Checking Serial Independence of Residuals from a Nonlinear Model

  • Luca Bagnato
  • Antonio PunzoEmail author
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


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.


Dependence Structure Nominal Size White Noise Process Serial Independence Portmanteau Test 
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  1. Bagnato L, Punzo A (2010) On the Use of χ2-Test to Check Serial Independence. Statistica Applicazioni 8(1):57–74Google Scholar
  2. Box GEP, Pierce DA (1970) Distribution of the autocorrelations in autoregressive moving average time series models. J Am Stat Assoc 65(332):1509–1526MathSciNetzbMATHCrossRefGoogle Scholar
  3. Diks C (2009) Nonparametric tests for independence. In: Meyers R (ed) Encyclopedia of complexity and systems science, Springer, BerlinGoogle Scholar
  4. Jianqing F, Qiwei Y (2003) Nonlinear time series: nonparametric and parametric methods. Springer, BerlinzbMATHGoogle Scholar
  5. Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrika 65(2):297–303MathSciNetzbMATHCrossRefGoogle Scholar
  6. Moran PAP (1953) The statistical analysis of the Canadian lynx cycle, 1. Structure and prediction. Aust J Zool 1(2):163–173Google Scholar
  7. Roy SN (1953) On a heuristic method of test construction and its use in multivariate analysis. Ann Math Stat 24(2):220–238zbMATHCrossRefGoogle Scholar
  8. Shaffer JP (1995) Multiple hypothesis testing. Ann Rev Psychol 46(1):561–584CrossRefGoogle Scholar
  9. Šidák Z (1967) Rectangular confidence regions for the means of multivariate normal distributions. J Am Stat Assoc 62(318):626–633zbMATHGoogle Scholar
  10. Tjøstheim D (1994) Non-linear time series: A selective review. Scand J Stat 21(2):97–130Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Dipartimento di Metodi Quantitativi per le Scienze Economiche e AziendaliUniversità di Milano-BicoccaMilanoItaly
  2. 2.Dipartimento di Impresa, Culture e SocietàUniversità di CataniaCataniaItaly

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