Reduced-Rank Envelope Vector Autoregressive Model

References

• Anderson, T. W. (1951), “Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions,” The Annals of Mathematical Statistics, 22, 327–351. DOI: 10.1214/aoms/1177729580.
   Google Scholar
• ———(1999), “Asymptotic Distribution of the Reduced Rank Regression Estimator Under General Conditions,” The Annals of Statistics, 27, 1141–1154.
   Web of Science ®Google Scholar
• ———(2002), “Canonical Correlation Analysis and Reduced Rank Regression in Autoregressive Models,” The Annals of Statistics, 30, 1134–1154.
   Web of Science ®Google Scholar
• Banbura, M., Giannone, D., and Reichlin, L. (2010), “Large Bayesian Vector Auto Regressions,” Journal of Applied Econometrics, 25, 71–92. DOI: 10.1002/jae.1137.
   Web of Science ®Google Scholar
• Basu, S., Li, X., and Michailidis, G. (2019), “Low Rank and Structured Modeling of High-Dimensional Vector Autoregressions,” IEEE Transactions on Signal Processing, 67, 1207–1222. DOI: 10.1109/TSP.2018.2887401.
   Web of Science ®Google Scholar
• Bernardini, E., and Cubadda, G. (2015), “Macroeconomic Forecasting and Structural Analysis through Regularized Reduced-Rank Regression,” International Journal of Forecasting, 31, 682–691. DOI: 10.1016/j.ijforecast.2013.10.005.
   Web of Science ®Google Scholar
• Billard, L., Douzal-Chouakria, A., and Samadi, S. Y. (2023), “Exploring Dynamic Structures in Matrix-Valued Time Series via Principal Component Analysis,” Axioms, 12, 570. DOI: 10.3390/axioms12060570.
   Web of Science ®Google Scholar
• Box, G. E., Jenkins, G. M., Reinsel, G. C., and Ljung, G. M. (2015), Time Series Analysis: Forecasting and Control, Hoboken, NJ: Wiley.
   Google Scholar
• Box, G. E. P., and Tiao, G. C. (1977), “A Canonical Analysis of Multiple Time Series,” Biometrika, 64, 355–365. DOI: 10.1093/biomet/64.2.355.
   Web of Science ®Google Scholar
• Brune, B., Scherrer, W., and Bura, E. (2022), “A State-Space Approach to Time-Varying Reduced-Rank Regression,” Econometric Reviews, 41, 895–917. DOI: 10.1080/07474938.2022.2073743.
   Web of Science ®Google Scholar
• Bura, E., and Cook, R. D. (2003), “Rank Estimation in Reduced-Rank Regression,” Journal of Multivariate Analysis, 87, 159–176. DOI: 10.1016/S0047-259X(03)00029-0.
   Web of Science ®Google Scholar
• Carriero, A., Kapetanios, G., and Marcellino, M. (2011), “Forecasting Large Datasets with Bayesian Reduced Rank Multivariate Models,” Journal of Applied Econometrics, 26, 735–761. DOI: 10.1002/jae.1150.
   Web of Science ®Google Scholar
• ———(2016), “Structural Analysis with Multivariate Autoregressive Index Models,” Journal of Econometrics, 192, 332–348.
   Web of Science ®Google Scholar
• Centoni M., and Cubadda, G. (2015), “Common Feature Analysis of Economic Time Series: An Overview and Recent Developments,” Communications for Statistical Applications and Methods, 22, 1–20. DOI: 10.5351/CSAM.2015.22.5.415.
   Google Scholar
• Chan, J. C. C., and Eisenstat, E. (2018), “Bayesian Model Comparison for Time-Varying Parameter VARs with Stochastic Volatility,” Journal of Applied Econometrics, 33, 509–532. DOI: 10.1002/jae.2617.
   Web of Science ®Google Scholar
• Chang, J., Jiang, Q., and Shao, X. (in press), “Testing the Martingale Difference Hypothesis in High Dimension,” Journal of Econometrics.
