BAC PARCIAL III
JOSE ALBERTO HERNANDEZ DADO
28/11/2019
BANK OF AMERICA CORPORATION (BAC)
La Corporación Bank of America es una empresa estadounidense de tipo bancario y de servicios financieros multinacional con sede central en Charlotte, Carolina del Norte. Es el segundo mayor holding bancario en los Estados Unidos por activos. A partir de 2010, Bank of America es la quinta compañía más grande de Estados Unidos por ingresos totales, y la tercera no petrolera (después de Wal-Mart y General Electric). En 2010, la revista Forbes enlistó a Bank of America como la tercera empresa más grande del mundo.
Con la adquisición de Merrill Lynch en 2008 hizo a Bank of America la mayor empresa de gestión de riqueza del mundo y juega un rol importante en el mercado de la banca de inversión.
La compañía llevó a cabo el 12,2% de todos los depósitos bancarios en los Estados Unidos en agosto de 2009, y es uno de los cuatro grandes bancos de Estados Unidos, junto con Citigroup, JPMorgan Chase y Wells Fargo, sus principales competidores. Bank of America opera en todo Estados Unidos y en más 40 países. Tiene un tamaño de banca minorista, que cubre aproximadamente el 80% de la población de los EE.UU. y atiende a cerca de 57 millones de consumidores y pequeñas empresas en 5600 centros bancarios y 16 200 cajeros automáticos (ATMs).
Fuente: Wikipedia
GRÁFICAS DE PRECIOS DE CIERRE A NIVELES Y RENDIMIENTOS
La gráfica de los precios de cierre a niveles, nos muestra grandes variaciones en su comportamiento, se observa que a partir del 2016 ha tenido un gran crecimiento, llegando en 2018 a su nivel más alto y siguiendo esa tendencia en la actualidad.
GRAFICA EN RENDIMIENTOS 
La gráfico de los rendimientos nos muestra una serie con un comportamiento similar, a excepción del año 2016, donde puede observarse un comportamiento de alta volatilidad. Este suceso se originó por lo siguiente: “La temporada de resultados entre los grandes bancos de Wall Street va ganando cuerpo y las cuentas van mostrando dónde están sus puntos débiles. Bank of America, el segundo grupo financio por activos de Estados Unidos, registró una caída del 16% en el beneficio del primer trimestre. Se debe a la fuerte contracción en el negocio de renta fija y variable. La tensión en el mercado de la energía le lleva a reforzar las reserva, como a Wells Fargo.”
https://elpais.com/economia/2016/04/14/actualidad/1460633496_775568.html [1]
GRÁFICOS DE AUTOCORRELACIÓN DE LOS RENDIMIENTOS
**Elaboración Propia con datos de Yahoo Finance**
PRUEBA ARCH A PARTIR DE MODELO AUTOARIMA
MODELO AUTOARIMA
## Series: BAC
## ARIMA(0,1,0) with drift
##
## Coefficients:
## drift
## 0.0120
## s.e. 0.0078
##
## sigma^2 estimated as 0.1048: log likelihood=-504.83
## AIC=1013.67 AICc=1013.68 BIC=1024.59PRUEBA ARCH
##
## Box-Ljung test
##
## data: fit1$residuals^2
## X-squared = 272.6, df = 30, p-value < 2.2e-16El valor P es de 2.2e-16, por lo que no se rechaza la H0, indicando que los residuales al cuadrado del ARIMA son homocedasticos.
