### HW4, R output ### Problem 1 ############# > da <- read.table("7cityMonth.txt",header=T) > head(da) Nanjing Dongtai Huoshan Hefei Shanghai Anqing Hangzhou 1 2.938710 3.374194 2.106452 2.290323 5.548387 3.577419 5.170968 2 4.185714 3.360714 4.742857 4.346429 5.175000 5.150000 5.614286 3 7.667742 6.129032 8.158065 8.000000 6.896774 8.738710 7.967742 4 14.576667 12.680000 15.090000 15.116667 13.323333 15.756667 14.686667 5 19.303226 18.232258 19.735484 19.967742 18.793548 20.474194 19.922581 6 22.376667 21.580000 22.613333 23.423333 21.853333 23.790000 23.063333 > zt <- da[,c(1,5)] > MTSplot(zt) > dzt <- diffM(zt,12) > MTSplot(dzt) > ccm(dzt) [1] "Covariance matrix:" Nanjing Shanghai Nanjing 2.82 2.5 Shanghai 2.50 2.6 CCM at lag: 0 [,1] [,2] [1,] 1.000 0.924 [2,] 0.924 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: > VARorder(dzt) selected order: aic = 13 selected order: bic = 12 selected order: hq = 12 Summary table: p AIC BIC HQ M(p) p-value [1,] 0 0.0074 0.0074 0.0074 0.0000 0.0000 [2,] 1 -0.0644 -0.0321 -0.0518 44.5131 0.0000 [3,] 2 -0.0528 0.0119 -0.0274 1.7800 0.7761 [4,] 3 -0.0471 0.0499 -0.0091 4.8061 0.3078 [5,] 4 -0.0368 0.0926 0.0139 2.4423 0.6550 [6,] 5 -0.0247 0.1370 0.0386 1.5535 0.8171 [7,] 6 -0.0120 0.1820 0.0639 1.2519 0.8695 [8,] 7 0.0024 0.2288 0.0910 0.3657 0.9852 [9,] 8 0.0103 0.2690 0.1116 3.6119 0.4611 [10,] 9 0.0213 0.3124 0.1352 2.0454 0.7274 [11,] 10 0.0249 0.3483 0.1515 5.7193 0.2211 [12,] 11 -0.0096 0.3462 0.1297 24.3688 0.0001 [13,] 12 -0.5221 -0.1340 -0.3702 258.2978 0.0000 [14,] 13 -0.5343 -0.1139 -0.3697 13.3412 0.0097 > > m1 <- sVARMA(dzt,order=c(1,0,0),sorder=c(0,0,1),s=12,include.mean=F) Number of parameters: 8 initial estimates: 0.1732758 -0.1215617 0.09604486 0.2170985 0.979506 -0.1196647 0.1443495 0.9430257 Coefficient(s): Estimate Std. Error t value Pr(>|t|) [1,] 0.14565 0.10622 1.371 0.1703 [2,] -0.01864 0.10908 -0.171 0.8643 [3,] -0.06502 0.10317 -0.630 0.5285 [4,] 0.25301 0.10575 2.392 0.0167 * [5,] 0.87247 0.04356 20.030 <2e-16 *** [6,] 0.02652 0.04718 0.562 0.5741 [7,] 0.03122 0.04036 0.773 0.4393 [8,] 0.88185 0.04079 21.618 <2e-16 *** --- --- Estimates in matrix form: Regular AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] 0.146 -0.0186 [2,] -0.065 0.2530 Seasonal MA coefficient matrix MA( 12 )-matrix [,1] [,2] [1,] 0.87246530 0.0265216 [2,] 0.03121629 0.8818488 Residuals cov-matrix: resi resi resi 1.526127 1.356899 resi 1.356899 1.422182 ---- aic= -1.0806 bic= -1.0159 > m1a <- refsVARMA(m1,thres=1) Number of parameters: 4 initial estimates: 0.1732758 0.2170985 0.979506 0.9430257 Coefficient(s): Estimate Std. Error t value Pr(>|t|) [1,] 0.18150 0.03076 5.901 3.6e-09 *** [2,] 0.24171 0.03076 7.859 4.0e-15 *** [3,] 0.87247 0.01120 77.932 < 2e-16 *** [4,] 0.88185 0.01143 77.149 < 2e-16 *** --- Estimates in matrix form: Regular AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] 0.182 0.000 [2,] 0.000 0.242 Seasonal MA coefficient matrix MA( 12 )-matrix [,1] [,2] [1,] 0.8724653 0.0000000 [2,] 0.0000000 0.8818488 Residuals cov-matrix: resi resi resi 1.513173 1.342330 resi 1.342330 1.413138 ---- aic= -1.0741 bic= -1.0417 > MTSdiag(m1a) [1] "Covariance matrix:" Nanjing Shanghai Nanjing 1.51 1.34 Shanghai 1.34 1.40 CCM at lag: 0 \ [,1] [,2] [1,] 1.00 0.92 [2,] 0.92 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,] 1.00 1.57 4.00 0.81 [2,] 2.00 4.59 8.00 0.80 [3,] 3.00 10.29 12.00 0.59 [4,] 4.00 13.39 16.00 0.64 [5,] 5.00 15.59 20.00 0.74 [6,] 6.00 27.32 24.00 0.29 [7,] 7.00 28.81 28.00 0.42 [8,] 8.00 32.33 32.00 0.45 [9,] 9.00 36.97 36.00 0.42 [10,] 10.00 39.74 40.00 0.48 [11,] 11.00 46.21 44.00 0.38 [12,] 12.00 50.30 48.00 0.38 [13,] 13.00 55.34 52.00 0.35 [14,] 14.00 56.03 56.00 0.47 [15,] 15.00 63.03 60.00 0.37 [16,] 16.00 71.28 64.00 0.25 [17,] 17.00 76.51 68.00 0.22 [18,] 18.00 83.60 72.00 0.17 [19,] 19.00 87.19 76.00 0.18 [20,] 20.00 94.47 80.00 0.13 [21,] 21.00 103.65 84.00 0.07 [22,] 22.00 104.54 88.00 0.11 [23,] 23.00 108.26 92.00 0.12 [24,] 24.00 111.50 96.00 0.13 Hit Enter to obtain residual plots: > > zt <- da[,6:7] > dzt <- diffM(zt,12) > MTSplot(dzt) > ccm(dzt) [1] "Covariance matrix:" Anqing Hangzhou Anqing 3.02 2.64 Hangzhou 2.64 2.85 CCM at lag: 0 [,1] [,2] [1,] 1.000 0.898 [2,] 0.898 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: > VARorder(dzt) selected order: aic = 12 selected order: bic = 12 selected order: hq = 12 Summary table: p AIC BIC HQ M(p) p-value [1,] 0 0.4534 0.4534 0.4534 0.0000 0.0000 [2,] 1 0.4058 0.4381 0.4185 32.1129 0.0000 [3,] 2 0.4086 0.4733 0.4339 6.3026 0.1777 [4,] 3 0.4145 0.5115 0.4525 4.6822 0.3215 [5,] 4 0.4139 0.5432 0.4645 7.9876 0.0920 [6,] 5 0.4160 0.5777 0.4793 6.5654 0.1607 [7,] 6 0.4237 0.6177 0.4996 3.7400 0.4423 [8,] 7 0.4249 0.6513 0.5135 6.9493 0.1386 [9,] 8 0.4297 0.6884 0.5310 5.1675 0.2705 [10,] 9 0.4429 0.7340 0.5568 0.9554 0.9165 [11,] 10 0.4480 0.7714 0.5746 4.9698 0.2904 [12,] 11 0.4442 0.8000 0.5835 9.2848 0.0544 [13,] 12 -0.0382 0.3499 0.1138 243.5543 0.0000 [14,] 13 -0.0379 0.3825 0.1267 7.2547 0.1230 > m2 <- sVARMA(dzt,order=c(1,0,0),sorder=c(0,0,1),s=12,include.mean=F) Number of parameters: 8 initial estimates: 0.1128605 -0.09828497 0.06137631 0.1424497 0.9680225 -0.1623031 0.1584617 0.96306 Coefficient(s): Estimate Std. Error t value Pr(>|t|) [1,] 0.1993108 0.0823546 2.420 0.0155 * [2,] -0.1303029 0.0884381 -1.473 0.1406 [3,] -0.0003668 0.0747264 -0.005 0.9961 [4,] 0.0998392 0.0800526 1.247 0.2123 [5,] 0.8953379 0.0410968 21.786 <2e-16 *** [6,] -0.0223220 0.0474771 -0.470 0.6382 [7,] 0.0055279 0.0369757 0.150 0.8812 [8,] 0.9028258 0.0408838 22.083 <2e-16 *** --- --- Estimates in matrix form: Regular AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] 0.199311 -0.1303 [2,] -0.000367 0.0998 Seasonal MA coefficient matrix MA( 12 )-matrix [,1] [,2] [1,] 0.895337856 -0.02232198 [2,] 0.005527868 0.90282578 Residuals cov-matrix: resi resi resi 1.702483 1.468231 resi 1.468231 1.543704 ---- aic= -0.7196 bic= -0.6549 > m2a <- refsVARMA(m2,thres=1) Number of parameters: 5 initial estimates: 0.1128605 -0.09828497 0.1424497 0.9680225 0.96306 Coefficient(s): Estimate Std. Error t value Pr(>|t|) [1,] 0.19931 0.03890 5.123 3e-07 *** [2,] -0.12987 0.05668 -2.291 0.0220 * [3,] 0.10063 0.04043 2.489 0.0128 * [4,] 0.89534 0.01140 78.567 <2e-16 *** [5,] 0.91929 0.01014 90.662 <2e-16 *** --- --- Estimates in matrix form: Regular AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] 0.199 -0.130 [2,] 0.000 0.101 Seasonal MA coefficient matrix MA( 12 )-matrix [,1] [,2] [1,] 0.8953379 0.0000000 [2,] 0.0000000 0.9192948 Residuals cov-matrix: resi resi resi 1.714114 1.476197 resi 1.476197 1.549546 ---- aic= -0.7214 bic= -0.681 > MTSdiag(m2a) [1] "Covariance matrix:" Anqing Hangzhou Anqing 1.69 1.46 Hangzhou 1.46 1.53 CCM at lag: 0 [,1] [,2] [1,] 1.000 0.904 [2,] 0.904 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 . . . . 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,] 1.00 2.45 4.00 0.65 [2,] 2.00 4.42 8.00 0.82 [3,] 3.00 8.12 12.00 0.78 [4,] 4.00 13.23 16.00 0.66 [5,] 5.00 14.52 20.00 0.80 [6,] 6.00 19.47 24.00 0.73 [7,] 7.00 26.70 28.00 0.53 [8,] 8.00 30.09 32.00 0.56 [9,] 9.00 32.67 36.00 0.63 [10,] 10.00 34.35 40.00 0.72 [11,] 11.00 36.79 44.00 0.77 [12,] 12.00 43.54 48.00 0.66 [13,] 13.00 44.22 52.00 0.77 [14,] 14.00 44.69 56.00 0.86 [15,] 15.00 47.98 60.00 0.87 [16,] 16.00 53.68 64.00 0.82 [17,] 17.00 56.67 68.00 0.83 [18,] 18.00 59.84 72.00 0.85 [19,] 19.00 62.90 76.00 0.86 [20,] 20.00 67.14 80.00 0.85 [21,] 21.00 71.38 84.00 0.84 [22,] 22.00 72.16 88.00 0.89 [23,] 23.00 72.45 92.00 0.93 [24,] 24.00 72.81 96.00 0.96 Hit Enter to obtain residual plots: > ### Problem 2 > setwd("C:/Users/rst/teaching/mts/sp2017") > da <- read.table("7cityMonth.txt",header=T) > head(da) Nanjing Dongtai Huoshan Hefei Shanghai Anqing Hangzhou 1 2.938710 3.374194 2.106452 2.290323 5.548387 3.577419 5.170968 2 4.185714 3.360714 4.742857 4.346429 5.175000 5.150000 5.614286 3 7.667742 6.129032 8.158065 8.000000 6.896774 8.738710 7.967742 4 14.576667 12.680000 15.090000 15.116667 13.323333 15.756667 14.686667 5 19.303226 18.232258 19.735484 19.967742 18.793548 20.474194 19.922581 6 22.376667 21.580000 22.613333 23.423333 21.853333 23.790000 23.063333 > X <- matrix(da$Shanghai,12,45) > mu <- apply(X,1,mean) > mseries <- rep(mu,45) > sha <- da$Shanghai-mseries > acf(sha,lag=36) > X <- matrix(da$Anqing,12,45) > mu <- apply(X,1,mean) > mseries <- rep(mu,45) > anq <- da$Anqing-mseries > X <- matrix(da$Hangzhou,12,45) > mu <- apply(X,1,mean) > mseries <- rep(mu,45) > han <- da$Hangzhou-mseries > acf(anq) > acf(han) > zt <- cbind(sha,anq,han) > VARorder(zt) Error: could not find function "VARorder" > require(MTS) Loading required package: MTS > VARorder(zt) selected order: aic = 3 selected order: bic = 1 selected order: hq = 2 Summary table: p AIC BIC HQ M(p) p-value [1,] 0 -2.5440 -2.5440 -2.5440 0.0000 0.0000 [2,] 1 -2.9480 -2.8765 -2.9201 228.5460 0.0000 [3,] 2 -2.9776 -2.8346 -2.9217 32.6817 0.0002 [4,] 3 -2.9936 -2.7790 -2.9096 25.4450 0.0025 [5,] 4 -2.9743 -2.6881 -2.8624 7.2068 0.6156 [6,] 5 -2.9648 -2.6072 -2.8249 12.1938 0.2026 [7,] 6 -2.9750 -2.5459 -2.8072 22.0958 0.0086 [8,] 7 -2.9582 -2.4576 -2.7624 8.3537 0.4989 [9,] 8 -2.9471 -2.3749 -2.7233 11.1410 0.2662 [10,] 9 -2.9436 -2.2998 -2.6918 14.8483 0.0952 [11,] 10 -2.9238 -2.2085 -2.6440 6.6999 0.6683 [12,] 11 -2.9162 -2.1294 -2.6085 12.6924 0.1770 [13,] 12 -2.9187 -2.0603 -2.5830 17.5235 0.0411 [14,] 13 -2.9095 -1.9797 -2.5459 11.7724 0.2264 > k1 <- VAR(zt,3) Constant term: Estimates: 0.005110481 0.006006501 0.003394544 Std.Error: 0.04844777 0.05271885 0.05091506 AR coefficient matrix AR( 1 )-matrix [,1] [,2] [,3] [1,] 0.3994 0.215 -0.3511 [2,] 0.1377 0.218 -0.2353 [3,] 0.0808 0.076 0.0228 standard error [,1] [,2] [,3] [1,] 0.135 0.0929 0.164 [2,] 0.147 0.1011 0.178 [3,] 0.142 0.0977 0.172 AR( 2 )-matrix [,1] [,2] [,3] [1,] 0.439 0.00390 -0.402 [2,] 0.434 0.00304 -0.434 [3,] 0.368 -0.04929 -0.309 standard error [,1] [,2] [,3] [1,] 0.142 0.0962 0.173 [2,] 0.154 0.1047 0.188 [3,] 0.149 0.1011 0.182 AR( 3 )-matrix [,1] [,2] [,3] [1,] 0.140 -0.193 0.143 [2,] 0.111 -0.219 0.175 [3,] 0.049 -0.204 0.195 standard error [,1] [,2] [,3] [1,] 0.132 0.0939 0.164 [2,] 0.143 0.1022 0.179 [3,] 0.138 0.0987 0.173 Residuals cov-mtx: [,1] [,2] [,3] [1,] 1.236513 1.123923 1.231359 [2,] 1.123923 1.464141 1.274769 [3,] 1.231359 1.274769 1.365663 det(SSE) = 0.04639213 AIC = -2.970625 BIC = -2.756047 HQ = -2.886704 > MTSdiag(k1) [1] "Covariance matrix:" sha anq han sha 1.24 1.13 1.23 anq 1.13 1.47 1.28 han 1.23 1.28 1.37 CCM at lag: 0 [,1] [,2] [,3] [1,] 1.000 0.835 0.948 [2,] 0.835 1.000 0.902 [3,] 0.948 0.902 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 . . . . . . . . . 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 0.164 9.000 1.00 [2,] 2.000 0.993 18.000 1.00 [3,] 3.000 2.282 27.000 1.00 [4,] 4.000 10.286 36.000 1.00 [5,] 5.000 22.502 45.000 1.00 [6,] 6.000 33.330 54.000 0.99 [7,] 7.000 42.927 63.000 0.98 [8,] 8.000 47.279 72.000 0.99 [9,] 9.000 64.837 81.000 0.91 [10,] 10.000 71.522 90.000 0.92 [11,] 11.000 80.127 99.000 0.92 [12,] 12.000 95.064 108.000 0.81 [13,] 13.000 103.490 117.000 0.81 [14,] 14.000 111.244 126.000 0.82 [15,] 15.000 115.738 135.000 0.88 [16,] 16.000 123.747 144.000 0.89 [17,] 17.000 130.154 153.000 0.91 [18,] 18.000 143.658 162.000 0.85 [19,] 19.000 152.365 171.000 0.84 [20,] 20.000 165.295 180.000 0.78 [21,] 21.000 168.545 189.000 0.85 [22,] 22.000 174.125 198.000 0.89 [23,] 23.000 182.068 207.000 0.89 [24,] 24.000 195.574 216.000 0.84 Hit Enter to obtain residual plots: > k1a <- refVAR(k1,thres=1) Constant term: Estimates: 0 0 0 Std.Error: 0 0 0 AR coefficient matrix AR( 1 )-matrix [,1] [,2] [,3] [1,] 0.3787 0.2046 -0.325 [2,] 0.1606 0.2279 -0.261 [3,] 0.0963 0.0835 0.000 standard error [,1] [,2] [,3] [1,] 0.1290 0.0905 0.155 [2,] 0.1402 0.0987 0.169 [3,] 0.0824 0.0762 0.000 AR( 2 )-matrix [,1] [,2] [,3] [1,] 0.400 0 -0.363 [2,] 0.475 0 -0.467 [3,] 0.388 0 -0.372 standard error [,1] [,2] [,3] [1,] 0.132 0 0.125 [2,] 0.142 0 0.134 [3,] 0.128 0 0.122 AR( 3 )-matrix [,1] [,2] [,3] \[1,] 0.235 -0.140 0.000 [2,] 0.000 -0.232 0.287 [3,] 0.000 -0.220 0.256 standard error [,1] [,2] [,3] [1,] 0.0754 0.0706 0.0000 [2,] 0.0000 0.0990 0.1010 [3,] 0.0000 0.0950 0.0971 Residuals cov-mtx: [,1] [,2] [,3] [1,] 1.238352 1.122525 1.230746 [2,] 1.122525 1.465874 1.275412 [3,] 1.230746 1.275412 1.366663 det(SSE) = 0.04804306 AIC = -2.961583 BIC = -2.802636 HQ = -2.89942 > MTSdiag(k1a) [1] "Covariance matrix:" sha anq han sha 1.24 1.12 1.23 anq 1.12 1.47 1.28 han 1.23 1.28 1.37 CCM at lag: 0 [,1] [,2] [,3] [1,] 1.000 0.833 0.946 [2,] 0.833 1.000 0.901 [3,] 0.946 0.901 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 . . . . . . . . . 