**A.4 Diagnostic test of student's t for serial correlation**


**Autocorrelation Partial Correlation AC PAC Q-Stat Prob**\* .|. | .|. | 28 -0.028 -0.038 20.471 0.847 .|\* | .|\* | 29 0.157 0.126 27.294 0.556 .|. | .|. | 30 0.024 0.004 27.457 0.599 .|. | .|. | 31 0.046 0.058 28.054 0.618 .|. | .|. | 32 0.013 0.045 28.101 0.664 .|. | .|. | 33 0.013 0.022 28.145 0.708 .|. | .|. | 34 0.054 0.053 28.981 0.712 \*|. | \*|. | 35 0.069 0.106 30.354 0.692 .|. | .|. | 36 0.003 0.036 30.357 0.734 \* no serial correlation since p-values >0.05%.

*Volatility Effects of the Global Oil Price on Stock Price in Nigeria: Evidence from Linear… DOI: http://dx.doi.org/10.5772/intechopen.93497*

**A.3 The probability density function of the generalized error**

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

*f x*ð Þ¼ j*μ*, *σ*, *κ*

**A.4 Diagnostic test of student's t for serial correlation**

Its log likelihood function in GARCH term is:

*e*�1 <sup>2</sup>j j *<sup>x</sup>*�*<sup>μ</sup>* <sup>1</sup> *n*

*<sup>n</sup>* � ð Þ *κ* þ 1 log 2ð Þ� log ð Þ� *h* log ð Þ� Γ log ð Þ *κ* þ 1 (13)

*<sup>σ</sup>*Γð Þ *<sup>κ</sup>* <sup>þ</sup> <sup>1</sup> (12)

2*<sup>κ</sup>*þ<sup>1</sup>

**Autocorrelation Partial Correlation AC PAC Q-Stat Prob**\* .|. | .|. | 1 �0.028 �0.028 0.1887 0.664 .|. | .|. | 2 �0.025 �0.025 0.3376 0.845 .|\* | .|\* | 3 0.107 0.106 3.1875 0.364 .|. | .|. | 4 0.040 0.045 3.5767 0.466 .|. | .|. | 5 0.024 0.031 3.7163 0.591 .|. | .|. | 6 �0.002 �0.010 3.7169 0.715 .|. | .|. | 7 0.039 0.032 4.1050 0.768 .|. | .|. | 8 0.014 0.009 4.1571 0.843 .|. | .|. | 9 �0.054 �0.054 4.9051 0.842 .|. | .|. | 10 �0.024 �0.036 5.0550 0.887 .|\* | .|\* | 11 0.101 0.093 7.6682 0.743 .|. | .|. | 12 0.023 0.038 7.8105 0.800 .|. | .|. | 13 �0.051 �0.036 8.4859 0.811 .|. | .|. | 14 �0.039 �0.059 8.8732 0.839 .|. | .|. | 15 �0.035 �0.054 9.1869 0.868 .|. | .|. | 16 �0.062 �0.063 10.192 0.856 .|. | .|. | 17 0.004 0.014 10.195 0.895 .|. | .|. | 18 0.004 0.010 10.199 0.925 .|. | .|. | 19 �0.039 �0.025 10.601 0.937 .|. | .|. | 20 �0.038 �0.023 10.977 0.947 .|. | .|. | 21 �0.023 �0.014 11.121 0.960 .|. | .|. | 22 �0.040 �0.048 11.545 0.966 .|. | .|. | 23 �0.050 �0.057 12.227 0.967 .|\* | .|\* | 24 0.136 0.146 17.252 0.838 .|. | .|. | 25 �0.052 �0.028 17.992 0.843 .|. | .|\* | 26 0.059 0.092 18.936 0.839 \*|. | \*|. | 27 �0.069 �0.083 20.253 0.820

**distribution is:**

� 1 2

**184**

j j *<sup>x</sup>* � *<sup>μ</sup>* <sup>1</sup>

**Date: 05/12/20 Time: 00:06 Sample: 2000:01 2020:12 Included observations: 243**
