Abstract
In this chapter, we consider multivariate (vector) time series analysis and forecasting problems. Unlike the univariate case, we now have two difficulties with multivariate time series: identifiability and curse of dimensionality. Thus, this chapter focuses on a special and useful VAR models. First, basic concepts on multivariate time series and general VARMA models are introduced. Then, we elaborate on VAR model building, forecasting, Granger causality test, and impulse response analysis.
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References
Akaike, H.: Fitting autoregressive models for prediction. Ann. Inst. Stat. Math. 21, 243–247 (1969)
Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods, 2nd edn. Springer, New York (1991)
Brockwell, P.J., Davis, R.A.: Introduction to Time Series and Forecasting, 3rd edn. Springer, Switzerland (2016)
Gómez, V.: Multivariate Time Series With Linear State Space Structure. Springer, Switzerland (2016)
Granger, C.W.J.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424–438 (1969)
Hosking, J.R.M.: The multivariate portmanteau statistic. J. Am. Stat. Assoc. 75, 602–608 (1980)
Li, W.K., McLeod, A.I.: Distribution of the residual autocorrelations in multivariate ARMA time series models. J. R. Stat. Soc. B43, 231–239 (1981)
Li, W.K.: Diagnostic Checks in Time Series. Chapman and Hall/CRC, Boca Raton, FL (2004)
Lütkepohl, H.: New Introduction to Multiple Time Series Analysis. Springer, Berlin (2005)
Mahdi, E., Mcleod, I.: Improved multivariate portmanteau test. J. Time Ser. Anal. 33, 2 (2012)
Thu, H.N.: Diagnostic checks in multiple time series modelling. In: Rojas, I., et al. (eds.) Advances in Time Series Analysis and Forecasting, Contributions to Statistics (2017)
Tsay, R.S.: Multivariate Time Series Analysis with R and Financial Applications. Wiley, Hoboken, NJ (2014)
Wei, W.W.S.: Multivariate Time Series Analysis and Applications. Wiley, Hoboken, NJ (2019)
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Huang, C., Petukhina, A. (2022). Multivariate Time Series Analysis. In: Applied Time Series Analysis and Forecasting with Python. Statistics and Computing. Springer, Cham. https://doi.org/10.1007/978-3-031-13584-2_7
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DOI: https://doi.org/10.1007/978-3-031-13584-2_7
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