Bai, Zhidong and Hui, Yongchang and Wong, Wing-Keung (2012): New Non-Linearity Test to Circumvent the Limitation of Volterra Expansion.
Download (205kB) | Preview
In this article we propose a quick, efficient, and easy method to detect whether a time series Yt possesses any nonlinear feature. The advantage of our proposed nonlinearity test is that it is not required to know the exact nonlinear features and the detailed nonlinear forms of Yt. Our proposed test could also be used to test whether the model, including linear and nonlinear, hypothesized to be used for the variable is appropriate as long as the residuals of the model being used could be estimated. Our simulation results show that our proposed test is stable and powerful while our illustration on Wolf's sunspots numbers is consistent with the findings from existing literature.
|Item Type:||MPRA Paper|
|Original Title:||New Non-Linearity Test to Circumvent the Limitation of Volterra Expansion|
|Keywords:||linearity; nonlinearity; U-statistics; Volterra expansion|
|Subjects:||C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General
C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics
|Depositing User:||Wing-Keung Wong|
|Date Deposited:||11 Oct 2012 12:33|
|Last Modified:||23 Feb 2017 14:56|
AKAIKE H. (1978). On the likelihood of a time series model. J. R. Statist. Soc. D, 27, 217-235.
BLOOMFIELD, P. (1976). Fourier Analysis of Time Series: An Introduction. New York: John Wiley.
BOLLERSLEV, T. (1986). Generalized autoregressive conditional heteroscedasticity. J. Econometrics, 31, 307-327.
BOX, G. E. P., JENKINS, G. M. & REINSEL, G. C. (1994). Time Series Analysis Forecasting and Control. Prentice-Hall.
BRILLINGER, D. R. (1970). The identification of polynomial systems by means of higher order spectra. J. Sound. Vib., 12, 301-313.
CARLIN, B. P., POLSON, N. G. & STOFFER, D. S. (1992). A Monte Carlo approach to nonnormal and nonlinear state space modeling. J. Am. Statist. Assoc., 87, 493-500.
CHAN, K. S. (1990b). Testing for threshold autoregression. Ann. Statist., 18, 1886-1894.
CHAN, K. S. & TONG, H. (1990). On likelihood ratio tests for threshold autoregression. J. R. Statist. Soc. B, 52, 469-476.
CHEN, R. & TSAY, R. S. (1993a). Functional-coefficient autoregressive models. J. Am. Statist. Assoc., 88, 298-308.
CHEN, R. & TSAY, R. S. (1993b). Nonlinear additive ARX models. J. Am. Statist. Assoc., 88, 955-967.
COX, D. R. (1981). Statistical analysis of time series: Some recent developments (with discussion). Scand. J. Statist., 8, 93-115.
CRADDOCK, J. M. (1967). An experiment in the analysis and prediction of time series. The Statistician, 17, 257-268.
DENKER, M. & KELLER, G. (1983). On U-statistics and v.Mises' Statistics for weakly Dependent Processes. Zeitschrift fur Wahrscheinlichkeitstheorie und verwandte Gebiete, 64, 505-522.
DENKER, M. & KELLER, G. (1986). Rigorous statistical procedures for data from dynamical system. J. Statist. Phys., 44, 67-93.
ENGLE, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987-1008.
FAN, J. Q. & YAO, Q. W. (2003). Nonlinear time series: nonparametric and parametric methods., New York: Springer-Verlag.
GHADDAR, D. K. (1980). Some diagnostic checks of non-linear time series models. M.sc. dissertation, University of Manchester, U.K.
GRANGER, C. W. J. & ANDERSEN, A. P. (1978). An Introduction to Bilinear Time Series Models., Gottingen: Vandenhoek and Ruprecht.
HAMILTON, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57, 357-384.
HARDLE, W., LUTKEPOHL, H. & CHEN, R. (1997). A review of nonparametric time series analysis. Int. Statist. Re., 65, 49-72.
HINICH, M. J. (1982). Testing for Gaussianity and linearity of a stationary time series. J. Time Series Anal., 3, 169-176.
HINICH, M. J. & PATTERSON, D. M. (1985). Evidence of nonlinearity in daily stock returns. J. Bus. Econ. Statist., 3, 69-77.
