84
Views
0
CrossRef citations to date
0
Altmetric
Articles

Generalized autocovariance matrices for multivariate time series

Pages 3797-3817 | Received 10 Feb 2022, Accepted 27 Dec 2022, Published online: 17 Jan 2023

References

  • Bartlett, M. S. 1955. An introduction to stochastic processes. Cambridge, UK: Cambridge University Press.
  • Battaglia, F. 1983. Inverse autocovariances and a measure of linear determinism for a stationary process. Journal of Time Series Analysis 4 (2):79–87. doi:10.1111/j.1467-9892.1983.tb00360.x.
  • Bhatia, R. 1997. Matrix analysis. New York, NY: Springer Verlag.
  • Bibi, A., and A. Ghezal. 2018. Markov-switching BILINEAR-GARCH models: Structure and estimation. Communications in Statistics - Theory and Methods 47 (2):307–33. doi:10.1080/03610926.2017.1303732.
  • Bibi, A., and A. Ghezal. 2019. QMLE of periodic time-varying bilinear-GARCH models. Communications in Statistics - Theory and Methods 48 (13):3291–310. doi:10.1080/03610926.2018.1476703.
  • Bibi, A., and K. Kimouche. 2019. Whittle estimation in multivariate CCC-GARCH processes. Communications in Statistics - Theory and Methods 48 (15):3921–40. doi:10.1080/03610926.2018.1484140.
  • Bibi, A., and F. Merahi. 2020. Yule–Walker type estimator of first-order time-varying periodic bilinear differential model for stochastic processes. Communications in Statistics - Theory and Methods 49 (16):4046–72. doi:10.1080/03610926.2019.1594300.
  • Box, G. E. P., and D. A. Pierce. 1970. Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association 65 (332):1509–26. doi:10.1080/01621459.1970.10481180.
  • Brillinger, D. R. 1981. Time series: Data analysis and theory. San Francisco, CA: Holden–Day Inc.
  • Brockwell, P. J., and R. A. Davis. 1987. Time series: Theory and methods. Berlin-Heidelberg, Germany/New York, NY: Springer-Verlag.
  • Cavicchioli, M. 2013. Spectral density of Markov-switching VARMA models. Economics Letters 121 (2):218–20. doi:10.1016/j.econlet.2013.07.022.
  • Cavicchioli, M. 2020a. Spectral representation and autocovariance structure of Markov switching DSGE models. Communications in Statistics - Theory and Methods 49 (7):1635–52. doi:10.1080/03610926.2018.1563184.
  • Cavicchioli, M. 2020b. Generalised cepstral models for the spectrum of vector time series. Electronic Journal of Statistics 14 (1):605–31. doi:10.1214/19-EJS1672.
  • Cavicchioli, M. 2022. Goodness-of-fit tests for Markov switching VAR models using spectral analysis. Journal of Statistical Planning and Inference 219:189–203. doi:10.1016/j.jspi.2021.12.008.
  • Chen, Z. G., and E. J. Hannan. 1980. The distribution of periodogram ordinates. Journal of Time Series Analysis 1 (1):73–82.
  • Cheng, J. 2016. Spectral density of Markov switching models: Derivation, simulation studies and application. Model Assisted Statistics and Applications 11 (4):277–91. doi:10.3233/MAS-160373.
  • Chitturi, R. V. 1974. Distribution of residual autocorrelations in multiple autoregressive schemes. Journal of the American Statistical Association 69 (348):928–34. doi:10.1080/01621459.1974.10480230.
  • Chiu, T. Y. M., T. Leonard, and K.-W. Tsui. 1996. The matrix-logarithmic covariance model. Journal of the American Statistical Association 91 (433):198–210. doi:10.1080/01621459.1996.10476677.
  • Cleveland, W. S. 1972. The inverse autocorrelations of a time series and their applications. Technometrics 14 (2):277–93. doi:10.1080/00401706.1972.10488914.
  • Dzhaparidze, K. 1986. Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series. Springer Science & Business Media.Springer-Verlag, Berlin-Heidelberg-New York.
  • Fackler, P. L. 2005. Notes on Matrix Calculus. North Carolina State University, U.S.
  • Fay, G., E. Moulines, and P. Soulier. 2002. Nonlinear functionals of the periodogram. Journal of Time Series Analysis 23 (5):523–53. doi:10.1111/1467-9892.00277.
  • Fay, G., and P. Soulier. 2001. The periodogram of an i.i.d. sequence. Stochastic Processes and Their Applications 92 (2):315–43. doi:10.1016/S0304-4149(00)00077-6.
  • Fishman, G. S. 2013. Spectral methods in econometrics. Cambridge, Massachusetts, USA: Harvard University Press, doi:10.4159/harvard.9780674334076.
  • Gleser, L. J. 1965. On the asymptotic theory of fixed-size sequential confidence bounds for linear regression parameters. The Annals of Mathematical Statistics 36 (2):463–7. doi:10.1214/aoms/1177700157.
  • Gleser, L. J. 1966. Correction to On the asymptotic theory of fixed-size sequential confidence bounds for linear regression parameters. The Annals of Mathematical Statistics 37 (4):1053–5. doi:10.1214/aoms/1177699388.
