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2012 | 269 Multivariate Statistical Analysis : Methodological Aspects and Applications | 49-62
Tytuł artykułu

Some Properties of the Robust Trend Tests

Treść / Zawartość
Warianty tytułu
Wybrane własności testów w odpornej analizie trendu
Języki publikacji
EN
Abstrakty
Formalne testowanie zagadnienia trendu w szeregu czasowym jest uzależnione od faktu znajomości postaci szeregu, w szczególności stopnia zintegrowania (I(0) lub I(1)) szeregu czasowego, czyli od słabej lub silnej autokorelacji. W artykule przedstawimy odporne testy (na rząd integracji danych w szeregu czasowym) zaproponowane w pracach Bunzel i Vogelsang (2005), Harvey i inni (2007) oraz Perron i Yabu (2009). Testy te są odporne w sensie asympotycznych własności wartości krytycznych w testowaniu wartości współczynnika kierunkowego funkcji trendu. (abstrakt oryginalny)
EN
Formal testing of whether a time series contains a trend is greatly complicated by the fact that in practice it is not known whether the trend is embedded in an I(0) or I(1), series, that is, within a weakly or strongly autocorrelated series. In this article we would like to present the properties of behavior of the robust (to the order of integration of the data) trend tests of Bunzel and Vogelsang (2005), Harvey et al. (2007) and Perron and Yabu (2009). These statistics are termed 'robust' in the sense that the asymptotic critical values for testing hypotheses on the trend coefficient. (original abstract)
Twórcy
  • University of Economics in Katowice, Poland
Bibliografia
  • Bianco, A., Garcia Ben, M., Martinez, E., and Yohai, V. (1996), "Robust Procedure for Regression Models with ARIMA Errors",in A. Prat (ed.) COMPSTAT 96 Proceedings Computational Statistics.
  • Bianco, A., Garcia Ben, M., Martinez, E., and Yohai, V.(2001), "Outlier Detection in Regression Rodéis with ARIMA Errors Using Robust Estimates," Journal of Forecasting, Vol. 20, 565-579.
  • Box, G., and Jenkins, G. (1976), Time Series Analysis: Forecasting and Control, San Francisco, Holden-Day.
  • Bunzel, H., Vogelsang, T.J., (2005), Powerful trend function tests that are robust to strong serial correlation with an application to the Prebisch-Singer hypothesis. Journal of Business and Economic Statistics 23, 381-394.
  • Chang, I., Tiao, G. C, and Chen. C (1988). "Estimation of Time Series Parameters in the Presence of Outliers", Technometrics, 30, 193-204.
  • Elliott, G., Rothenberg, T. J. and Stock, J. H. (1996) Efficient tests for an autoregressive unit root. Econometrica 64, 813-36.
  • Grambsch, P., Stahel,W. A. (1990). Forecasting demand for special services. International Journal of Forecasting 6, 53-64.
  • Harvey David I., Leybourne Stephen J., Taylor A.M. Robert. A simple, robust and powerful test of the trend hypothesis Journal of Econometrics 141 (2007) 1302-1330
  • Harvey David L, Leybourne Stephen J., Taylor A.M. Robert. The impact of initial condition on robust tests for linear trend, Journal of Times Series Analysis, (2010)
  • Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., Shin, Y., 1992. Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? Journal of Econometrics 54, 159-178.
  • Martin, R. D., Samarov, A., and Vandaele, W. (1983). "Robust Methods for ARIMA Models", in E. Zellner (ed.) Applied Time Series Analysis of Economic Data, U.S. Census Bureau, Government Printing Office.
  • Martin, R.D., and V. J. Yohai (1996). "Highly Robust Estimation of Autoregressive Integrated Time Series Models," Publicaciones Previas No. 89, Facultad de Ciencias Exactas y Naturales, Universidad de
  • Masreliesz, C. J. (1975). "Approximate non-Gaussian Filtering with Linear State and Observation Relations", IEEE Transactions on Automatic Control, AC-20, 107-110.
  • Parzen, E. (1982). ARARMA models for time series analysis and forecasting. Journal of Forecasting 1, 67-82.
  • Perron, P. and Yabu, T. (2009) Estimating deterministic trends with an integrated or stationary noise component. Journal of Econometrics 151, 56-69.
  • Roy, A. and Fuller, W. A. (2001) Estimation for autoregressive processes with a root near one. Journal of Business and Economic Statistics 19, 482-93.
  • Roy, A., Falk, B. and Fuller, W. A. (2004) Testing for trend in the presence of autoregressive errors. Journal of the American Statistical Association 99.
  • Sarnaglia A.J.Q., Reisen V.A., Lévy-Leduc C, Robust estimation of periodic autoregressive processes in the presence of additive outliers, Journal of Multivariate Analysis 101 (2010) 2168-2183
  • Tsay, R. S. (1988). "Outliers, Level Shifts and Variance Changes in Time Series", Journal of Forecasting, 7, 1-20.
  • Vogelsang, T. J. (1998) Trend function hypothesis testing in the presence of serial correlation. Econometrica 66, 123-148.
  • Yohai, V. J., and Zamar, R. H. (1988). "High Breakdown-Point Estimates of Regression by Means of the Minimization of an Efficient Scale", Journal of the American Statistical Association, 83, 406-413.
Typ dokumentu
Bibliografia
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