   Web of Science ®Google Scholar
• Chen, K., Dong, H., and Chan, K. S. (2013), “Reduced Rank Regression via Adaptive Nuclear Norm Penalization,” Biometrika, 100, 901–920. DOI: 10.1093/biomet/ast036.
   PubMed Web of Science ®Google Scholar
• Conway, J. (1990), A Course in Functional Analysis, New York: Spring-Verlag.
   Google Scholar
• Cook, R. D., and Zhang, X. (2015a), “Foundations for Envelope Models and Methods,” Journal of the American Statistical Association, 110, 599–611. DOI: 10.1080/01621459.2014.983235.
   Web of Science ®Google Scholar
• ———(2015b), “Simultaneous Envelopes for Multivariate Linear Regression,” Technometrics, 57, 11–25.
   Web of Science ®Google Scholar
• ———(2016), “Algorithms for Envelope Estimation,” Journal of Computational and Graphical Statistics, 25, 284–300.
   Web of Science ®Google Scholar
• Cook, R. D., and Zhang, X. (2018), “Fast Envelope Algorithms,” Statistica Sinica, 28, 1179–1197.
   Web of Science ®Google Scholar
• Cook, R. D., Li, B., and Chiaromonte, F. (2010), “Envelope Models for Parsimonious and Efficient Multivariate Linear Regression,” (with discussion), Statistica Sinica, 20, 927–960.
   Web of Science ®Google Scholar
• Cook, R. D., Helland, I. S., and Su, Z. (2013), “Envelopes and Partial Least Squared Regression,” Journal of the Royal Statistical Society, Series B, 75, 851–877. DOI: 10.1111/rssb.12018.
   Google Scholar
• Cook, R. D., Forzani, L., and Zhang, X. (2015), “Envelopes and Reduced-Rank Regression,” Biometrika, 102, 439–456. DOI: 10.1093/biomet/asv001.
   Web of Science ®Google Scholar
• Cubadda, G., and Guardabascio, B. (2019), “Representation, Estimation and Forecasting of the Multivariate Index-Augmented Autoregressive Model,” International Journal of Forecasting, 35, 67–79. DOI: 10.1016/j.ijforecast.2018.08.002.
   Web of Science ®Google Scholar
• Cubadda G., Guardabascio B., and Hecq, A. (2017), “A Vector Heterogeneous Autoregressive Index Model for Realized Volatility Measures,” International Journal of Forecasting, 33, 337–344. DOI: 10.1016/j.ijforecast.2016.09.002.
   Web of Science ®Google Scholar
• Cubadda, G., and Hecq, A. (2011), “Testing for common autocorrelation in data-rich environments,” Journal of Forecasting, 30, 325–335. DOI: 10.1002/for.1186.
   Web of Science ®Google Scholar
• Cubadda, G., and Hecq, A. (2022a), “Reduced Rank Regression Models in Economics and Finance,” in Oxford Research Encyclopedia of Economics and Finance, Oxford University Press.
   Google Scholar
• ———(2022b), “Dimension Reduction for High Dimensional Vector Autoregressive Models,” Oxford Bulletin of Economics and Statistics, 84, 1123–1152.
   Web of Science ®Google Scholar
• Cubadda, G., Hecq, A., and Telg, S. (2019), “Detecting Co-movements in Noncausal Time Series,” Oxford Bulletin of Economics and Statistics, 81, 697–715. DOI: 10.1111/obes.12281.
   Web of Science ®Google Scholar
• Ding, S., and Cook, R. D. (2018), “Matrix Variate Regressions and Envelope Models,” Journal of the Royal Statistical Society, Series B, 80, 387–408. DOI: 10.1111/rssb.12247.
   Google Scholar
• Davis, R. A., Zang, P., and Zheng, T. (2016), “Sparse Vector Autoregressive Modeling,” Journal of Computational and Graphical Statistics, 25, 1077–1096. DOI: 10.1080/10618600.2015.1092978.
