**Author details**

Raed Alzghool1,2

1 Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt, Jordan

2 Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa, Saudi Arabia

\*Address all correspondence to: raedalzghool@bau.edu.jo; ralzghool@kfu.edu.sa

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

from the fourth column in **Table 6**, which favors the QL method and gives smaller

*μ α***<sup>0</sup>** *α***<sup>1</sup>** *β***<sup>1</sup>** *μ α***<sup>0</sup>** *α***<sup>1</sup>** *β***<sup>1</sup>**

0.037 0.012 0.007 0.014 0.066 0.014 0.013 0.018

0.149 0.422 0.007 0.016 0.137 0.326 0.018 0.021

0.027 0.012 0.007 0.013 0.022 0.014 0.012 0.016

0.121 0.289 0.007 0.018 0.119 0.307 0.018 0.021

0.019 0.012 0.007 0.011 0.014 0.013 0.012 0.015

0.012 0.012 0.007 0.011 0.012 0.013 0.012 0.015

0.012 0.011 0.007 0.011 0.011 0.013 0.012 0.015

*μ*^**<sup>0</sup>** *α*^**<sup>0</sup>** *α*^**<sup>1</sup>** ^*β***<sup>1</sup>** ^*ξ<sup>t</sup>*

*<sup>S</sup>:<sup>d</sup>* ^*<sup>ξ</sup>* ð Þ*<sup>t</sup>*

True 0.16 0.37 0.90 0.08 �0.10 0.48 0.89 0.08 QL 0.17 0.42 0.89 0.07 �0.09 0.51 0.90 0.06

AQL 0.16 0.38 0.89 0.07 �0.10 0.47 0.90 0.07

QL 0.16 0.42 0.89 0.07 �0.09 0.51 0.91 0.06

QL 0.16 0.42 0.89 0.07 �0.09 0.52 0.91 0.06

QL 0.16 0.42 0.89 0.07 �0.10 0.51 0.90 0.06 0.100 0.159 0.007 0.017 0.108 0.248 0.018 0.021

QL 0.16 0.42 0.89 0.07 �0.10 0.51 0.90 0.06 0.100 0.159 0.007 0.018 0.101 0.242 0.018 0.021

T = 20 0.176 0.511 0.008 0.016 0.169 0.451 0.018 0.022

*Linear and Non-Linear Financial Econometrics - Theory and Practice*

T = 40 AQL 0.16 0.38 0.89 0.07 �0.10 0.47 0.90 0.07

T = 60 AQL 0.16 0.38 0.89 0.07 �0.10 0.47 0.90 0.07

T = 80 AQL 0.16 0.38 0.89 0.07 �0.10 0.47 0.90 0.07

T = 100 AQL 0.16 0.38 0.89 0.07 �0.10 0.47 0.90 0.07

*The QL and AQL estimates and the RMSE of each estimate is stated below that estimate for GARCH model*

QL 0.0008 0.566 0.912 0.0004 0.002 AQL 0.0089 0.630 0.972 0.041 0.185

In this chapter, two alternative approaches, QL and AQL, have been developed to estimate the parameters in ARCH and GARCH models. Parameter estimation for ARCH and GARCH models, which include nonlinear and non-Gaussian models is given. The estimations of unknown parameters are considered without any distribution assumptions concerning the processes involved, and the estimation is based

standardized residuals, better than AQL method.

*Estimation of μ*, *α*0, *α*1, *β*<sup>1</sup> *for the rates of change prices data.*

**5. Conclusions**

**Table 5.**

**Table 6.**

**92**

*with different sample size.*
