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Year 2018, Volume: 31 Issue: 4, 1268 - 1282, 01.12.2018

Abstract

References

  • Cochrane, D. and Orcutt, G.H., “Application of least squares regression to relationships containing autocorrelated error terms”, Journal of the American Statistical Association, 44(245): 32-61, (1949).
  • Gallant, A.R. and Goebel, J.J., “Nonlinear regression with autocorrelated errors”, Journal of the American Statistical Association, 71(356): 961-967, (1976).
  • Glasbey, C.A., “Correlated residuals in nonlinear regression applied to growth data”, Applied Statistics, 28(3): 251-259, (1979).
  • Glasbey, C.A., “Nonlinear regression with autoregressive time series errors”, Biometrics, 36(1): 135-140, (1980).
  • Glasbey, C.A., “Examples of regression with serially correlated errors”, The Statistician, 37(3): 277-291, (1988).
  • Huang, M.N.L. and Huang, M.K., “A parameter-elimination method for nonlinear regression with linear parameters and autocorrelated errors”, Biometrical Journal, 33(8): 937-950, (1991).
  • Asikgil, B. and Erar, A., “Polynomial tapered two-stage least squares method in nonlinear regression”, Applied Mathematics and Computation, 219(18): 9743-9754, (2013).
  • Asikgil, B., “A novel approach for estimating seemingly unrelated regressions with high-order autoregressive disturbances”, Communications in Statistics: Simulation and Computation, 43(9): 2061-2080, (2014).
  • Tong, H., “On a threshold model”, In: Chen, C. H. ed., Pattern Recognition and Signal Processing, Sijhoff and Noordhoff, Amsterdam, (1978).
  • Tong, H., Threshold Models in Nonlinear Time Series Analysis, Lecture Notes in Statistics, Springer-Verlag, New York, (1983).
  • Tsay, R.S., “Testing and modeling threshold autoregressive processes”, Journal of the American Statistical Association, 84(405): 231-240, (1989).
  • Tsay, R.S., Analysis of Financial Time Series, John Wiley and Sons, Canada, (2002).
  • Yadav, P.K., Pope, P.F. and Paudyal, K., “Threshold autoregressive modeling in finance: the price differences of equivalent assests”, Mathematical Finance, 4(2): 205-221, (1994).
  • Feucht, M., Möller, U., Witte, H., Schmidt, K., Arnold, M., Benninger, F., Steinberger, K. and Friedrich, M.H., “Nonlinear dynamics of 3 Hz spike-and-wave discharges recorded during typical absence seizures in children”, Cerebral Cortex, 8(6): 524-533, (1998).
  • Chan, W.S., Wong, A.C.S. and Tong, H., “Some nonlinear threshold autoregressive time series models for actuarial use”, North American Actuarial Journal, 8(4): 37-61, (2004).
  • Chan, K.S. and Tong, H., “On estimating thresholds in autoregressive models”, Journal of Time Series Analysis, 7(3): 179-190, (1986).
  • Chan, K.S., “Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model”, The Annals of Statistics, 21(1): 520-533, (1993).
  • Chan, W.S. and Cheung, S.H., “On robust estimation of threshold autoregressions”, Journal of Forecasting, 13(1): 37-49, (1994).
  • Baragona, R., Battaglia, F. and Cucina, D., “Fitting piecewise linear threshold autoregressive models by means of genetic algorithms”, Computational Statistics and Data Analysis, 47(2): 277-295, (2004).
  • Jaras, J. and Gishani, A.M., “Threshold Detection in Autoregressive Nonlinear Models”, MSc. Thesis, Lund University, Sweden, (2010).
  • Tong, H. and Lim, K.S., “Threshold autoregression, limit cycles and cyclical data”, Journal of the Royal Statistical Society: Series B (Methodological), 42(3): 245-292, (1980).
  • Gibson, D. and Nur, D., “Threshold autoregressive models in finance: a comparative approach”, Proceedings of the Fourth Annual ASEARC Conference, University of Western Sydney, Australia, (2011).
  • Petruccelli, J. and Woolford, S.W., “A threshold AR(1) model”, Journal of Applied Probability, 21(2): 270-286, (1984).

An Adapted Approach for Self-Exciting Threshold Autoregressive Disturbances in Multiple Linear Regression

Year 2018, Volume: 31 Issue: 4, 1268 - 1282, 01.12.2018

Abstract

Ordinary
least squares method is usually used for parameter estimation in multiple
linear regression models when all regression assumptions are satisfied. One of
the problems in multiple linear regression analysis is the presence of serially
correlated disturbances. Serial correlation can be formed by autoregressive or
moving average models. There are many studies in the literature including
parameter estimation in regression models especially with autoregressive
disturbances. The motivation of this study is that whether serially correlated
disturbances are defined by a different type of nonlinear process and how this
process is analyzed in multiple linear regression. For this purpose, a
nonlinear time series process known as self-exciting threshold autoregressive
model is used to generate disturbances in multiple linear regression models.
Two-stage least squares method used in the presence of autoregressive
disturbances is adapted for dealing with this new situation and comprehensive
experiments are performed in order to compare efficiencies of the proposed
method with the others. According to numerical results, the proposed method can
outperform under the type of self-exciting threshold autoregressive
autocorrelation problem when compared to ordinary least squares and two-stage
least squares.

