##### R output for HW3 ##### May 12, 2017 > require(MTS) ##### Problem 1 > da <- read.table("hw3p1.txt") > fix(da) > zt <- as.matrix(da) > colnames(zt) <- c("z1t","z2t") > VMAorder(zt) Q(j,m) Statistics: j Q(j,m) p-value [1,] 1.00 168.04 0.00 [2,] 2.00 86.25 0.20 [3,] 3.00 80.98 0.22 [4,] 4.00 74.45 0.28 [5,] 5.00 69.70 0.29 [6,] 6.00 67.39 0.24 [7,] 7.00 63.69 0.22 [8,] 8.00 62.48 0.15 [9,] 9.00 60.51 0.11 [10,] 10.00 52.47 0.18 [11,] 11.00 46.01 0.24 [12,] 12.00 43.64 0.18 [13,] 13.00 30.25 0.56 [14,] 14.00 20.00 0.86 [15,] 15.00 17.90 0.81 [16,] 16.00 14.58 0.80 [17,] 17.00 9.89 0.87 [18,] 18.00 7.70 0.81 [19,] 19.00 5.39 0.71 [20,] 20.00 2.24 0.69 > m1 <- VMA(zt,1,include.mean=F) Number of parameters: 4 initial estimates: 0.341 0.159 -0.5009 1.1 Par. Lower-bounds: 0.1732 -0.0521 -0.6427 0.9216 Par. Upper-bounds: 0.5087 0.3701 -0.3591 1.2785 Final Estimates: 0.3414631 0.2393855 -0.4595239 1.091897 Coefficient(s): Estimate Std. Error t value Pr(>|t|) [1,] 0.34146 0.06349 5.378 7.53e-08 *** [2,] 0.23939 0.07489 3.197 0.00139 ** [3,] -0.45952 0.04684 -9.811 < 2e-16 *** [4,] 1.09190 0.05447 20.046 < 2e-16 *** --- Estimates in matrix form: MA coefficient matrix MA( 1 )-matrix [,1] [,2] [1,] 0.341 0.239 [2,] -0.460 1.092 Residuals cov-matrix: [,1] [,2] [1,] 1.600675 0.4665200 [2,] 0.466520 0.9571321 ---- aic= 0.3133932 bic= 0.3793595 > MTSdiag(m1,gof=12) [1] "Covariance matrix:" z1t z2t z1t 1.594 0.458 z2t 0.458 0.954 CCM at lag: 0 [,1] [,2] [1,] 1.000 0.371 [2,] 0.371 1.000 Simplified matrix: CCM at lag: 1 . . . . CCM at lag: 2 . . . . CCM at lag: 3 . . . . CCM at lag: 4 . . . . CCM at lag: 5 . . . . CCM at lag: 6 . . . . CCM at lag: 7 . . . . CCM at lag: 8 . . . . CCM at lag: 9 . . . . CCM at lag: 10 . . . . CCM at lag: 11 . . . . CCM at lag: 12 . . . . Hit Enter for p-value plot of individual ccm: Hit Enter to compute MQ-statistics: Ljung-Box Statistics: m Q(m) df p-value [1,] 1.000 0.925 4.000 0.92 [2,] 2.000 6.222 8.000 0.62 [3,] 3.000 10.200 12.000 0.60 [4,] 4.000 13.247 16.000 0.65 [5,] 5.000 13.829 20.000 0.84 [6,] 6.000 18.045 24.000 0.80 [7,] 7.000 21.063 28.000 0.82 [8,] 8.000 22.624 32.000 0.89 [9,] 9.000 27.820 36.000 0.83 [10,] 10.000 34.199 40.000 0.73 [11,] 11.000 37.526 44.000 0.74 [12,] 12.000 43.381 48.000 0.66 Hit Enter to obtain residual plots: > VMApred(m1,2) Forecasts at origin: 200 z1t z2t -0.5675 -1.596 fcst 0.0000 0.000 Standard Errors of predictions: [,1] [,2] [1,] 1.265 0.9783 [2,] 1.385 1.4029 > VARorder(zt) selected order: aic = 9 selected order: bic = 2 selected order: hq = 4 Summary table: p AIC BIC HQ M(p) p-value [1,] 0 1.1783 