Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We define one-sided dynamic principal components (ODPC) for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared error. Usually dynamic principal components have been defined as functions of past and future values of the series and therefore they are not appropriate for forecasting purposes. On the contrary, it is shown that the ODPC introduced in this article can be successfully used for forecasting high-dimensional multiple time series. An alternating least-squares algorithm to compute the proposed ODPC is presented. We prove that for stationary and ergodic time series the estimated values converge to their population analogs. We also prove that asymptotically, when both the number of series and the sample size go to infinity, if the data follow a dynamic factor model, the reconstruction obtained with ODPC converges in mean square to the common part of the factor model. The results of a simulation study show that the forecasts obtained with ODPC compare favorably with those obtained using other forecasting methods based on dynamic factor models. Supplementary materials for this article are available online. © 2019, © 2019 American Statistical Association.

Registro:

Documento: Artículo
Título:Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
Autor:Peña, D.; Smucler, E.; Yohai, V.J.
Filiación:Department of Statistics and Institute of Financial Big Data, Universidad Carlos III de Madrid, Getafe, Spain
Department of Mathematics and Statistics, Universidad Torcuato Di Tella, Buenos Aires, Argentina
Department of Mathematics, Instituto de Calculo, Universidad de Buenos Aires, Buenos Aires, Argentina
School of Exact and Natural Sciences, Universidad de Buenos Aires, Argentina
CONICET, Buenos Aires, Argentina
Palabras clave:Dimensionality reduction; Dynamic factor models; High-dimensional time series
Año:2019
DOI: http://dx.doi.org/10.1080/01621459.2018.1520117
Título revista:Journal of the American Statistical Association
Título revista abreviado:J. Am. Stat. Assoc.
ISSN:01621459
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_01621459_v_n_p_Pena

Referencias:

