Electronic Journal of Statistics

Periodic dynamic factor models: estimation approaches and applications

Changryong Baek, Richard A. Davis, and Vladas Pipiras

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Abstract

A periodic dynamic factor model (PDFM) is introduced as a dynamic factor modeling approach to multivariate time series data exhibiting cyclical behavior and, in particular, periodic dependence structure. In the PDFM, the loading matrices are allowed to depend on the “season” and the factors are assumed to follow a periodic vector autoregressive (PVAR) model. Estimation of the loading matrices and the underlying PVAR model is studied. A simulation study is presented to assess the performance of the introduced estimation procedures, and applications to several real data sets are provided.

Article information

Source
Electron. J. Statist., Volume 12, Number 2 (2018), 4377-4411.

Dates
Received: April 2018
First available in Project Euclid: 18 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1545123627

Digital Object Identifier
doi:10.1214/18-EJS1518

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62H12: Estimation
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.)

Keywords
Dynamic factor model periodic vector autoregressive (PVAR) model dimension reduction adaptive lasso

Rights
Creative Commons Attribution 4.0 International License.

Citation

Baek, Changryong; Davis, Richard A.; Pipiras, Vladas. Periodic dynamic factor models: estimation approaches and applications. Electron. J. Statist. 12 (2018), no. 2, 4377--4411. doi:10.1214/18-EJS1518. https://projecteuclid.org/euclid.ejs/1545123627


