Data forecasting NSEI data
What is forecasting and its example?
Forecasting is the step of the statistical process. Here, we can understand with an example analysis of trends.
AR, ARIMA GARCH
head(NSEI)
NSEI.Open NSEI.High NSEI.Low
2007-09-17 4518.45 4549.05 4482.85
2007-09-18 4494.10 4551.80 4481.55
2007-09-19 4550.25 4739.00 4550.25
2007-09-20 4734.85 4760.85 4721.15
2007-09-21 4752.95 4855.70 4733.70
2007-09-24 4837.15 4941.15 4837.15
NSEI.Close NSEI.Volume
2007-09-17 4494.65 0
2007-09-18 4546.20 0
2007-09-19 4732.35 0
2007-09-20 4747.55 0
2007-09-21 4837.55 0
2007-09-24 4932.20 0
NSEI.Adjusted
2007-09-17 4494.65
2007-09-18 4546.20
2007-09-19 4732.35
2007-09-20 4747.55
2007-09-21 4837.55
2007-09-24 4932.20
> tail(NSEI)
NSEI.Open NSEI.High NSEI.Low
2020-05-29 9422.20 9598.85 9376.90
2020-06-01 9726.85 9931.60 9706.95
2020-06-02 9880.85 9995.60 9824.05
2020-06-03 10108.30 10176.20 10035.55
2020-06-04 10054.25 10123.85 9944.25
2020-06-05 10093.80 10177.80 10040.75
NSEI.Close NSEI.Volume
2020-05-29 9580.30 967000
2020-06-01 9826.15 794200
2020-06-02 9979.10 770200
2020-06-03 10061.55 794700
2020-06-04 10029.10 775100
2020-06-05 10142.15 987100
NSEI.Adjusted
2020-05-29 9580.30
2020-06-01 9826.15
2020-06-02 9979.10
2020-06-03 10061.55
2020-06-04 10029.10
2020-06-05 10142.15
> chartSeries(Cl(NSEI))
> addRSI()
addBBands()
> addMACD()
> ret <- dailyReturn(Cl(NSEI), type='log')
Warning message:
In to_period(xx, period = on.opts[[period]], ...) :
missing values removed from data
> par(mfrow=c(2,2))
> acf(ret, main="Return ACF");
> pacf(ret, main="Return PACF");
> acf(ret^2, main="Squared return ACF");
> pacf(ret^2, main="Squared return PACF")
> par(mfrow=c(1,1))
> m=mean(ret);s=sd(ret);
> par(mfrow=c(1,2))
> hist(ret, nclass=40, freq=FALSE, main='Return histogram');curve(dnorm(x,
+ mean=m,sd=s), from = -0.3, to = 0.2, add=TRUE, col="red")
> plot(density(ret), main='Return empirical distribution');curve(dnorm(x,
+ mean=m,sd=s), from = -0.3, to = 0.2, add=TRUE, col="red")
> par(mfrow=c(1,1))
> library("moments", lib.loc="~/R/win-library/3.6")
Attaching package: ‘moments’
The following objects are masked from ‘package:timeDate’:
kurtosis, skewness
> kurtosis(ret)
daily.returns
16.71434
> moment(ret)
daily.returns
0.0002622663
> skewness(ret)
daily.returns
-0.224163
plot(density(ret), main='Return EDF - upper tail', xlim = c(0.1, 0.2),ylim=c(0,2));
> curve(dnorm(x, mean=m,sd=s), from = -0.3, to = 0.2, add=TRUE, col="red")
> plot(density(ret), xlim=c(-5*s,5*s),log='y', main='Density on log-scale')
Warning message:
In xy.coords(x, y, xlabel, ylabel, log) :
55 y values <= 0 omitted from logarithmic plot
> curve(dnorm(x, mean=m,sd=s), from=-5*s, to=5*s, log="y", add=TRUE,
+ col="red")
