Abstract
This chapter discusses the problem of testing the equality of two nonparametric autoregressive functions against two-sided alternatives. The heteroscedastic error and stationary densities of the two independent strong mixing strictly stationary time series can be possibly different. The chapter adapts the partial sum process idea used in the independent observations settings to construct the tests and derives their asymptotics under both null and alternative hypotheses. Then, a Monte Carlo simulation is conducted to study the finite sample level and power behavior of these tests at both fixed and local alternatives.
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References
Berkes I, Philipp W (1997) Approximation theorems for independent and weakly dependent random vectors. Ann Probab 7:29–54
Bloomfield P (1992) Trends in global temperatures. Climatic Change 21:275–287
Bosq D (1998) Nonparametric Statistics for Stochastic Processes: Estimation and Prediction. Springer, New York
Delgado MA (1993) Testing the equality of nonparametric regression curves. Stat Probab Lett 17:199–204
Dehling H, Mikosch T, Sφrensen M (2002) Empirical Process Techniques for Dependent Data. Birkhauser, Boston. MR1958776
Fan J, Yao Q (2003) Nonlinear Time Series: Nonparametric and Parametric Methods. Springer Verlag, New York
Hall P, Hart JD (1990) Bootstrap test for difference between means in nonparametric regression. J Amer Stat Assoc 85:1039–1049
Hall P, Heyde CC (1980) Martingale limit theory and its Applications. Academic Press, Inc., New York
Koul HL (2002) Weighted Empirical Processes in Dynamic Nonlinear Models. Springler, New York
Koul HL, Li F (2005) Testing for Superiority among two time series. Statistical Inference for Stochastic Processes. 8:109–135
Koul HL, Schick A (1997) Testing the equality of two nonparametric regression curves.J Stat Plann Inference 65:293–314
Kulasekera KB (1995) Comparison of regression curves using quasi-residuals. J Am Stat Assoc 90:1085–1093
Li F (2008) Asymptotic properties of some kernel smoothers. Preprint. pr08-03, Department of Mathematical Sciences. Indiana University Purdue University Indianapolis.
Li F (2009) Testing for the equality of two autoregressive functions using quasi residual. Communicat Stat-Theory Meth 38(9):1404–1421
Nadaraya EA (1964) On estimating regression. Theory Probab Appl 9:141–142
Resnick SI (1992) Adventures in Stochastic Processes. Springer, New York
Scheike TH (2000) Comparison of non-parametric regression functions through their cumulatives. Stat Probab Lett 46:21–32
Watson GS (1964) Smooth regression analysis. Sankhy\(\bar {a}\) Ser A 26:359–372
Acknowledgement
The author is Dr. Hira L. Koul’s 22nd Ph.D. student. She graduated in 2004 and would like to thank Hira for his patient guidance and generous support for more than ten years now. The author is also very grateful to Hira for his academic advice and knowledge and many insightful discussions and suggestions. This manuscript is specially dedicated to him on the occasion of his 70th Birthday.
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Li, F. (2014). Comparison of Autoregressive Curves Through Partial Sums of Quasi-Residuals. In: Lahiri, S., Schick, A., SenGupta, A., Sriram, T. (eds) Contemporary Developments in Statistical Theory. Springer Proceedings in Mathematics & Statistics, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-319-02651-0_15
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DOI: https://doi.org/10.1007/978-3-319-02651-0_15
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