# UNIVERSIDAD NACIONAL DEL ALTIPLANO
# INGENIERIA ESTADISTICA E INFORMATICA
# CURSO: SERIES DE TIEMPO
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library(mFilter)
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library(stats)
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library(fGarch)
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library(kableExtra)
ipc <- read_excel("E:/SERIES DE TIEMPO/TAREA 08/ipc.xls")
#View(ipc)
attach(ipc)
names(ipc)
## [1] "IPCREND"
# Rentabilidad de tu variable
#Descargar precios de Acciones de Yahoo Finance
startDate <- as.Date("2007-02-03") #Peridodo de tiempo que nosotros estamos interesados
endDate <- as.Date("2021-08-03")
getSymbols("IBM", from = startDate, to = endDate)
## 'getSymbols' currently uses auto.assign=TRUE by default, but will
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## options("getSymbols.warning4.0"=FALSE). See ?getSymbols for details.
## [1] "IBM"
rIBM2 <- dailyReturn(IBM)
head(rIBM2)
## daily.returns
## 2007-02-05 0.0122013157
## 2007-02-06 -0.0052799241
## 2007-02-07 -0.0031047081
## 2007-02-08 0.0008037303
## 2007-02-09 -0.0107407883
## 2007-02-12 0.0003043961
chartSeries(rIBM2)
# Con lso Datos
IPCREND <- ipc$IPCREND
#Generar Serie de Teimpo de los rendimeintos
ipcrents <- ts(IPCREND, start = c(2000,02), end = c(2021,12), frequency = 12)
chartSeries(ipcrents)
# 1. Estimar Modelo
arima22 <- arima(ipcrents, order = c(2,0,2))
arima22
##
## Call:
## arima(x = ipcrents, order = c(2, 0, 2))
##
## Coefficients:
## ar1 ar2 ma1 ma2 intercept
## -0.3691 -0.9408 0.4119 0.8594 1.2715
## s.e. 0.0812 0.0440 0.1205 0.0787 0.3371
##
## sigma^2 estimated as 30.89: log likelihood = -824.57, aic = 1661.15
# 2. Calcular Residuales al 2
rescuad <- resid(arima22)^2
rescuad
## Jan Feb Mar Apr May
## 2000 1.035513e+02 6.922266e-03 1.083708e+02 1.264297e+02
## 2001 9.727145e+01 8.244875e+01 1.535968e+00 1.595475e+00 2.178268e+01
## 2002 1.078626e+02 6.509171e+00 3.227793e+01 4.360079e-01 1.750207e+01
## 2003 8.785178e+00 1.171259e+01 4.087135e+00 1.081217e+02 8.779729e-01
## 2004 3.533052e+01 2.373438e+01 1.755241e+01 4.493129e+01 3.781467e-03
## 2005 7.860589e-01 1.982777e+01 7.780724e+01 1.542015e+01 8.094713e+00
## 2006 1.826541e+01 1.242034e+00 5.386227e+00 1.857714e+01 1.158128e+02
## 2007 2.273624e+01 3.177304e+01 3.513057e+01 1.098133e-02 6.364367e+01
## 2008 2.566964e+01 8.273033e-01 4.201191e+01 1.532412e+01 1.965913e+01
## 2009 1.892159e+02 5.381601e+01 5.201190e+01 5.116716e+01 1.751755e+02
## 2010 2.082273e+01 2.803664e+00 3.606709e+00 1.316866e+00 3.498857e+00
## 2011 4.512109e+01 2.065681e+00 5.992118e-01 7.740512e+00 2.415389e+01
## 2012 9.688435e-02 1.197208e+00 9.108061e+00 5.446485e-01 2.567146e+01
## 2013 1.290542e+00 1.735606e+01 2.084332e-02 3.565998e+01 1.452511e+01
## 2014 2.557719e+01 3.868208e+01 5.470365e+00 1.358683e+00 2.051335e+00
## 2015 3.927949e+01 3.692205e+01 8.840998e+00 4.330461e+00 1.522015e+00
## 2016 1.644370e+02 7.565100e+01 2.715697e+01 5.758237e+01 9.010468e+00
## 2017 7.161073e+00 9.817563e-01 5.489639e+01 2.906530e+02 2.745064e+01
## 2018 8.605062e+01 1.187803e+02 6.820896e+00 5.924814e+01 5.330519e+00
## 2019 1.256998e+01 1.369390e+01 5.161773e+00 1.388325e+00 3.496195e+00
## 2020 2.440475e-01 9.247628e+00 1.125885e+00 2.517501e+01 1.219149e+01
## 2021 6.674113e+00 4.587882e+01 7.777152e+00 1.341933e+02 1.421673e+01
## Jun Jul Aug Sep Oct
## 2000 1.531378e+02 6.873317e+01 3.070940e+01 6.582846e+01 8.767593e+00
## 2001 9.809887e+00 1.308236e+00 5.948420e+01 2.808676e+02 2.863400e+01
## 2002 8.938570e+01 1.184765e+02 7.585237e+00 6.036962e+01 4.911458e+00
## 2003 1.299381e+01 