Abstract
In this paper the serial independence tests known as SIS (Serial Independence Simultaneous) and SICS (Serial Independence Chi-Square) are considered. These tests are here contextualized in the model validation phase for nonlinear models in which the underlying assumption of serial independence is tested on the estimated residuals. Simulations are used to explore the performance of the tests, in terms of size and power, once a linear/nonlinear model is fitted on the raw data. Results underline that both tests are powerful against various types of alternatives.
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References
Bagnato L, Punzo A (2010) On the Use of χ2-Test to Check Serial Independence. Statistica Applicazioni 8(1):57–74
Box GEP, Pierce DA (1970) Distribution of the autocorrelations in autoregressive moving average time series models. J Am Stat Assoc 65(332):1509–1526
Diks C (2009) Nonparametric tests for independence. In: Meyers R (ed) Encyclopedia of complexity and systems science, Springer, Berlin
Jianqing F, Qiwei Y (2003) Nonlinear time series: nonparametric and parametric methods. Springer, Berlin
Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrika 65(2):297–303
Moran PAP (1953) The statistical analysis of the Canadian lynx cycle, 1. Structure and prediction. Aust J Zool 1(2):163–173
Roy SN (1953) On a heuristic method of test construction and its use in multivariate analysis. Ann Math Stat 24(2):220–238
Shaffer JP (1995) Multiple hypothesis testing. Ann Rev Psychol 46(1):561–584
Šidák Z (1967) Rectangular confidence regions for the means of multivariate normal distributions. J Am Stat Assoc 62(318):626–633
Tjøstheim D (1994) Non-linear time series: A selective review. Scand J Stat 21(2):97–130
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Bagnato, L., Punzo, A. (2012). Checking Serial Independence of Residuals from a Nonlinear Model. In: Gaul, W., Geyer-Schulz, A., Schmidt-Thieme, L., Kunze, J. (eds) Challenges at the Interface of Data Analysis, Computer Science, and Optimization. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24466-7_21
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DOI: https://doi.org/10.1007/978-3-642-24466-7_21
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