   Web of Science ®Google Scholar
• De Mol, C., Giannone, D., and Reichlin, L. (2008), “Forecasting Using a Large Number of Predictors: Is Bayesian Regression a Valid Alternative to Principal Components?” Journal of Econometrics, 146, 318–328. DOI: 10.1016/j.jeconom.2008.08.011.
   Web of Science ®Google Scholar
• Escanciano, J. C., and Velasco, C. (2006), “Generalized Spectral Tests for the Martingale Difference Hypothesis,” Journal of Econometrics, 134, 151–185. DOI: 10.1016/j.jeconom.2005.06.019.
   Web of Science ®Google Scholar
• Forni, M., Hallin, M., Lippi, M., and Reichlin, L. (2005), “The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting,” Journal of the American Statistical Association, 100, 830–840. DOI: 10.1198/016214504000002050.
   Web of Science ®Google Scholar
• Forzani, L., and Su, Z. (2021), “Envelopes for Elliptical Multivariate Linear Regression,” Statistica Sinica, 31, 301–332. DOI: 10.5705/ss.202017.0424.
   Web of Science ®Google Scholar
• Franchi, M., and Paruolo, P. (2011), “A Characterization of Vector Autoregressive Processes with Common Cyclical Features,” Journal of Econometrics, 163, 105–117. DOI: 10.1016/j.jeconom.2010.11.009.
   Web of Science ®Google Scholar
• Hamilton, J. (1994), Time Series Analysis, Princeton, NJ: Princeton University Press.
   Google Scholar
• Hecq, A., Palm, F., and Urbain, J. (2006), “Common Cyclical Features Analysis in VAR Models with Cointegration,” Journal of Econometrics, 132, 117–141. DOI: 10.1016/j.jeconom.2005.01.025.
   Web of Science ®Google Scholar
• Henderson, H. V., and Searle, S. R. (1979), “Vec and vech Operators for Matrices, with Some Uses in Jacobians and Multivariate Statistics,” Canadian Journal of Statistics, 7, 65–81. DOI: 10.2307/3315017.
   Google Scholar
• Herath, H. M. W. B. and Samadi, S. Y. (2023a), “Partial Envelope and Reduced-Rank Partial Envelope Vector Autoregressive Models,” preprint.
   Google Scholar
• ———(2023b), “Scaled Envelope Models for Multivariate Time Series,” preprint.
   Google Scholar
• Hetland, S., Pedersen, R. S., and Rahbek, A. (in press), “Dynamic Conditional Eigenvalue GARCH,” Journal of Econometrics.
   Web of Science ®Google Scholar
• Izenman, A. J. (1975), “Reduced-Rank Regression for the Multivariate Linear Model,” Journal of Multivariate Analysis, 5, 248–264. DOI: 10.1016/0047-259X(75)90042-1.
   Google Scholar
• Koop, G. M. (2013), “Forecasting with Medium and Large Bayesian VARs,” Journal of Applied Econometrics, 28, 177–203. DOI: 10.1002/jae.1270.
   Web of Science ®Google Scholar
• Lam, K. S., and Tam, L. H. (2011), “Liquidity and Asset Pricing: Evidence from the Hong Kong Stock Market,” Journal of Banking & Finance, 35, 2217–2230. DOI: 10.1016/j.jbankfin.2011.01.015.
   Web of Science ®Google Scholar
• Lam, C., and Yao, Q. (2012), “Factor Modeling for High-Dimensional Time Series: Inference for the Number of Factors,” The Annals of Statistics, 40, 694–726. DOI: 10.1214/12-AOS970.
   Web of Science ®Google Scholar
• Lee, M., and Su, Z. (2020), “A Review of Envelope Models,” International Statistical Review, 88, 658–676. DOI: 10.1111/insr.12361.
   Web of Science ®Google Scholar
• Li, L., and Zhang, X. (2017), “Parsimonious Tensor Response Regression,” Journal of the American Statistical Association, 112, 1131–1146. DOI: 10.1080/01621459.2016.1193022.
