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Tests of Equal Accuracy for Nested Models with Estimated Factors

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In this paper we develop asymptotics for tests of equal predictive ability between nested models when factor-augmented regression models are used to forecast. We provide conditions under which the estimation of the factors does not affect the asymptotic distributions developed in Clark and McCracken (2001) and McCracken (2007). This enables researchers to use the existing tabulated critical values when conducting inference. As an intermediate result, we derive the asymptotic properties of the principal components estimator over recursive windows. We provide simulation evidence on the finite sample effects of factor estimation and apply the tests to the case of forecasting excess returns to the S&P 500 Composite Index.

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  • Silvia Goncalves & Michael W. McCracken & Benoit Perron, 2015. "Tests of Equal Accuracy for Nested Models with Estimated Factors," Working Papers 2015-25, Federal Reserve Bank of St. Louis.
    • Handle: RePEc:fip:fedlwp:2015-025
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    Cited by:

    1. Marine Carrasco & Barbara Rossi, 2016. "In-Sample Inference and Forecasting in Misspecified Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 313-338, July.
    2. Massacci, Daniele & Kapetanios, George, 2024. "Forecasting in factor augmented regressions under structural change," International Journal of Forecasting, Elsevier, vol. 40(1), pages 62-76.
    3. Giovannelli, Alessandro & Massacci, Daniele & Soccorsi, Stefano, 2021. "Forecasting stock returns with large dimensional factor models," Journal of Empirical Finance, Elsevier, vol. 63(C), pages 252-269.
    4. Arabinda Basistha, 2023. "Estimation of short‐run predictive factor for US growth using state employment data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(1), pages 34-50, January.
    5. Arabinda Basistha & Richard Startz, 2024. "Measuring persistent global economic factors with output, commodity price, and commodity currency data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(7), pages 2860-2885, November.
    6. Luiz Renato Lima & Lucas Lúcio Godeiro, 2023. "Equity‐premium prediction: Attention is all you need," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(1), pages 105-122, January.
    7. Luiz Renato Lima & Lucas Lúcio Godeiro & Mohammed Mohsin, 2021. "Time-Varying Dictionary and the Predictive Power of FED Minutes," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 149-181, January.
    8. Karen Miranda & Pilar Poncela & Esther Ruiz, 2022. "Dynamic factor models: Does the specification matter?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 13(1), pages 397-428, May.
    9. Luca Margaritella & Ovidijus Stauskas, 2024. "New Tests of Equal Forecast Accuracy for Factor-Augmented Regressions with Weaker Loadings," Papers 2409.20415, arXiv.org, revised Oct 2024.
    10. Andreou, Elena & Ghysels, Eric, 2021. "Predicting the VIX and the volatility risk premium: The role of short-run funding spreads Volatility Factors," Journal of Econometrics, Elsevier, vol. 220(2), pages 366-398.
    11. In Choi & Hanbat Jeong, 2020. "Differencing versus nondifferencing in factor‐based forecasting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(6), pages 728-750, September.
    12. Antoine A. Djogbenou, 2021. "Model selection in factor-augmented regressions with estimated factors," Econometric Reviews, Taylor & Francis Journals, vol. 40(5), pages 470-503, April.
    13. Daniel Borup & Bent Jesper Christensen & Yunus Emre Ergemen, 2019. "Assessing predictive accuracy in panel data models with long-range dependence," CREATES Research Papers 2019-04, Department of Economics and Business Economics, Aarhus University.
    14. Daniel Borup & Martin Thyrsgaard, 2017. "Statistical tests for equal predictive ability across multiple forecasting methods," CREATES Research Papers 2017-19, Department of Economics and Business Economics, Aarhus University.
    15. Fosten, Jack, 2017. "Confidence intervals in regressions with estimated factors and idiosyncratic components," Economics Letters, Elsevier, vol. 157(C), pages 71-74.
    16. Corradi, Valentina & Fosten, Jack & Gutknecht, Daniel, 2024. "Predictive ability tests with possibly overlapping models," Journal of Econometrics, Elsevier, vol. 241(1).
    17. Michael W. McCracken, 2020. "Tests of Conditional Predictive Ability: Existence, Size, and Power," Working Papers 2020-050, Federal Reserve Bank of St. Louis.
    18. Daniel Borup & Jonas N. Eriksen & Mads M. Kjær & Martin Thyrsgaard, 2024. "Predicting Bond Return Predictability," Management Science, INFORMS, vol. 70(2), pages 931-951, February.

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    More about this item

    Keywords

    factor models; out-of-sample forecasts; recursive estimation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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