MGM VOLATILIDAD
Sandra Gonzalez Arzate
21 de Junio de 2020
MGM
MGM Resorts International (NYSE: MGM)
MGM MGM Resorts International (NYSE: MGM) es un grupo empresarial con sede en la ciudad de Paradise (Nevada) que posee y gestiona casinos, hoteles y espectĆ”culos alrededor del mundo. La compaƱĆa empezĆ³ a operar el 31 de mayo de 2000 despuĆ©s de la uniĆ³n de las empresas MGM Grand Inc.Ā y Mirage Resorts, Inc.. Actualmente es la segunda compaƱĆa de juegos mĆ”s grande del mundo.1 El multimillonario Kirk Kerkorian y su CorporaciĆ³n Tracinda son los que tienen la mayorĆa de las acciones del MGM Mirage. Kerkorian tambiĆ©n fue el antiguo dueƱo de los estudios de pelĆculas Metro-Goldwyn-Mayer, de ahĆ el nombre del MGM Grand, Inc.
NOTICIA: La compaƱĆa estadounidense MGM Resorts International acordĆ³ vender su emblemĆ”tico MGM Grand de Las Vegas a un grupo conformado por MGM Growth Properties y Blackstone Group, por US$ 2.500 millones. La firma sigue avanzando asĆ desprendiĆ©ndose de activos pesados para enfocarse en la gestiĆ³n de casinos.
ComposiciĆ³n de MGM
Augmented Dickey-Fuller Test
data: MGM_R
Dickey-Fuller = -9.6968, Lag order = 11, p-value = 0.01
alternative hypothesis: stationary
Phillips-Perron Unit Root Test
data: MGM_R
Dickey-Fuller = -34.41, Truncation lag parameter = 7, p-value = 0.01
ARCH LM-test; Null hypothesis: no ARCH effects
data: MGM_R
Chi-squared = 501.96, df = 12, p-value < 2.2e-16
*---------------------------------*
* 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 0.00004 0.00000 2085.3 0
alpha1 0.77419 0.00037 2091.1 0
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
omega 0.00004 0.000000 8260.2 0
alpha1 0.77419 0.000106 7322.4 0
LogLikelihood : 1393.268
Information Criteria
------------------------------------
Akaike -2.0781
Bayes -2.0703
Shibata -2.0781
Hannan-Quinn -2.0752
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 0.01134 0.9152
Lag[2*(p+q)+(p+q)-1][2] 2.74434 0.1646
Lag[4*(p+q)+(p+q)-1][5] 5.41039 0.1234
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 0.1495 0.6990
Lag[2*(p+q)+(p+q)-1][2] 0.3879 0.7487
Lag[4*(p+q)+(p+q)-1][5] 0.9069 0.8804
d.o.f=1
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[2] 0.4754 0.500 2.000 0.4905
ARCH Lag[4] 0.4998 1.397 1.611 0.8682
ARCH Lag[6] 90.7784 2.222 1.500 0.0000
Nyblom stability test
------------------------------------
Joint Statistic: 0.6119
Individual Statistics:
omega 0.01915
alpha1 0.59262
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 1.5623 0.1185
Negative Sign Bias 0.6242 0.5326
Positive Sign Bias 1.5956 0.1108
Joint Effect 4.8943 0.1797
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 375.3 5.883e-68
2 30 575.7 7.022e-103
3 40 720.5 2.600e-126
4 50 880.2 8.083e-153
Elapsed time : 0.3853612 
*---------------------------------*
* 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 0.000261 0.000017 15.0708 0
alpha1 0.234718 0.043218 5.4310 0
alpha2 0.355818 0.048766 7.2965 0
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
omega 0.000261 0.000031 8.4326 0.000000
alpha1 0.234718 0.080530 2.9147 0.003561
alpha2 0.355818 0.097645 3.6440 0.000268
LogLikelihood : 3235.381
Information Criteria
------------------------------------
Akaike -4.8281
Bayes -4.8164
Shibata -4.8281
Hannan-Quinn -4.8237
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 0.001953 0.9648
Lag[2*(p+q)+(p+q)-1][2] 0.025964 0.9756
Lag[4*(p+q)+(p+q)-1][5] 0.831423 0.8965
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 0.1454 0.7030