1.385550e+01 4.893561e+00 1.402751e+00 3.681527e+00
## 2004 2.291674e-01 9.359321e+00 1.170217e+00 2.524673e+01 1.204708e+01
## 2005 6.681195e+00 4.601369e+01 7.806550e+00 1.340454e+02 1.416283e+01
## 2006 1.218280e+01 3.194945e+00 5.124632e+00 2.729820e+01 1.636042e+01
## 2007 1.043255e+01 6.438904e+00 2.125456e+00 4.775894e+00 4.135123e+00
## 2008 8.695524e+01 4.993008e+01 4.073014e+01 5.264552e+01 3.394817e+02
## 2009 3.676393e-01 4.794002e+01 3.613112e+00 3.671062e+01 1.478884e+01
## 2010 3.971802e+01 4.326904e+00 2.397306e+00 1.507333e+01 1.296222e+01
## 2011 1.376958e+00 8.143019e+00 4.852422e+00 5.638620e+01 4.844353e+01
## 2012 1.847846e+01 3.800027e-01 1.079508e+01 6.920367e+00 9.326226e-01
## 2013 9.097379e+00 6.267617e-02 3.052091e+01 3.469359e-01 1.537199e+00
## 2014 3.879498e+00 7.839436e-02 1.187793e+01 4.416654e+00 2.473695e+00
## 2015 2.215764e+00 1.921952e+00 1.492484e+01 9.800020e+01 9.208689e-01
## 2016 1.230195e+02 6.549646e-01 1.059263e+02 9.058204e+01 2.206748e+00
## 2017 5.228746e+00 2.665593e+01 1.026031e+02 5.852820e+00 3.414063e+01
## 2018 2.750620e-03 1.067677e-01 8.201558e+00 1.176414e+01 4.428761e+00
## 2019 2.871497e+01 1.486808e+00 3.491637e+01 2.361197e+01 1.784827e+01
## 2020 1.904037e+01 3.517736e+01 7.702229e-01 1.992364e+01 7.802203e+01
## 2021 4.942161e+01 1.286711e+01 1.825873e+01 1.255162e+00 5.400576e+00
## Nov Dec
## 2000 1.133564e+02 3.157459e-01
## 2001 3.839706e+00 2.707132e+01
## 2002 2.265344e-02 8.234690e-02
## 2003 2.844168e+01 1.411071e+00
## 2004 1.906146e+01 3.537718e+01
## 2005 4.945744e+01 1.281547e+01
## 2006 2.551436e+01 2.795308e+01
## 2007 3.608009e+01 1.866248e+00
## 2008 7.927146e-02 2.879428e+01
## 2009 1.983772e+01 1.144039e+01
## 2010 9.827160e+00 2.498924e+01
## 2011 1.716799e-01 4.854706e-03
## 2012 2.485440e-02 1.897861e+01
## 2013 4.158737e+00 9.893299e-01
## 2014 1.319364e+01 9.315179e+00
## 2015 1.098690e+02 1.167004e+02
## 2016 3.206232e+00 2.195685e+01
## 2017 7.022816e-01 1.811095e+01
## 2018 1.090023e+02 9.819373e-01
## 2019 4.498381e+01 1.076923e-03
## 2020 1.545357e+01 8.164506e+00
## 2021 1.860972e+01 1.159035e+02
chartSeries(rescuad)
# 3. Hacer una Regresion con los Residuales al cuadrado rezagados
ipc.arch <- dynlm(rescuad ~ L(rescuad), data = ipc)
summary(ipc.arch)
##
## Time series regression with "ts" data:
## Start = 2000(3), End = 2021(12)
##
## Call:
## dynlm(formula = rescuad ~ L(rescuad), data = ipc)
##
## Residuals:
## Min 1Q Median 3Q Max
## -66.106 -26.288 -17.217 7.333 306.326
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 27.09298 3.44691 7.860 1.02e-13 ***
## L(rescuad) 0.11515 0.06171 1.866 0.0632 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.7 on 260 degrees of freedom
## Multiple R-squared: 0.01322, Adjusted R-squared: 0.00942
## F-statistic: 3.482 on 1 and 260 DF, p-value: 0.06317
#Funcion de Autocorrelacion parcial y Autocorrelacion
acf.res2 <- acf(rescuad, main = 'ACF Residuales al Cuadrado', lag.max = 100, ylim = c(-0.5,1))
acf.res2 <- pacf(rescuad, main = 'PACF Residuales al Cuadrado', lag.max = 100, ylim = c(-0.5,1))
# Observamos las graficas y no es un ruido blanco
#Probamos con archtest
ipcarchtest <- ArchTest(ipcrents, lags = 1, demean = T)
ipcarchtest
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: ipcrents
## Chi-squared = 3.0036, df = 1, p-value = 0.08308
#Probamos con archtest con 2 rezagos
ipcarchtest1 <- ArchTest(ipcrents, lags = 2, demean = T)
ipcarchtest1
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: ipcrents
## Chi-squared = 15.488, df = 2, p-value = 0.0004333
#Estimar el Modelo GARCH con default
ug_spec <- ugarchspec()
ug_spec