> qqnorm(ret);qqline(ret);
GARCH
chartSeries(ret)
> garch11.spec = ugarchspec(variance.model = list(model="sGARCH",
+ garchOrder=c(1,1)), mean.model = list(armaOrder=c(0,0)))
>
> nsei.garch11.fit = ugarchfit(spec=garch11.spec, data=ret)
> coef(nsei.garch11.fit)
mu omega alpha1
6.980502e-04 1.395972e-06 9.533248e-02
beta1
9.011659e-01
> vcov(nsei.garch11.fit)
[,1] [,2]
[1,] 2.933090e-08 4.043859e-11
[2,] 4.043859e-11 2.211391e-12
[3,] 6.311625e-07 2.712701e-08
[4,] -6.134868e-07 -2.722442e-08
[,3] [,4]
[1,] 6.311625e-07 -6.134868e-07
[2,] 2.712701e-08 -2.722442e-08
[3,] 4.282120e-04 -4.073095e-04
[4,] -4.073095e-04 3.967103e-04
> infocriteria(nsei.garch11.fit)
Akaike -6.125997
Bayes -6.118211
Shibata -6.126000
Hannan-Quinn -6.123201
> uncvariance(nsei.garch11.fit)
[1] 0.0003986693
> uncmean(nsei.garch11.fit)
[1] 0.0006980502
signbias(nsei.garch11.fit)#Engle - Ng sign bias test
t-value prob sig
Sign Bias 2.1857499 0.02890853 **
Negative Sign Bias 0.1352497 0.89242325
Positive Sign Bias 0.3995563 0.68951090
Joint Effect 9.5498170 0.02280725 **
>
residuals(msft.garch11.fit) #obtain the residuals
2007-09-18 1.070593e-02
2007-09-19 3.943212e-02
2007-09-20 2.508676e-03
2007-09-21 1.808165e-02
2007-09-24 1.867877e-02
2007-09-25 6.493047e-04
2007-09-26 -3.640400e-04
2007-09-27 1.138328e-02
2007-09-28 3.452924e-03
2007-10-01 8.736842e-03
2007-10-03 2.690157e-02
2007-10-04 -1.110721e-03
2007-10-05 -5.084955e-03
2007-10-08 -2.031712e-02
2007-10-09 4.582239e-02
2007-10-10 2.051240e-02
2007-10-11 1.451246e-02
2007-10-12 -1.833737e-02
2007-10-15 4.294480e-02
2007-10-16 -1.112586e-03
2007-10-17 -2.007099e-02
2007-10-18 -3.888676e-02
2007-10-19 -2.638493e-02
2007-10-22 -6.717667e-03
2007-10-23 5.367983e-02
2007-10-24 3.394939e-03
2007-10-25 1.246068e-02
2007-10-26 2.296496e-02
2007-10-29 3.438422e-02
2007-10-30 -7.008221e-03
2007-10-31 4.722784e-03
2007-11-01 -6.510834e-03
2007-11-02 1.048107e-02
2007-11-05 -1.514690e-02
2007-11-06 -1.115041e-02
2007-11-07 -1.415477e-03
2007-11-08 -1.526139e-02
2007-11-12 -1.512937e-02
2007-11-13 1.314523e-02
2007-11-14 4.099865e-02
2007-11-15 -5.052454e-03
2007-11-16 -1.586454e-03
2007-11-19 -5.626566e-04
2007-11-20 -2.238679e-02
2007-11-21 -3.947051e-02
2007-11-22 -8.224837e-03
2007-11-23 1.534298e-02
2007-11-26 2.101300e-02
2007-11-27 -6.568712e-03
2007-11-28 -1.494400e-02
2007-11-29 2.332536e-03
2007-11-30 2.179056e-02
2007-12-03 1.688964e-02
2007-12-04 -1.832522e-03
2007-12-05 1.314307e-02
2007-12-06 1.773673e-03
2007-12-07 2.587997e-03
2007-12-10 -2.993790e-03
2007-12-11 2.196864e-02
2007-12-12 9.427203e-03
2007-12-13 -1.726492e-02
2007-12-14 -2.416219e-03
2007-12-17 -4.649160e-02
2007-12-18 -6.722774e-03
2007-12-19 8.419745e-04
