Improved inference for moving average disturbances in nonlinear regression models. (English) Zbl 1307.62174

Summary: This paper proposes an improved likelihood-based method to test for first-order moving average in the disturbances of nonlinear regression models. The proposed method has a third-order distributional accuracy which makes it particularly attractive for inference in small sample sizes models. Compared to the commonly used first-order methods such as likelihood ratio and Wald tests which rely on large samples and asymptotic properties of the maximum likelihood estimation, the proposed method has remarkable accuracy. Monte Carlo simulations are provided to show how the proposed method outperforms the existing ones. Two empirical examples including a power regression model of aggregate consumption and a Gompertz growth model of mobile cellular usage in the US are presented to illustrate the implementation and usefulness of the proposed method in practice.


62J02 General nonlinear regression
62P20 Applications of statistics to economics


Full Text: DOI


[1] P. E. Nguimkeu and M. Rekkas, “Third-order inference for autocorrelation in nonlinear regression models,” Journal of Statistical Planning and Inference, vol. 141, no. 11, pp. 3413-3425, 2011. · Zbl 1221.62102
[2] D. F. Nicholls, A. R. Pagan, and R. D. Terrell, “The estimation and use of models with moving average disturbance terms: a survey,” International Economic Review, vol. 16, pp. 113-134, 1975. · Zbl 0303.62056
[3] P. H. Franses, Time Series Models for Business and Economic Forecasting, Cambridge University Press, Cambridge, Mass, USA, 1998.
[4] J. D. Hamilton, Time Series Analysis, Princeton University Press, Princeton, NJ, USA, 1994. · Zbl 0831.62061
[5] H. Lütkepohl and M. Kratzig, Applied Time Series Econometrics, Cambridge University Press, Cambridge, Mass, USA, 2004.
[6] D. A. S. Fraser and N. Reid, “Ancillaries and third order significance,” Utilitas Mathematica, vol. 47, pp. 33-53, 1995. · Zbl 0829.62006
[7] F. Chang, M. Rekkas, and A. Wong, “Improved likelihood-based inference for the MA(1) model,” Journal of Statistical Planning and Inference, vol. 143, no. 1, pp. 209-219, 2013. · Zbl 1250.62044
[8] D. A. S. Fraser, N. Reid, and J. Wu, “A simple general formula for tail probabilities for frequentist and Bayesian inference,” Biometrika, vol. 86, no. 2, pp. 249-264, 1999. · Zbl 0932.62003
[9] G. E. P. Box and G. M. Jenkins, Time Series Analysis: Forecasting and Control, Holden-Day, San Francisco, Calif, USA, 1976. · Zbl 0363.62069
[10] A. R. Pagan and D. F. Nicholls, “Exact maximum likelihood estimation of regression models with finite order moving average errors,” Review of Economic Studies, vol. 43, pp. 483-487, 1976. · Zbl 0358.62046
[11] P. Whittle, Prediction and Regulation by Linear Least-Square Methods, University of Minnesota Press, Minneapolis, Minn, USA, 2nd edition, 1983. · Zbl 0646.62079
[12] J. W. Galbraith and V. Zinde-Walsh, “A simple noniterative estimator for moving average models,” Biometrika, vol. 81, no. 1, pp. 143-155, 1994. · Zbl 0800.62522
[13] J. H. Stock, “Unit roots, structural breaks and trends,” in Handbook of Econometrics, Vol. IV, R. F. Engle and D. L. McFadden, Eds., vol. 2, chapter 46, pp. 2739-2841, North-Holland, Amsterdam, The Netherlands, 1994.
[14] O. E. Barndorff-Nielsen, “Modified signed log likelihood ratio,” Biometrika, vol. 78, no. 3, pp. 557-563, 1991. · Zbl 1192.62052
[15] O. E. Barndorff-Nielsen, “Inference on full and partial parameters based on the standardized signed log-likelihood ratio,” Biometrika, vol. 73, pp. 307-322, 1986. · Zbl 0605.62020
[16] P. Balestra, “A note on the exact transformation associated with the first-order moving average process,” Journal of Econometrics, vol. 14, no. 3, pp. 381-394, 1980. · Zbl 0458.62079
[17] A. Ullah, H. D. Vinod, and R. S. Singh, “Estimation of linear models with moving average disturbances,” Journal of Quantitative Economics, vol. 2, no. 1, pp. 137-152, 1986.
[18] D. A. S. Fraser, M. Rekkas, and A. Wong, “Highly accurate likelihood analysis for the seemingly unrelated regression problem,” Journal of Econometrics, vol. 127, no. 1, pp. 17-33, 2005. · Zbl 1336.62140
[19] F. Chang and A. C. M. Wong, “Improved likelihood-based inference for the stationary AR (2) model,” Journal of Statistical Planning and Inference, vol. 140, no. 7, pp. 2099-2110, 2010. · Zbl 1184.62150
[20] A. C. Harvey, “Time series forecasting based on the logistic curve,” Journal of the Operational Research Society, vol. 35, no. 7, pp. 641-646, 1984. · Zbl 0544.62097
[21] D. Fekedulegn, M. P. Mac Siurtain, and J. J. Colbert, “Parameter estimation of nonlinear growth models in forestry,” Silva Fennica, vol. 33, no. 4, pp. 327-336, 1999.
[22] P. Young, “Technological growth curves. A competition of forecasting models,” Technological Forecasting and Social Change, vol. 44, no. 4, pp. 375-389, 1993.
[23] A. Tsoularis and J. Wallace, “Analysis of logistic growth models,” Mathematical Biosciences, vol. 179, no. 1, pp. 21-55, 2002. · Zbl 0993.92028
[24] P. H. Franses, “Fitting of Gompertz curve,” Journal of the Operational Research Society, vol. 45, no. 1, pp. 109-113, 1994. · Zbl 0800.62815
[25] M. Bengisu and R. Nekhili, “Forecasting emerging technologies with the aid of science and technology databases,” Technological Forecasting and Social Change, vol. 73, no. 7, pp. 835-844, 2006.
[26] N. Meade and T. Islam, “Technological forecasting-model selection, model stability, and combining models,” Management Science, vol. 44, no. 8, pp. 1115-1130, 1998. · Zbl 0988.90532
[27] W. H. Greene, Econometric Analysis, Prentice Hall, Englewood Cliffs, NJ, USA, 7th edition, 2012.
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