Testing for changes in polynomial regression

We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability in the regression parameters against the alternative of a break at an unknown time. We derive the extreme value distribution of a maximum-type test statistic which is asymptotically equivalent to the maximally selected likelihood ratio. The resulting test is easy to apply and has good size and power, even in small samples.

[1]  Bruce E. Hansen,et al.  Testing for structural change in conditional models , 2000 .

[2]  D. Jarušková.  Testing appearance of linear trend , 1998 .

[3]  Chung-Ming Kuan.  Tests for changes in models with a polynomial trend , 1998 .

[4]  Holger Rootzén,et al.  Extreme Values in Finance, Telecommunications, and the Environment , 2003 .

[5]  J. Doob.  Stochastic processes , 1953 .

[6]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[7]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[8]  J. Albin.  On Extremal Theory for Stationary Processes , 1990 .

[9]  Pierre Perron,et al.  Dealing with Structural Breaks , 2005 .

[10]  V. K. Jandhyala,et al.  Residual partial sum limit process for regression models with applications to detecting parameter changes at unknown times , 1989 .

[11]  Ernst Eberlein,et al.  On Strong Invariance Principles Under Dependence Assumptions , 1986 .

[12]  Testing Appearance of Polynomial Trend , 1999 .

[13]  D. Andrews.  Tests for Parameter Instability and Structural Change with Unknown Change Point , 1993 .

[14]  Q. Shao.  Almost sure invariance principles for mixing sequences of random variables , 1993 .

[15]  C. R. Rao,et al.  Linear Statistical Inference and its Applications , 1968 .

[16]  Jean-Marie Dufour,et al.  Editors' introduction recent developments in the econometrics of structural change , 1996 .

[17]  K. Hornik,et al.  The generalized fluctuation test: A unifying view , 1995 .

[18]  L. Horváth,et al.  Limit Theorems in Change-Point Analysis , 1997 .

[19]  On a Test Statistic for Linear Trend , 2003 .

[20]  A. Banerjee,et al.  Modelling structural breaks, long memory and stock market volatility: an overview , 2005 .

[21]  V. Jandhyala.  A property of partial sums of regression least squares residuals and its applications , 1993 .

[22]  R. Quandt.  The Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regimes , 1958 .

[23]  P. Perron,et al.  Estimating and Testing Structural Changes in Multivariate Regressions , 2007 .

[24]  R. Quandt.  Tests of the Hypothesis That a Linear Regression System Obeys Two Separate Regimes , 1960 .

[25]  Ian B. MacNeill,et al.  Properties of Sequences of Partial Sums of Polynomial Regression Residuals with Applications to Tests for Change of Regression at Unknown Times , 1978 .

[26]  M. Kupperman.  Linear Statistical Inference and Its Applications 2nd Edition (C. Radhakrishna Rao) , 1975 .

[27]  J. Hüsler.  Extremes and related properties of random sequences and processes , 1984 .

[28]  Lajos Horváth,et al.  Detecting Changes in Linear Regressions , 1995 .

[29]  J. Stock,et al.  Testing for and Dating Common Breaks in Multivariate Time Series , 1998 .

[30]  D. L. Hawkins.  A u-i approach to retrospective testing for shifting parameters in a linear model , 1989 .

[31]  Iterated Partial Sum Sequences of Regression Residuals and Tests for Changepoints with Continuity Constraints , 1997 .

[32]  Marie Husková,et al.  Extreme value theory for stochastic integrals of Legendre polynomials , 2009, J. Multivar. Anal..

[33]  J. Nyblom.  Testing for the Constancy of Parameters over Time , 1989 .

[34]  J. Albin,et al.  On the general law of iterated logarithm with application to selfsimilar processes and to Gaussian processes in Rn and Hilbert space , 1992 .

[35]  D. Andrews,et al.  Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative , 1992 .

[36]  P. Protter,et al.  Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations , 1991 .

[37]  On extremes and streams of upcrossings , 2001 .