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 0.702 9.000 1.00 [2,] 2.000 5.430 18.000 1.00 [3,] 3.000 22.066 27.000 0.73 [4,] 4.000 32.104 36.000 0.65 [5,] 5.000 47.070 45.000 0.39 [6,] 6.000 55.404 54.000 0.42 [7,] 7.000 65.543 63.000 0.39 [8,] 8.000 69.088 72.000 0.58 [9,] 9.000 86.804 81.000 0.31 [10,] 10.000 93.490 90.000 0.38 [11,] 11.000 102.882 99.000 0.37 [12,] 12.000 119.189 108.000 0.22 [13,] 13.000 127.765 117.000 0.23 [14,] 14.000 136.600 126.000 0.24 [15,] 15.000 141.043 135.000 0.34 [16,] 16.000 148.808 144.000 0.37 [17,] 17.000 154.881 153.000 0.44 [18,] 18.000 168.150 162.000 0.35 [19,] 19.000 175.808 171.000 0.38 [20,] 20.000 187.033 180.000 0.34 [21,] 21.000 190.666 189.000 0.45 [22,] 22.000 197.430 198.000 0.50 [23,] 23.000 204.283 207.000 0.54 [24,] 24.000 217.276 216.000 0.46 Hit Enter to obtain residual plots: > ### Problem 3 > g1 <- sVARMA(ddzt,order=c(2,0,2),sorder=c(1,0,1),s=7,include.mean=F) Number of parameters: 24 initial estimates: 0.73557 0.277588 -0.1300863 -0.2448572 0.1404201 0.6208903 -0.07298733 -0.1147411 0.04601783 0.005662857 0.01981644 0.06718089 0.9640656 0.2021145 -0.03307971 -0.2169084 0.00907268 0.9177437 -0.1603777 0.003621249 0.9999987 -0.1111652 0.02563328 0.9923012 Coefficient(s): Estimate Std. Error t value Pr(>|t|) [1,] 0.399384 0.280719 1.423 0.154818 [2,] 0.726932 0.280553 2.591 0.009568 ** [3,] 0.029538 0.156626 0.189 0.850416 [4,] -0.523285 0.139117 -3.761 0.000169 *** [5,] 0.213805 0.123325 1.734 0.082977 . [6,] 0.233011 0.140353 1.660 0.096878 . [7,] -0.019454 0.083173 -0.234 0.815067 [8,] -0.009514 0.074642 -0.127 0.898578 [9,] -0.004331 0.038180 -0.113 0.909680 [10,] 0.056650 0.055948 1.013 0.311278 [11,] 0.045775 0.028105 1.629 0.103374 [12,] 0.014818 0.035694 0.415 0.678034 [13,] 0.611900 0.289741 2.112 0.034696 * [14,] 0.616668 0.279415 2.207 0.027314 * [15,] 0.210862 0.229523 0.919 0.358254 [16,] -0.610364 0.255677 -2.387 0.016975 * [17,] 0.062630 0.121975 0.513 0.607626 [18,] 0.621925 0.138136 4.502 6.72e-06 *** [19,] -0.023812 0.109524 -0.217 0.827885 [20,] 0.241003 0.125984 1.913 0.055752 . [21,] 0.988347 0.005987 165.086 < 2e-16 *** [22,] -0.014872 0.007898 -1.883 0.059704 . [23,] -0.002208 0.004724 -0.467 0.640197 [24,] 0.980797 0.005559 176.449 < 2e-16 *** --- --- Estimates in matrix form: Regular AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] 0.399 0.727 [2,] 0.214 0.233 AR( 2 )-matrix [,1] [,2] [1,] 0.0295 -0.52329 [2,] -0.0195 -0.00951 Seasonal AR coefficient matrix AR( 7 )-matrix [,1] [,2] [1,] -0.00433 0.0566 [2,] 0.04577 0.0148 Regular MA coefficient matrix MA( 1 )-matrix [,1] [,2] [1,] 0.6119 0.617 [2,] 0.0626 0.622 MA( 2 )-matrix [,1] [,2] [1,] 0.2109 -0.610 [2,] -0.0238 0.241 Seasonal MA coefficient matrix MA( 7 )-matrix [,1] [,2] [1,] 0.98834683 -0.01487235 [2,] -0.00220826 0.98079664 Residuals cov-matrix: resi resi resi 0.07033381 0.03911878 resi 0.03911878 0.04438876 ---- aic= -6.4162 bic= -6.3428 > MTSdiag(g1,gof=28) [1] "Covariance matrix:" ºþ.. X.... ºþ.. 0.0703 0.0391 X.... 0.0391 0.0444 CCM at lag: 0 [,1] [,2] [1,] 1.0 0.7 [2,] 0.7 1.0 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 - - . . CCM at lag: 25 . . . . CCM at lag: 26 . . . . CCM at lag: 27 . . . . CCM at lag: 28 + + + + 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 12.7 4.0 0.01 [2,] 2.0 19.4 8.0 0.01 [3,] 3.0 23.0 12.0 0.03 [4,] 4.0 27.1 16.0 0.04 [5,] 5.0 28.2 20.0 0.10 [6,] 6.0 40.0 24.0 0.02 [7,] 7.0 45.7 28.0 0.02 [8,] 8.0 58.5 32.0 0.00 [9,] 9.0 62.0 36.0 0.00 [10,] 10.0 68.7 40.0 0.00 [11,] 11.0 94.7 44.0 0.00 [12,] 12.0 99.7 48.0 0.00 [13,] 13.0 105.7 52.0 0.00 [14,] 14.0 107.1 56.0 0.00 [15,] 15.0 109.6 60.0 0.00 [16,] 16.0 113.6 64.0 0.00 [17,] 17.0 118.3 68.0 0.00 [18,] 18.0 125.8 72.0 0.00 [19,] 19.0 130.3 76.0 0.00 [20,] 20.0 134.3 80.0 0.00 [21,] 21.0 138.0 84.0 0.00 [22,] 22.0 145.7 88.0 0.00 [23,] 23.0 148.7 92.0 0.00 [24,] 24.0 157.6 96.0 0.00 [25,] 25.0 159.5 100.0 0.00 [26,] 26.0 160.5 104.0 0.00 [27,] 27.0 165.3 108.0 0.00 [28,] 28.0 191.9 112.0 0.00 Hit Enter to obtain residual plots: > > > > g2 <- refsVARMA(g1,thres=1) Number of parameters: 15 initial estimates: 0.73557 0.277588 -0.2448572 0.1404201 0.6208903 0.005662857 0.01981644 0.9640656 0.2021145 -0.2169084 0.9177437 0.003621249 0.9999987 -0.1111652 0.9923012 Coefficient(s): Estimate Std. Error t value Pr(>|t|) [1,] 0.6180306 0.0282470 21.880 < 2e-16 *** [2,] 0.7271034 0.1335895 5.443 5.24e-08 *** [3,] -0.5720149 0.0534174 -10.708 < 2e-16 *** [4,] 0.0954553 0.0200690 4.756 1.97e-06 *** [5,] 0.3063977 0.0553486 5.536 3.10e-08 *** [6,] -0.0004511 0.0253120 -0.018 0.985782 [7,] 0.0154974 0.0157156 0.986 0.324077 [8,] 0.9333060 0.0120985 77.142 < 2e-16 *** [9,] 0.6140923 0.1285762 4.776 1.79e-06 *** [10,] -0.6332582 0.1076284 -5.884 4.01e-09 *** [11,] 0.6903999 0.0512561 13.470 < 2e-16 *** [12,] 0.1870869 0.0372363 5.024 5.05e-07 *** [13,] 0.9883468 0.0023702 416.992 < 2e-16 *** [14,] -0.0122458 0.0033655 -3.639 0.000274 *** [15,] 0.9807966 0.0017898 547.987 < 2e-16 *** --- --- Estimates in matrix form: Regular AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] 0.6180 0.727 [2,] 0.0955 0.306 AR( 2 )-matrix [,1] [,2] [1,] 0 -0.572 [2,] 0 0.000 Seasonal AR coefficient matrix AR( 7 )-matrix [,1] [,2] [1,] 0.0000 -0.000451 [2,] 0.0155 0.000000 Regular MA coefficient matrix MA( 1 )-matrix [,1] [,2] [1,] 0.933 0.614 [2,] 0.000 0.690 MA( 2 )-matrix [,1] [,2] [1,] 0 -0.633 [2,] 0 0.187 Seasonal MA coefficient matrix MA( 7 )-matrix [,1] [,2] [1,] 0.9883468 -0.01224581 [2,] 0.0000000 0.98079664 Residuals cov-matrix: resi resi resi 0.06968810 0.03940999 resi 0.03940999 0.04491671 ---- aic= -6.4355 bic= -6.3897 > > g3 <- refsVARMA(g2,thres=1) Number of parameters: 13 initial estimates: 0.73557 0.277588 -0.2448572 0.1404201 0.6208903 0.9640656 0.2021145 -0.2169084 0.9177437 0.003621249 0.9999987 -0.1111652 0.9923012 Coefficient(s): Estimate Std. Error t value Pr(>|t|) [1,] 0.620621 0.027343 22.698 < 2e-16 *** [2,] 0.727103 0.110193 6.598 4.15e-11 *** [3,] -0.566389 0.044095 -12.845 < 2e-16 *** [4,] 0.095277 0.019692 4.838 1.31e-06 *** [5,] 0.309861 0.051592 6.006 1.90e-09 *** [6,] 0.937215 0.010837 86.481 < 2e-16 *** [7,] 0.611145 0.102464 5.965 2.45e-09 *** [8,] -0.627536 0.084601 -7.418 1.19e-13 *** [9,] 0.691881 0.046675 14.824 < 2e-16 *** [10,] 0.184159 0.034261 5.375 7.65e-08 *** [11,] 0.988347 0.002321 425.885 < 2e-16 *** [12,] -0.012054 0.003300 -3.652 0.00026 *** [13,] 0.980797 0.001785 549.502 < 2e-16 *** --- Estimates in matrix form: Regular AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] 0.6206 0.727 [2,] 0.0953 0.310 AR( 2 )-matrix [,1] [,2] [1,] 0 -0.566 [2,] 0 0.000 Seasonal AR coefficient matrix AR( 7 )-matrix [,1] [,2] [1,] 0 0 [2,] 0 0 Regular MA coefficient matrix MA( 1 )-matrix [,1] [,2] [1,] 0.937 0.611 [2,] 0.000 0.692 MA( 2 )-matrix [,1] [,2] [1,] 0 -0.628 [2,] 0 0.184 Seasonal MA coefficient matrix MA( 7 )-matrix [,1] [,2] [1,] 0.9883468 -0.01205448 [2,] 0.0000000 0.98079664 Residuals cov-matrix: resi resi resi 0.06963620 0.03943252 resi 0.03943252 0.04499309 ---- aic= -6.437 bic= -6.3972 > > MTSdiag(g3,gof=28) [1] "Covariance matrix:" ºþ.. X.... ºþ.. 0.0697 0.0395 X.... 0.0395 0.0450 CCM at lag: 0 [,1] [,2] [1,] 1.000 0.704 [2,] 0.704 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 . . . . 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 - - . . CCM at lag: 25 . . . . CCM at lag: 26 . . . . CCM at lag: 27 . . . . CCM at lag: 28 + + + + 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 3.86 4.00 0.43 [2,] 2.00 11.20 8.00 0.19 [3,] 3.00 20.53 12.00 0.06 [4,] 4.00 29.53 16.00 0.02 [5,] 5.00 30.64 20.00 0.06 [6,] 6.00 37.34 24.00 0.04 [7,] 7.00 58.70 28.00 0.00 [8,] 8.00 70.83 32.00 0.00 [9,] 9.00 73.06 36.00 0.00 [10,] 10.00 77.90 40.00 0.00 [11,] 11.00 103.16 44.00 0.00 [12,] 12.00 109.44 48.00 0.00 [13,] 13.00 118.70 52.00 0.00 [14,] 14.00 122.65 56.00 0.00 [15,] 15.00 126.74 60.00 0.00 [16,] 16.00 130.94 64.00 0.00 [17,] 17.00 136.40 68.00 0.00 [18,] 18.00 142.46 72.00 0.00 [19,] 19.00 146.83 76.00 0.00 [20,] 20.00 150.89 80.00 0.00 [21,] 21.00 154.28 84.00 0.00 [22,] 22.00 162.10 88.00 0.00 [23,] 23.00 164.05 92.00 0.00 [24,] 24.00 173.12 96.00 0.00 [25,] 25.00 175.41 100.00 0.00 [26,] 26.00 175.57 104.00 0.00 [27,] 27.00 179.81 108.00 0.00 [28,] 28.00 210.06 112.00 0.00 Hit Enter to obtain residual plots: #### Problem 4 > da <- read.csv("clothing.csv") > da <- da[1:1805,] > m1 <- princomp(da) > names(m1) [1] "sdev" "loadings" "center" "scale" "n.obs" "scores" "call" > score <- m1$scores > zt <- score[,1:3] > MTSplot(zt) > dzt <- diffM(zt,7) > acf(dzt[,3],lag=28) > y <- diffM(dzt[,1:2]) > ddzt <- cbind(y,dzt[2:nrow(dzt),3]) > MTSplot(ddzt) > VARorder(ddzt) selected order: aic = 13 selected order: bic = 8 selected order: hq = 9 Summary table: p AIC BIC HQ M(p) p-value [1,] 0 -2.6441 -2.6441 -2.6441 0.0000 0.0000 [2,] 1 -2.7861 -2.7586 -2.7760 270.5410 0.0000 [3,] 2 -2.8462 -2.7912 -2.8259 124.5070 0.0000 [4,] 3 -2.8701 -2.7875 -2.8396 60.1514 0.0000 [5,] 4 -2.8742 -2.7641 -2.8335 24.9342 0.0030 [6,] 5 -2.8790 -2.7414 -2.8282 26.1740 0.0019 [7,] 6 -2.9123 -2.7472 -2.8514 76.5278 0.0000 [8,] 7 -3.6487 -3.4561 -3.5776 1314.7679 0.0000 [9,] 8 -3.6942 -3.4741 -3.6129 97.6160 0.0000 [10,] 9 -3.7174 -3.4697 -3.6260 58.3140 0.0000 [11,] 10 -3.7163 -3.4411 -3.6147 15.6344 0.0749 [12,] 11 -3.7142 -3.4116 -3.6025 13.9660 0.1235 [13,] 12 -3.7184 -3.3882 -3.5965 24.6686 0.0034 [14,] 13 -3.7327 -3.3750 -3.6006 42.4173 0.0000 ### I started with order=c(2,0,0), but increased it to c(4,0,0) ### > m3 <- sVARMA(ddzt,order=c(4,0,0),sorder=c(1,0,1),s=7,include.mean=F) Number of parameters: 54 Coefficient(s): Estimate Std. Error t value Pr(>|t|) [1,] 0.001150 0.024370 0.047 0.96236 [2,] 0.180452 0.072427 2.492 0.01272 * [3,] 0.076661 0.062978 1.217 0.22350 [4,] -0.215413 0.023835 -9.038 < 2e-16 *** [5,] -0.102545 0.077189 -1.328 0.18402 [6,] 0.032960 0.064939 0.508 0.61176 [7,] -0.160396 0.023919 -6.706 2.00e-11 *** [8,] 0.001203 0.080364 0.015 0.98805 [9,] 0.057591 0.065454 0.880 0.37893 [10,] -0.204081 0.024742 -8.248 2.22e-16 *** [11,] -0.171084 0.073911 -2.315 0.02063 * [12,] 0.120833 0.064465 1.874 0.06088 . [13,] -0.018680 0.007573 -2.467 0.01364 * [14,] -0.424447 0.023170 -18.318 < 2e-16 *** [15,] -0.081132 0.020199 -4.017 5.91e-05 *** [16,] 0.016734 0.007546 2.218 0.02659 * [17,] -0.225435 0.024624 -9.155 < 2e-16 *** [18,] 0.043311 0.020710 2.091 0.03650 * [19,] 0.003831 0.007597 0.504 0.61413 [20,] -0.167630 0.024504 -6.841 7.86e-12 *** [21,] 0.029737 0.020725 1.435 0.15133 [22,] 0.013054 0.007857 1.661 0.09661 . [23,] -0.105258 0.023571 -4.466 7.98e-06 *** [24,] 0.014467 0.020517 0.705 0.48074 [25,] -0.009597 0.009000 -1.066 0.28629 [26,] -0.117054 0.028094 -4.167 3.09e-05 *** [27,] 0.254549 0.024014 10.600 < 2e-16 *** [28,] -0.016812 0.008945 -1.880 0.06017 . [29,] -0.095227 0.029837 -3.192 0.00141 ** [30,] 0.197688 0.024412 8.098 6.66e-16 *** [31,] -0.022591 0.009032 -2.501 0.01237 * [32,] -0.065328 0.029768 -2.195 0.02819 * [33,] 0.126617 0.024422 5.185 2.17e-07 *** [34,] 0.012309 0.009212 1.336 0.18150 [35,] 0.024237 0.028095 0.863 0.38832 [36,] 0.111187 0.024115 4.611 4.01e-06 *** [37,] 0.012979 0.025106 0.517 0.60519 [38,] 0.068474 0.073266 0.935 0.34999 [39,] 0.058055 0.062755 0.925 0.35491 [40,] -0.005057 0.007416 -0.682 0.49533 [41,] -0.030732 0.024361 -1.262 0.20712 [42,] 0.007460 0.014460 0.516 0.60591 [43,] -0.010161 0.008383 -1.212 0.22546 [44,] 0.016954 0.023762 0.713 0.47555 [45,] 0.008117 0.025935 0.313 0.75430 [46,] 0.988307 0.006145 160.832 < 2e-16 *** [47,] -0.058790 0.026204 -2.244 0.02486 * [48,] 0.085913 0.036216 2.372 0.01768 * [49,] 0.001489 0.001789 0.833 0.40512 [50,] 0.974531 0.005241 185.955 < 2e-16 *** [51,] 0.004331 0.007130 0.607 0.54356 [52,] -0.011479 0.004644 -2.472 0.01345 * [53,] 0.017151 0.011641 1.473 0.14066 [54,] 0.923278 0.014249 64.796 < 2e-16 *** --- --- Estimates in matrix form: Regular AR coefficient matrix AR( 1 )-matrix [,1] [,2] [,3] [1,] 0.00115 0.180 0.0767 [2,] -0.01868 -0.424 -0.0811 [3,] -0.00960 -0.117 0.2545 AR( 2 )-matrix [,1] [,2] [,3] [1,] -0.2154 -0.1025 0.0330 [2,] 0.0167 -0.2254 0.0433 [3,] -0.0168 -0.0952 0.1977 AR( 3 )-matrix [,1] [,2] [,3] [1,] -0.16040 0.0012 0.0576 [2,] 0.00383 -0.1676 0.0297 [3,] -0.02259 -0.0653 0.1266 AR( 4 )-matrix [,1] [,2] [,3] [1,] -0.2041 -0.1711 0.1208 [2,] 0.0131 -0.1053 0.0145 [3,] 0.0123 0.0242 0.1112 Seasonal AR coefficient matrix AR( 7 )-matrix [,1] [,2] [,3] [1,] 0.01298 0.0685 0.05806 [2,] -0.00506 -0.0307 0.00746 [3,] -0.01016 0.0170 0.00812 Seasonal MA coefficient matrix MA( 7 )-matrix [,1] [,2] [,3] [1,] 0.988306631 -0.05878954 0.08591291 [2,] 0.001489227 0.97453142 0.00433110 [3,] -0.011478884 0.01715135 0.92327778 Residuals cov-matrix: resi resi resi resi 0.85404190 -0.037293922 -0.018705963 resi -0.03729392 0.086199871 0.001309535 resi -0.01870596 0.001309535 0.122304120 ---- aic= -4.6725 bic= -4.5074 > MTSdiag(m3,gof=28) [1] "Covariance matrix:" Comp.1 Comp.2 Comp.1 0.8522 -0.03748 -0.01815 Comp.2 -0.0375 0.08624 0.00135 -0.0181 0.00135 0.12223 CCM at lag: 0 [,1] [,2] [,3] [1,] 1.0000 -0.1383 -0.0562 [2,] -0.1383 1.0000 0.0132 [3,] -0.0562 0.0132 1.0000 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 . . . . . . . . . CCM at lag: 25 . . . . . . . . . CCM at lag: 26 . . . . . . . - . CCM at lag: 27 + . . . . . . . . CCM at lag: 28 + . . . . . . . . 