Anexos Pruebas de estacionariedad Null Hypothesis: TES has a unit root Augmented Dickey-Fuller test statistic -1.739333 0.4042 Test critical values: 1% level -3.610453 5% level -2.938987 10% level -2.607932 Dependent Variable: D(TES) Date: 01/23/18 Time: 16:28 Sample (adjusted): 2008Q1 2017Q3 Included observations: 39 after adjustments TES(-1) -0.113710 0.065375-1.739333 0.0903 C 0.733568 0.500486 1.465711 0.1512 R-squared 0.075584 Mean dependent var -0.111769 Adjusted R-squared 0.050600 S.D. dependent var 0.765869 S.E. of regression 0.746241 Akaike info criterion 2.302385 Sum squared resid 20.60442 Schwarz criterion 2.387696 Log likelihood -42.89651 Hannan-Quinn criter. 2.332994 F-statistic 3.025278 Durbin-Watson stat 1.656137 Prob(F-statistic) 0.090291 Null Hypothesis: D(TES) has a unit root Augmented Dickey-Fuller test statistic -5.653135 0.0000 Test critical values: 1% level -3.615588 5% level -2.941145 10% level -2.609066
Dependent Variable: D(TES,2) Date: 01/23/18 Time: 16:29 Sample (adjusted): 2008Q2 2017Q3 Included observations: 38 after adjustments D(TES(-1)) -0.899734 0.159157-5.653135 0.0000 C -0.134639 0.123210-1.092767 0.2818 R-squared 0.470260 Mean dependent var -0.030105 Adjusted R-squared 0.455546 S.D. dependent var 1.017674 S.E. of regression 0.750913 Akaike info criterion 2.316141 Sum squared resid 20.29932 Schwarz criterion 2.402330 Log likelihood -42.00668 Hannan-Quinn criter. 2.346807 F-statistic 31.95793 Durbin-Watson stat 2.041372 Prob(F-statistic) 0.000002 Null Hypothesis: EMBI has a unit root Augmented Dickey-Fuller test statistic -2.301936 0.1764 Test critical values: 1% level -3.610453 5% level -2.938987 10% level -2.607932 Dependent Variable: D(EMBI) Date: 01/23/18 Time: 16:33 Sample (adjusted): 2008Q1 2017Q3 Included observations: 39 after adjustments EMBI(-1) -0.248701 0.108040-2.301936 0.0271 C 0.552525 0.254282 2.172883 0.0363 R-squared 0.125273 Mean dependent var 0.004872 Adjusted R-squared 0.101632 S.D. dependent var 0.591461 S.E. of regression 0.560600 Akaike info criterion 1.730302 Sum squared resid 11.62807 Schwarz criterion 1.815613
Log likelihood -31.74089 Hannan-Quinn criter. 1.760911 F-statistic 5.298910 Durbin-Watson stat 1.498400 Prob(F-statistic) 0.027068 Null Hypothesis: D(EMBI) has a unit root Augmented Dickey-Fuller test statistic -5.287640 0.0001 Test critical values: 1% level -3.615588 5% level -2.941145 10% level -2.609066 Dependent Variable: D(EMBI,2) Date: 01/23/18 Time: 16:33 Sample (adjusted): 2008Q2 2017Q3 Included observations: 38 after adjustments D(EMBI(-1)) -0.855821 0.161853-5.287640 0.0000 C -0.013649 0.095672-0.142661 0.8874 R-squared 0.437141 Mean dependent var -0.015000 Adjusted R-squared 0.421506 S.D. dependent var 0.775401 S.E. of regression 0.589761 Akaike info criterion 1.832997 Sum squared resid 12.52145 Schwarz criterion 1.919186 Log likelihood -32.82695 Hannan-Quinn criter. 1.863663 F-statistic 27.95914 Durbin-Watson stat 1.865027 Prob(F-statistic) 0.000006 Null Hypothesis: INF has a unit root Lag Length: 1 (Automatic - based on SIC, maxlag=9) Augmented Dickey-Fuller test statistic -2.797326 0.0681 Test critical values: 1% level -3.615588 5% level -2.941145 10% level -2.609066
