Computes forecasts from a fitted multivariate Threshold Autoregressive (TAR) model.
Usage
# S3 method for class 'mtar'
predict(
object,
...,
newdata,
n.ahead = NULL,
row.names,
credible = 0.95,
out.of.sample = FALSE,
rolling = NULL
)Arguments
- object
An object of class
mtarobtained from a call tomtar().- ...
Additional arguments that may affect the prediction method.
- newdata
An optional
data.framecontaining future values of the threshold series (if included in the fitted model), the exogenous series (if included in the fitted model), and, whenout.of.sample = TRUE, the realized values of the output series.- n.ahead
A positive integer specifying the number of steps ahead to forecast.
- row.names
An optional variable in
newdataspecifying labels for the time- credible
An optional numeric value in \((0,1)\) specifying the level of the required credible intervals. By default,
credibleis set to0.95.- out.of.sample
An optional logical indicator. If
TRUEthen the log-score, Energy-Score (ES), Absolute Error (AE), Absolute Percentage Error (APE), Squared Error (SE), are computed as measures of predictive accuracy. In this case,newdatamust include the observed values of the output series.- rolling
An optional positive integer specifying the rolling-window size used for forecasting with fixed parameters. By default,
rolling = NULL, indicating that rolling-window forecasting is not performed.
References
Nieto, F.H. (2005) Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics - Theory and Methods, 34, 905-930.
Romero, L.V. and Calderon, S.A. (2021) Bayesian estimation of a multivariate TAR model when the noise process follows a Student-t distribution. Communications in Statistics - Theory and Methods, 50, 2508-2530.
Calderon, S.A. and Nieto, F.H. (2017) Bayesian analysis of multivariate threshold autoregressive models with missing data. Communications in Statistics - Theory and Methods, 46, 296-318.
Karlsson, S. (2013) Chapter 15-Forecasting with Bayesian Vector Autoregression. In Elliott, G. and Timmermann, A. Handbook of Economic Forecasting, Volume 2, 791–89, Elsevier.
Vanegas, L.H. and Calderón, S.A. and Rondón, L.M. (2025) Bayesian estimation of a multivariate tar model when the noise process distribution belongs to the class of gaussian variance mixtures. International Journal of Forecasting.
Examples
# \donttest{
###### Example 1: Returns of the closing prices of three financial indexes
data(returns)
fit1 <- mtar(~ COLCAP + BOVESPA | SP500, data=returns, row.names=Date,
subset={Date<="2015-12-07"}, dist="Student-t",
ars=ars(nregim=3,p=c(1,1,2)), n.burnin=100, n.sim=200,
n.thin=2)
p1 <- predict(fit1, newdata=subset(returns,Date>"2015-12-07"), n.ahead=75,
credible=0.8, out.of.sample=TRUE)
with(p1,summary)
#> COLCAP.Mean COLCAP.Lower COLCAP.Upper BOVESPA.Mean BOVESPA.Lower
#> 1 -7.589411e-03 -0.018714818 0.0031440465 -9.714299e-03 -0.0246243674
#> 2 -7.837729e-04 -0.008177396 0.0090916414 -1.715733e-05 -0.0119996635
#> 3 -3.496193e-03 -0.018603009 0.0062566602 -8.408984e-03 -0.0242862765
#> 4 -1.496247e-03 -0.010383864 0.0074713539 1.011381e-03 -0.0156045649
#> 5 6.115571e-03 -0.003394287 0.0164650908 1.089255e-02 -0.0036374408
#> 6 5.255667e-03 -0.003688259 0.0164235197 1.333250e-02 -0.0019368649
#> 7 -1.524151e-03 -0.015262946 0.0098409205 -1.111201e-02 -0.0263925022
#> 8 -5.443799e-03 -0.015502469 0.0098247941 -1.083407e-02 -0.0262977418