ESTIMACIÓN DE MODELOS ARCH GARCH
MODELO ARCH(1,0)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,0)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000211 0.000009 23.7195 0e+00
## alpha1 0.140258 0.030623 4.5802 5e-06
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000211 0.000014 14.608 0.000000
## alpha1 0.140258 0.046063 3.045 0.002327
##
## LogLikelihood : 4769.487
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.4957
## Bayes -5.4894
## Shibata -5.4957
## Hannan-Quinn -5.4933
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.212 0.2710
## Lag[2*(p+q)+(p+q)-1][2] 1.213 0.4340
## Lag[4*(p+q)+(p+q)-1][5] 3.116 0.3863
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.03957 0.842316
## Lag[2*(p+q)+(p+q)-1][2] 3.04225 0.136668
## Lag[4*(p+q)+(p+q)-1][5] 11.70424 0.003329
## d.o.f=1
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[2] 5.992 0.500 2.000 0.0143747
## ARCH Lag[4] 14.460 1.397 1.611 0.0003545
## ARCH Lag[6] 17.753 2.222 1.500 0.0001471
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.4375
## Individual Statistics:
## omega 0.2703
## alpha1 0.2553
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 0.61 0.749 1.07
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.4765 0.63376
## Negative Sign Bias 1.7555 0.07934 *
## Positive Sign Bias 1.5605 0.11882
## Joint Effect 8.7986 0.03209 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 88.53 6.043e-11
## 2 30 109.14 3.202e-11
## 3 40 129.00 1.463e-11
## 4 50 153.56 1.031e-12
##
##
## Elapsed time : 0.4260089MODELO ARCH(2)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(2,0)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## omega 0.00019 0.000009 20.0957 0.000000
## alpha1 0.12609 0.030166 4.1797 0.000029
## alpha2 0.10154 0.028528 3.5594 0.000372
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.00019 0.000014 13.9983 0.000000
## alpha1 0.12609 0.045195 2.7898 0.005273
## alpha2 0.10154 0.039535 2.5684 0.010217
##
## LogLikelihood : 4779.815
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.5064
## Bayes -5.4970
## Shibata -5.5064
## Hannan-Quinn -5.5029
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.099 0.2945
## Lag[2*(p+q)+(p+q)-1][2] 1.132 0.4573
## Lag[4*(p+q)+(p+q)-1][5] 2.655 0.4737
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.02573 0.8726
## Lag[2*(p+q)+(p+q)-1][5] 2.48866 0.5083
## Lag[4*(p+q)+(p+q)-1][9] 6.26076 0.2693
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 1.349 0.500 2.000 0.2455
## ARCH Lag[5] 4.195 1.440 1.667 0.1571
## ARCH Lag[7] 6.624 2.315 1.543 0.1045
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.8843
## Individual Statistics:
## omega 0.2020
## alpha1 0.2767
## alpha2 0.4288
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 0.846 1.01 1.35
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.5224 0.6015
## Negative Sign Bias 1.7357 0.0828 *
## Positive Sign Bias 1.5686 0.1169
## Joint Effect 8.4837 0.0370 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 87.44 9.381e-11
## 2 30 109.49 2.809e-11
## 3 40 129.65 1.160e-11
## 4 50 163.01 3.630e-14
##
##
## Elapsed time : 0.457005MODELO ARCH(3)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(3,0)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000181 0.000010 17.9676 0.000000
## alpha1 0.121478 0.029101 4.1743 0.000030
## alpha2 0.087275 0.029078 3.0014 0.002688
## alpha3 0.057012 0.026073 2.1867 0.028768
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000181 0.000015 11.8743 0.000000
## alpha1 0.121478 0.042693 2.8454 0.004436
## alpha2 0.087275 0.039867 2.1892 0.028584
## alpha3 0.057012 0.039651 1.4378 0.150483
##
## LogLikelihood : 4783.195
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.5092
## Bayes -5.4966
## Shibata -5.5092
## Hannan-Quinn -5.5045
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.296 0.2550
## Lag[2*(p+q)+(p+q)-1][2] 1.344 0.3988
## Lag[4*(p+q)+(p+q)-1][5] 2.843 0.4366
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.005434 0.9412