  • Granger, C. W. J., and R. Engle. 1983. Applications of spectral analysis in econometrics. in Time series in the frequency domain, ed. D.R. Brillinger and P.R. Krishnaiah, Amsterdam, Netherlands/New York, NY/Oxford, UK: North-Holland.
  • Hamilton, J. D. 1994. Time series analysis. Princeton, NJ: Princeton University Press.
  • Hannan, E. J., and M. Deistler. 2012. The statistical theory of linear systems. Philadelphia, USA: SIAM.
  • Holan, S. H., T. S. McElroy, and G. Wu. 2017. The cepstral model for multivariate time series: The vector exponential model. Statistica Sinica 27:23–42. doi:10.5705/ss.202014.0024.
  • Horn, R. A., and C. R. Johnson. 2013. Matrix Analysis. 2nd ed. Cambridge, UK: Cambridge University Press.
  • Hosking, J. R. M. 1980. The multivariate portmanteau statistic. Journal of the American Statistical Association 75 (371):602–8. doi:10.1080/01621459.1980.10477520.
  • Hosking, JR. M. 1981. Equivalent forms of the multivariate portmanteau statistic. Journal of the Royal Statistical Society B 43 (2):261–2. Corrigendum 51 (2), 303. doi:10.1111/j.2517-6161.1981.tb01179.x.
  • Huhtanen, M., and O. Seiskari. 2012. Computational geometry of positive definiteness. Linear Algebra and Its Applications 437 (7):1562–78. doi:10.1016/j.laa.2012.05.002.
  • Ioannidis, E. E. 2007. Spectra of bivariate VAR(p) models. Journal of Statistical Planning and Inference 137 (2):554–66. doi:10.1016/j.jspi.2005.12.013.
  • Li, W. K., and A. I. McLeod. 1981. Distribution of the residual autocorrelations in multivariate ARMA time series models. Journal of the Royal Statistical Society B 43 (2):231–9. doi:10.1111/j.2517-6161.1981.tb01175.x.
  • Ljung, G. M., and G. E. P. Box. 1978. On a measure of lack of fit in time series models. Biometrika 65 (2):297–303. doi:10.1093/biomet/65.2.297.
  • Lütkepohl, H. 2007. New Introduction to Multiple Time Series Analysis. 2nd ed. Berlin-Heidelberg, Germany/New York, NY: Springer-Verlag.
  • Magnus, J. R., and H. Neudecker. 1986. Symmetry, 0−1 matrices and Jacobians. A review. Econometric Theory 2:157–90.
  • Magnus, J. R., and H. Neudecker. 1999. Matrix differential calculus with applications in statistics and econometrics. Second ed. Chichester, UK/New York, NY: John Wiley and Sons.
  • Marée, S. 2012. Correcting non positive definite correlation matrices. BSc thesis, Applied Mathematics, Delft University of Technology, Delft, Netherlands.
  • McElroy, T. S., and S. H. Holan. 2012. On the computation of autocovariances for generalized Gegenbauer processes. Statistica Sinica 22:1661–87. doi:10.5705/ss.2010.186.
  • Milhoj, A. 1981. A test of fit in time series models. Biometrika 68 (1):167–77.
  • Paparoditis, E. 2005. Testing the fit of a vector autoregressive moving average model. Journal of Time Series Analysis 26 (4):543–68. doi:10.1111/j.1467-9892.2005.00419.x.
  • Pataracchia, B. 2011. The spectral representation of Markov switching ARMA models. Economics Letters 112 (1):11–5. doi:10.1016/j.econlet.2011.03.003.
  • Pourahmadi, M. 1983. Exact factorization of the spectral density and its application to forecasting and time series analysis. Communications in Statistics - Theory and Methods 12 (18):2085–94. doi:10.1080/03610928308828592.
  • Pourahmadi, M. 2001. Foundations of Time series Analysis and prediction Theory. Chichester, UK/New York, NY: John Wiley & Sons.
  • Proietti, T., and A. Luati. 2015. The generalised autocovariance function. Journal of Econometrics 186 (1):245–57. doi:10.1016/j.jeconom.2014.07.004.
  • Proietti, T., and A. Luati. 2016. Generalised partial autocorrelations and the mutual information between past and future. In The Fascination of Probability, Statistics and their Applications, eds. M. Podolskij, R. Stelzer, S. Thorbjornsen and A. Veraart, 303–15. Cham, Switzerland: Springer Verlag.
  • Proietti, T., and A. Luati. 2019. Generalised linear cepstral models for the spectrum of a time series. Statistica Sinica 29:1561–83. doi:10.5705/ss.202017.0322.
  • Rump, S. M. 2006. Verification of positive definiteness. BIT Numerical Mathematics 46 (2):433–52. doi:10.1007/s10543-006-0056-1.
  • Velasco, C. 2000. Non-Gaussian log-periodogram regression. Econometric Theory 16 (1):44–79. doi:10.1017/S0266466600161031.
  • Velilla, S., and H. N. Thu. 2018. A goodness-of-fit test for VARMA(p, q) models. Journal of Statistical Planning and Inference 197:126–40. doi:10.1016/j.jspi.2018.01.002.
  • Walker, A. M. 1965. Some asymptotic results for the periodogram of a stationary time series. Journal of the Australian Mathematical Society 5 (1):107–28. doi:10.1017/S1446788700025921.
  • Wang, P. 2008. Financial econometrics. Routledge advanced texts in economics and finance. London, UK/New York, NY: Taylor & Francis Group.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.