A semiparametric first-order nonlinear autoregressive model with dependent and skew normal errors

Subject Areas : Statistics

Leila Sakhabakhsh ¹ , rahman Farnoosh ² , Afshin Fallah ³ , Mohammad Hassan Behzadi ⁴

1 - Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Science and Research Unit, Tehran, Iran
2 - Department of Mathematics, Faculty of Mathematics, Iran University of Science and Technology, Tehran, Iran
3 - Department of Statistics, Faculty of Basic Sciences, Imam Khomeini International University, Qazvin, Iran
4 - Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Science and Research Unit, Tehran, Iran

Received: 2021-03-03 Accepted : 2022-09-07 Published : 2022-12-22

Keywords: الگوریتم EM, مدل اتورگرسیو غیرخطی, خطاهای چوله نرمال, برآورد نیمه پارامتری,

Abstract :

The common ways for analyzing the nonlinear autoregressive models are based on normality assumption of errors, whereas in many practical situations, the residuals show a nonnormal structure. The use of these methods leads to misleading and unreliable forecasts. Also, in these conditions, parametric and nonparametric methods do not have the necessary efficiency in estimating the nonlinear regression function. In this paper, a first-order nonlinear autoregressive model with dependent skew normal errors is introduced and a semiparametric method is proposed to estimate the nonlinear part of model. The parameters are estimated by the maximum likelihood (ML) method using Expectation-Maximization (EM) algorithm. The performance of the proposed model is investigated by a simulation study and analysis of a real data set of daily data on the exchange rate of the euro to the dollar.

References:

 

[1] Farnoosh, R, Hajebi, M. and Samadi, Y. (2019). A semiparametric estimation for the first-order nonlinear autoregressive time series model with independendent and dependent errors. Iranian Journal of Science and Technology, Transaction A: Science, 43: 905-917.

 

[2] Mortazavi, S. J. and Farnoosh, R. (2013). The prediction nonlinear autoregressive model for annual ring width of pinus eldarica with semiparametric approach. World Applied Sciences Jornal, 26(6): 783-787.

 

[3] Zhuoxi, Y., Dehui, W. and Ningzhong, S. (2009). Semiparametric estimation of regression function in autoregressive models. Statistics & Probability Letters, 61: 165-172.

 

[4] Farnoosh, R. and Mortazavi, S. J. (2011). A semiparametric method for estimating nonlinear autoregressive model with dependent errors. Nonlinear Analysis, 74: 6358-6370.

 

[5] Tong, H. (1990). Nonlinear time series, Oxford university press, Oxford.

 

[6] Li, Q. (1999). Consistent model specification tests for time series econometric models. Journal of econometrics, 92: 101-147.

 

[7] Azzalini, A. (1985). A class of distribution which includes the normal ones. Scandinavian Journal of statistics, 12: 171-178.

 

[8] Hajrajabi, A. and Fallah, S. J. (2018). Nonlinear semiparametric AR(1) model with skew symmetric innovations. Communications in Statistics-Simulation and computation, 47: 1453-1462.

 

[9] Hajrajabi, A. and Mortazavi, S. J. (2019). The first-order nonlinear autoregressive Model with skew normal innovations: A semiparametric approach. Iranian Journal of Science and Technology, Transaction A: Science, 43: 579-587

 

[10] Henz N (1986). A probabilistic representation of the skew-normal. Scandinavian Journal of statistics, 13:171-178

 

[11] Azzalini A (1986). Further results on a class of distributions which includes the normal ones. Scandinavian Journal of statistics, 12:171-178.

]

12[ بهرامی، محمد (1389)، توزیع نرمال چوله و برآورد ماکسیمم درستنمایی پارامترهای آن، دهمین کنفرانس آمار ایران، دانشگاه تبریز.

 

[13] Farnoosh, R. and Nademi, A. (2014). Mixture of autoregressive-autoregressive conditionally heteroscedastic models: Semi- parametric approach. Journal of Applied Statistics, 41: 275-293.