   Web of Science ®Google Scholar
• Lütkepohl, H. (2005), New Introduction to Multiple Time Series Analysis, Berlin: Springer.
   Google Scholar
• McCracken, M. W., and Ng, S. (2020), “FRED-QD: A Quarterly Database for Macroeconomic Research,” Federal Reserve Bank of St. Louis Working Paper 2020-005, DOI: 10.20955/wp.2020.005.
   Google Scholar
• Negahban, S., and Wainwright, M. J. (2011), “Estimation of (near) Low-Rank Matrices with Noise and High-Dimensional Scaling,” The Annals of Statistics, 39, 1069–1097. DOI: 10.1214/10-AOS850.
   Web of Science ®Google Scholar
• Park, J. H., and Samadi, S. Y. (2014), “Heteroscedastic Modelling via the Autoregressive Conditional Variance Subspace,” Canadian Journal of Statistics, 42, 423–435. DOI: 10.1002/cjs.11222.
   Web of Science ®Google Scholar
• Park, J. H., and Samadi, S. Y. (2020), “Dimension Reduction for the Conditional Mean and Variance Functions in Time Series,” Scandinavian Journal of Statistics, 47, 134–155. DOI: 10.1111/sjos.12405.
   Web of Science ®Google Scholar
• Politis, D. N., and Romano, J. P. (1994), “The Stationary Bootstrap,” Journal of the American Statistical Association, 89, 1303–1313. DOI: 10.1080/01621459.1994.10476870.
   Web of Science ®Google Scholar
• Rao, C. R. (1964), “The Use and Interpretation of Principal Component Analysis in Applied Research,” Sankhyā: The Indian Journal of Statistics, Series A, (1961-2002), 26, 329–358.
   Google Scholar
• Raskutti, G., Yuan, M., and Chen, H. (2019), “Convex Regularization for High-Dimensional Multi-Response Tensor Regression,” The Annals of Statistics, 47, 1554–1584. DOI: 10.1214/18-AOS1725.
   Web of Science ®Google Scholar
• Reinsel, G. C., and Velu, R. P. (1998), Multivariate Reduced-rank Regression: Theory and Applications, New York: Springer.
   Google Scholar
• Reinsel, G. C., Velu, R. P., and Chen, K. (2022), Multivariate Reduced-Rank Regression: Theory, Methods and Applications, New York: Springer.
   Google Scholar
• Rekabdarkolaee, H. M., Wang, Q., Naji, Z., and Fuente, M. (2020), “New Parsimonious Multivariate Spatial Model,” Statistica Sinica, 30, 1583–1604. DOI: 10.5705/ss.202017.0455.
   Web of Science ®Google Scholar
• Samadi, S. Y. (2014), “Matrix Time Series Analysis,” Ph.D. Dissertation, University of Georgia, Athens, GA.
   Google Scholar
• Samadi, S. Y., Billard, L., Meshkani, M. R., and Khodadadi, A. (2017), “Canonical Correlation for Principal Components of Time Series,” Computational Statistics, 32, 1191–1212. DOI: 10.1007/s00180-016-0667-1.
   Web of Science ®Google Scholar
• Samadi, S. Y., and DeAlwis, T. P. (2023a), “Fourier Methods for Sufficient Dimension Reduction in Time Series,” preprint.
   Google Scholar
• ———(2023b), “Envelope Matrix Autoregressive Models,” preprint.
   Google Scholar
• Samadi, S. Y., Hajebi, M., and Farnoosh, R. (2019), “A Semiparametric Approach for Modelling Multivariate Nonlinear Time Series,” Canadian Journal of Statistics, 47, 668–687. DOI: 10.1002/cjs.11518.
   Web of Science ®Google Scholar
• Shapiro, A. (1986), “Asymptotic Theory of Overparameterized Structural Models,” Journal of the American Statistical Association, 81, 142–149. DOI: 10.1080/01621459.1986.10478251.