IZENMAN, A. J., Wolf, J. R. & Wolfer, H. A. (1983). An historical note on Zurich sunspot relative numbers. J. R. Statist. Soc. A, 146, 311-318.
KEENAN, D. M. (1985). A Tukey non-additivity-type test for time series nonlinearity. Biometrika, 72, 39-44.
KOWALSKI, J. & Tu, X. M. (2007). Modern Applied U-Statistics. New York: John Wiley & Sons.
LEWIS, P. A. W. & STEVENS, J. G. (1991). Nonlinear modeling of time series using multivariate adaptive regression spline (MARS). J. Am. Statist. Assoc., 86, 864-877.
LIM, K.S. (1981). On threshold time series modelling. Unpublished Ph.D. Thesis. University of Manchester, U.K.
MARAVELL, A. (1983). An application of nonlinear time series forecasting. J. Bus. Econ. Statist., 1, 66-74.
MASRY, E. & FAN, J. (1997). Local polynomial estimation of regression functions for mixing processes. Scand. J. Statist., 24, 165-179.
MORAN, P. A. P. (1954). Some experiments on the prediction of sunspot numbers. J. R. Statist. Soc. B, 116, 112-117.
NEWEY, W. K. & WEST, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation constistent covariance matrix. Econometrica, 55, 703-708.
PRIESTLEY, M. B. (1980). State-dependent models: a general approach to nonlinear time series analysis. J. Time Series Anal., 1, 47-71.
RAMSEY, J. B. (1969). Tests for specification errors in classical linear least squares regression analysis. J. R. Statist. Soc. B, 31, 350-371.
SCHAERF, M. C. (1964). Estimation of the covariance and autoregressive structure of a stationary time series. Tech. Rep., Department of Statistics, Stanford University, Stanford, California, U.S.A.
SERFLING, R. (1980). Approximation Theorems of Mathematical Statistics. New York: John Wiley & Sons.
SUBBA RAO, T. & GABR, M. M. (1980). A test for linearity of stationary time series. J. Time Series Anal., 1, 145-158.
TIAO, G. C. & TSAY, R. S. (1994). Some advances in nonlinear and adaptive modeling in time series. J. Forecasting, 13, 109-131.
TJOTHEIM, D. (1994). Non-linear time series: A selective review. Scand. J. Statist., 21, 97-130.
TUKEY, J. W. (1949). One degree of freedom for non-additivity. Biometrics, 5, 232-242.
TONG, H. (1978). On a threshold model. In C. H. Chen (ed.), Pattern Recognition and Signal Processing. Amsterdam: Sijhoff & Noordhoff.
TONG, H. (1983). Threshold Models in Non-linear Time Series Analysis. New York: Springer-Verlag.
TONG, H. (1990). Non-linear Time Series: A Dynamical Systems Approach. Oxford: Oxford University Press.
TONG, H. (1995). A personal overview of non-linear time series analysis from a chaos perspective (with discussion). Scand. J. Statist., 22, 399-445.
TONG, H. & LIM, K. S. (1980). Threshold autoregression, limit cycles and cyclical data (with discussion). J. R. Statist. Soc. B, 42, 245-292.
TSAY, R. S. (1986). Nonlinearity tests for time series. Biometrika, 73, 461-466.
TSAY, R. S. (1989). Testing and modeling threshold autoregressive processes. J. Am. Statist. Assoc., 84, 231-240.
WIENER, N. (1958). Non-linear Problems in Random Theory. Cambridge, Mass: M.I.T. Press.
YAO, Q. & TONG, H. (1995a). On initial-condition sensitivity and prediction in nonlinear stochastic systems. Bull. Int. Statist. Inst., 10, 395-412.
YAO, Q. & TONG, H. (1995b). On prediction and chaos in stochastic systems. In Chaos and Forecasting ed. by H Tong, World Scientific, Singapore, pp. 57-86.
YULE, G. U. (1927). On a method of investigating periodicities in disturbed series with special reference to Wolfer's sunspot numbers. Philosophical Transactions of the Royal Society (London) A, 226, 267-298.
Available Versions of this Item
- New Non-Linearity Test to Circumvent the Limitation of Volterra Expansion. (deposited 11 Oct 2012 12:33) [Currently Displayed]