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TIME-VARYING PARAMETER REGRESSIONS WITH STATIONARY PERSISTENT DATA

Published online by Cambridge University Press:  01 April 2024

ZHISHUI HU Open the ORCID record for ZHISHUI HU [Opens in a new window] ,
IOANNIS KASPARIS Open the ORCID record for IOANNIS KASPARIS [Opens in a new window]  and
QIYING WANG Open the ORCID record for QIYING WANG [Opens in a new window]
ZHISHUI HU
Affiliation:
University of Science and Technology of China
IOANNIS KASPARIS*
Affiliation:
University of Cyprus
QIYING WANG
Affiliation:
The University of Sydney
*
Address correspondence to Ioannis Kasparis, Department of Economics, University of Cyprus, Nicosia, Cyprus, email: kasparis@ucy.ac.cy.
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Abstract

We consider local level and local linear estimators for estimation and inference in time-varying parameter (TVP) regressions with general stationary covariates. The latter estimator also yields estimates for parameter derivatives that are utilized for the development of time invariance tests for the regression coefficients. Our theoretical framework is general enough to allow for a wide range of stationary regressors, including stationary long memory. We demonstrate that neglecting time variation in the regression parameters has a range of adverse effects in inference, in particular, when regressors exhibit long-range dependence. For instance, parametric tests diverge under the null hypothesis when the memory order is strictly positive. The finite sample performance of the methods developed is investigated with the aid of a simulation experiment. The proposed methods are employed for exploring the predictability of SP500 returns by realized variance. We find evidence of time variability in the intercept as well as episodic predictability when realized variance is utilized as a predictor in TVP specifications.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 27
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Footnotes

The authors thank the co-editor and two referees for their very helpful comments on the original version and revision of this paper. Hu acknowledges research support from the NSFC (Grant No. 11671373) and Wang acknowledges research support from the Australian Research Council.

