco, C., Wang, X.: A joint portmanteau test for conditional mean and variance time-series models. J. Time Ser. Anal. 36(1), 39–60 (2015)
Welsh, A.K., Jernigan, R.W.: A statistic to identify asymmetric time series. In: Proceedings of the Business and Economics Statistics Section, pp. 390–395. American Statistical Association, Alexandria (1983)
Wong, H., Ling, S.: Mixed portmanteau tests for time-series models. J. Time Ser. Anal. 26(4), 569–579 (2005)
Zhu, K.: A mixed portmanteau test for ARMA-GARCH models by the quasi-maximum exponential likelihood estimation approach. J. Time Ser. Anal. 34(2), 230–237 (2013)