Lag[2*(p+q)+(p+q)-1][5] 5.1885 0.1387
Lag[4*(p+q)+(p+q)-1][9] 8.4978 0.1028
d.o.f=2
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[3] 2.656 0.500 2.000 0.10316
ARCH Lag[5] 5.391 1.440 1.667 0.08339
ARCH Lag[7] 7.198 2.315 1.543 0.07869
Nyblom stability test
------------------------------------
Joint Statistic: 2.1571
Individual Statistics:
omega 0.5566
alpha1 0.3634
alpha2 0.7671
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 1.1442 0.2528
Negative Sign Bias 0.3984 0.6904
Positive Sign Bias 0.8097 0.4182
Joint Effect 1.4314 0.6982
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 99.19 7.497e-13
2 30 112.27 9.740e-12
3 40 124.33 7.747e-11
4 50 119.07 9.173e-08
Elapsed time : 0.256238 
*---------------------------------*
* 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 0.000229 0.000018 12.8779 0.000000
alpha1 0.219711 0.041445 5.3013 0.000000
alpha2 0.331882 0.050159 6.6165 0.000000
alpha3 0.102107 0.032899 3.1036 0.001912
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
omega 0.000229 0.000029 7.7881 0.000000
alpha1 0.219711 0.079037 2.7798 0.005439
alpha2 0.331882 0.093856 3.5361 0.000406
alpha3 0.102107 0.045753 2.2317 0.025636
LogLikelihood : 3247.045
Information Criteria
------------------------------------
Akaike -4.8440
Bayes -4.8284
Shibata -4.8440
Hannan-Quinn -4.8382
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 0.01731 0.8953
Lag[2*(p+q)+(p+q)-1][2] 0.02978 0.9725
Lag[4*(p+q)+(p+q)-1][5] 0.71675 0.9197
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 0.4952 0.4816
Lag[2*(p+q)+(p+q)-1][8] 5.5446 0.2842
Lag[4*(p+q)+(p+q)-1][14] 7.9967 0.3844
d.o.f=3
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[4] 1.733 0.500 2.000 0.1880
ARCH Lag[6] 2.939 1.461 1.711 0.3169
ARCH Lag[8] 3.159 2.368 1.583 0.5142
Nyblom stability test
------------------------------------
Joint Statistic: 1.8468
Individual Statistics:
omega 0.4191
alpha1 0.3305
alpha2 0.6223
alpha3 0.1293
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 0.9594 0.3375
Negative Sign Bias 0.2781 0.7810
Positive Sign Bias 0.9253 0.3550
Joint Effect 1.2412 0.7431
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 95.82 3.041e-12
2 30 113.26 6.678e-12
3 40 120.75 2.740e-10
4 50 138.33 1.880e-10
Elapsed time : 0.2272141 
*---------------------------------*
* 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 0.000203 0.000018 11.5455 0.000000
alpha1 0.214741 0.040000 5.3685 0.000000
alpha2 0.253098 0.050368 5.0249 0.000001
alpha3 0.089674 0.029939 2.9952 0.002742
alpha4 0.133004 0.038458 3.4584 0.000543
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
omega 0.000203 0.000030 6.8808 0.000000
alpha1 0.214741 0.071036 3.0230 0.002503
alpha2 0.253098 0.093672 2.7020 0.006893
alpha3 0.089674 0.042634 2.1033 0.035435
alpha4 0.133004 0.050425 2.6377 0.008348
LogLikelihood : 3258.667
Information Criteria
------------------------------------
Akaike -4.8598
Bayes -4.8404
Shibata -4.8599
Hannan-Quinn -4.8526
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 0.006014 0.9382
Lag[2*(p+q)+(p+q)-1][2] 0.010502 0.9892
Lag[4*(p+q)+(p+q)-1][5] 0.388772 0.9734
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 0.0645 0.7995
Lag[2*(p+q)+(p+q)-1][11] 2.8880 0.8816
Lag[4*(p+q)+(p+q)-1][19] 8.3304 0.6382
d.o.f=4
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[5] 0.5029 0.500 2.000 0.4782
ARCH Lag[7] 0.9169 1.473 1.746 0.7807
ARCH Lag[9] 1.1973 2.402 1.619 0.9025
Nyblom stability test
------------------------------------