References

REFERENCES

Amihud, Y., & Hurvich, C. M. (2004). Predictive regressions: A reduced-bias estimation method. Journal of Financial and Quantitative Analysis , 39(4), 813–841.CrossRefGoogle Scholar
Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2001). The distribution of realized exchange rate volatility. Journal of the American Statistical Association , 96, 42–55.CrossRefGoogle Scholar
Andersen, T. G., & Varneskov, R. T. (2021). Consistent inference for predictive regressions in persistent economic systems. Journal of Econometrics , 224(1), 215–244.CrossRefGoogle Scholar
Ang, A., & Bekaert, G. (2007). Stock return predictability: Is it there? Review of Financial Studies , 20(3), 651–707.CrossRefGoogle Scholar
Baillie, R. T., Chung, C.-F., & Tieslau, M. T. (1996). Analysing inflation by the fractionally integrated ARFIMA-GARCH model. Journal of Applied Econometrics , 11, 23–40.3.0.CO;2-M>CrossRefGoogle Scholar
Bandi, F. M., Perron, B., Tamoni, A., & Tebaldi, C. (2019). The scale of predictability. Journal of Econometrics , 208(1), 120–140.CrossRefGoogle Scholar
Bollerslev, T., Osterrieder, D., Sizova, N., & Tauchen, G. (2013). Risk and return: Long-run relations, fractional cointegration, and return predictability. Journal of Financial Economics , 108(2), 409–424.CrossRefGoogle Scholar
Bollerslev, T., Tauchen, G., & Zhou, H. (2009). Expected stock returns and variance risk premia. Review of Financial Studies , 22(11), 4463–4492.CrossRefGoogle Scholar
Breitung, J., & Demetrescu, M. (2015). Instrumental variable and variable addition based inference in predictive regressions. Journal of Econometrics , 187(1), 358–375.CrossRefGoogle Scholar
Brockwell, P. J., & Davis, R. A. (1991). Time series: Theory and methods . Springer.CrossRefGoogle Scholar
Chen, W. W., & Deo, R. (2009). Bias reduction and likelihood-based almost exactly sized hypothesis testing in predictive regressions using the restricted likelihood. Econometric Theory , 25(5), 1143–1179.CrossRefGoogle Scholar
Christensen, B. J., & Nielsen, M. Ø. (2006). Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting. Journal of Econometrics , 133(1), 343–371.CrossRefGoogle Scholar
Dahlhaus, R. (2000). A likelihood approximation for locally stationary processes. Annals of Statistics , 28(6), 1762–1794.CrossRefGoogle Scholar
Dahlhaus, R., Richter, S., & Wu, W. B. (2019). Towards a general theory for nonlinear locally stationary processes. Bernoulli , 25(2), 1013–1044.CrossRefGoogle Scholar
Demetrescu, M., Georgiev, I., Rodrigues, P., & Taylor, R. (2022). Testing for episodic predictability in stock returns. Journal of Econometrics , 227(1), 85–113.CrossRefGoogle Scholar
Duffy, J. A., & Kasparis, I. (2021). Estimation and inference in the presence of fractional $d=1/2$ and weakly nonstationary processes. Annals of Statistics , 49(2), 1195–1217.CrossRefGoogle Scholar
Francq, C., & Zakoian, J.-M. (2010). GARCH models: Structure, statistical inference and financial applications . John Wiley & Sons.CrossRefGoogle Scholar
Giraitis, L., Kapetanios, G., & Marcellino, M. (2021). Time-varying instrumental variable estimation. Journal of Econometrics , 224(2), 394–415.CrossRefGoogle Scholar
Giraitis, L., Kapetanios, G., & Price, S. (2013). Adaptive forecasting in the presence of recent and ongoing structural change, Journal of Econometrics , 177(2), 153–170.CrossRefGoogle Scholar
Giraitis, L., Kapetanios, G., & Yates, T. (2014). Inference on stochastic time-varying coefficient models. Journal of Econometrics , 179(1), 46–65.CrossRefGoogle Scholar
Hassler, U., & Pohle, J.-M. (2019). Forecasting under long memory and nonstationarity. Working paper, Goethe University Frankfurt.Google Scholar
Hassler, U., & Wolters, J. (1995). Long memory in inflation rates: International evidence. Journal of Business and Economic Statistics , 13(1), 37–45.CrossRefGoogle Scholar
Hu, Z., Kasparis, I., & Wang, Q. (2021). Chronological trimming methods for nonlinear predictive regressions with persistent data . Mimeo, University of Cyprus.Google Scholar
Ibragimov, I. A., & Linnik, Y. V. (1971). Independent and stationary sequences of random variables . Wolters-Noordhoff Publishing.Google Scholar
Kasparis, I. (2011). The Bierens test for certain nonstationary models. Journal of Econometrics , 158(2), 221–230.CrossRefGoogle Scholar
Kasparis, I., Andreou, E., & Phillips, P. C. B. (2015). Nonparametric predictive regression. Journal of Econometrics , 185(2), 468–494.CrossRefGoogle Scholar
Kolmogorov, A. N., & Rozanov, U. A. (1960). On strong mixing conditions for stationary Gaussian processes. Theory of Probability and Its Applications , 5(2), 204–208.CrossRefGoogle Scholar
Kostakis, A., Magdalinos, T., & Stamatogiannis, M. P. (2015). Robust econometric inference for stock return predictability. Review of Financial Studies , 28(5), 1506–1553.CrossRefGoogle Scholar
Kristensen, D. (2012). Non-parametric detection and estimation of structural change. Econometrics Journal , 15(3), 420–461.CrossRefGoogle Scholar
Lewellen, J. (2004). Predicting returns with financial ratios. Journal of Financial Economics , 74(2), 209–235.CrossRefGoogle Scholar
Li, Q., & Racine, J. S. (2006). Nonparametric econometrics: Theory and practice . Princeton University Press.Google Scholar
Magdalinos, T., & Phillips, P. C. B. (2009). Econometric inference in the vicinity of unity . Mimeo, Singapore Management University.Google Scholar
Marmer, V. (2008). Nonlinearity, nonstationarity and spurious forecasts. Journal of Econometrics , 142(1), 1–27.CrossRefGoogle Scholar
Park, J. Y., & Phillips, P. C. B. (1999). Asymptotics for nonlinear transformations of integrated time series. Econometric Theory , 15(3), 269–298.CrossRefGoogle Scholar
Park, J. Y., & Phillips, P. C. B. (2000). Nonstationary binary choice, Econometrica , 68(5), 1249–1280.CrossRefGoogle Scholar
Park, J. Y., & Phillips, P. C. B. (2001). Nonlinear regressions with integrated time series, Econometrica , 69(1), 117–161.CrossRefGoogle Scholar
Petrova, K. (2019). A quasi-Bayesian local likelihood approach to time varying parameter VAR models. Journal of Econometrics , 212(1), 286–306.CrossRefGoogle Scholar
Phillips, P. C. B. (1995). Fully modified least squares and vector autoregression. Econometrica, 63(5), 1023–78.CrossRefGoogle Scholar
Phillips, P. C. B. (2015). Pitfalls and possibilities in predictive regression. Journal of Financial Econometrics , 13(3), 521–555.CrossRefGoogle Scholar
Phillips, P. C. B., Li, D., & Gao, J. (2017). Estimating smooth structural change in cointegration models. Journal of Econometrics , 196(1), 180–195.CrossRefGoogle Scholar
Phillips, P. C. B., & Magdalinos, T. (2007). Limit theory for moderate deviations from a unit root. Journal of Econometrics , 136(1), 115–130.CrossRefGoogle Scholar
Robinson, P. M. (1989). Nonparametric estimation of time varying parameters. In Hackl, P. (Ed.), Economic structural change: Analysis and forecasting (pp. 253–264). Springer.CrossRefGoogle Scholar
Robinson, P. M. (1991). Time varying nonlinear regression. In Hackl, P. (Ed.), Economic structural change: Analysis and forecasting (pp. 179–190). Springer.CrossRefGoogle Scholar
Robinson, P. M. (1995). Gaussian semiparametric estimation of long range dependence. Annals of Statistics , 23(5), 1630–1661.CrossRefGoogle Scholar
Samorodnitsky, G., & Taqqu, M. S. (1994). Stable non-Gaussian random processes . Chapman & Hall.Google Scholar
Shimotsu, K., & Phillips, P. C. B. (2005). Exact local Whittle estimation of fractional integration. Annals of Statistics , 33(4), 1890–1933.CrossRefGoogle Scholar
Shiryaev, A. N. (1996). Probability . (2nd ed.) Springer.CrossRefGoogle Scholar
Wang, Q. (2014). Martingale limit theorem revisited and nonlinear cointegrating regression. Econometric Theory , 30(3), 509–535.CrossRefGoogle Scholar
Wang, Q. (2015). Limit theorems for nonlinear cointegrating regression . World Scientific.CrossRefGoogle Scholar
Wang, Q., & Phillips, P. C. B. (2009). Asymptotic theory for local time density estimation and nonparametric cointegrating regression. Econometric Theory , 25(3), 710–738.CrossRefGoogle Scholar
Welch, I., & Goyal, A. (2008). A comprehensive look at the empirical performance of equity premium prediction. Review of Financial Studies , 21(4), 1455–1508.CrossRefGoogle Scholar
Yang, B., Long, W., Peng, L., &Cai, Z. (2020). Testing the predictability of U.S. housing price index returns based on an IVX-AR model. Journal of the American Statistical Association , 115(532), 1598–1619.CrossRefGoogle Scholar
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