2007-12-20 1.967443e-03
2007-12-24 3.650970e-02
2007-12-26 1.351104e-02
2007-12-27 1.071170e-03
2007-12-28 -9.940416e-04
2007-12-31 8.943284e-03
2008-01-01 2.382070e-04
2008-01-02 4.990137e-03
2008-01-03 -8.356292e-04
2008-01-04 1.468026e-02
2008-01-07 6.672954e-05
2008-01-08 6.944915e-04
2008-01-09 -3.221983e-03
2008-01-10 -1.921178e-02
2008-01-11 6.285830e-03
2008-01-14 3.819468e-04
2008-01-15 -2.228496e-02
2008-01-16 -2.376319e-02
2008-01-17 -4.504266e-03
2008-01-18 -3.648969e-02
2008-01-21 -9.174412e-02
2008-01-22 -6.195522e-02
2008-01-23 5.952189e-02
2008-01-24 -3.390462e-02
2008-01-25 6.650715e-02
2008-01-28 -2.120086e-02
2008-01-29 5.714469e-04
2008-01-30 -2.236723e-02
2008-01-31 -6.549548e-03
2008-02-01 3.370132e-02
2008-02-04 2.643531e-02
2008-02-05 3.028849e-03
2008-02-06 -3.056208e-02
2008-02-07 -3.691154e-02
2008-02-08 -3.214222e-03
2008-02-11 -5.349990e-02
2008-02-12 -4.565929e-03
2008-02-13 1.797632e-02
2008-02-14 5.311766e-02
2008-02-15 1.851260e-02
2008-02-18 -5.613087e-03
2008-02-19 4.072871e-05
2008-02-20 -2.491516e-02
2008-02-21 6.521913e-03
2008-02-22 -1.643231e-02
2008-02-25 1.674905e-02
2008-02-26 1.254849e-02
2008-02-27 -1.011171e-03
2008-02-28 2.466816e-03
2008-02-29 -1.242193e-02
2008-03-03 -5.387227e-02
2008-03-04 -1.877896e-02
2008-03-05 1.098243e-02
2008-03-07 -3.160937e-02
2008-03-10 5.319478e-03
2008-03-11 1.285440e-02
2008-03-12 5.548069e-04
2008-03-13 -5.302894e-02
2008-03-14 2.538828e-02
2008-03-17 -5.319196e-02
2008-03-18 5.919851e-03
2008-03-19 8.295185e-03
2008-03-24 7.120083e-03
2008-03-25 5.573940e-02
2008-03-26 -1.072248e-02
2008-03-27 -4.081885e-04
2008-03-28 2.217383e-02
2008-03-31 -4.359203e-02
2008-04-01 3.679787e-04
2008-04-02 2.388275e-03
2008-04-03 2.955170e-03
2008-04-04 -2.715790e-02
2008-04-07 2.357988e-02
2008-04-08 -1.158425e-02
2008-04-09 7.211707e-03
2008-04-10 -3.662131e-03
2008-04-11 8.722848e-03
2008-04-15 2.039528e-02
2008-04-16 8.684377e-04
2008-04-17 1.374507e-02
2008-04-21 1.502953e-02
2008-04-22 1.740864e-03
2008-04-23 -5.960123e-03
2008-04-24 -5.277627e-03
2008-04-25 2.142609e-02
2008-04-28 -5.021072e-03
2008-04-29 1.988577e-02
2008-04-30 -6.411598e-03
2008-05-02 1.128972e-02
2008-05-05 -7.598009e-03
2008-05-06 -9.907859e-03
2008-05-07 -2.478161e-03
2008-05-08 -1.122937e-02
2008-05-09 -2.039208e-02
2008-05-12 5.314785e-03
2008-05-13 -1.170069e-02
2008-05-14 1.012505e-02
2008-05-15 1.974307e-02
2008-05-16 7.566457e-03
2008-05-20 -1.097814e-02
2008-05-21 1.786584e-03
2008-05-22 -1.887834e-02
2008-05-23 -1.652277e-02
2008-05-26 -1.525805e-02
2008-05-27 -3.831126e-03
2008-05-28 1.127783e-02
2008-05-29 -1.772804e-02
2008-05-30 6.473306e-03
2008-06-02 -2.785978e-02
2008-06-03 -5.711058e-03
2008-06-04 -2.871683e-02