##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : sGARCH(1,1)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(1,0,1)
## Include Mean : TRUE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSE
#Estimar otro modelo con ARMA
ug_spec1 <- ugarchspec(mean.model = list(armaOrder = c(1,0)))
ug_spec1
##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : sGARCH(1,1)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(1,0,0)
## Include Mean : TRUE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSE
#Estimar otro modelo con ARMA 2
ug_spec2 <- ugarchspec(mean.model = list(armaOrder = c(2,2)))
ug_spec2
##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : sGARCH(1,1)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(2,0,2)
## Include Mean : TRUE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSE
#Estimar Modelo
ugfit <- ugarchfit(spec = ug_spec, data = ipcrents)
ugfit
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,1)
## Mean Model : ARFIMA(1,0,1)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 1.42777 0.332887 4.2891 0.000018
## ar1 0.54586 0.455801 1.1976 0.231079
## ma1 -0.49892 0.472866 -1.0551 0.291385
## omega 1.84995 0.984054 1.8799 0.060118
## alpha1 0.14543 0.046777 3.1089 0.001878
## beta1 0.79846 0.051867 15.3942 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 1.42777 0.350022 4.0791 0.000045
## ar1 0.54586 0.222217 2.4564 0.014033
## ma1 -0.49892 0.227403 -2.1940 0.028238
## omega 1.84995 0.742707 2.4908 0.012745
## alpha1 0.14543 0.040335 3.6055 0.000312
## beta1 0.79846 0.040320 19.8028 0.000000
##
## LogLikelihood : -817.7611
##
## Information Criteria
## ------------------------------------
##
## Akaike 6.2643
## Bayes 6.3458
## Shibata 6.2633
## Hannan-Quinn 6.2971
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.04609 0.83001
## Lag[2*(p+q)+(p+q)-1][5] 1.57244 0.99646
## Lag[4*(p+q)+(p+q)-1][9] 8.65877 0.03254
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.026 0.3112
## Lag[2*(p+q)+(p+q)-1][5] 2.712 0.4622
## Lag[4*(p+q)+(p+q)-1][9] 5.212 0.3990
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.001655 0.500 2.000 0.9676
## ARCH Lag[5] 2.267553 1.440 1.667 0.4151
## ARCH Lag[7] 3.400527 2.315 1.543 0.4413
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.5122
## Individual Statistics:
## mu 0.13816
## ar1 0.03553
## ma1 0.03511
## omega 0.08013
## alpha1 0.04858
## beta1 0.07678
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.49 1.68 2.12
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 2.0274 0.04365 **
## Negative Sign Bias 1.1937 0.23369
## Positive Sign Bias 0.3245 0.74581
## Joint Effect 8.0244 0.04551 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 22.55 0.2576821
## 2 30 38.03 0.1217455
## 3 40 60.50 0.0152213
## 4 50 89.28 0.0003861
##
##
## Elapsed time : 1.506551
ugfit1 <- ugarchfit(spec = ug_spec1, data = ipcrents)
ugfit1
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,1)
## Mean Model : ARFIMA(1,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 1.430307 0.317965 4.49832 0.000007
## ar1 0.041174 0.065039 0.63307 0.526690
## omega 1.818985 0.982407 1.85156 0.064089
## alpha1 0.145484 0.047037 3.09294 0.001982
## beta1 0.799692 0.051654 15.48166 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 1.430307 0.347244 4.11902 0.000038
## ar1 0.041174 0.052107 0.79019 0.429420
## omega 1.818985 0.745100 2.44126 0.014636
## alpha1 0.145484 0.041278 3.52449 0.000424
## beta1 0.799692 0.041245 19.38890 0.000000
##
## LogLikelihood : -817.9684
##
## Information Criteria
## ------------------------------------
##
## Akaike 6.2583
## Bayes 6.3262
## Shibata 6.2576
## Hannan-Quinn 6.2856
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1128 0.7369