## Lag[2*(p+q)+(p+q)-1][8] 2.666561 0.7462
## Lag[4*(p+q)+(p+q)-1][14] 6.115118 0.6233
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 1.979 0.500 2.000 0.1595
## ARCH Lag[6] 3.277 1.461 1.711 0.2691
## ARCH Lag[8] 4.744 2.368 1.583 0.2773
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.1265
## Individual Statistics:
## omega 0.1379
## alpha1 0.2059
## alpha2 0.4548
## alpha3 0.3340
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.4847 0.62798
## Negative Sign Bias 1.7464 0.08092 *
## Positive Sign Bias 1.6143 0.10664
## Joint Effect 9.0152 0.02909 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 83.25 5.091e-10
## 2 30 108.97 3.419e-11
## 3 40 133.80 2.578e-12
## 4 50 149.18 4.726e-12
##
##
## Elapsed time : 0.639977MODELO ARCH(4)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(4,0)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000172 0.000010 16.9642 0.000000
## alpha1 0.116476 0.028981 4.0190 0.000058
## alpha2 0.088945 0.029485 3.0166 0.002556
## alpha3 0.038714 0.024203 1.5995 0.109699
## alpha4 0.056894 0.023750 2.3955 0.016597
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000172 0.000016 10.9017 0.000000
## alpha1 0.116476 0.042446 2.7441 0.006068
## alpha2 0.088945 0.041260 2.1557 0.031106
## alpha3 0.038714 0.034701 1.1156 0.264574
## alpha4 0.056894 0.032503 1.7504 0.080042
##
## LogLikelihood : 4787.316
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.5128
## Bayes -5.4970
## Shibata -5.5128
## Hannan-Quinn -5.5069
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.540 0.2146
## Lag[2*(p+q)+(p+q)-1][2] 1.601 0.3386
## Lag[4*(p+q)+(p+q)-1][5] 2.862 0.4329
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.07497 0.7842
## Lag[2*(p+q)+(p+q)-1][11] 2.32428 0.9368
## Lag[4*(p+q)+(p+q)-1][19] 7.89961 0.6870
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.04864 0.500 2.000 0.8255
## ARCH Lag[7] 1.22538 1.473 1.746 0.6951
## ARCH Lag[9] 2.86217 2.402 1.619 0.5911
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.2833
## Individual Statistics:
## omega 0.1201
## alpha1 0.1691
## alpha2 0.4546
## alpha3 0.2661
## alpha4 0.3264
##
## 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 0.5119 0.60880
## Negative Sign Bias 1.7853 0.07439 *
## Positive Sign Bias 1.6038 0.10894
## Joint Effect 9.0528 0.02860 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 90.97 2.231e-11
## 2 30 108.07 4.805e-11
## 3 40 129.65 1.160e-11
## 4 50 148.08 6.894e-12
##
##
## Elapsed time : 0.743005MODELO GARCH(1,1)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000028 0.000009 3.0097 0.002615
## alpha1 0.082505 0.019130 4.3128 0.000016
## beta1 0.804338 0.051487 15.6221 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000028 0.000017 1.6213 0.104944
## alpha1 0.082505 0.033938 2.4311 0.015054
## beta1 0.804338 0.095923 8.3853 0.000000
##
## LogLikelihood : 4792.465
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.5210
## Bayes -5.5116
## Shibata -5.5210
## Hannan-Quinn -5.5175
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.099 0.1474
## Lag[2*(p+q)+(p+q)-1][2] 2.144 0.2400
## Lag[4*(p+q)+(p+q)-1][5] 3.598 0.3087
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.735 0.1878
## Lag[2*(p+q)+(p+q)-1][5] 2.517 0.5022
## Lag[4*(p+q)+(p+q)-1][9] 3.442 0.6842
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.5027 0.500 2.000 0.4783
## ARCH Lag[5] 1.5993 1.440 1.667 0.5666
## ARCH Lag[7] 2.0571 2.315 1.543 0.7052
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.4573
## Individual Statistics:
## omega 0.07943
## alpha1 0.15599
## beta1 0.08286
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 0.846 1.01 1.35
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.5656 0.571713
