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OxMetrics ARMA-GARCH Results.txt
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OxMetrics ARMA-GARCH Results.txt
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dataForGARCH.csv loaded from C:\Users\Reginald\Desktop\Q5\dataForGARCH.csv
Ox 9.10 (Windows_64/Parallel) (C) J.A. Doornik, 1994-2023 (oxlang.dev)
Copyright for this package: S. Laurent, 2000-2021.
G@RCH package version 9.0, object created on 28-03-2024
Copyright for this package: S. Laurent, 2000-2021.
Starting estimation process...
******************************
** G@RCH(1) SPECIFICATIONS **
******************************
The dataset is: C:\Users\Reginald\Desktop\Q5\dataForGARCH.csv
The estimation sample is: 2006-01-03 - 2008-12-31
The dependent variable is: DLclose
Mean Equation: ARMA (0, 0) model.
No regressor in the conditional mean
Variance Equation: GARCH (1, 1) model.
No regressor in the conditional variance
Normal distribution.
Strong convergence using numerical derivatives
Log-likelihood = 1870.36
Please wait : Computing the Std Errors ...
Robust Standard Errors (Sandwich formula)
Coefficient Std.Error t-value t-prob
Cst(M) 0.000821 0.00052731 1.557 0.1200
Cst(V) x 10^4 0.067645 0.034520 1.960 0.0504
ARCH(Alpha1) 0.173502 0.041712 4.160 0.0000
GARCH(Beta1) 0.832814 0.036735 22.67 0.0000
No. Observations : 755 No. Parameters : 4
Mean (Y) : -0.00020 Variance (Y) : 0.00102
Skewness (Y) : 0.17230 Kurtosis (Y) : 10.84318
Log Likelihood : 1870.356 Alpha[1]+Beta[1]: 1.00632
The sample mean of squared residuals was used to start recursion.
The positivity constraint for the GARCH (1,1) is observed.
This constraint is alpha[L]/[1 - beta(L)] >= 0.
The unconditional variance does not exist and/or is not positive.
The conditions are alpha[0] > 0, alpha[L] + beta[L] < 1 and alpha[i] + beta[i] >= 0.
=> See Doornik & Ooms (2001) for more details.
The condition for existence of the fourth moment of the GARCH is not observed.
The constraint equals 1.07288 and should be < 1.
=> See Ling & McAleer (2001) for details.
Estimated Parameters Vector :
0.000821; 0.067645; 0.173502; 0.832819
Elapsed Time : 0.015 seconds (or 0.00025 minutes).
***********
** TESTS **
***********
TESTS :
---------
Information Criteria (to be minimized)
Akaike -4.943990 Shibata -4.944046
Schwarz -4.919478 Hannan-Quinn -4.934548
---------------
Normality Test
Statistic t-Test P-Value
Skewness 0.15513 1.7436 0.081227
Excess Kurtosis 1.9466 10.954 6.3687e-28
Jarque-Bera 122.23 .NaN 2.8749e-27
---------------
Q-Statistics on Standardized Residuals
Q( 5) = 6.53864 [0.2572736]
Q( 10) = 14.4739 [0.1524534]
Q( 20) = 19.9099 [0.4635757]
Q( 50) = 48.9643 [0.5149355]
H0 : No serial correlation ==> Accept H0 when prob. is High [Q < Chisq(lag)]
---------------
Q-Statistics on Squared Standardized Residuals
--> P-values adjusted by 2 degree(s) of freedom
Q( 5) = 1.37499 [0.7114082]
Q( 10) = 2.58037 [0.9578776]
Q( 20) = 9.86379 [0.9362616]
Q( 50) = 43.0707 [0.6746233]
H0 : No serial correlation ==> Accept H0 when prob. is High [Q < Chisq(lag)]
---------------
Diagnostic test based on the news impact curve (EGARCH vs. GARCH)
Test P-value
Sign Bias t-Test 0.22549 0.82160
Negative Size Bias t-Test 0.66076 0.50877
Positive Size Bias t-Test 0.38061 0.70349
Joint Test for the Three Effects 1.28668 0.73230
---------------
ARCH 1-2 test: F(2,748) = 0.58516 [0.5573]
ARCH 1-5 test: F(5,742) = 0.26853 [0.9303]
ARCH 1-10 test: F(10,732) = 0.25772 [0.9896]
---------------
CondV [ 1 - 755] saved to dataForGARCH.csv
dataForGARCH.csv saved to C:\Users\Reginald\Desktop\Q5\dataForGARCH.csv