  • Ahn, S.K., Reinsel, G.C., “Nested Reduced-rank Autogressive Models for Multiple Time Series,” (1988) Journal of the American Statistical Association, 83, pp. 849-856
  • Amengual, D., Watson, M.W., “Consistent Estimation of the Number of Dynamic Factors in a Large n and t Panel,” (2007) Journal of Business & Economic Statistics, 25, pp. 91-96
  • Bai, J., Ng, S., “Determining the Number of Factors in Approximate Factor Models,” (2002) Econometrica, 70, pp. 191-221
  • Bai, J., Ng, S., “Determining the Number of Primitive Shocks in Factor Models,” (2007) Journal of Business & Economic Statistics, 25, pp. 52-60
  • Box, G.E.P., Tiao, G.C., “A Canonical Analysis of Multiple Time Series,” (1977) Biometrika, 64, p. 355
  • Brillinger, D.R., The Generalization of the Techniques of Factor Analysis, Canonical Correlation and Principal Components to Stationary Time Series (1964) Invited Paper at the Royal Statistical Society Conference in Cardiff, , Wales
  • Brillinger, D.R., “Time Series: Data Analysis and Theory,” (1981) Classics in Applied Mathematics, , San Francisco, CA: Society for Industrial and Applied Mathematics, in
  • Bühlmann, P., Van De Geer, S., (2011) Statistics for High-dimensional Data: Methods, Theory and Applications, , New York: Springer Science & Business Media
  • Connor, G., Korajczyk, R.A., “A Test for the Number of Factors in an Approximate Factor Model,” (1993) The Journal of Finance, 48, pp. 1263-1291
  • Fan, J., Liao, Y., Mincheva, M., “Large Covariance Estimation by Thresholding Principal Orthogonal Complements,” (2013) Journal of the Royal Statistical Society, Series B, 75, pp. 603-680
  • Forni, M., Hallin, M., Lippi, M., Reichlin, L., “The Generalized Dynamic-Factor Model: Identification and Estimation (2000) The Review of Economics and Statistics, 82, pp. 540-554
  • Forni, M., Hallin, M., Lippi, M., Reichlin, L., “The Generalized Dynamic Factor Model: One-sided Estimation and Forecasting,” (2005) Journal of the American Statistical Association, 100, pp. 830-840
  • Forni, M., Giannone, D., Lippi, M., Reichlin, L., “Opening the Black Box: Structural Factor Models with Large Cross Sections,” (2009) Econometric Theory, 25, pp. 1319-1347
  • Forni, M., Hallin, M., Lippi, M., Zaffaroni, P., “Dynamic Factor Models with Infinite-Dimensional Factor Spaces: One-Sided Representations,” (2015) Journal of Econometrics, 185, pp. 359-371
  • Forni, M., Giovannelli, A., Lippi, M., Soccorsi, S., (2016), Dynamic Factor Model with Infinite Dimensional Factor Space: Forecasting, Technical Report DP11161, CEPR; Forni, M., Hallin, M., Lippi, M., Zaffaroni, P., “Dynamic Factor Models with Infinite-Dimensional Factor Space: Asymptotic Analysis,” (2017) Journal of Econometrics, 199, pp. 74-92
  • Garcia-Ferrer, A., Highfield, R.A., Palm, F., Zellner, A., “Macroeconomic Forecasting Using Pooled International Data,” (1987) Journal of Business & Economic Statistics, 5, pp. 53-67
  • Hallin, M., Lippi, M., “Factor Models in High-Dimensional Time Series—a Time-Domain Approach,” (2013) Stochastic Processes and Their Applications, 123, pp. 2678-2695
  • Hallin, M., Liška, R., “Determining the Number of Factors in the General Dynamic Factor Model,” (2007) Journal of the American Statistical Association, 102, pp. 603-617
  • Hyndman, R., Khandakar, Y., “Automatic Time Series Forecasting: The Forecast Package for R,” (2008) Journal of Statistical Software, 27, pp. 1-22
  • Litterman, R.B., “Forecasting with Bayesian Vector Autoregressions: Five Years of Experience,” (1986) Journal of Business & Economic Statistics, 4, pp. 25-38
  • McCracken, M.W., Ng, S., “Fred-md: A Monthly Database for Macroeconomic Research,” (2016) Journal of Business & Economic Statistics, 4, pp. 574-589
  • Onatski, A., “Determining the Number of Factors from Empirical Distribution of Eigenvalues,” (2010) The Review of Economics and Statistics, 92, pp. 1004-1016
  • Peña, D., Box, G.E.P., “Identifying a Simplifying Structure in Time Series,” (1987) Journal of the American Statistical Association, 82, pp. 836-843
  • Peña, D., Poncela, P., “Forecasting with Nonstationary Dynamic Factor Models,” (2004) Journal of Econometrics, 119, pp. 291-321
  • Peña, D., Yohai, V.J., “Generalized Dynamic Principal Components,” (2016) Journal of the American Statistical Association, 111, pp. 1121-1131
  • Poncela, P., Ruiz, E., “More is Not Always Better: Back to the Kalman Filter in Dynamic Factor Models,” (2015) Unobserved Components and Time Series Econometrics, , Koopman S.J., Shephard N.G., (eds), Oxford, UK: Oxford University Press, and, eds
  • Poncela, P., Ruiz, E., “Small-versus Big-data Factor Extraction in Dynamic Factor Models: An Empirical Assessment,” (2016) Dynamic Factor Models, pp. 401-434. , Hillebrand E., Koopman S.J., (eds), Emerald Group Publishing Limited, and, eds
  • Smucler, E., Yohai, V.J., “Robust and Sparse Estimators for Linear Regression Models,” (2017) Computational Statistics & Data Analysis, 111, pp. 116-130
  • Stock, J.H., Watson, M.W., “Forecasting Using Principal Components from a Large Number of Predictors,” (2002) Journal of the American Statistical Association, 97, pp. 1167-1179
  • Tiao, G.C., Tsay, R.S., “Model Specification in Multivariate Time Series,” (1989) Journal of the Royal Statistical Society, Series B, 51, pp. 157-213
  • Tibshirani, R., “Regression Shrinkage and Selection Via the Lasso,” (1996) Royal Statistical Society, Series B, 58, pp. 267-288
  • Wright, S.J., “Coordinate Descent Algorithms,” (2015) Mathematical Programming, 151, pp. 3-34
  • Yohai, V.J., “High Breakdown-point and High Efficiency Robust Estimates for Regression,” (1987) The Annals of Statistics, 15, pp. 642-656

Citas:

---------- APA ----------
Peña, D., Smucler, E. & Yohai, V.J. (2019) . Forecasting Multiple Time Series With One-Sided Dynamic Principal Components. Journal of the American Statistical Association.
http://dx.doi.org/10.1080/01621459.2018.1520117
---------- CHICAGO ----------
Peña, D., Smucler, E., Yohai, V.J. "Forecasting Multiple Time Series With One-Sided Dynamic Principal Components" . Journal of the American Statistical Association (2019).
http://dx.doi.org/10.1080/01621459.2018.1520117
---------- MLA ----------
Peña, D., Smucler, E., Yohai, V.J. "Forecasting Multiple Time Series With One-Sided Dynamic Principal Components" . Journal of the American Statistical Association, 2019.
http://dx.doi.org/10.1080/01621459.2018.1520117
---------- VANCOUVER ----------
Peña, D., Smucler, E., Yohai, V.J. Forecasting Multiple Time Series With One-Sided Dynamic Principal Components. J. Am. Stat. Assoc. 2019.
http://dx.doi.org/10.1080/01621459.2018.1520117