I am working with a TS that shows me the electricity price from 1998 to 2022 with the avg mean pr month. I have used ann arma-garch to look for changes in vlolatility.
Im am not sure how to quality check the model. dose anybody know, and or have any sugestions on how i can improve and quality check?
> ts <- ts(df$`NP system`, start = c(1998,1), frequency = 8760)
> tsav <- aggregate(ts, nfrequency = 30, FUN = mean)
> tsavfill <- na.approx(tsavfill)
> str(tsavfill)
Time-Series [1:723] from 1998 to 2022: 9.3 8.15 10.42 12.71 12.06
> log_tsavfill=log(tsavfill)
> diff_log=diff(log_tsavfill)
> auto.arima(log_tsavfill`
Series: log_tsavfill ARIMA(2,1,3)
Coefficients: ar1 ar2 ma1 ma2 ma3 0.0367 -0.7365 0.0331 0.6476 -0.0628 s.e. 0.1032 0.0970 0.1082 0.1105 0.0489
sigma^2 = 0.03344: log likelihood = 204.65 AIC=-397.3 AICc=-397.19 BIC=-369.81
> model_g <- ugarchspec(variance.model = list(model = "iGARCH", garchOrder = c(10,10)),
mean.model = list(armaOrder = c(2,1,3)),
distribution.model = "norm")
> ugift = ugarchfit(spec = model_g, data = diff_log, solver = "hybrid")
GARCH Model Fit \*
*---------------------------------*
Conditional Variance Dynamics
-
GARCH Model : iGARCH(10,10)
Mean Model : ARFIMA(2,0,1)
Distribution : norm
Optimal Parameters
-
Estimate Std. Error t value Pr(>|t|)
mu -0.005274 0.004261 -1.237724 0.215818
ar1 0.373841 0.223977 1.669103 0.095097
ar2 -0.120043 0.035796 -3.353532 0.000798
ma1 -0.293279 0.214782 -1.365476 0.172104
omega 0.003792 0.001039 3.650704 0.000262
alpha1 0.204792 0.033618 6.091779 0.000000
alpha2 0.374888 0.046542 8.054890 0.000000
alpha3 0.170857 0.288112 0.593023 0.553165
alpha4 0.000000 0.133136 0.000000 1.000000
alpha5 0.054604 0.038612 1.414188 0.157307
alpha6 0.000001 0.076762 0.000012 0.999990
alpha7 0.010392 0.057162 0.181795 0.855744
alpha8 0.000000 0.075458 0.000000 1.000000
alpha9 0.000000 0.039127 0.000003 0.999997
alpha10 0.000000 0.035620 0.000003 0.999998
beta1 0.000000 0.295547 0.000000 1.000000
beta2 0.000000 0.538345 0.000000 1.000000
beta3 0.000000 0.282598 0.000000 1.000000
beta4 0.000000 0.112154 0.000003 0.999998
beta5 0.000000 0.053896 0.000001 0.999999
beta6 0.000000 0.032104 0.000000 1.000000
beta7 0.000000 0.081059 0.000000 1.000000
beta8 0.000000 0.034391 0.000002 0.999998
beta9 0.000000 0.067957 0.000001 0.999999
beta10 0.184465 NA NA NA
Robust Standard Errors:
Estimate Std. Error t value Pr(\>|t|)
mu -0.005274 0.005516 -0.956174 0.33898
ar1 0.373841 0.403778 0.925858 0.35452
ar2 -0.120043 0.124221 -0.966364 0.33386
ma1 -0.293279 0.470120 -0.623838 0.53273
omega 0.003792 0.008231 0.460681 0.64503
alpha1 0.204792 0.267927 0.764357 0.44466
alpha2 0.374888 0.291419 1.286422 0.19830
alpha3 0.170857 1.183286 0.144392 0.88519
alpha4 0.000000 0.781875 0.000000 1.00000
alpha5 0.054604 0.586068 0.093171 0.92577
alpha6 0.000001 0.188080 0.000005 1.00000
alpha7 0.010392 0.109661 0.094763 0.92450
alpha8 0.000000 0.298520 0.000000 1.00000
alpha9 0.000000 0.158561 0.000001 1.00000
alpha10 0.000000 0.306701 0.000000 1.00000
beta1 0.000000 1.148654 0.000000 1.00000
beta2 0.000000 2.345333 0.000000 1.00000
beta3 0.000000 1.689488 0.000000 1.00000
beta4 0.000000 0.383614 0.000001 1.00000
beta5 0.000000 0.236929 0.000000 1.00000
beta6 0.000000 0.619670 0.000000 1.00000
beta7 0.000000 0.366661 0.000000 1.00000
beta8 0.000000 0.505519 0.000000 1.00000
beta9 0.000000 0.290965 0.000000 1.00000
beta10 0.184465 NA NA NA
LogLikelihood : 366.9737
Information Criteria
-
Akaike -0.95007
Bayes -0.79775
Shibata -0.95218
Hannan-Quinn -0.89127
Weighted Ljung-Box Test on Standardized Residuals
-
statistic p-value
Lag\[1\] 0.002932 0.9568
Lag\[2\*(p+q)+(p+q)-1\]\[8\] 3.237259 0.9877
Lag\[4\*(p+q)+(p+q)-1\]\[14\] 6.296019 0.6973
d.o.f=3
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
-
statistic p-value
Lag\[1\] 0.1051 0.7459
Lag\[2\*(p+q)+(p+q)-1\]\[59\] 15.1838 0.9976
Lag\[4\*(p+q)+(p+q)-1\]\[99\] 26.7622 0.9997
d.o.f=20
Weighted ARCH LM Tests
-
Statistic Shape Scale P-Value
ARCH Lag\[21\] 0.5316 0.500 2.000 0.4659
ARCH Lag\[23\] 0.9574 1.498 1.916 0.8007
ARCH Lag\[25\] 1.2364 2.491 1.847 0.9299
Nyblom stability test
-
Joint Statistic: no.parameters\>20 (not available)
Individual Statistics:
mu 0.09430
ar1 0.18384
ar2 0.07998
ma1 0.19519
omega 0.04841
alpha1 0.09145
alpha2 0.16028
alpha3 0.05535
alpha4 0.18453
alpha5 0.08339
alpha6 0.16953
alpha7 0.03458
alpha8 0.89098
alpha9 0.03897
alpha10 0.14245
beta1 0.05728
beta2 0.14306
beta3 0.28425
beta4 0.21429
beta5 0.24878
beta6 0.86303
beta7 0.29692
beta8 0.10914
beta9 0.47839
Asymptotic Critical Values (10% 5% 1%)
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
-
t-value prob sig
Sign Bias 0.8425 0.3998
Negative Sign Bias 0.4347 0.6639
Positive Sign Bias 0.6097 0.5423
Joint Effect 0.7953 0.8506
Adjusted Pearson Goodness-of-Fit Test:
-
group statistic p-value(g-1)
1 20 36.67 0.008723
2 30 42.46 0.051030
3 40 57.28 0.029615
4 50 60.41 0.127187
Elapsed time : 0.6795101
I have run the arma-garch but i am not sure if the code be improved or the results can be quality checked