1.1783 1.1783 0.0000 0.0000 [2,] 1 0.7396 0.8055 0.7663 87.8526 0.0000 [3,] 2 0.5302 0.6621 0.5836 45.2618 0.0000 [4,] 3 0.5134 0.7113 0.5935 10.1950 0.0373 [5,] 4 0.4663 0.7302 0.5731 15.4632 0.0038 [6,] 5 0.4820 0.8118 0.6155 4.2657 0.3712 [7,] 6 0.4829 0.8787 0.6431 6.7752 0.1483 [8,] 7 0.4606 0.9224 0.6475 10.6904 0.0303 [9,] 8 0.4343 0.9620 0.6479 11.2357 0.0240 [10,] 9 0.4284 1.0221 0.6687 7.6858 0.1038 [11,] 10 0.4602 1.1198 0.7271 1.3676 0.8498 [12,] 11 0.4511 1.1768 0.7448 8.0184 0.0909 [13,] 12 0.4577 1.2493 0.7780 5.4024 0.2484 [14,] 13 0.4816 1.3392 0.8287 2.5586 0.6342 > m2 <- VAR(zt,4,include.mean=F) AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] -0.293 -0.165 [2,] 0.478 -0.931 standard error [,1] [,2] [1,] 0.0793 0.0941 [2,] 0.0648 0.0769 AR( 2 )-matrix [,1] [,2] [1,] -0.135 -0.239 [2,] 0.541 -0.670 standard error [,1] [,2] [1,] 0.0976 0.1209 [2,] 0.0798 0.0989 AR( 3 )-matrix [,1] [,2] [1,] 0.029 -0.176 [2,] 0.321 -0.414 standard error [,1] [,2] [1,] 0.1033 0.1163 [2,] 0.0844 0.0951 AR( 4 )-matrix [,1] [,2] [1,] -0.00203 -0.0529 [2,] 0.26848 -0.1525 standard error [,1] [,2] [1,] 0.0906 0.0871 [2,] 0.0741 0.0712 Residuals cov-mtx: [,1] [,2] [1,] 1.6079138 0.5422538 [2,] 0.5422538 1.0744246 det(SSE) = 1.433543 AIC = 0.5201489 BIC = 0.7840143 HQ = 0.6269312 > m2a <- refVAR(m2,thres=1) AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] -0.296 -0.146 [2,] 0.478 -0.931 standard error [,1] [,2] [1,] 0.0755 0.0833 [2,] 0.0648 0.0769 AR( 2 )-matrix [,1] [,2] [1,] -0.143 -0.207 [2,] 0.541 -0.670 standard error [,1] [,2] [1,] 0.0799 0.0893 [2,] 0.0798 0.0989 AR( 3 )-matrix [,1] [,2] [1,] 0.000 -0.133 [2,] 0.321 -0.414 standard error [,1] [,2] [1,] 0.0000 0.0745 [2,] 0.0844 0.0951 AR( 4 )-matrix [,1] [,2] [1,] 0.000 0.000 [2,] 0.268 -0.152 standard error [,1] [,2] [1,] 0.0000 0.0000 [2,] 0.0741 0.0712 Residuals cov-mtx: [,1] [,2] [1,] 1.6132110 0.5422538 [2,] 0.5422538 1.0744246 det(SSE) = 1.439234 AIC = 0.4941113 BIC = 0.7085019 HQ = 0.5808719 > MTSdiag(m2a) [1] "Covariance matrix:" z1t z2t z1t 1.608 0.539 z2t 0.539 1.077 CCM at lag: 0 [,1] [,2] [1,] 1.00 0.41 [2,] 0.41 1.00 Simplified matrix: CCM at lag: 1 . . . . CCM at lag: 2 . . . . CCM at lag: 3 . . . . CCM at lag: 4 . . . . CCM at lag: 5 . . . . CCM at lag: 6 . . . . CCM at lag: 7 . . . . CCM at lag: 8 . . . . CCM at lag: 9 . . - . CCM at lag: 10 . . . . CCM at lag: 11 . . . . CCM at lag: 12 . . . . CCM at lag: 13 . . . . CCM at lag: 14 . . . . CCM at lag: 15 . . . . CCM at lag: 16 . . . . CCM at lag: 17 . . . . CCM at lag: 18 . . . . CCM at lag: 19 . . . . CCM at lag: 20 . . . . CCM