References

  • Cochrane, D. and Orcutt, G.H., “Application of least squares regression to relationships containing autocorrelated error terms”, Journal of the American Statistical Association, 44(245): 32-61, (1949).
  • Gallant, A.R. and Goebel, J.J., “Nonlinear regression with autocorrelated errors”, Journal of the American Statistical Association, 71(356): 961-967, (1976).
  • Glasbey, C.A., “Correlated residuals in nonlinear regression applied to growth data”, Applied Statistics, 28(3): 251-259, (1979).
  • Glasbey, C.A., “Nonlinear regression with autoregressive time series errors”, Biometrics, 36(1): 135-140, (1980).
  • Glasbey, C.A., “Examples of regression with serially correlated errors”, The Statistician, 37(3): 277-291, (1988).
  • Huang, M.N.L. and Huang, M.K., “A parameter-elimination method for nonlinear regression with linear parameters and autocorrelated errors”, Biometrical Journal, 33(8): 937-950, (1991).
  • Asikgil, B. and Erar, A., “Polynomial tapered two-stage least squares method in nonlinear regression”, Applied Mathematics and Computation, 219(18): 9743-9754, (2013).
  • Asikgil, B., “A novel approach for estimating seemingly unrelated regressions with high-order autoregressive disturbances”, Communications in Statistics: Simulation and Computation, 43(9): 2061-2080, (2014).
  • Tong, H., “On a threshold model”, In: Chen, C. H. ed., Pattern Recognition and Signal Processing, Sijhoff and Noordhoff, Amsterdam, (1978).
  • Tong, H., Threshold Models in Nonlinear Time Series Analysis, Lecture Notes in Statistics, Springer-Verlag, New York, (1983).
  • Tsay, R.S., “Testing and modeling threshold autoregressive processes”, Journal of the American Statistical Association, 84(405): 231-240, (1989).
  • Tsay, R.S., Analysis of Financial Time Series, John Wiley and Sons, Canada, (2002).
  • Yadav, P.K., Pope, P.F. and Paudyal, K., “Threshold autoregressive modeling in finance: the price differences of equivalent assests”, Mathematical Finance, 4(2): 205-221, (1994).
  • Feucht, M., Möller, U., Witte, H., Schmidt, K., Arnold, M., Benninger, F., Steinberger, K. and Friedrich, M.H., “Nonlinear dynamics of 3 Hz spike-and-wave discharges recorded during typical absence seizures in children”, Cerebral Cortex, 8(6): 524-533, (1998).
  • Chan, W.S., Wong, A.C.S. and Tong, H., “Some nonlinear threshold autoregressive time series models for actuarial use”, North American Actuarial Journal, 8(4): 37-61, (2004).
  • Chan, K.S. and Tong, H., “On estimating thresholds in autoregressive models”, Journal of Time Series Analysis, 7(3): 179-190, (1986).
  • Chan, K.S., “Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model”, The Annals of Statistics, 21(1): 520-533, (1993).
  • Chan, W.S. and Cheung, S.H., “On robust estimation of threshold autoregressions”, Journal of Forecasting, 13(1): 37-49, (1994).
  • Baragona, R., Battaglia, F. and Cucina, D., “Fitting piecewise linear threshold autoregressive models by means of genetic algorithms”, Computational Statistics and Data Analysis, 47(2): 277-295, (2004).
  • Jaras, J. and Gishani, A.M., “Threshold Detection in Autoregressive Nonlinear Models”, MSc. Thesis, Lund University, Sweden, (2010).
  • Tong, H. and Lim, K.S., “Threshold autoregression, limit cycles and cyclical data”, Journal of the Royal Statistical Society: Series B (Methodological), 42(3): 245-292, (1980).
  • Gibson, D. and Nur, D., “Threshold autoregressive models in finance: a comparative approach”, Proceedings of the Fourth Annual ASEARC Conference, University of Western Sydney, Australia, (2011).
  • Petruccelli, J. and Woolford, S.W., “A threshold AR(1) model”, Journal of Applied Probability, 21(2): 270-286, (1984).
There are 23 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Statistics
Authors

Barış Asıkgıl

Publication Date December 1, 2018
Published in Issue Year 2018 Volume: 31 Issue: 4

Cite

APA Asıkgıl, B. (2018). An Adapted Approach for Self-Exciting Threshold Autoregressive Disturbances in Multiple Linear Regression. Gazi University Journal of Science, 31(4), 1268-1282.
AMA Asıkgıl B. An Adapted Approach for Self-Exciting Threshold Autoregressive Disturbances in Multiple Linear Regression. Gazi University Journal of Science. December 2018;31(4):1268-1282.
Chicago Asıkgıl, Barış. “An Adapted Approach for Self-Exciting Threshold Autoregressive Disturbances in Multiple Linear Regression”. Gazi University Journal of Science 31, no. 4 (December 2018): 1268-82.
EndNote Asıkgıl B (December 1, 2018) An Adapted Approach for Self-Exciting Threshold Autoregressive Disturbances in Multiple Linear Regression. Gazi University Journal of Science 31 4 1268–1282.
IEEE B. Asıkgıl, “An Adapted Approach for Self-Exciting Threshold Autoregressive Disturbances in Multiple Linear Regression”, Gazi University Journal of Science, vol. 31, no. 4, pp. 1268–1282, 2018.
ISNAD Asıkgıl, Barış. “An Adapted Approach for Self-Exciting Threshold Autoregressive Disturbances in Multiple Linear Regression”. Gazi University Journal of Science 31/4 (December 2018), 1268-1282.
JAMA Asıkgıl B. An Adapted Approach for Self-Exciting Threshold Autoregressive Disturbances in Multiple Linear Regression. Gazi University Journal of Science. 2018;31:1268–1282.
MLA Asıkgıl, Barış. “An Adapted Approach for Self-Exciting Threshold Autoregressive Disturbances in Multiple Linear Regression”. Gazi University Journal of Science, vol. 31, no. 4, 2018, pp. 1268-82.
Vancouver Asıkgıl B. An Adapted Approach for Self-Exciting Threshold Autoregressive Disturbances in Multiple Linear Regression. Gazi University Journal of Science. 2018;31(4):1268-82.