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 4.4 9.0 0.88 [2,] 2.0 10.9 18.0 0.90 [3,] 3.0 20.4 27.0 0.81 [4,] 4.0 38.1 36.0 0.37 [5,] 5.0 86.3 45.0 0.00 [6,] 6.0 139.6 54.0 0.00 [7,] 7.0 150.6 63.0 0.00 [8,] 8.0 158.8 72.0 0.00 [9,] 9.0 171.9 81.0 0.00 [10,] 10.0 181.0 90.0 0.00 [11,] 11.0 196.4 99.0 0.00 [12,] 12.0 204.8 108.0 0.00 [13,] 13.0 221.4 117.0 0.00 [14,] 14.0 239.9 126.0 0.00 [15,] 15.0 247.0 135.0 0.00 [16,] 16.0 259.1 144.0 0.00 [17,] 17.0 274.1 153.0 0.00 [18,] 18.0 284.5 162.0 0.00 [19,] 19.0 298.6 171.0 0.00 [20,] 20.0 306.8 180.0 0.00 [21,] 21.0 329.6 189.0 0.00 [22,] 22.0 331.6 198.0 0.00 [23,] 23.0 349.5 207.0 0.00 [24,] 24.0 358.5 216.0 0.00 [25,] 25.0 370.5 225.0 0.00 [26,] 26.0 384.8 234.0 0.00 [27,] 27.0 399.9 243.0 0.00 [28,] 28.0 421.1 252.0 0.00 Hit Enter to obtain residual plots: > m3a <- refsVARMA(m3,thres=1) Number of parameters: 38 Coefficient(s): Estimate Std. Error t value Pr(>|t|) [1,] 0.242240 0.070262 3.448 0.000565 *** [2,] 0.053201 0.053864 0.988 0.323311 [3,] -0.223216 0.023581 -9.466 < 2e-16 *** [4,] -0.104194 0.071547 -1.456 0.145309 [5,] -0.172848 0.022877 -7.555 4.17e-14 *** [6,] -0.210309 0.024102 -8.726 < 2e-16 *** [7,] -0.206862 0.068443 -3.022 0.002508 ** [8,] 0.125173 0.052639 2.378 0.017408 * [9,] -0.018922 0.007372 -2.567 0.010266 * [10,] -0.428751 0.022923 -18.704 < 2e-16 *** [11,] -0.069152 0.019304 -3.582 0.000341 *** [12,] 0.016734 0.007466 2.241 0.024996 * [13,] -0.209770 0.024594 -8.529 < 2e-16 *** [14,] 0.048884 0.019499 2.507 0.012175 * [15,] -0.163626 0.023770 -6.884 5.84e-12 *** [16,] 0.041550 0.019147 2.170 0.030003 * [17,] 0.016983 0.007712 2.202 0.027664 * [18,] -0.090539 0.023391 -3.871 0.000109 *** [19,] -0.008469 0.008934 -0.948 0.343157 [20,] -0.117054 0.027478 -4.260 2.05e-05 *** [21,] 0.260163 0.024059 10.814 < 2e-16 *** [22,] -0.016482 0.008924 -1.847 0.064754 . [23,] -0.083130 0.028981 -2.868 0.004125 ** [24,] 0.196176 0.024442 8.026 1.11e-15 *** [25,] -0.019979 0.008927 -2.238 0.025214 * [26,] -0.077645 0.027534 -2.820 0.004802 ** [27,] 0.127846 0.024370 5.246 1.55e-07 *** [28,] 0.014592 0.008911 1.637 0.101530 [29,] 0.099580 0.023700 4.202 2.65e-05 *** [30,] -0.030990 0.023527 -1.317 0.187768 [31,] 0.001009 0.007566 0.133 0.893863 [32,] 0.988307 NA NA NA [33,] -0.051824 0.016846 -3.076 0.002095 ** [34,] -0.040672 NA NA NA [35,] 0.971761 0.005485 177.168 < 2e-16 *** [36,] 0.006310 NA NA NA [37,] 0.017151 0.011902 1.441 0.149569 [38,] 0.922313 0.009579 96.281 < 2e-16 *** --- --- Estimates in matrix form: Regular AR coefficient matrix AR( 1 )-matrix [,1] [,2] [,3] [1,] 0.00000 0.242 0.0532 [2,] -0.01892 -0.429 -0.0692 [3,] -0.00847 -0.117 0.2602 AR( 2 )-matrix [,1] [,2] [,3] [1,] -0.2232 -0.1042 0.0000 [2,] 0.0167 -0.2098 0.0489 [3,] -0.0165 -0.0831 0.1962 AR( 3 )-matrix [,1] [,2] [,3] [1,] -0.173 0.0000 0.0000 [2,] 0.000 -0.1636 0.0416 [3,] -0.020 -0.0776 0.1278 AR( 4 )-matrix [,1] [,2] [,3] [1,] -0.2103 -0.2069 0.1252 [2,] 0.0170 -0.0905 0.0000 [3,] 0.0146 0.0000 0.0996 Seasonal AR coefficient matrix AR( 7 )-matrix [,1] [,2] [,3] [1,] 0.00000 0.000 0 [2,] 0.00000 -0.031 0 [3,] 0.00101 0.000 0 Seasonal MA coefficient matrix MA( 7 )-matrix [,1] [,2] [,3] [1,] 0.988306631 -0.05182412 -0.0406722 [2,] 0.000000000 0.97176130 0.0000000 [3,] 0.006310236 0.01715135 0.9223127 Residuals cov-matrix: resi resi resi resi 0.87245970 -0.038733827 -0.008972650 resi -0.03873383 0.086447334 0.002035884 resi -0.00897265 0.002035884 0.122067467 ---- aic= -4.6667 bic= -4.5505 Warning message: In sqrt(diag(solve(Hessian))) : NaNs produced > ##### Problem 5 > zt <- score[,24:25] > MTSplot(zt) > acf(zt[,1],lag=28) > acf(zt[,2],lag=28) > VARorder(zt) selected order: aic = 5 selected order: bic = 3 selected order: hq = 4 Summary table: p AIC BIC HQ M(p) p-value [1,] 0 -9.1541 -9.1541 -9.1541 0.0000 0.0000 [2,] 1 -9.4523 -9.4401 -9.4478 541.2893 0.0000 [3,] 2 -9.5048 -9.4804 -9.4958 101.6638 0.0000 [4,] 3 -9.5188 -9.4822 -9.5053 32.8705 0.0000 [5,] 4 -9.5236 -9.4749 -9.5056 16.4854 0.0024 [6,] 5 -9.5237 -9.4627 -9.5012 7.9980 0.0917 [7,] 6 -9.5231 -9.4500 -9.4961 6.8649 0.1432 [8,] 7 -9.5223 -9.4370 -9.4908 6.3694 0.1732 [9,] 8 -9.5224 -9.4249 -9.4864 8.1363 0.0867 [10,] 9 -9.5199 -9.4102 -9.4794 3.3503 0.5010 [11,] 10 -9.5176 -9.3957 -9.4726 3.7550 0.4402 [12,] 11 -9.5152 -9.3812 -9.4657 3.6893 0.4497 [13,] 12 -9.5130 -9.3668 -9.4591 3.9971 0.4064 [14,] 13 -9.5116 -9.3532 -9.4531 5.2617 0.2615 > k1 <- VAR(zt,5) Constant term: Estimates: 5.195509e-05 5.692626e-05 Std.Error: 0.002263864 0.002085592 AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] 0.2832 -0.012 [2,] 0.0253 0.299 standard error [,1] [,2] [1,] 0.0236 0.0256 [2,] 0.0218 0.0236 AR( 2 )-matrix [,1] [,2] [1,] 0.15635 -0.0360 [2,] 0.00141 0.0885 standard error [,1] [,2] [1,] 0.0245 0.0268 [2,] 0.0226 0.0247 AR( 3 )-matrix [,1] [,2] [1,] 0.0186 -0.00102 [2,] -0.0177 0.11082 standard error [,1] [,2] [1,] 0.0248 0.0267 [2,] 0.0228 0.0246 AR( 4 )-matrix [,1] [,2] [1,] 0.074954 -0.0207 [2,] 0.000582 0.0199 standard error [,1] [,2] [1,] 0.0245 0.0268 [2,] 0.0226 0.0247 AR( 5 )-matrix [,1] [,2] [1,] 0.0413 -0.0268 [2,] 0.0249 0.0390 standard error [,1] [,2] [1,] 0.0236 0.0257 [2,] 0.0217 0.0237 Residuals cov-mtx: [,1] [,2] [1,] 0.0091687107 0.0001121846 [2,] 0.0001121846 0.0077815556 det(SSE) = 7.133425e-05 AIC = -9.525973 BIC = -9.46505 HQ = -9.503487 > MTSdiag(k1,gof=28) [1] "Covariance matrix:" Comp.24 Comp.25 Comp.24 0.009174 0.000112 Comp.25 0.000112 0.007786 CCM at lag: 0 [,1] [,2] [1,] 1.0000 0.0133 [2,] 0.0133 1.0000 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 . . . . CCM at lag: 25 . . . . CCM at lag: 26 . . + . CCM at lag: 27 . . . . CCM at lag: 28 + . . . 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 0.018 4.000 1.00 [2,] 2.000 0.118 8.000 1.00 [3,] 3.000 0.291 12.000 1.00 [4,] 4.000 0.961 16.000 1.00 [5,] 5.000 2.955 20.000 1.00 [6,] 6.000 4.674 24.000 1.00 [7,] 7.000 10.499 28.000 1.00 [8,] 8.000 20.879 32.000 0.93 [9,] 9.000 25.096 36.000 0.91 [10,] 10.000 28.765 40.000 0.91 [11,] 11.000 32.401 44.000 0.90 [12,] 12.000 36.402 48.000 0.89 [13,] 13.000 40.046 52.000 0.89 [14,] 14.000 49.231 56.000 0.73 [15,] 15.000 58.305 60.000 0.54 [16,] 16.000 60.837 64.000 0.59 [17,] 17.000 62.359 68.000 0.67 [18,] 18.000 64.479 72.000 0.72 [19,] 19.000 65.467 76.000 0.80 [20,] 20.000 69.829 80.000 0.78 [21,] 21.000 72.516 84.000 0.81 [22,] 22.000 77.539 88.000 0.78 [23,] 23.000 78.993 92.000 0.83 [24,] 24.000 81.642 96.000 0.85 [25,] 25.000 83.132 100.000 0.89 [26,] 26.000 95.350 104.000 0.72 [27,] 27.000 97.987 108.000 0.74 [28,] 28.000 108.184 112.000 0.58 Hit Enter to obtain residual plots: > k1a <- refVAR(k1,thres=1) Constant term: Estimates: 0 0 Std.Error: 0 0 AR coefficient matrix AR( 1 )-matrix [,1] [,2] [1,] 0.2861 0.000 [2,] 0.0211 0.301 standard error [,1] [,2] [1,] 0.0233 0.0000 [2,] 0.0201 0.0234 AR( 2 )-matrix [,1] [,2] [1,] 0.161 -0.0437 [2,] 0.000 0.0890 standard error [,1] [,2] [1,] 0.0238 0.0241 [2,] 0.0000 0.0246 AR( 3 )-matrix [,1] [,2] [1,] 0 0.000 [2,] 0 0.116 standard error [,1] [,2] [1,] 0 0.0000 [2,] 0 0.0238 AR( 4 )-matrix [,1] [,2] [1,] 0.079 0 [2,] 0.000 0 standard error [,1] [,2] [1,] 0.0238 0 [2,] 0.0000 0 AR( 5 )-matrix [,1] [,2] [1,] 0.0434 -0.0356 [2,] 0.0212 0.0454 standard error [,1] [,2] [1,] 0.0233 0.0241 [2,] 0.0201 0.0226 Residuals cov-mtx: [,1] [,2] [1,] 0.0091767902 0.0001064415 [2,] 0.0001064415 0.0077872831 det(SSE) = 7.145093e-05 AIC = -9.533203 BIC = -9.496649 HQ = -9.519712 > MTSdiag(k1a,gof=14) [1] "Covariance matrix:" Comp.24 Comp.25 Comp.24 0.009182 0.000106 Comp.25 0.000106 0.007792 CCM at lag: 0 [,1] [,2] [1,] 1.0000 0.0126 [2,] 0.0126 1.0000 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 . . . + 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 0.410 4.000 0.98 [2,] 2.000 0.738 8.000 1.00 [3,] 3.000 1.433 12.000 1.00 [4,] 4.000 3.146 16.000 1.00 [5,] 5.000 5.264 20.000 1.00 [6,] 6.000 7.131 24.000 1.00 [7,] 7.000 13.260 28.000 0.99 [8,] 8.000 23.698 32.000 0.86 [9,] 9.000 27.784 36.000 0.83 [10,] 10.000 31.776 40.000 0.82 [11,] 11.000 35.158 44.000 0.83 [12,] 12.000 39.319 48.000 0.81 [13,] 13.000 42.918 52.000 0.81 [14,] 14.000 52.216 56.000 0.62 Hit Enter to obtain residual plots: >