New Fractional Dickey and Fuller Test

Bensalma, Ahmed (2015): New Fractional Dickey and Fuller Test. Forthcoming in: IEEE Conference paper

Abstract

The aim of this paper is motivated by the following question: “If a series were best characterized by fractional process, would a researcher be able to detect that fact by using conventional Dickey-Fuller (1979) test?” To answer this question, in simple framework, we propose a new fractional Dickey-Fuller (F-DF) test, different from the test of Dolado, Gonzalo and Mayoral (2002).

• Item Type: MPRA Paper
• Language: English
• Keywords: Fractional unit root, Dickey-Fuller Test, Fractional integration parameter.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy; E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit

References

Bensalma, A. (2013a) ‘Simple fractional Dickey-Fuller test’, 29th European Meeting of Statisticians, Budapest (Hongrie), July, pp.46–47.

Bensalma, A. (2013b) ‘Unified theoretical framework for unit root and fractional unit root’, arXiv: 1209.1031v2.

Bensalma, A. (2015) ‘ A consistent test for unit root against fractional alternative’, Forthcoming in International Journal of Operational Research’ Inderscience Editor.

Dickey, D.A. and Fuller, W.A. (1979) ‘Distribution of the estimators for autoregressive time series with a unit root’, Journal of the American Statistical Association, Vol. 74, No. 366a, pp.427–431.

Dickey, D.A. and Fuller, W.A. (1981) ‘Likelihood ratio tests for autoregressive time series with a unit root’, Econometrica, Vol. 49, No.4, pp.1057–1072.

Dickey, D.A. and Pantula, S.G. (1987) ‘Determining the order of differencing in autoregressive processes’, Journal of Business and Economic Statistics, Vol. 15, No. 4, pp.455–461.

Diebold, F.X., and Rudebush, G.D. (1991) ‘On the power of the Dickey-Fuller test against fractional alternatives’, Economic Letters, Vol. 35, No. 2, pp.155–160.

Dolado, J.J., Gonzalo, J. and Mayoral, M. (2002) ‘A fractional Dickey- Fuller test for unit root’, Econometrica, Vol. 70, No. 5, pp.1963–2006.

Granger, C.W.J. and Joyeux, R. (1980) ‘An introduction to long memory time series models and fractional differencing’, Journal of Time Series Analysis, Vol. 1, No. 1, pp.15–29.

Hosking, J.R.M. (1981) ‘Fractional differencing’, Biom´etrika, Vol. 68, No. 1, pp.165–176.

Johansen, S. and Nilsen, M.O., (2010), ’Likelihood inference for a stationary fractional autoregressive model’, Journal of Econometrics, 158, 51-66.

Li, H. (1995) ‘A reexamination of the Nelson-Plosser data set using recursive and sequential tests’, Empirical Economics, Vol. 20, No. 3, pp.501–518.

Liu, M. (1998) ‘Asymptotics of nonstationary fractional integrated series’, Econometric Theory, Vol. 14, No. 5, pp.641–662.

Lobato, I.N. and Velasco, C. (2006) ‘Optimal fractional Dickey-Fuller tests’, Econometrics Journal, Vol. 9, No. 3, pp.492–510.

Lobato, I.N. and Velasco, C. (2007) ‘Efficient Wald tests for fractional unit roots’, Econometrica, Vol. 75, No. 2, pp.575–589.

Nelson, C.R. and Plosser, C.I. (1982) ‘Trends and random walks in macroeconomic time series: some evidence and implications’, Journal of Monetary Economics, Vol. 10, No. 2, pp.139–162.

Nilsen, M.O. (2004) ‘Efficient likelihood inference in stationary univariate models’, Econometric Theory, Vol. 20, No. 1, pp.116–146.

Sowell, F.B. (1990) ‘The fractional unit root distribution’, Econometrica, Vol. 58, No. 2, pp.494–505.