Dependent Variable: D(INF) Date: 01/23/18 Time: 16:34 Sample (adjusted): 2008Q2 2017Q3 Included observations: 38 after adjustments INF(-1) -0.150187 0.053689-2.797326 0.0083 D(INF(-1)) 0.637284 0.127795 4.986755 0.0000 C 0.603526 0.247804 2.435502 0.0201 R-squared 0.447760 Mean dependent var -0.051579 Adjusted R-squared 0.416203 S.D. dependent var 0.834805 S.E. of regression 0.637846 Akaike info criterion 2.014218 Sum squared resid 14.23968 Schwarz criterion 2.143501 Log likelihood -35.27015 Hannan-Quinn criter. 2.060216 F-statistic 14.18911 Durbin-Watson stat 1.967987 Prob(F-statistic) 0.000031 Null Hypothesis: D(INF) has a unit root Augmented Dickey-Fuller test statistic -3.154147 0.0309 Test critical values: 1% level -3.615588 5% level -2.941145 10% level -2.609066 Dependent Variable: D(INF,2) Date: 01/23/18 Time: 16:34 Sample (adjusted): 2008Q2 2017Q3 Included observations: 38 after adjustments D(INF(-1)) -0.431438 0.136784-3.154147 0.0032 C -0.026143 0.113021-0.231313 0.8184 R-squared 0.216517 Mean dependent var -0.006842 Adjusted R-squared 0.194753 S.D. dependent var 0.775263 S.E. of regression 0.695687 Akaike info criterion 2.163361 Sum squared resid 17.42328 Schwarz criterion 2.249550 Log likelihood -39.10386 Hannan-Quinn criter. 2.194027 F-statistic 9.948642 Durbin-Watson stat 1.771602
Prob(F-statistic) 0.003243 Examen de residuales de las estimaciones de regresión por MCO de la metodología Engle- Granger Examen de residuales de EQ03 Null Hypothesis: RESIDDEEQ03 has a unit root Lag Length: 1 (Automatic - based on SIC, maxlag=9) Augmented Dickey-Fuller test statistic -2.301083 0.1768 Test critical values: 1% level -3.615588 5% level -2.941145 10% level -2.609066 Dependent Variable: D(RESIDDEEQ03) Date: 01/29/18 Time: 10:14 Sample (adjusted): 2008Q2 2017Q3 Included observations: 38 after adjustments RESIDDEEQ03(-1) -0.195295 0.084871-2.301083 0.0275 D(RESIDDEEQ03(-1)) 0.351881 0.154218 2.281711 0.0287 C 0.006129 0.112343 0.054559 0.9568 R-squared 0.191599 Mean dependent var 0.009120 Adjusted R-squared 0.145404 S.D. dependent var 0.748838 S.E. of regression 0.692259 Akaike info criterion 2.177942 Sum squared resid 16.77277 Schwarz criterion 2.307225 Log likelihood -38.38090 Hannan-Quinn criter. 2.223940 F-statistic 4.147663 Durbin-Watson stat 1.644520 Prob(F-statistic) 0.024181 Examen de residuales de EQ04 Null Hypothesis: RESIDDEEQ04 has a unit root
