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Structural-break models under mis-specification: Implications for forecasting

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  • Koo, Bonsoo
  • Seo, Myung Hwan

Abstract

This paper revisits the least squares estimator of the linear regression with a structural break. We view the model as an approximation to the true data generating process whose exact nature is unknown but perhaps changing over time either continuously or with some jumps. This view is widely held in the forecasting literature and under this view, the time series dependence property of all the observed variables is unstable as well. We establish that the rate of convergence of the estimator to a properly defined limit is at most the cube root of T, where T is the sample size, which is much slower than the standard super consistent rate. We also provide an asymptotic distribution of the estimator and that of the Gaussian quasi likelihood ratio statistic for a certain class of true data generating processes. We relate our finding to current forecast combination methods and propose a new averaging scheme. Our method compares favourably with various contemporary forecasting methods in forecasting a number of macroeconomic series.

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  • Koo, Bonsoo & Seo, Myung Hwan, 2015. "Structural-break models under mis-specification: Implications for forecasting," Journal of Econometrics, Elsevier, vol. 188(1), pages 166-181.
  • Handle: RePEc:eee:econom:v:188:y:2015:i:1:p:166-181
    DOI: 10.1016/j.jeconom.2015.03.046
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    Cited by:

    1. Koo, Bonsoo & Anderson, Heather M. & Seo, Myung Hwan & Yao, Wenying, 2020. "High-dimensional predictive regression in the presence of cointegration," Journal of Econometrics, Elsevier, vol. 219(2), pages 456-477.
    2. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    3. Gantungalag Altansukh & Denise R. Osborn, 2022. "Using structural break inference for forecasting time series," Empirical Economics, Springer, vol. 63(1), pages 1-41, July.
    4. Yan Gao & Xinyu Zhang & Shouyang Wang & Terence Tai-leung Chong & Guohua Zou, 2019. "Frequentist model averaging for threshold models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 275-306, April.
    5. Christian Balcells, 2022. "Determinants of firm boundaries and organizational performance: an empirical investigation of the Chilean truck market," Journal of Evolutionary Economics, Springer, vol. 32(2), pages 423-461, April.
    6. Hirano, Keisuke & Wright, Jonathan H., 2022. "Analyzing cross-validation for forecasting with structural instability," Journal of Econometrics, Elsevier, vol. 226(1), pages 139-154.

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    More about this item

    Keywords

    Structural break; Forecasting; Mis-specification; Cube-root asymptotics;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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