e16068c2-7499-42b9-b1d4-7d57d4684ac920210216094032550wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS1109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40512720202720201910.37394/23206.2020.19http://wseas.org/wseas/cms.action?id=23185The Influence of Covariance Hankel Matrix Dimension on Algorithms for VARMA ModelsCelinaPestano-GabinoDepartamento de Economía Aplicada y Métodos Cuantitativos, Universidad de La Laguna (ULL), 38071 Campus de Guajara, La Laguna, SPAINConcepciónGonzález-ConcepciónDepartamento de Economía Aplicada y Métodos Cuantitativos, Universidad de La Laguna (ULL), 38071 Campus de Guajara, La Laguna, SPAINMaríaCandelaria Gil-FariñaDepartamento de Economía Aplicada y Métodos Cuantitativos, Universidad de La Laguna (ULL), 38071 Campus de Guajara, La Laguna, SPAINSome methods for estimating VARMA models, and Multivariate Time Series Models in general, rely on the use of a Hankel matrix. Some authors suggest taking a larger dimension than theoretically necessary for this matrix. If the data sample is populous enough and the Hankel matrix dimension is unnecessarily large, this may result in an unnecessary number of computations, as well as in worse numerical and statistical results. We provide some theoretical results to know which is the Hankel matrix with the lowest dimension that is theoretically necessary and illustrate, with several simulated VARMA models, that using a dimension of the Hankel matrix greater than the theoretical minimal dimension proposed as valid does not necessarily lead to improved estimates. Although we use two algorithms, our main contributions are independent of the estimation method considered. We note that our paper does not include any comparisons between different algorithms for estimating VARMA models, as this is not our aim.272020272020110https://www.wseas.org/multimedia/journals/mathematics/2020/a025106-071.pdf10.37394/23206.2020.19.1http://www.wseas.org/multimedia/journals/mathematics/2020/a025106-071.pdfH. Lütkepohl, The New Introduction to Multiple Time Series Analysis, Springer-Verlag, Berlin, 2005. 10.1006/jmva.1996.0011S. Nsiri and R. Roy, Identification of Refined ARMA Echelon Form Models for Multivariate Time Series, Journal of Multivariate Analysis 56, 207-231(1996). 10.2307/1391530R.S. Tsay, Parsimonious Parameterization of Vector Autoregressive Moving Average Models, Journal of Business & Economic Statistics, Vol. 7, No. 3, 327-341(1989).10.1111/j.2517-6161.1989.tb01756.xG.C. Tiao and R.S. Tsay, Model Specification in Multivariate Time Series, Journal of the Royal Statistical Society B 51 (2): 157-213 (1989). 10.1109/78.847793J. Mari, P. Stoica and T. McKelvey, Vector ARMA Estimation: A Reliable Subspace Approach, IEEE Transactions on Signal Processing, Vol. 48, No. 7, 2092-2104 (2000). 10.1137/110853996M. Fazel, T.K. Pong, D. Sun and P. Tseng, Hankel Matrix Rank Minimization with Applications to System Identification and Realization, SIAM Journal Matrix Analysis and Applications, 34(3), 946-977 (2013). 10.1017/s0266466615000043B.D. Anderson, M. Deistler, E. Felsenstein, B. Funovits, L. Koelbl and M. Zamani, Multivariate AR systems and mixed frequency data: G-identifiability and estimation, Econometric Theory, 32(4), 793-826 (2016).10.1016/j.jeconom.2016.02.004B.D. Anderson, M. Deistler, E. Felsenstein and L. Koelbl, The structure of multivariate AR and ARMA systems: Regular and singular systems; the single and the mixed frequency case. Journal of Econometrics, 192(2), 366-373 (2016). 10.1108/s0731-9053(1998)0000013005B. Chen and P.A. Zadrozny, An extended Yule-Walker method for estimating a v ector autoregressive model with mixed-frequencey data, Advances in Econometrics 13, 47-73 (1998). 10.1016/j.jeconom.2016.04.017P.A. Zadrozny, Extended Yule–Walker identification of VARMA models with single-or mixed-frequency data. Journal of Econometrics, 193(2), 438-446 (2016). 10.1108/s0731-905320150000035002L. Koelbl, A. Braumann, E. Felsenstein and M. Deistler, Estimation of VAR Systems from Mixed-Frequency Data: The Stock and the Flow Case. In Dynamic Factor Models. Publ ished online: 07 Jan 2016,43-73 (2016).C. Pestano-Gabino, C. González-Concepción and M.C. Gil-Fariña, Sure Overall Orders to Identify Scalar Component Models, WSEAS Transactions on Mathematics, 2006, Vol. 5(1), 97-102.