at lag: 21 . . . . CCM at lag: 22 . . . . CCM at lag: 23 . . . . CCM at lag: 24 . . . . Hit Enter for p-value plot of individual ccm: Hit Enter to compute MQ-statistics: Ljung-Box Statistics: m Q(m) df p-value [1,] 1.000 0.209 4.000 0.99 [2,] 2.000 0.954 8.000 1.00 [3,] 3.000 3.467 12.000 0.99 [4,] 4.000 9.848 16.000 0.87 [5,] 5.000 20.039 20.000 0.46 [6,] 6.000 23.150 24.000 0.51 [7,] 7.000 24.474 28.000 0.66 [8,] 8.000 26.017 32.000 0.76 [9,] 9.000 31.956 36.000 0.66 [10,] 10.000 37.464 40.000 0.58 [11,] 11.000 41.916 44.000 0.56 [12,] 12.000 47.960 48.000 0.47 [13,] 13.000 51.507 52.000 0.49 [14,] 14.000 53.595 56.000 0.57 [15,] 15.000 55.390 60.000 0.64 [16,] 16.000 58.714 64.000 0.66 [17,] 17.000 59.948 68.000 0.75 [18,] 18.000 62.077 72.000 0.79 [19,] 19.000 64.417 76.000 0.83 [20,] 20.000 66.489 80.000 0.86 [21,] 21.000 71.560 84.000 0.83 [22,] 22.000 74.419 88.000 0.85 [23,] 23.000 79.176 92.000 0.83 [24,] 24.000 83.028 96.000 0.82 Hit Enter to obtain residual plots: > VARpred(m2a,2) orig 200 Forecasts at origin: 200 z1t z2t -0.1558 -1.4644 -0.2821 0.7426 Standard Errors of predictions: [,1] [,2] [1,] 1.270 1.037 [2,] 1.351 1.375 Root mean square errors of predictions: [,1] [,2] [1,] 1.295 1.057 [2,] 1.379 1.482 > ############ Problem 2 > m1a <- VMAe(zt,1,include.mean=F) Number of parameters: 4 initial estimates: 0.3409647 0.1589919 -0.5009143 1.100035 Par. Lower-bounds: 0.1732237 -0.05211085 -0.6427206 0.9215711 Par. Upper-bounds: 0.5087058 0.3700947 -0.359108 1.278499 Final Estimates: 0.3406082 0.2123193 -0.4694092 1.119853 Coefficient(s): Estimate Std. Error t value Pr(>|t|) [1,] 0.34061 0.06398 5.323 1.02e-07 *** [2,] 0.21232 0.07240 2.932 0.00336 ** [3,] -0.46941 0.04634 -10.130 < 2e-16 *** [4,] 1.11985 0.05264 21.272 < 2e-16 *** --- Estimates in matrix form: MA coefficient matrix MA( 1 )-matrix [,1] [,2] [1,] 0.341 0.212 [2,] -0.469 1.120 Residuals cov-matrix: [,1] [,2] [1,] 1.6110684 0.4786888 [2,] 0.4786888 0.9753231 ---- aic= 0.3342872 bic= 0.2942872 > MTSdiag(m1a,gof=12) [1] "Covariance matrix:" z1t z2t z1t 1.598 0.456 z2t 0.456 0.950 CCM at lag: 0 [,1] [,2] [1,] 1.00 0.37 [2,] 0.37 1.00 Simplified matrix: CCM at lag: 1 . . . . CCM at lag: 2 . . . . CCM at lag: 3 . . . . CCM at lag: 4 . . . . CCM at lag: 5 . . . . CCM at lag: 6 . . . . CCM at lag: 7 . . . . CCM at lag: 8 . . . . CCM at lag: 9 . . . . CCM at lag: 10 . . . . CCM at lag: 11 . . . . CCM at lag: 12 . . . . Hit Enter for p-value plot of individual ccm: Hit Enter to compute MQ-statistics: Ljung-Box Statistics: m Q(m) df p-value [1,] 1.000 0.609 4.000 0.96 [2,] 2.000 7.586 8.000 0.47 [3,] 3.000 11.688 12.000 0.47 [4,] 4.000 15.503 16.000 0.49 [5,] 5.000 16.458 20.000 0.69 [6,] 6.000 20.464 24.000 0.67 [7,] 7.000 23.930 28.000 0.69 [8,] 8.000 25.425 32.000 0.79 [9,] 9.000 30.272 36.000 0.74 [10,] 10.000 36.725 40.000 0.62 [11,] 11.000 39.638 44.000 0.66 [12,] 12.000 45.085 48.000 0.59 Hit Enter to obtain residual plots: ##### Problem 3 > da <- read.table("m-dec238-6116.txt",header=T) > fix(da) > yt <- as.matrix(da[,2:4]) > yt <- log(yt+1)*100 > m3 <- VMA(yt,1) Coefficient(s): Estimate Std. Error t value Pr(>|t|) dec2 0.86290 0.20104 4.292 1.77e-05 *** dec3 0.92650 0.21453 4.319 1.57e-05 *** dec8 0.99531 0.27815 3.578 0.000346 *** -0.20472 0.17568 -1.165 0.243890 -0.02665 0.19028 -0.140 0.888620 0.09015 0.07374 1.223 0.221514 -0.20882 0.18757 -1.113 0.265580 -0.04634 0.20268 -0.229 0.819167 0.10589 0.07896 1.341 0.179929 -0.08249 0.23449 -0.352 0.725011 -0.38692 0.25436 -1.521 0.128227 0.18188 0.10011 1.817 0.069232 . --- Estimates in matrix form: Constant term: Estimates: 0.8628979 0.9264984 0.9953095 MA coefficient matrix MA( 1 )-matrix [,1] [,2] [,3] [1,] -0.2047 -0.0266 0.0901 [2,] -0.2088 -0.0463 0.1059 [3,] -0.0825 -0.3869 0.1819 Residuals cov-matrix: [,1] [,2] [,3] [1,] 21.41721 22.50954 25.53188 [2,] 22.50954 24.80825 28.35773 [3,] 25.53188 28.35773 37.83724 ---- aic= 4.92342 bic= 5.00396 > m3a <- refVMA(m3,thres=1.645) Number of parameters: 4 initial estimates: 0.8629 0.9265 0.9953 -0.1819 Par. Lower-bounds: 0.4608 0.4974 0.439 -0.3821 Par. Upper-bounds: 1.265 1.3556 1.5516 0.0183 Final Estimates: 0.8617287 0.9252887 0.9948264 -0.08088782 Coefficient(s): Estimate Std. Error t value Pr(>|t|) 0.86173 0.17984 4.792 1.65e-06 *** 0.92529 0.19351 4.782 1.74e-06 *** 0.99483 0.25972 3.830 0.000128 *** -0.08089 0.01462 -5.534 3.12e-08 *** --- Estimates in matrix form: Constant term: Estimates: 0.8617287 0.9252887 0.9948264 MA coefficient matrix MA( 1 )-matrix [,1] [,2] [,3] [1,] 0 0 0.0000 [2,] 0 0 0.0000 [3,] 0 0 -0.0809 Residuals cov-matrix: [,1] [,2] [,3] [1,] 21.73599 22.84694 26.05427 [2,] 22.84694 25.16583 28.91687 [3,] 26.05427 28.91687 38.80897 ---- aic= 4.944083 bic= 4.97093 > MTSdiag(m3a,gof=12) [1] "Covariance matrix:" dec2 dec3 dec8 dec2 21.8 22.9 26.1 dec3 22.9 25.2 29.0 dec8 26.1 29.0 38.9 CCM at lag: 0 [,1] [,2] [,3] [1,] 1.000 0.977 0.897 [2,] 0.977 1.000 0.925 [3,] 0.897 0.925 1.000 Simplified matrix: CCM at lag: 1 + + + + + + + + . CCM at lag: 2 . . - . . . . . . CCM at lag: 3 . . . . . . . . . CCM at lag: 4 . . . . . . . . . CCM at lag: 5 . . . . . . . . . CCM at lag: 6 . . . . . . . . . CCM at lag: 7 . . . . . . . . . CCM