## Negative Sign Bias 2.5447 0.011022 **
## Positive Sign Bias 1.3115 0.189865
## Joint Effect 12.5927 0.005606 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 87.65 8.624e-11
## 2 30 109.84 2.463e-11
## 3 40 124.90 6.339e-11
## 4 50 146.64 1.131e-11
##
##
## Elapsed time : 0.6509778MODELO GARCH(1,2)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,2)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Convergence Problem:
## Solver Message:MODELO GARCH(2,1)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(2,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000028 0.000013 2.0860 0.036980
## alpha1 0.082636 0.022347 3.6979 0.000217
## alpha2 0.000000 0.033648 0.0000 1.000000
## beta1 0.804103 0.078729 10.2136 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000028 0.000030 0.91951 0.357829
## alpha1 0.082636 0.033507 2.46624 0.013654
## alpha2 0.000000 0.067744 0.00000 1.000000
## beta1 0.804103 0.180602 4.45234 0.000008
##
## LogLikelihood : 4792.635
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.5200
## Bayes -5.5075
## Shibata -5.5201
## Hannan-Quinn -5.5154
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.108 0.1466
## Lag[2*(p+q)+(p+q)-1][2] 2.153 0.2385
## Lag[4*(p+q)+(p+q)-1][5] 3.608 0.3072
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.708 0.1912
## Lag[2*(p+q)+(p+q)-1][8] 3.279 0.6343
## Lag[4*(p+q)+(p+q)-1][14] 4.776 0.7967
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.1934 0.500 2.000 0.6601
## ARCH Lag[6] 1.7122 1.461 1.711 0.5574
## ARCH Lag[8] 1.9636 2.368 1.583 0.7489
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.0081
## Individual Statistics:
## omega 0.08094
## alpha1 0.15664
## alpha2 0.21166
## beta1 0.08327
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.5701 0.568712
## Negative Sign Bias 2.5405 0.011156 **
## Positive Sign Bias 1.3161 0.188299
## Joint Effect 12.5573 0.005699 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 86.66 1.289e-10
## 2 30 108.69 3.797e-11
## 3 40 123.10 1.198e-10
## 4 50 145.61 1.613e-11
##
##
## Elapsed time : 0.669992MODELO GARCH(2,2)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(2,2)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000031 0.000019 1.58899 0.112064
## alpha1 0.095941 0.019346 4.95932 0.000001
## alpha2 0.000000 0.072871 0.00000 1.000000
## beta1 0.549210 0.553100 0.99297 0.320726
## beta2 0.229106 0.401076 0.57123 0.567845
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000031 0.000037 0.83501 0.403713
## alpha1 0.095941 0.037822 2.53667 0.011191
## alpha2 0.000000 0.119725 0.00000 1.000000
## beta1 0.549210 1.124669 0.48833 0.625316
## beta2 0.229106 0.886474 0.25845 0.796062
##
## LogLikelihood : 4793.417
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.5198
## Bayes -5.5041
## Shibata -5.5198
## Hannan-Quinn -5.5140
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.057 0.1516
## Lag[2*(p+q)+(p+q)-1][2] 2.105 0.2459
## Lag[4*(p+q)+(p+q)-1][5] 3.614 0.3062
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7302 0.3928
## Lag[2*(p+q)+(p+q)-1][11] 2.7699 0.8946
## Lag[4*(p+q)+(p+q)-1][19] 6.7609 0.8068
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 1.442 0.500 2.000 0.2299
## ARCH Lag[7] 1.836 1.473 1.746 0.5411
## ARCH Lag[9] 1.877 2.402 1.619 0.7822
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.6888
## Individual Statistics:
## omega 0.08505
## alpha1 0.14656
## alpha2 0.18093
## beta1 0.08444
## beta2 0.08024
##
## 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 0.5064 0.612671
## Negative Sign Bias 2.2355 0.025513 **
## Positive Sign Bias 1.5062 0.132203
## Joint Effect 11.6486 0.008689 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 85.09 2.427e-10
## 2 30 106.41 8.985e-11
## 3 40 123.97 8.791e-11
## 4 50 145.03 1.964e-11
##
##
## Elapsed time : 0.561007TABLA DE COEFICIENTES
MEJORES MODELOS
GARCH(1,1) En este modelo GACH(1,1), se cumplen las condiciones de no negatividad en los parámetros, la suma de los mismos no es mayor a 1 como se muestra en la tabla y además, el criterio de AIC es mayor (negativamente) por lo que se aproxima a los principios de parsimonia.