2008-06-05 1.902720e-02
2008-06-06 -1.126273e-02
2008-06-09 -2.849107e-02
2008-06-10 -1.212747e-02
2008-06-11 1.575100e-02
2008-06-12 2.777643e-03
2008-06-13 -5.611685e-03
2008-06-16 1.149183e-02
2008-06-17 1.675402e-02
2008-06-18 -1.598737e-02
2008-06-19 -1.789951e-02
2008-06-20 -3.610702e-02
2008-06-23 -1.954012e-02
2008-06-24 -1.850515e-02
2008-06-25 1.388099e-02
2008-06-26 1.405397e-02
2008-06-27 -4.310611e-02
2008-06-30 -2.420347e-02
2008-07-01 -3.693601e-02
2008-07-02 4.852281e-02
2008-07-03 -4.250436e-02
2008-07-04 2.203092e-02
2008-07-07 2.781943e-03
2008-07-08 -1.103666e-02
2008-07-09 4.069192e-02
2008-07-10 5.280379e-04
2008-07-11 -2.827194e-02
2008-07-14 -2.997568e-03
2008-07-15 -4.591633e-02
2008-07-16 -1.226403e-02
2008-07-17 3.292224e-02
2008-07-18 3.539044e-02
2008-07-21 1.560188e-02
2008-07-22 1.849395e-02
2008-07-23 5.362353e-02
2008-07-24 -1.040594e-02
2008-07-25 -2.853155e-02
2008-07-28 3.987316e-03
2008-07-29 -3.408553e-02
2008-07-30 2.839818e-02
2008-07-31 3.789412e-03
2008-08-01 1.773261e-02
2008-08-04 -4.830174e-03
2008-08-05 2.346531e-02
2008-08-06 2.561167e-03
2008-08-07 6.956043e-04
2008-08-08 5.500850e-04
2008-08-11 1.917165e-02
2008-08-12 -1.555769e-02
2008-08-13 -5.807505e-03
2008-08-14 -2.265258e-02
2008-08-18 -9.231977e-03
2008-08-19 -6.359281e-03
2008-08-20 1.011717e-02
2008-08-21 -3.102358e-02
2008-08-22 9.428288e-03
2008-08-25 1.125818e-03
2008-08-26 -2.022727e-04
2008-08-27 -1.122005e-02
2008-08-28 -1.906188e-02
2008-08-29 3.336169e-02
2008-09-01 -3.304678e-03
2008-09-02 3.440241e-02
2008-09-04 -1.326559e-02
2008-09-05 -2.239200e-02
2008-09-08 2.873382e-02
2008-09-09 -3.736732e-03
2008-09-10 -1.613427e-02
2008-09-11 -2.600279e-02
2008-09-12 -1.521912e-02
2008-09-15 -3.817834e-02
2008-09-16 -2.071202e-04
2008-09-17 -1.718950e-02
2008-09-18 6.733855e-03
2008-09-19 4.931602e-02
2008-09-22 -5.941191e-03
2008-09-23 -2.372912e-02
2008-09-24 7.590964e-03
2008-09-25 -1.295677e-02
2008-09-26 -3.165480e-02
2008-09-29 -3.521195e-02
2008-09-30 1.761352e-02
2008-10-01 6.809667e-03
2008-10-03 -3.479817e-02
2008-10-06 -5.891692e-02
2008-10-07 4.810397e-04
2008-10-08 -2.680822e-02
2008-10-10 -6.952524e-02
2008-10-13 6.157606e-02
2008-10-14 7.277040e-03
2008-10-15 -5.328379e-02
2008-10-16 -2.161376e-02
2008-10-17 -6.218043e-02
2008-10-20 1.493847e-02
2008-10-21 3.456988e-02
2008-10-22 -5.459956e-02
2008-10-23 -4.131412e-02
2008-10-24 -1.308399e-01
2008-10-27 -2.411247e-02
2008-10-29 6.553639e-02
2008-10-31 6.687623e-02
2008-11-03 5.269226e-02
2008-11-04 3.107015e-02
2008-11-05 -4.866193e-02
2008-11-06 -3.545257e-02
2008-11-07 2.670049e-02
2008-11-10 5.657715e-02
2008-11-11 -6.959453e-02
2008-11-12 -3.187334e-02
2008-11-14 -1.416395e-02
2008-11-17 -4.548408e-03