at lag: 8 . . - . . - . . . CCM at lag: 9 . . . . . . . . . CCM at lag: 10 . . . . . . . . . CCM at lag: 11 . . . . . . . . . CCM at lag: 12 . . . . . . . . . Hit Enter for p-value plot of individual ccm: Hit Enter to compute MQ-statistics: Ljung-Box Statistics: m Q(m) df p-value [1,] 1.0 26.6 9.0 0.00 [2,] 2.0 41.7 18.0 0.00 [3,] 3.0 51.2 27.0 0.00 [4,] 4.0 65.2 36.0 0.00 [5,] 5.0 81.8 45.0 0.00 [6,] 6.0 94.5 54.0 0.00 [7,] 7.0 101.7 63.0 0.00 [8,] 8.0 114.0 72.0 0.00 [9,] 9.0 123.5 81.0 0.00 [10,] 10.0 132.8 90.0 0.00 [11,] 11.0 138.2 99.0 0.01 [12,] 12.0 167.6 108.0 0.00 Hit Enter to obtain residual plots: > VMApred(m3a,2) Forecasts at origin: 672 dec2 dec3 dec8 0.8617 0.9253 1.1058 fcst 0.8617 0.9253 0.9948 Standard Errors of predictions: [,1] [,2] [,3] [1,] 4.662 5.017 6.23 [2,] 4.662 5.017 6.25 > ################### Problem 4 > da <- read.csv("FDHBFIN.csv") > da1 <- read.csv("FDHBFRBN.csv") > fix(da) > dim(da) [1] 188 2 > zt <- cbind(da[,2],da1[,2]) > xt <- log(zt) > dxt <- diffM(xt) > VMAorder(dxt) Q(j,m) Statistics: j Q(j,m) p-value [1,] 1.000 240.992 0.00 [2,] 2.000 158.674 0.00 [3,] 3.000 121.929 0.00 [4,] 4.000 100.125 0.01 [5,] 5.000 79.461 0.09 [6,] 6.000 69.614 0.19 [7,] 7.000 67.251 0.14 [8,] 8.000 61.951 0.16 [9,] 9.000 54.547 0.24 [10,] 10.000 52.095 0.19 [11,] 11.000 44.042 0.30 [12,] 12.000 30.905 0.71 [13,] 13.000 25.573 0.78 [14,] 14.000 17.921 0.93 [15,] 15.000 15.817 0.89 [16,] 16.000 14.527 0.80 [17,] 17.000 8.587 0.93 [18,] 18.000 2.826 1.00 [19,] 19.000 0.395 1.00 [20,] 20.000 0.132 1.00 > n1 <- VMA(dxt,4) Number of parameters: 18 Coefficient(s): Estimate Std. Error t value Pr(>|t|) dbfi 0.029482 0.006118 4.819 1.44e-06 *** dbfr 0.020875 0.006517 3.203 0.00136 ** -0.294537 0.072792 -4.046 5.20e-05 *** 0.035876 0.070994 0.505 0.61332 -0.228047 0.073702 -3.094 0.00197 ** -0.085722 0.070835 -1.210 0.22622 -0.172804 0.071388 -2.421 0.01549 * -0.014841 0.071909 -0.206 0.83649 -0.282143 0.071619 -3.940 8.16e-05 *** 0.045628 0.071334 0.640 0.52241 -0.054373 0.085559 -0.635 0.52510 -0.462948 0.086226 -5.369 7.92e-08 *** -0.166191 0.090432 -1.838 0.06610 . -0.302439 0.113622 -2.662 0.00777 ** -0.251177 0.088977 -2.823 0.00476 ** -0.158923 0.131200 -1.211 0.22578 0.002495 0.089325 0.028 0.97771 -0.080744 0.093991 -0.859 0.39031 --- Estimates in matrix form: Constant term: Estimates: 0.02948155 0.02087545 MA coefficient matrix MA( 1 )-matrix [,1] [,2] [1,] -0.2945 0.0359 [2,] -0.0544 -0.4629 MA( 2 )-matrix [,1] [,2] [1,] -0.228 -0.0857 [2,] -0.166 -0.3024 MA( 3 )-matrix [,1] [,2] [1,] -0.173 -0.0148 [2,] -0.251 -0.1589 MA( 4 )-matrix [,1] [,2] [1,] -0.2821 0.0456 [2,] 0.0025 -0.0807 Residuals cov-matrix: [,1] [,2] [1,] 0.0018020779 -0.0002746742 [2,] -0.0002746742 0.0020164233 ---- aic= -12.35371 bic= -12.0427 ## > MTSdiag(n1,gof=12) [1] "Covariance matrix:" dbfi dbfr dbfi 0.001809 -0.000275 dbfr -0.000275 0.002027 CCM at lag: 0 [,1] [,2] [1,] 1.000 -0.144 [2,] -0.144 1.000 Simplified matrix: CCM at lag: 1 . . . . CCM at lag: 2 . . . . CCM at lag: 3 . . . . CCM at lag: 4 . . . . CCM at lag: 5 . . . - CCM at lag: 6 . . . . CCM at lag: 7 . . . . CCM at lag: 8 . . . + CCM at lag: 9 . . . . CCM at lag: 10 . . . . CCM at lag: 11 . . . - CCM at lag: 12 . . . . Hit Enter for p-value plot of individual ccm: Hit Enter to compute MQ-statistics: Ljung-Box Statistics: m Q(m) df p-value [1,] 1.00 3.00 4.00 0.56 [2,] 2.00 4.23 8.00 0.84 [3,] 3.00 5.30 12.00 0.95 [4,] 4.00 6.05 16.00 0.99 [5,] 5.00 18.09 20.00 0.58 [6,] 6.00 22.09 24.00 0.57 [7,] 7.00 24.30 28.00 0.67 [8,] 8.00 30.44 32.00 0.55 [9,] 9.00 32.38 36.00 0.64 [10,] 10.00 38.22 40.00 0.55 [11,] 11.00 48.66 44.00 0.29 [12,] 12.00 49.00 48.00 0.43 Hit Enter to obtain residual plots: ## > VMApred(n1,3) Forecasts at origin: 187 dbfi dbfr [1,] 0.008160 0.0008027 [2,] 0.008589 0.0015491 [3,] 0.012537 0.0102848 Standard Errors of predictions: [,1] [,2] [1,] 0.04245 0.04490 [2,] 0.04435 0.04940 [3,] 0.04544 0.05145 > ############# Problem 5 > VARorder(dxt) selected order: aic = 6 selected order: bic = 1 selected order: hq = 1 Summary table: p AIC BIC HQ M(p) p-value [1,] 0 -12.3988 -12.3988 -12.3988 0.0000 0.0000 [2,] 1 -12.6783 -12.6092 -12.6503 54.9609 0.0000 [3,] 2 -12.6528 -12.5146 -12.5968 2.9103 0.5729 [4,] 3 -12.6897 -12.4824 -12.6057 13.2671 0.0100 [5,] 4 -12.6887 -12.4122 -12.5767 6.8661 0.1431 [6,] 5 -12.6945 -12.3489 -12.5545 7.8963 0.0955 [7,] 6 -12.7532 -12.3385 -12.5852 16.2864 0.0027 [8,] 7 -12.7279 -12.2441 -12.5319 2.7778 0.5957 [9,] 8 -12.6955 -12.1426 -12.4714 1.6164 0.8058 [10,] 9 -12.7017 -12.0797 -12.4496 7.5683 0.1087 [11,] 10 -12.6927 -12.0015 -12.4126 5.1515 0.2721 [12,] 11 -12.6635 -11.9033 -12.3555 2.0494 0.7267 [13,] 12 -12.6334 -11.8041 -12.2974 1.8854 0.7568 [14,] 13 -12.6184 -11.7199 -12.2543 4.0623 0.3976 > n3 <- VAR(dxt,6) Constant term: Estimates: 0.01645353 0.007900423 Std.Error: 0.004617536 0.005413275 AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] 0.1945 -0.0294 [2,] 0.0512 0.4611 standard error [,1] [,2] [1,] 0.0747 0.0634 [2,] 0.0876 0.0744 AR( 2 )-matrix [,1] [,2] [1,] 0.0672 0.0559 [2,] 0.0907 0.0512 standard error [,1] [,2] [1,] 0.0737 0.0683 [2,] 0.0864 0.0801 AR( 3 )-matrix [,1] [,2] [1,] 0.0243 -0.0728 [2,] 0.1085 -0.0631 standard error [,1] [,2] [1,] 0.0727 0.0680 [2,] 0.0852 0.0797 AR( 4 )-matrix [,1] [,2] [1,] 0.190 -0.0417 [2,] -0.197 -0.0215 standard error [,1] [,2] [1,] 0.0725 0.0678 [2,] 0.0850 0.0795 AR( 5 )-matrix [,1] [,2] [1,] -0.1402 0.0812 [2,] -0.0799 -0.2616 standard error [,1] [,2] [1,] 0.0734 0.0676 [2,] 0.0860 0.0793 AR( 6 )-matrix [,1] [,2] [1,] 0.0445 -0.0166 [2,] 0.1417 0.2794 standard error [,1] [,2] [1,] 0.0693 0.0628 [2,] 0.0812 0.0737 Residuals cov-mtx: [,1] [,2] [1,] 0.0013626381 -0.0002247259 [2,] -0.0002247259 0.0018727518 det(SSE) = 2.501381e-06 AIC = -12.64198 BIC = -12.2273 HQ = -12.47395 > n3a <- refVAR(n3,thres=1) Constant term: Estimates: 0.01680316 0.007659259 Std.Error: 0.004144434 0.00501658 AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] 0.194 0.00 [2,] 0.000 0.47 standard error [,1] [,2] [1,] 0.0712 0.0000 [2,] 0.0000 0.0658 AR( 2 )-matrix [,1] [,2] [1,] 0.0718 0 [2,] 0.0916 0 standard error [,1] [,2] [1,] 0.0676 0 [2,] 0.0815 0 AR( 3 )-matrix [,1] [,2] [1,] 0.000 -0.0674 [2,] 0.116 0.0000 standard error [,1] [,2] [1,] 0.0000 0.0551 [2,] 0.0815 0.0000 AR( 4 )-matrix [,1] [,2] [1,] 0.212 0 [2,] -0.207 0 standard error [,1] [,2] [1,] 0.0663 0 [2,] 0.0793 0 AR( 5 )-matrix [,1] [,2] [1,] -0.117 0.0598 [2,] 0.000 -0.2784 standard error [,1] [,2] [1,] 0.0659 0.0551 [2,] 0.0000 0.0708 AR( 6 )-matrix [,1] [,2] [1,] 0.0000 0.000 [2,] 0.0981 0.282 standard error [,1] [,2] [1,] 0.0000 0.0000 [2,] 0.0737 0.0723 Residuals cov-mtx: [,1] [,2] [1,] 0.0013751081 -0.0002162579 [2,] -0.0002162579 0.0018965338 det(SSE) = 2.561172e-06 AIC = -12.73601 BIC = -12.51139 HQ = -12.64499 > MTSdiag(n3a,gof=12) [1] "Covariance matrix:" dbfi dbfr dbfi 0.001383 -0.000217 dbfr -0.000217 0.001907 CCM at lag: 0 [,1] [,2] [1,] 1.000 -0.134 [2,] -0.134 1.000 Simplified matrix: CCM at lag: 1 . . . . CCM at lag: 2 . . . . CCM at lag: 3 . . . . CCM at lag: 4 . . . . CCM at lag: 5 . . . . CCM at lag: 6 . . . . CCM at lag: 7 . . . . CCM at lag: 8 . . . . CCM at lag: 9 . . . . CCM at lag: 10 . . . . CCM at lag: 11 . . . - CCM at lag: 12 . . . . Hit Enter for p-value plot of individual ccm: Hit Enter to compute MQ-statistics: Ljung-Box Statistics: m Q(m) df p-value [1,] 1.000 0.589 4.000 0.96 [2,] 2.000 2.098 8.000 0.98 [3,] 3.000 3.794 12.000 0.99 [4,] 4.000 5.437 16.000 0.99 [5,] 5.000 5.514 20.000 1.00 [6,] 6.000 6.447 24.000 1.00 [7,] 7.000 8.576 28.000 1.00 [8,] 8.000 12.639 32.000 1.00 [9,] 9.000 15.544 36.000 1.00 [10,] 10.000 19.672 40.000 1.00 [11,] 11.000 26.175 44.000 0.98 [12,] 12.000 27.307 48.000 0.99 Hit Enter to obtain residual plots: >