   Web of Science ®Google Scholar
• Shojaie, A., and Michailidis, G. (2010), “Discovering Graphical Granger Causality Using the Truncating Lasso Penalty,” Bioinformatics, 26, i517–i523. DOI: 10.1093/bioinformatics/btq377.
   PubMed Web of Science ®Google Scholar
• Song, S., and Bickel, P. J. (2011), “Large Vector Autoregressions,” arXiv preprint arXiv: 1106.3915.
   Google Scholar
• Stock, J. H., and Watson, M. W. (2005), “Implications of Dynamic Factor Models for VAR Analysis,” NBER working paper series w11467.
   Google Scholar
• Stoica, P., and Viberg, M. (1996), “Maximum Likelihood Parameter and Rank Estimation in Reduced-Rank Multivariate Linear Regressions,” IEEE Transactions on Signal Processing, 44, 3069–3078. DOI: 10.1109/78.553480.
   Web of Science ®Google Scholar
• Su, Z., and Cook, R. D. (2011), “Partial Envelopes for Efficient Estimation in Multivariate Linear Regression,” Biometrika, 98, 133–146. DOI: 10.1093/biomet/asq063.
   Web of Science ®Google Scholar
• Su, Z., Zhu, G., Chen, X., and Yang, Y. (2016), “Sparse Envelope Model: Efficient Estimation and Response Variable Selection in Multivariate Linear Regression,” Biometrika, 103, 579–593. DOI: 10.1093/biomet/asw036.
   Web of Science ®Google Scholar
• Tiao, G. C., and Tsay, R. S. (1989), “Model Specification in Multivariate Time Series,” Journal of the Royal Statistical Society, Series B, 51, 157–195. DOI: 10.1111/j.2517-6161.1989.tb01756.x.
   Google Scholar
• Tsay, R. S. (2014), Multivariate Time Series Analysis: With R and Financial Applications, Hoboken, NJ: Wiley.
   Google Scholar
• Velu, R. P., Reinsel, G. C., and Wichern, D. W. (1986), “Reduced Rank Models for Multiple Time Series,” Biometrika, 73, 105–118. DOI: 10.1093/biomet/73.1.105.
   Web of Science ®Google Scholar
• Wang, D., Zheng, Y., Lian, H., and Li, G. (2022a), “High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition,” Journal of the American Statistical Association, 117, 1338–1356. DOI: 10.1080/01621459.2020.1855183.
   Web of Science ®Google Scholar
• Wang, D., Zhang, X., Li, G., and Tsay, R. (2022b), “High-Dimensional Vector Autoregression with Common Response and Predictor Factors,” arXiv:2203.15170.
   Google Scholar
• Wang, D., Zheng, Y., and Li, G. (2021), “High-Dimensional Low-Rank Tensor Autoregressive Time Series Modeling,” arXiv preprint arXiv:2101.04276.
   Google Scholar
• Wang, L., and Ding, S. (2018), “Vector Autoregression and Envelope Model,” Stat, 7, e203. DOI: 10.1002/sta4.203.
   Web of Science ®Google Scholar
• Wei, W. W. (2019), Multivariate Time Series Analysis and Applications, Hoboke, NJ: Wiley.
   Google Scholar
• Zhou, X. C., and Lin, J. G. (2013), “Semiparametric Regression Estimation for Longitudinal Data in Models with Martingale Difference Error’s Structure,” Statistics, 47, 521–534. DOI: 10.1080/02331888.2011.617819.
   Web of Science ®Google Scholar
• Zhao, Z. W., Wang, D. H., and Zhang, Y. (2011), “Limit Theory for Random Coefficient First-Order Autoregressive Process Under Martingale Difference Error Sequence,” Journal of Computational and Applied Mathematics, 235, 2515–2522. DOI: 10.1016/j.cam.2010.11.004.
   Web of Science ®Google Scholar