## Lag[2*(p+q)+(p+q)-1][2] 0.1196 0.9999
## Lag[4*(p+q)+(p+q)-1][5] 1.6901 0.7979
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.048 0.3059
## Lag[2*(p+q)+(p+q)-1][5] 2.697 0.4653
## Lag[4*(p+q)+(p+q)-1][9] 5.311 0.3852
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 2.564e-05 0.500 2.000 0.9960
## ARCH Lag[5] 2.482e+00 1.440 1.667 0.3742
## ARCH Lag[7] 3.689e+00 2.315 1.543 0.3936
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.4741
## Individual Statistics:
## mu 0.15921
## ar1 0.03259
## omega 0.08128
## alpha1 0.04769
## beta1 0.07729
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 2.0275 0.04364 **
## Negative Sign Bias 1.1688 0.24358
## Positive Sign Bias 0.2863 0.77489
## Joint Effect 8.0417 0.04516 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 23.92 0.19923
## 2 30 28.22 0.50635
## 3 40 58.67 0.02232
## 4 50 68.37 0.03507
##
##
## Elapsed time : 0.7869971
ugfit2 <- ugarchfit(spec = ug_spec2, data = ipcrents)
ugfit2
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 1.45611 0.308282 4.7233 0.000002
## ar1 -0.28095 0.005462 -51.4353 0.000000
## ar2 -1.01291 0.001806 -560.9958 0.000000
## ma1 0.28061 0.008486 33.0683 0.000000
## ma2 1.00788 0.001637 615.7106 0.000000
## omega 1.81023 0.977792 1.8513 0.064120
## alpha1 0.13522 0.043732 3.0921 0.001988
## beta1 0.80429 0.052725 15.2544 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 1.45611 0.359660 4.0486 0.000052
## ar1 -0.28095 0.002559 -109.8026 0.000000
## ar2 -1.01291 0.001333 -759.8792 0.000000
## ma1 0.28061 0.004403 63.7260 0.000000
## ma2 1.00788 0.000447 2254.4072 0.000000
## omega 1.81023 0.834521 2.1692 0.030069
## alpha1 0.13522 0.039425 3.4299 0.000604
## beta1 0.80429 0.048912 16.4436 0.000000
##
## LogLikelihood : -812.0082
##
## Information Criteria
## ------------------------------------
##
## Akaike 6.2358
## Bayes 6.3445
## Shibata 6.2340
## Hannan-Quinn 6.2795
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.476 2.244e-01
## Lag[2*(p+q)+(p+q)-1][11] 8.868 1.394e-05
## Lag[4*(p+q)+(p+q)-1][19] 16.400 9.714e-03
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3337 0.5635
## Lag[2*(p+q)+(p+q)-1][5] 2.5705 0.4911
## Lag[4*(p+q)+(p+q)-1][9] 5.5903 0.3481
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.000354 0.500 2.000 0.9850
## ARCH Lag[5] 3.946008 1.440 1.667 0.1789
## ARCH Lag[7] 4.873507 2.315 1.543 0.2376
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.0547
## Individual Statistics:
## mu 0.23219
## ar1 0.04018
## ar2 0.05339
## ma1 0.04614
## ma2 0.07996
## omega 0.05516
## alpha1 0.04639
## beta1 0.06071
##
## 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 1.8611 0.06386 *
## Negative Sign Bias 0.5204 0.60325
## Positive Sign Bias 0.2486 0.80387
## Joint Effect 8.7034 0.03351 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 33.96 0.018587
## 2 30 50.57 0.007827
## 3 40 57.46 0.028587
## 4 50 71.03 0.021480
##
##
## Elapsed time : 2.008999
#Imprimir coeficientes de tu modelo ARMA(2,2)+GARCH(1,1)
ugfit2@fit$coef
## mu ar1 ar2 ma1 ma2 omega alpha1
## 1.4561066 -0.2809535 -1.0129144 0.2806130 1.0078815 1.8102265 0.1352214
## beta1
## 0.8042917
#Pronostico
ugfore <- ugarchforecast(ugfit2, n, ahead =10)
ugfore
##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: sGARCH
## Horizon: 10
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=Dic. 2021]:
## Series Sigma
## T+1 -0.9021 5.494
## T+2 3.6595 5.492
## T+3 3.2257 5.491
## T+4 -1.2730 5.490
## T+5 0.4304 5.489
## T+6 4.5086 5.488
## T+7 1.6375 5.487
## T+8 -1.6867 5.486
## T+9 2.1554 5.485
## T+10 4.4431 5.484