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Forecast comparison of principal component regression and principal covariate regression

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  • Heij, Christiaan
  • Groenen, Patrick J.F.
  • van Dijk, Dick

Abstract

Forecasting with many predictors is of interest, for instance, in macroeconomics and finance. This paper compares two methods for dealing with many predictors, that is, principal component regression (PCR) and principal covariate regression (PCovR). The forecast performance of these methods is compared by simulating data from factor models and from regression models. The simulations show that, in general, PCR performs better for the first type of data and PCovR performs better for the second type of data. The simulations also clarify the effect of the choice of the PCovR weight on the orecast quality.
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Suggested Citation

  • Heij, Christiaan & Groenen, Patrick J.F. & van Dijk, Dick, 2007. "Forecast comparison of principal component regression and principal covariate regression," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3612-3625, April.
    • Handle: RePEc:eee:csdana:v:51:y:2007:i:7:p:3612-3625
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    1. Marianne Sensier & Dick van Dijk, 2004. "Testing for Volatility Changes in U.S. Macroeconomic Time Series," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 833-839, August.
    2. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    3. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
    4. Heij, C. & Groenen, P.J.F. & van Dijk, D.J.C., 2006. "Time series forecasting by principal covariate regression," Econometric Institute Research Papers EI 2006-37, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October.
    6. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    7. Stock, James H. & Watson, Mark W., 2006. "Forecasting with Many Predictors," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 10, pages 515-554, Elsevier.
    8. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
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    Cited by:

    1. Cornillon, P.-A. & Imam, W. & Matzner-Lober, E., 2008. "Forecasting time series using principal component analysis with respect to instrumental variables," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1269-1280, January.
    2. Vortelinos, Dimitrios I., 2017. "Forecasting realized volatility: HAR against Principal Components Combining, neural networks and GARCH," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 824-839.
    3. Mestekemper, Thomas & Windmann, Michael & Kauermann, Göran, 2010. "Functional hourly forecasting of water temperature," International Journal of Forecasting, Elsevier, vol. 26(4), pages 684-699, October.
    4. Tsay, Ruey S. & Ando, Tomohiro, 2012. "Bayesian panel data analysis for exploring the impact of subprime financial crisis on the US stock market," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3345-3365.
    5. Peter Exterkate & Dick Van Dijk & Christiaan Heij & Patrick J. F. Groenen, 2013. "Forecasting the Yield Curve in a Data‐Rich Environment Using the Factor‐Augmented Nelson–Siegel Model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(3), pages 193-214, April.
    6. Poncela, Pilar & Rodríguez, Julio & Sánchez-Mangas, Rocío & Senra, Eva, 2011. "Forecast combination through dimension reduction techniques," International Journal of Forecasting, Elsevier, vol. 27(2), pages 224-237.
    7. Guidolin, Massimo & Hyde, Stuart, 2012. "Simple VARs cannot approximate Markov switching asset allocation decisions: An out-of-sample assessment," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3546-3566.
    8. Heij, C. & Groenen, P.J.F. & van Dijk, D.J.C., 2006. "Time series forecasting by principal covariate regression," Econometric Institute Research Papers EI 2006-37, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Aguilera, Ana M. & Escabias, Manuel & Valderrama, Mariano J., 2008. "Forecasting binary longitudinal data by a functional PC-ARIMA model," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3187-3197, February.
    10. Simon Lineu Umbach, 2020. "Forecasting with supervised factor models," Empirical Economics, Springer, vol. 58(1), pages 169-190, January.
    11. Aguilera, Ana M. & Escabias, Manuel & Valderrama, Mariano J., 2008. "Discussion of different logistic models with functional data. Application to Systemic Lupus Erythematosus," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 151-163, September.

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