2008-11-18 -4.316532e-02
2008-11-19 -1.880631e-02
2008-11-20 -3.225338e-02
2008-11-21 5.279698e-02
2008-11-24 4.781738e-03
2008-11-25 -2.093278e-02
2008-11-26 3.565277e-02
2008-11-28 3.369659e-04
2008-12-01 -2.725356e-02
2008-12-02 -1.009758e-02
2008-12-03 -1.206155e-03
2008-12-04 4.763582e-02
2008-12-05 -2.745164e-02
2008-12-08 2.461979e-02
2008-12-10 4.981818e-02
2008-12-11 -3.468074e-03
2008-12-12 -2.871298e-04
2008-12-15 1.958197e-02
2008-12-16 1.940907e-02
2008-12-17 -2.985236e-02
2008-12-18 3.468324e-02
2008-12-19 4.759545e-03
2008-12-22 -1.318839e-02
2008-12-23 -2.421802e-02
2008-12-24 -1.830102e-02
2008-12-26 -2.134273e-02
2008-12-29 2.177907e-02
2008-12-30 1.872071e-02
2008-12-31 -7.551520e-03
2009-01-02 2.847537e-02
2009-01-05 2.352412e-02
2009-01-06 -3.473014e-03
2009-01-07 -6.450015e-02
2009-01-09 -1.706183e-02
2009-01-12 -3.608897e-02
2009-01-13 -1.090107e-02
2009-01-14 3.168688e-02
2009-01-15 -3.609302e-02
2009-01-16 3.227799e-02
2009-01-19 5.557863e-03
2009-01-20 -1.827838e-02
2009-01-21 -3.357555e-02
2009-01-22 2.124910e-03
2009-01-23 -1.377231e-02
2009-01-27 3.336093e-02
2009-01-28 2.711089e-02
2009-01-29 -9.704994e-03
2009-01-30 1.714848e-02
2009-02-02 -3.904401e-02
2009-02-03 5.517570e-03
2009-02-04 6.157290e-03
2009-02-05 -8.937247e-03
2009-02-06 2.172806e-02
2009-02-09 2.595624e-02
2009-02-10 4.289695e-03
2009-02-11 -3.701380e-03
2009-02-12 -1.192048e-02
2009-02-13 1.823635e-02
2009-02-16 -3.515124e-02
2009-02-17 -2.846278e-02
2009-02-18 1.339181e-03
2009-02-19 4.045538e-03
2009-02-20 -1.984524e-02
2009-02-24 -1.630367e-03
2009-02-25 9.708891e-03
2009-02-26 7.647087e-03
2009-02-27 -8.627020e-03
2009-03-02 -3.345041e-02
2009-03-03 -2.040803e-02
2009-03-04 7.958716e-03
2009-03-05 -2.693522e-02
2009-03-06 1.602399e-02
2009-03-09 -1.879879e-02
2009-03-12 1.637170e-02
2009-03-13 3.745751e-02
2009-03-16 2.040707e-02
2009-03-17 -7.852958e-03
2009-03-18 1.272038e-02
2009-03-19 3.746900e-03
2009-03-20 -7.336218e-04
2009-03-23 4.554336e-02
2009-03-24 -1.106294e-03
2009-03-25 1.471666e-02
2009-03-26 3.157980e-02
2009-03-27 7.830617e-03
2009-03-30 -4.358430e-02
2009-03-31 1.357102e-02
2009-04-01 1.225994e-02
2009-04-02 4.737063e-02
2009-04-06 1.338768e-02
2009-04-08 2.547185e-02
2009-04-09 -9.672805e-04
2009-04-13 1.136222e-02
2009-04-15 2.888136e-02
2009-04-16 -3.415777e-02
2009-04-17 3.714193e-03
2009-04-20 -2.857277e-03
2009-04-21 -4.198306e-03
2009-04-22 -1.115277e-02
2009-04-23 2.696137e-02
2009-04-24 1.582791e-02
2009-04-27 -3.791244e-03
2009-04-28 -3.221248e-02
2009-04-29 3.195405e-02
2009-05-04 4.983215e-02
2009-05-05 1.461603e-03
2009-05-06 -1.081207e-02
2009-05-07 1.540580e-02
2009-05-08 -1.800263e-02
2009-05-11 -1.912285e-02