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000028 0.000009 3.0097 0.002615
## alpha1 0.082505 0.019130 4.3128 0.000016
## beta1 0.804338 0.051487 15.6221 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000028 0.000017 1.6213 0.104944
## alpha1 0.082505 0.033938 2.4311 0.015054
## beta1 0.804338 0.095923 8.3853 0.000000
##
## LogLikelihood : 4792.465
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.5210
## Bayes -5.5116
## Shibata -5.5210
## Hannan-Quinn -5.5175
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.099 0.1474
## Lag[2*(p+q)+(p+q)-1][2] 2.144 0.2400
## Lag[4*(p+q)+(p+q)-1][5] 3.598 0.3087
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.735 0.1878
## Lag[2*(p+q)+(p+q)-1][5] 2.517 0.5022
## Lag[4*(p+q)+(p+q)-1][9] 3.442 0.6842
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.5027 0.500 2.000 0.4783
## ARCH Lag[5] 1.5993 1.440 1.667 0.5666
## ARCH Lag[7] 2.0571 2.315 1.543 0.7052
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.4573
## Individual Statistics:
## omega 0.07943
## alpha1 0.15599
## beta1 0.08286
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 0.846 1.01 1.35
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.5656 0.571713
## Negative Sign Bias 2.5447 0.011022 **
## Positive Sign Bias 1.3115 0.189865
## Joint Effect 12.5927 0.005606 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 87.65 8.624e-11
## 2 30 109.84 2.463e-11
## 3 40 124.90 6.339e-11
## 4 50 146.64 1.131e-11
##
##
## Elapsed time : 1.274987GARCH(2,1) En este modelo GACH(2,1), se cumplen las condiciones de no negatividad en los parámetros, la suma de los mismos no es mayor a 1 como se muestra en la tabla y además, el criterio de AIC es mayor (negativamente) por lo que se aproxima a los principios de parsimonia.
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(2,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000028 0.000013 2.0860 0.036980
## alpha1 0.082636 0.022347 3.6979 0.000217
## alpha2 0.000000 0.033648 0.0000 1.000000
## beta1 0.804103 0.078729 10.2136 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.000028 0.000030 0.91951 0.357829
## alpha1 0.082636 0.033507 2.46624 0.013654
## alpha2 0.000000 0.067744 0.00000 1.000000
## beta1 0.804103 0.180602 4.45234 0.000008
##
## LogLikelihood : 4792.635
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.5200
## Bayes -5.5075
## Shibata -5.5201
## Hannan-Quinn -5.5154
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.108 0.1466
## Lag[2*(p+q)+(p+q)-1][2] 2.153 0.2385
## Lag[4*(p+q)+(p+q)-1][5] 3.608 0.3072
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.708 0.1912
## Lag[2*(p+q)+(p+q)-1][8] 3.279 0.6343
## Lag[4*(p+q)+(p+q)-1][14] 4.776 0.7967
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.1934 0.500 2.000 0.6601
## ARCH Lag[6] 1.7122 1.461 1.711 0.5574
## ARCH Lag[8] 1.9636 2.368 1.583 0.7489
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.0081
## Individual Statistics:
## omega 0.08094
## alpha1 0.15664
## alpha2 0.21166
## beta1 0.08327
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.5701 0.568712
## Negative Sign Bias 2.5405 0.011156 **
## Positive Sign Bias 1.3161 0.188299
## Joint Effect 12.5573 0.005699 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 86.66 1.289e-10
## 2 30 108.69 3.797e-11
## 3 40 123.10 1.198e-10
## 4 50 145.61 1.613e-11
##
##
## Elapsed time : 0.5509961CONSLUSIÓN
</center
La compañia Bank of America Corporation se ve afectada en sus rendimientos debido a la volatilidad, las noticias tienen un alto impacto. La volatilidad se encuentra en un rango de 0.05-0.010.