Joint Statistic: 1.7721
Individual Statistics:
omega 0.25237
alpha1 0.23889
alpha2 0.55528
alpha3 0.09659
alpha4 0.37798
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 1.1338 0.2571
Negative Sign Bias 0.3010 0.7635
Positive Sign Bias 0.9821 0.3262
Joint Effect 1.5869 0.6624
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 86.38 1.445e-10
2 30 107.97 4.998e-11
3 40 116.50 1.197e-09
4 50 135.65 4.591e-10
Elapsed time : 0.346324
*---------------------------------*
* 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 0.000034 0.000010 3.5842 0.000338
alpha1 0.170683 0.033184 5.1435 0.000000
beta1 0.773809 0.041732 18.5425 0.000000
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
omega 0.000034 0.000017 1.9965 0.045875
alpha1 0.170683 0.064713 2.6376 0.008351
beta1 0.773809 0.075669 10.2262 0.000000
LogLikelihood : 3268.481
Information Criteria
------------------------------------
Akaike -4.8775
Bayes -4.8658
Shibata -4.8775
Hannan-Quinn -4.8731
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 0.0001511 0.9902
Lag[2*(p+q)+(p+q)-1][2] 0.0779280 0.9354
Lag[4*(p+q)+(p+q)-1][5] 0.6464630 0.9329
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 0.4613 0.4970
Lag[2*(p+q)+(p+q)-1][5] 0.6093 0.9396
Lag[4*(p+q)+(p+q)-1][9] 1.1813 0.9775
d.o.f=2
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[3] 0.2014 0.500 2.000 0.6536
ARCH Lag[5] 0.2747 1.440 1.667 0.9469
ARCH Lag[7] 0.4300 2.315 1.543 0.9843
Nyblom stability test
------------------------------------
Joint Statistic: 1.0662
Individual Statistics:
omega 0.2299
alpha1 0.2122
beta1 0.1487
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 1.1102 0.2671
Negative Sign Bias 0.1586 0.8740
Positive Sign Bias 0.7687 0.4422
Joint Effect 1.7114 0.6344
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 73.47 2.413e-08
2 30 87.31 9.388e-08
3 40 96.85 7.971e-07
4 50 117.80 1.354e-07
Elapsed time : 0.215199 
*---------------------------------*
* GARCH Model Fit *
*---------------------------------*
Conditional Variance Dynamics
-----------------------------------
GARCH Model : sGARCH(1,2)
Mean Model : ARFIMA(0,0,0)
Distribution : norm
Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
omega 0.000034 0.000010 3.579472 0.000344
alpha1 0.170691 0.035762 4.773040 0.000002
beta1 0.773839 0.190478 4.062628 0.000049
beta2 0.000003 0.172187 0.000018 0.999986
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
omega 0.000034 0.000017 2.020783 0.043302
alpha1 0.170691 0.053259 3.204920 0.001351
beta1 0.773839 0.277318 2.790443 0.005264
beta2 0.000003 0.284068 0.000011 0.999991
LogLikelihood : 3268.483
Information Criteria
------------------------------------
Akaike -4.8760
Bayes -4.8605
Shibata -4.8760
Hannan-Quinn -4.8702
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 0.0001485 0.9903
Lag[2*(p+q)+(p+q)-1][2] 0.0775669 0.9357
Lag[4*(p+q)+(p+q)-1][5] 0.6462559 0.9330
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 0.4610 0.4972
Lag[2*(p+q)+(p+q)-1][8] 0.9599 0.9767
Lag[4*(p+q)+(p+q)-1][14] 2.8715 0.9622
d.o.f=3
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[4] 0.01578 0.500 2.000 0.9000
ARCH Lag[6] 0.12655 1.461 1.711 0.9835
ARCH Lag[8] 1.10843 2.368 1.583 0.9078
Nyblom stability test
------------------------------------
Joint Statistic: 1.2385
Individual Statistics:
omega 0.2298
alpha1 0.2121
beta1 0.1483
beta2 0.1437
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 1.1113 0.2666
Negative Sign Bias 0.1597 0.8731