2009-05-12 3.427103e-02
2009-05-13 -1.323181e-02
2009-05-14 -1.226320e-02
2009-05-15 2.083035e-02
2009-05-18 1.626451e-01
2009-05-19 -1.785744e-03
2009-05-20 -1.191060e-02
2009-05-21 -1.470571e-02
2009-05-22 5.835005e-03
2009-05-25 -9.222573e-04
2009-05-26 -2.963136e-02
2009-05-27 3.727967e-02
2009-05-28 1.347825e-02
2009-05-29 2.476416e-02
2009-06-01 1.733364e-02
2009-06-02 -1.725069e-03
2009-06-03 5.056215e-04
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2011-06-28 2.679821e-03
2011-06-29 9.198249e-03
2011-06-30 7.650208e-03
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2011-08-03 -1.022732e-02
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2011-08-05 -2.356716e-02
2011-08-08 -1.865637e-02
2011-08-09 -9.656668e-03
2011-08-10 1.652950e-02
2011-08-11 -5.106162e-03
2011-08-12 -1.349776e-02
2011-08-16 -8.048229e-03
2011-08-17 3.423927e-03
2011-08-18 -2.318735e-02
2011-08-19 -2.082171e-02
2011-08-22 1.021081e-02
2011-08-23 9.477022e-03
2011-08-24 -1.289605e-02
2011-08-25 -1.083327e-02
2011-08-26 -1.984883e-02
2011-08-29 3.484788e-02
2011-08-30 1.571260e-02
2011-09-02 7.070139e-03
2011-09-05 -5.232084e-03
2011-09-06 8.645788e-03
2011-09-07 1.114827e-02
2011-09-08 4.867322e-03
2011-09-09 -1.906781e-02
2011-09-12 -2.321501e-02
2011-09-13 -1.881254e-03
2011-09-14 1.368902e-02
2011-09-15 1.182171e-02
2011-09-16 9.849909e-04
2011-09-19 -1.103795e-02
2011-09-20 2.058636e-02
2011-09-21 -2.051091e-03
2011-09-22 -4.238693e-02
2011-09-23 -1.211634e-02
2011-09-26 -7.366033e-03
2011-09-27 2.700943e-02
2011-09-28 -5.810437e-03
2011-09-29 1.326621e-02
2011-09-30 -1.519823e-02
2011-10-03 -1.984545e-02
2011-10-04 -1.677674e-02
2011-10-05 -5.076743e-03
2011-10-07 2.767714e-02
2011-10-10 1.785812e-02
2011-10-11 -1.752908e-03
2011-10-12 2.413009e-02
2011-10-13 -4.932954e-03
2011-10-14 9.967851e-03
2011-10-17 -3.439330e-03
2011-10-18 -1.660071e-02
[ reached getOption("max.print") -- omitted 2103 rows ]
newsimpact(nsei.garch11.fit)
$zy
[1] 0.0089405865 0.0085974245 0.0082612659
[4] 0.0079321106 0.0076099586 0.0072948099
[7] 0.0069866645 0.0066855224 0.0063913837
[10] 0.0061042482 0.0058241160 0.0055509871
[13] 0.0052848616 0.0050257393 0.0047736203
[16] 0.0045285047 0.0042903923 0.0040592833
[19] 0.0038351776 0.0036180751 0.0034079760
[22] 0.0032048802 0.0030087876 0.0028196984
[25] 0.0026376125 0.0024625299 0.0022944506
[28] 0.0021333746 0.0019793019 0.0018322325
[31] 0.0016921664 0.0015591036 0.0014330442
[34] 0.0013139880 0.0012019351 0.0010968855
[37] 0.0009988393 0.0009077963 0.0008237567
[40] 0.0007467203 0.0006766873 0.0006136575
[43] 0.0005576311 0.0005086080 0.0004665882
[46] 0.0004315716 0.0004035584 0.0003825485
[49] 0.0003685419 0.0003615386 0.0003615386