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References

  • Alonso, A. M., García-Martos, C., Rodríguez, J. & Sánchez, M. J. (2011), ‘Seasonal dynamic factor analysis and bootstrap inference: Application to electricity market forecasting’, Technometrics 53(2), 137–151.
  • Baek, C., Davis, R. A. & Pipiras, V. (2017), ‘Sparse seasonal and periodic vector autoregressive modeling’, Computational Statistics & Data Analysis 106, 103–126.
    Zentralblatt MATH: 06917863
    Digital Object Identifier: doi:10.1016/j.csda.2016.09.005
  • Bai, J. & Ng, S. (2007), ‘Determining the number of primitive shocks in factor models’, Journal of Business & Economic Statistics 25(1), 52–60.
  • Bai, J. & Ng, S. (2008), Large Dimensional Factor Analysis, Now Publishers Inc.
  • Bai, J. & Wang, P. (2015), ‘Identification and Bayesian Estimation of Dynamic Factor Models’, Journal of Business & Economic Statistics 33(2), 221–240.
  • Brockwell, P. & Davis, R. A. (2009), Time Series: Theory and Methods, Springer Series in Statistics, Springer, New York. Reprint of the second (1991) edition.
    Zentralblatt MATH: 0709.62080
  • Chamberlain, G. & Rothschild, M. (1983), ‘Arbitrage, factor structure, and mean-variance analysis on large asset markets’, Econometrica 51(5), 1281–1304.
    Zentralblatt MATH: 0523.90017
    Digital Object Identifier: doi:10.2307/1912275
  • Dordonnat, V., Koopman, S. J. & Ooms, M. (2012), ‘Dynamic factors in periodic time-varying regressions with an application to hourly electricity load modelling’, Computational Statistics & Data Analysis 56(11), 3134–3152.
    Zentralblatt MATH: 1254.91652
    Digital Object Identifier: doi:10.1016/j.csda.2011.04.002
  • Doz, C., Giannone, D. & Reichlin, L. (2011), ‘A two-step estimator for large approximate dynamic factor models based on Kalman filtering’, Journal of Econometrics 164, 188–205.
    Zentralblatt MATH: 06616663
    Digital Object Identifier: doi:10.1016/j.jeconom.2011.02.012
  • Doz, C., Giannone, D. & Reichlin, L. (2012), ‘A quasi-maximum likelihood approach for large approximate dynamic factor model’, Review of Economics and Statistics 94, 1014–1024.
  • Dudek, A., Hurd, H. & Wójtowicz, W., (2016a), ‘PARMA methods based on Fourier representation of periodic coefficients’, Wiley Interdisciplinary Reviews: Computational Statistics 8(3), 130–149.
  • Dudek, A., Hurd, H. & Wojtowicz, W., (2016b), perARMA: Periodic Time Series Analysis. R package version 1.6.
  • Engle, R. & Watson, M. (1981), ‘A one-factor multivariate time series model of metropolitan wage rates’, Journal of the American Statistical Association 76(376), 774–781.
  • Forni, M., Hallin, M., Lippi, M. & Reichlin, L. (2000), ‘The generalized dynamic-factor model: identification and estimation’, The Review of Economics and Statistics 82(4), 540–554.
  • Franses, P. H. & Paap, R. (2004), Periodic Time Series Models, Advanced Texts in Econometrics, Oxford University Press, Oxford.
    Zentralblatt MATH: 1058.62112
  • Ghysels, E. & Osborn, D. R. (2001), The Econometric Analysis of Seasonal Time Series, Themes in Modern Econometrics, Cambridge University Press, Cambridge.
    Zentralblatt MATH: 0994.62086
  • Hurd, H. & Gerr, N. (2008), ‘Graphical method for determining the presence of periodic correlation’, Journal of Time Series Analysis 12, 337–350.
  • Hurd, H. L. & Miamee, A. (2007), Periodically Correlated Random Sequences, Wiley Series in Probability and Statistics, Wiley-Interscience, Hoboken, NJ.
    Zentralblatt MATH: 1138.60003
  • Jones, R. H. & Brelsford, W. M. (1967), ‘Time series with periodic structure’, Biometrika 54, 403–408.
    Zentralblatt MATH: 0153.47706
    Digital Object Identifier: doi:10.1093/biomet/54.3-4.403
  • Lund, R. (2011), Choosing seasonal autocovariance structures: PARMA or SARMA, in W. Bell, S. Holan & T. McElroy, eds, ‘Economic Time Series: Modelling and Seasonality’, Chapman and Hall, pp. 63–80.
  • Nieto, F. H., Pena, D. & Saboyá, D. (2016), ‘Common seasonality in multivariate time series’, Statistica Sinica 26(4), 1389–1410.
    Zentralblatt MATH: 1356.62153
  • Peña, D. & Poncela, P. (2006), ‘Nonstationary dynamic factor analysis’, Journal of Statistical Planning and Inference 136(4), 1237 – 1257.
    Zentralblatt MATH: 1088.62077
    Digital Object Identifier: doi:10.1016/j.jspi.2004.08.020
  • Shumway, R. H. & Stoffer, D. S. (2006), Time Series Analysis and Its Applications: With R examples, Springer.
    Mathematical Reviews (MathSciNet): MR2228626
    Zentralblatt MATH: 1096.62088
  • Stock, J. H. & Watson, M. W. (2002), ‘Forecasting using principal components from a large number of predictors’, Journal of the American Statistical Association 97(460), 1167–1179.
    Zentralblatt MATH: 1041.62081
    Digital Object Identifier: doi:10.1198/016214502388618960
  • Stock, J. H. & Watson, M. W. (2009), Forecasting in dynamic factor models subject to structural instability, in ‘The Methodology and Practice of Econometrics: Festschrift in Honor of D.F. Hendry’, Oxford University Press, pp. 1–57.
  • Stock, J. H. & Watson, M. W. (2011), ‘Dynamic factor models’, Oxford Handbook of Economic Forecasting. Oxford University Press, USA pp. 35–59.
    Mathematical Reviews (MathSciNet): MR3204189
  • Su, L. & Wang, X. (2017), ‘On time-varying factor models: Estimation and testing’, Journal of Econometrics 198(1), 84 – 101.
  • Wang, W. & Fan, J. (2017), ‘Asymptotics of empirical eigenstructure for high dimensional spiked covariance’, The Annals of Statistics 45(3), 1342–1374.
    Zentralblatt MATH: 1373.62299
    Digital Object Identifier: doi:10.1214/16-AOS1487
    Project Euclid: euclid.aos/1497319697

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