Positive Sign Bias 0.7690 0.4420
Joint Effect 1.7160 0.6334
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 73.47 2.413e-08
2 30 87.31 9.388e-08
3 40 97.03 7.533e-07
4 50 117.80 1.354e-07
Elapsed time : 0.255245 
*---------------------------------*
* 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 0.000044 0.000013 3.3084 0.000938
alpha1 0.142142 0.040009 3.5528 0.000381
alpha2 0.061066 0.053722 1.1367 0.255666
beta1 0.725051 0.059690 12.1469 0.000000
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
omega 0.000044 0.000025 1.75609 0.079072
alpha1 0.142142 0.057457 2.47388 0.013365
alpha2 0.061066 0.107974 0.56556 0.571692
beta1 0.725051 0.122358 5.92563 0.000000
LogLikelihood : 3269.098
Information Criteria
------------------------------------
Akaike -4.8769
Bayes -4.8614
Shibata -4.8769
Hannan-Quinn -4.8711
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 0.00688 0.9339
Lag[2*(p+q)+(p+q)-1][2] 0.06592 0.9442
Lag[4*(p+q)+(p+q)-1][5] 0.60954 0.9395
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 0.09531 0.7575
Lag[2*(p+q)+(p+q)-1][8] 0.94516 0.9777
Lag[4*(p+q)+(p+q)-1][14] 2.83291 0.9641
d.o.f=3
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[4] 0.0009949 0.500 2.000 0.9748
ARCH Lag[6] 0.0796386 1.461 1.711 0.9915
ARCH Lag[8] 1.1732894 2.368 1.583 0.8973
Nyblom stability test
------------------------------------
Joint Statistic: 1.1977
Individual Statistics:
omega 0.2444
alpha1 0.2031
alpha2 0.2683
beta1 0.1506
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 1.05324 0.2924
Negative Sign Bias 0.08158 0.9350
Positive Sign Bias 0.61811 0.5366
Joint Effect 1.26368 0.7378
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 69.11 1.292e-07
2 30 91.07 2.485e-08
3 40 96.73 8.276e-07
4 50 118.92 9.605e-08
Elapsed time : 0.654614 
*---------------------------------*
* 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 0.000066 0.000019 3.47275 0.000515
alpha1 0.135661 0.037862 3.58306 0.000340
alpha2 0.161976 0.056554 2.86406 0.004182
beta1 0.237134 0.246137 0.96342 0.335336
beta2 0.357210 0.195112 1.83080 0.067131
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
omega 0.000066 0.000030 2.15721 0.030989
alpha1 0.135661 0.054120 2.50666 0.012188
alpha2 0.161976 0.095853 1.68983 0.091060
beta1 0.237134 0.246742 0.96106 0.336522
beta2 0.357210 0.213405 1.67386 0.094159
LogLikelihood : 3269.977
Information Criteria
------------------------------------
Akaike -4.8767
Bayes -4.8573
Shibata -4.8768
Hannan-Quinn -4.8695
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 0.009448 0.9226
Lag[2*(p+q)+(p+q)-1][2] 0.068403 0.9424
Lag[4*(p+q)+(p+q)-1][5] 0.623891 0.9370
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 0.05707 0.8112
Lag[2*(p+q)+(p+q)-1][11] 1.81688 0.9710
Lag[4*(p+q)+(p+q)-1][19] 4.80181 0.9492
d.o.f=4
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[5] 0.0561 0.500 2.000 0.8128
ARCH Lag[7] 0.5129 1.473 1.746 0.8937
ARCH Lag[9] 1.7334 2.402 1.619 0.8095
Nyblom stability test
------------------------------------
Joint Statistic: 1.2909
Individual Statistics:
omega 0.2436
alpha1 0.1059
alpha2 0.3107
beta1 0.1469
beta2 0.1436
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 1.0727 0.2836
Negative Sign Bias 0.1615 0.8718
Positive Sign Bias 0.5761 0.5646
Joint Effect 1.2450 0.7422
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 66.00 4.190e-07
2 30 85.52 1.754e-07
3 40 98.46 4.786e-07
4 50 117.42 1.518e-07
Elapsed time : 0.4374089 
Fuente: elaboraciĆ³n propia con salida de R.