NON- AND SEMIPARAMETRIC IDENTIFICATION OF SEASONAL NONLINEAR AUTOREGRESSION MODELS

Non- or semiparametric estimation and lag selection methods are proposed for three seasonal nonlinear autoregressive models of varying seasonal flexibility. All procedures are based on either local constant or local linear estimation. For the semiparametric models, after preliminary estimation of the seasonal parameters, the function estimation and lag selection are the same as nonparametric estimation and lag selection for standard models. A Monte Carlo study demonstrates good performance of all three methods. The semiparametric methods are applied to German real gross national product and UK public investment data. For these series our procedures provide evidence of nonlinear dynamics.

[1]  H. Rootzén.  On the functional central limit theorem for martingales, II , 1977 .

[2]  Leslie Godfrey,et al.  Testing the adequacy of a time series model , 1979 .

[3]  Bernard W. Silverman,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[4]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[5]  R. Fildes.  Journal of the American Statistical Association : William S. Cleveland, Marylyn E. McGill and Robert McGill, The shape parameter for a two variable graph 83 (1988) 289-300 , 1989 .

[6]  Byung Sam Yoo,et al.  Seasonal integration and cointegration , 1990 .

[7]  D. Tjøstheim,et al.  Identification of nonlinear time series: First order characterization and order determination , 1990 .

[8]  Denise R. Osborn,et al.  A survey of seasonality in UK macroeconomic variables , 1990 .

[9]  Persistence and Seasonality in Output and Employment of the Federal Republic of Germany , 1992 .

[10]  Critères d'ergodicité de quelques modèles à représentation markovienne , 1992 .

[11]  Ian T. Jolliffe,et al.  Introduction to Multiple Time Series Analysis , 1993 .

[12]  G. C. Tiao,et al.  An introduction to multiple time series analysis. , 1993, Medical care.

[13]  Ruey S. Tsay,et al.  Nonlinear Additive ARX Models , 1993 .

[14]  Agustín Maravall,et al.  Unobserved Components in Economic Time Series , 1993 .

[15]  P. Doukhan.  Mixing: Properties and Examples , 1994 .

[16]  J. Rosenthal.  Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo , 1995 .

[17]  Dag Tjøstheim,et al.  Nonparametric Identification of Nonlinear Time Series: Selecting Significant Lags , 1994 .

[18]  Dag Tjøstheim,et al.  Nonparametric Identification of Nonlinear Time Series: Projections , 1994 .

[19]  Eric Ghysels,et al.  Série Scientifique Scientific Series N o 95 s19 IS SEASONAL ADJUSTMENT A LINEAR OR NONLINEAR DATA FILTERING PROCESS ? , 1997 .

[20]  Dag Tjøstheim,et al.  Nonparametric tests of linearity for time series , 1995 .

[21]  Philip Hans Franses,et al.  Periodicity and Stochastic Trends in Economic Time Series , 1996 .

[22]  Wolfgang Karl Härdle,et al.  Nonparametric Vector Autoregression , 1998 .

[23]  Vidar Hjellvik,et al.  Nonparametric statistics for testing of linearity and serial independence , 1996 .

[24]  David F Findley.  Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process? Comment , 1996 .

[25]  Dag Tjøstheim,et al.  Additive Nonlinear ARX Time Series and Projection Estimates , 1997, Econometric Theory.

[26]  Robert H. Shumway,et al.  Semiparametric Modeling of Seasonal Time Series , 1998 .

[27]  Jens Perch Nielsen,et al.  Nonparametric Autoregression with Multiplicative Volatility and Additive mean , 1999 .

[28]  Lijian Yang,et al.  Multivariate bandwidth selection for local linear regression , 1999 .

[29]  Huay-min H. Pu,et al.  GEOMETRIC ERGODICITY OF NONLINEAR TIME SERIES , 1999 .

[30]  Finite nonparametric grach model for foreign exchange volatility , 2000 .

[31]  Juan M. Rodríguez-Póo,et al.  A nonparametric method to estimate time varying coefficients under seasonal constraints , 2000 .

[32]  Lijian Yang,et al.  Nonparametric Lag Selection for Time Series , 2000 .

[33]  S. Zacks,et al.  Journal of Statistical Planning and Inference , 2016 .