Augmented Dickey-Fuller test statistic -3.194636 0.0279 Test critical values: 1% level -3.610453 5% level -2.938987 10% level -2.607932 Dependent Variable: D(RESIDDEEQ04) Date: 01/29/18 Time: 10:23 Sample (adjusted): 2008Q1 2017Q3 Included observations: 39 after adjustments RESIDDEEQ04(-1) -0.431542 0.135083-3.194636 0.0029 C -0.053226 0.110963-0.479676 0.6343 R-squared 0.216196 Mean dependent var -0.067754 Adjusted R-squared 0.195013 S.D. dependent var 0.771701 S.E. of regression 0.692379 Akaike info criterion 2.152553 Sum squared resid 17.73737 Schwarz criterion 2.237864 Log likelihood -39.97479 Hannan-Quinn criter. 2.183162 F-statistic 10.20570 Durbin-Watson stat 1.782162 Prob(F-statistic) 0.002860 Prueba de cointegración de Johansen Date: 01/25/18 Time: 17:32 Sample (adjusted): 2008Q3 2017Q3 Included observations: 37 after adjustments Trend assumption: Linear deterministic trend Series: INF TES EMBI Lags interval (in first differences): 1 to 2 Unrestricted Cointegration Rank Test (Trace) Hypothesized Trace 0.05 No. of CE(s) Eigenvalue Statistic Critical Value * None * 0.589340 47.49852 29.79707 0.0002 At most 1 0.218863 14.56890 15.49471 0.0686 At most 2 * 0.136489 5.429719 3.841466 0.0198 Trace test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized Max-Eigen 0.05 No. of CE(s) Eigenvalue Statistic Critical Value * None * 0.589340 32.92962 21.13162 0.0007 At most 1 0.218863 9.139178 14.26460 0.2747 At most 2 * 0.136489 5.429719 3.841466 0.0198 Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unrestricted Cointegrating Coefficients (normalized by b'*s11*b=i): INF TES EMBI -0.465777-0.662641 1.842287 0.122112-0.012241-1.694436 0.725391-0.522119-0.395473 Unrestricted Adjustment Coefficients (alpha): D(INF) 0.164655 0.172698-0.156191 D(TES) 0.308637 0.246124 0.069940 D(EMBI) -0.244512 0.157592-0.057493 1 Cointegrating Equation(s): Log likelihood -72.88301 Normalized cointegrating coefficients (standard error in parentheses) INF TES EMBI 1.000000 1.422657-3.955299 (0.27945) (0.66648) Adjustment coefficients (standard error in parentheses) D(INF) -0.076693 (0.04998) D(TES) -0.143756 (0.05325) D(EMBI) 0.113888 (0.03663) 2 Cointegrating Equation(s): Log likelihood -68.31342 Normalized cointegrating coefficients (standard error in parentheses) INF TES EMBI 1.000000 0.000000-13.22309 (4.00583) 0.000000 1.000000 6.514422 (2.83447) Adjustment coefficients (standard error in parentheses) D(INF) -0.055604-0.111221 (0.04931) (0.06786)
D(TES) -0.113702-0.207529 (0.05046) (0.06945) D(EMBI) 0.133132 0.160095 (0.03515) (0.04838) El modelo MCE Vector Error Correction Estimates Date: 01/25/18 Time: 17:33 Sample (adjusted): 2008Q3 2017Q3 Included observations: 37 after adjustments Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq: CointEq1 INF(-1) 1.000000 TES(-1) 1.422657 (0.27945) [ 5.09093] EMBI(-1) -3.955299 (0.66648) [-5.93459] C -5.716436 Error Correction: D(INF) D(TES) D(EMBI) CointEq1-0.076693-0.143756 0.113888 (0.04998) (0.05325) (0.03663) [-1.53450] [-2.69979] [ 3.10919] D(INF(-1)) 0.454726 0.086354-0.152902 (0.21954) (0.23390) (0.16090) [ 2.07124] [ 0.36919] [-0.95027] D(INF(-2)) 0.057567 0.138311 0.093022 (0.19661) (0.20947) (0.14410) [ 0.29280] [ 0.66030] [ 0.64555] D(TES(-1)) 0.371378 0.128561 0.105296 (0.17691) (0.18848) (0.12966) [ 2.09922] [ 0.68209] [ 0.81210] D(TES(-2)) 0.241248-0.044005 0.131058 (0.17509) (0.18654) (0.12832) [ 1.37788] [-0.23591] [ 1.02133] D(EMBI(-1)) -0.197184-0.303465 0.339416 (0.22837) (0.24330) (0.16737) [-0.86344] [-1.24727] [ 2.02792]