[52] 0.0003685419 0.0003825485 0.0004035584
[55] 0.0004315716 0.0004665882 0.0005086080
[58] 0.0005576311 0.0006136575 0.0006766873
[61] 0.0007467203 0.0008237567 0.0009077963
[64] 0.0009988393 0.0010968855 0.0012019351
[67] 0.0013139880 0.0014330442 0.0015591036
[70] 0.0016921664 0.0018322325 0.0019793019
[73] 0.0021333746 0.0022944506 0.0024625299
[76] 0.0026376125 0.0028196984 0.0030087876
[79] 0.0032048802 0.0034079760 0.0036180751
[82] 0.0038351776 0.0040592833 0.0042903923
[85] 0.0045285047 0.0047736203 0.0050257393
[88] 0.0052848616 0.0055509871 0.0058241160
[91] 0.0061042482 0.0063913837 0.0066855224
[94] 0.0069866645 0.0072948099 0.0076099586
[97] 0.0079321106 0.0082612659 0.0085974245
[100] 0.0089405865
$zx
[1] -0.300000000 -0.293939394 -0.287878788
[4] -0.281818182 -0.275757576 -0.269696970
[7] -0.263636364 -0.257575758 -0.251515152
[10] -0.245454545 -0.239393939 -0.233333333
[13] -0.227272727 -0.221212121 -0.215151515
[16] -0.209090909 -0.203030303 -0.196969697
[19] -0.190909091 -0.184848485 -0.178787879
[22] -0.172727273 -0.166666667 -0.160606061
[25] -0.154545455 -0.148484848 -0.142424242
[28] -0.136363636 -0.130303030 -0.124242424
[31] -0.118181818 -0.112121212 -0.106060606
[34] -0.100000000 -0.093939394 -0.087878788
[37] -0.081818182 -0.075757576 -0.069696970
[40] -0.063636364 -0.057575758 -0.051515152
[43] -0.045454545 -0.039393939 -0.033333333
[46] -0.027272727 -0.021212121 -0.015151515
[49] -0.009090909 -0.003030303 0.003030303
[52] 0.009090909 0.015151515 0.021212121
[55] 0.027272727 0.033333333 0.039393939
[58] 0.045454545 0.051515152 0.057575758
[61] 0.063636364 0.069696970 0.075757576
[64] 0.081818182 0.087878788 0.093939394
[67] 0.100000000 0.106060606 0.112121212
[70] 0.118181818 0.124242424 0.130303030
[73] 0.136363636 0.142424242 0.148484848
[76] 0.154545455 0.160606061 0.166666667
[79] 0.172727273 0.178787879 0.184848485
[82] 0.190909091 0.196969697 0.203030303
[85] 0.209090909 0.215151515 0.221212121
[88] 0.227272727 0.233333333 0.239393939
[91] 0.245454545 0.251515152 0.257575758
[94] 0.263636364 0.269696970 0.275757576
[97] 0.281818182 0.287878788 0.293939394
[100] 0.300000000
$yexpr
expression(sigma[t]^2)
$xexpr
expression(epsilon[t - 1])
FORECAST ARIMAORDER AND GARCH MODEL Attaching package: ‘forecast’ The following object is masked from ‘package:Ecfun’: BoxCox > arma.aparch.t = ugarchspec(mean.model=list(armaOrder=c(1,0)), + variance.model=list(model="apARCH", + garchOrder=c(1,1)), distribution.model = "std") > ret.aparch.t = ugarchfit(ret, spec=arma.aparch.t) > show(ret.aparch.t) ret means NSEI LOG DATA *---------------------------------* * GARCH Model Fit * *---------------------------------* Conditional Variance Dynamics ----------------------------------- GARCH Model : apARCH(1,1) Mean Model : ARFIMA(1,0,0) Distribution : std Optimal Parameters ------------------------------------ Estimate Std. Error t value mu 0.000036 0.000247 0.14737 ar1 -0.048548 0.015318 -3.16936 omega 0.000004 0.000002 2.36223 alpha1 0.061980 0.009038 6.85804 beta1 0.929079 0.012530 74.14894 gamma1 0.067265 0.047143 1.42682 delta 2.029480 0.032782 61.90755 shape 5.851426 0.518903 11.27654 Pr(>|t|) mu 0.882840 ar1 0.001528 omega 0.018165 alpha1 0.000000 beta1 0.000000 gamma1 0.153631 delta 0.000000 shape 0.000000 Robust Standard Errors: Estimate Std. Error t value mu 0.000036 0.000259 0.14057 ar1 -0.048548 0.013808 -3.51589 omega 0.000004 0.000002 1.88772 alpha1 0.061980 0.015451 4.01136 beta1 0.929079 0.021014 44.21271 gamma1 0.067265 0.056776 1.18474 delta 2.029480 0.169875 11.94690 shape 5.851426 0.525345 11.13825 Pr(>|t|) mu 0.888208 ar1 0.000438 omega 0.059063 alpha1 0.000060 beta1 0.000000 gamma1 0.236122 delta 0.000000 shape 0.000000 LogLikelihood : 10531.7 Information Criteria ------------------------------------ Akaike -5.0425 Bayes -5.0304 Shibata -5.0425 Hannan-Quinn -5.0382 Weighted Ljung-Box Test on Standardized Residuals ------------------------------------ statistic Lag[1] 0.6906 Lag[2*(p+q)+(p+q)-1][2] 1.1329 Lag[4*(p+q)+(p+q)-1][5] 2.6692 p-value Lag[1] 0.4060 Lag[2*(p+q)+(p+q)-1][2] 0.6582 Lag[4*(p+q)+(p+q)-1][5] 0.5188 d.o.f=1 H0 : No serial correlation Weighted Ljung-Box Test on Standardized Squared Residuals ------------------------------------ statistic Lag[1] 0.2302 Lag[2*(p+q)+(p+q)-1][5] 5.2651 Lag[4*(p+q)+(p+q)-1][9] 9.1664 p-value Lag[1] 0.63135 Lag[2*(p+q)+(p+q)-1][5] 0.13324 Lag[4*(p+q)+(p+q)-1][9] 0.07512 d.o.f=2 Weighted ARCH LM Tests ------------------------------------ Statistic Shape Scale ARCH Lag[3] 1.953 0.500 2.000 ARCH Lag[5] 7.602 1.440 1.667 ARCH Lag[7] 9.344 2.315 1.543 P-Value ARCH Lag[3] 0.16227 ARCH Lag[5] 0.02500 ARCH Lag[7] 0.02609 Nyblom stability test ------------------------------------ Joint Statistic: 131.3225 Individual Statistics: mu 0.4580 ar1 0.1933 omega 0.8532 alpha1 0.5161 beta1 0.4291 gamma1 0.0970 delta 0.4220 shape 0.2261 Asymptotic Critical Values (10% 5% 1%) Joint Statistic: 1.89 2.11 2.59 Individual Statistic: 0.35 0.47 0.75 Sign Bias Test ------------------------------------ t-value prob sig Sign Bias 0.65217 0.5143 Negative Sign Bias 0.02349 0.9813 Positive Sign Bias 0.37243 0.7096 Joint Effect 1.46310 0.6908 Adjusted Pearson Goodness-of-Fit Test: ------------------------------------ group statistic p-value(g-1) 1 20 11.45 0.90767 2 30 33.88 0.24378 3 40 45.17 0.22993 4 50 63.76 0.07654 Elapsed time : 2.417678
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