Fong, P. W.; Li, W. K.; Yau, C. W.; Wong, C. S. On a mixture vector autoregressive model. (English) Zbl 1124.62059 Can. J. Stat. 35, No. 1, 135-150 (2007). Summary: The authors show how to extend univariate mixture autoregressive models to a multivariate time series context. Similar to the univariate case, the multivariate model consists of a mixture of stationary or nonstationary autoregressive components. The authors give first and second order stationarity conditions for a multivariate case up to order 2. They also derive the second order stationarity condition for the univariate mixture model up to arbitrary order. They describe an EM algorithm for estimation, as well as a diagnostic checking procedure. They study the performance of their method via simulations and include a real application. Cited in 1 ReviewCited in 17 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62H12 Estimation in multivariate analysis Keywords:diagnostic checking; EM algorithm; multivariate time series; stationarity Software:FinTS; DerivaGem PDFBibTeX XMLCite \textit{P. W. Fong} et al., Can. J. Stat. 35, No. 1, 135--150 (2007; Zbl 1124.62059) Full Text: DOI References: [1] BenesÌ, Existence of finite invariant measures for Markov processes, Proceedings of the American Mathematical Society 18 pp 1058– (1967) · Zbl 0241.60059 [2] Berchtold, Mixture transition distribution (MTD) modeling of heteroscedastic time series, Computational Statistics & Data Analysis 41 pp 399– (2003) · Zbl 1256.62048 [3] Berchtold, Optimisation of mixture models: comparison of different strategies, Computational Statistics 19 pp 385– (2004) · Zbl 1068.65020 [4] Biernacki, Choosing starting value for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models, Computational Statistics & Data Analysis 41 pp 561– (2003) · Zbl 1429.62235 [5] Box, Time Series Analysis: Forecasting and Control (1994) · Zbl 0858.62072 [6] Carvalho, Modeling nonlinear time series with local mixtures of generalized linear models, The Canadian Journal of Statistics 33 pp 97– (2005) · Zbl 1063.62121 [7] P. W. Fong, W. K. Li, C. W. Yau & C. S. Wong (2004). On a Mixture Vector Autoregressive Model. Research Report no 369, Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, China. · Zbl 1124.62059 [8] Goldberg, Difference Equations. (1958) [9] Hull, Fundamentals of Futures and Options Markets. (2002) · Zbl 1019.91025 [10] Lanne, Nonlinear dynamics of interest rate and inflation, Journal of Applied Econometrics 21 pp 1157– (2006) [11] Lanne, Modeling the U.S. Short-term interest rate by mixture autoregressive processes., Journal of Financial Econometrics 1 pp 96– (2003) [12] Le, Modeling flat stretches, bursts, and outliers in time series using mixture transition distribution models, Journal of the American Statistical Association 91 pp 1504– (1996) · Zbl 0881.62096 [13] Li, On the squared residual autocorrelations in non-linear time series with conditional heteroscedasticity, Journal of Time Series Analysis 15 pp 627– (1994) [14] McLachlan, Mixture Models: Inference and Application to Clustering. (1988) · Zbl 0697.62050 [15] Martin, Threshold time series models as multimodal distribution jump processes, Journal of Time Series Analysis 13 pp 79– (1992) · Zbl 0850.62667 [16] Saikkonen, Stability of mixtures of vector autoregressions with autoregressive conditional heteroskedasticity, Statistica Sinica 17 pp 221– (2007) · Zbl 1145.62074 [17] Titterington, Statistical Analysis of Finite Mixture Distributions. (1985) · Zbl 0646.62013 [18] Tsay, Analysis of Financial Time Series. (2002) [19] Wong, On a mixture autoregressive model, Journal of the Royal Statistical Society Series B 62 pp 95– (2000) · Zbl 0941.62095 [20] Wong, On a mixture autoregressive conditional heteroscedastic model, Journal of the American Statistical Association 96 pp 982– (2001) · Zbl 1051.62091 [21] Wong, A mixture time series model for the Heng Sang Index, Hong Kong Statistical Society Bulletin 23 pp 6– (2001) [22] Wong, On a logistic mixture autoregressive model, Biometrika 88 pp 833– (2001) · Zbl 0985.62074 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.