D(EMBI(-2)) -0.202503-0.081787-0.172533 (0.21871) (0.23301) (0.16029) [-0.92589] [-0.35100] [-1.07636] C 0.019761-0.164645 0.027395 (0.11203) (0.11936) (0.08211) [ 0.17638] [-1.37940] [ 0.33364] R-squared 0.486210 0.248573 0.476984 Adj. R-squared 0.362192 0.067194 0.350739 Sum sq. resids 12.35429 14.02285 6.635986 S.E. equation 0.652694 0.695375 0.478359 F-statistic 3.920476 1.370460 3.778232 Log likelihood -32.20780-34.55148-20.71013 Akaike AIC 2.173395 2.300080 1.551899 Schwarz SC 2.521701 2.648387 1.900205 Mean dependent -0.086757-0.182675-0.004595 S.D. dependent 0.817269 0.719985 0.593668 Determinant resid covariance (dof adj.) 0.021426 Determinant resid covariance 0.010317 Log likelihood -72.88301 Akaike information criterion 5.399082 Schwarz criterion 6.574616 Prueba de normalidad residual del MCE VEC Residual Normality Tests Orthogonalization: Cholesky (Lutkepohl) Null Hypothesis: residuals are multivariate normal Date: 01/30/18 Time: 09:00 Sample: 2007Q4 2017Q3 Included observations: 37 Component Skewness Chi-sq df Prob. 1-0.238462 0.350661 1 0.5537 2 0.755429 3.519154 1 0.0607 3-0.045535 0.012786 1 0.9100 Joint 3.882602 3 0.2744 Component Kurtosis Chi-sq df Prob. 1 2.737621 0.106132 1 0.7446 2 3.415613 0.266299 1 0.6058 3 2.045561 1.404386 1 0.2360 Joint 1.776818 3 0.6200
Component Jarque-Bera df Prob. 1 0.456793 2 0.7958 2 3.785453 2 0.1507 3 1.417172 2 0.4923 Joint 5.659419 6 0.4624 No existen problemas de no normalidad con ninguna de las ecuaciones, ya que las probabilidades resultan ser mayores que 0,05 en todos los casos (0,7958; 0,1507; 0,4923 y 0,4624), y por tanto, se puede aceptar la normalidad de los errores. Prueba de Autocorrelación VEC Residual Serial Correlation LM Tests Null Hypothesis: no serial correlation at lag order h Date: 01/30/18 Time: 09:04 Sample: 2007Q4 2017Q3 Included observations: 37 Lags LM-Stat Prob 1 13.00979 0.1622 2 7.644761 0.5703 Probs from chi-square with 9 df. No hay problema de autocorrelación, ya que 0,5703 > 0,05 y se acepta la hipótesis Ho: No correlación serial. Prueba de Heteroscedasticidad VEC Residual Heteroskedasticity Tests: No Cross Terms (only levels and squares) Date: 01/30/18 Time: 09:05 Sample: 2007Q4 2017Q3 Included observations: 37 Joint test: Chi-sq df Prob. 89.78147 84 0.3130
Individual components: Dependent R-squared F(14,22) Prob. Chi-sq(14) Prob. res1*res1 0.462130 1.350151 0.2566 17.09883 0.2509 res2*res2 0.355191 0.865618 0.6012 13.14208 0.5154 res3*res3 0.293305 0.652203 0.7936 10.85229 0.6976 res2*res1 0.645280 2.858625 0.0134 23.87536 0.0474 res3*res1 0.395976 1.030172 0.4615 14.65112 0.4024 res3*res2 0.446436 1.267320 0.3005 16.51814 0.2828 No hay problemas de heteroscedasticidad por cuanto 0,3130 > 0,05, es decir, se acepta la Ho: la varianza de los errores es homoscedástica.