#> 9 4.454151e-03 -0.007183341 0.0144940520 1.106011e-02 -0.0044481425
#> 10 5.509470e-03 -0.003473936 0.0169084373 9.666824e-03 -0.0105464427
#> 11 4.453158e-03 -0.003576756 0.0157942624 9.877290e-03 -0.0132126557
#> 12 7.731380e-04 -0.008955003 0.0088818260 -2.088271e-03 -0.0158261525
#> 13 -5.303413e-04 -0.010948600 0.0083024578 -1.863078e-03 -0.0133692533
#> 14 5.227813e-03 -0.006522643 0.0139293776 1.161567e-02 -0.0043627214
#> 15 -1.850578e-03 -0.017698890 0.0070588634 -1.054374e-02 -0.0300970874
#> 16 -6.878931e-03 -0.017782953 0.0039794540 -9.413944e-03 -0.0252370929
#> 17 -5.487508e-04 -0.008524473 0.0089718434 -2.018857e-04 -0.0130407624
#> 18 -6.204858e-03 -0.018610300 0.0052723761 -1.146236e-02 -0.0272300948
#> 19 -6.963238e-03 -0.017459872 0.0033173017 -1.003449e-02 -0.0261315888
#> 20 -8.047500e-03 -0.023909394 0.0001883247 -1.201699e-02 -0.0302815667
#> 21 3.617336e-03 -0.008548523 0.0151775718 1.328195e-02 -0.0009473293
#> 22 -3.408104e-03 -0.018126415 0.0087494589 -1.004037e-02 -0.0272856229
#> 23 2.966233e-03 -0.006230707 0.0141385150 1.081141e-02 -0.0044545604
#> 24 -3.296270e-03 -0.015445600 0.0084395149 -9.813703e-03 -0.0253324787
#> 25 -1.221231e-03 -0.008125142 0.0099599784 -7.164014e-04 -0.0129817165
#> 26 2.685131e-04 -0.007429735 0.0080621392 -5.502987e-04 -0.0180974683
#> 27 -6.222609e-03 -0.018583191 0.0062390775 -1.110656e-02 -0.0262174920
#> 28 -1.367421e-03 -0.010339448 0.0080052008 3.505790e-04 -0.0123300919
#> 29 5.151484e-03 -0.005117672 0.0174979788 1.237984e-02 -0.0080019926
#> 30 -1.966182e-03 -0.015718866 0.0096707092 -8.065291e-03 -0.0235426631
#> 31 3.619240e-03 -0.004535258 0.0163055615 1.153202e-02 -0.0026330872
#> 32 -3.406885e-03 -0.015966110 0.0097693457 -1.106600e-02 -0.0249066242
#> 33 -1.552691e-03 -0.009276484 0.0074110637 -4.291012e-04 -0.0130387355
#> 34 5.219249e-03 -0.004584252 0.0174338137 1.174510e-02 -0.0050316971
#> 35 2.465024e-03 -0.005598513 0.0119004557 8.945811e-05 -0.0123396981
#> 36 -4.032289e-03 -0.015742612 0.0079948801 -1.008536e-02 -0.0326346292
#> 37 -1.354671e-03 -0.010383651 0.0075793439 -3.198675e-04 -0.0115646984
#> 38 7.872993e-04 -0.008389906 0.0098531627 -9.391111e-04 -0.0147825651
#> 39 -4.941881e-03 -0.015056908 0.0093675016 -1.139374e-02 -0.0331709271
#> 40 -6.066334e-03 -0.022395179 0.0037930935 -1.158034e-02 -0.0269032119
#> 41 -1.765779e-03 -0.011206665 0.0096596557 6.618504e-04 -0.0128943155
#> 42 -7.713759e-04 -0.008452473 0.0093162475 -5.281688e-04 -0.0118786835
#> 43 -4.469495e-03 -0.016322007 0.0082209811 -1.056502e-02 -0.0245538855
#> 44 3.091669e-03 -0.006400154 0.0143437351 1.096379e-02 -0.0068487551
#> 45 1.416915e-03 -0.006506057 0.0099883117 -5.409138e-04 -0.0143438706
#> 46 2.907097e-04 -0.007324106 0.0092934332 9.300761e-05 -0.0120040930
#> 47 5.400560e-03 -0.004371520 0.0165656402 1.109871e-02 -0.0034909614
#> 48 1.069844e-04 -0.009143645 0.0090997550 -1.306099e-03 -0.0131302592
#> 49 1.454454e-04 -0.007892689 0.0085800078 -6.328246e-04 -0.0105999297
#> 50 4.806222e-03 -0.006765357 0.0130503799 1.121410e-02 -0.0025135048
#> 51 -3.712897e-03 -0.015903942 0.0095794268 -1.181790e-02 -0.0305990186
#> 52 6.037475e-04 -0.006863622 0.0117098134 6.958025e-04 -0.0138546224
#> 53 5.800845e-03 -0.005299115 0.0167825429 1.150761e-02 -0.0023683829
#> 54 1.560347e-03 -0.006248804 0.0117977117 2.250480e-03 -0.0114724718
#> 55 -4.163585e-03 -0.017155080 0.0075728318 -1.073118e-02 -0.0302818483
#> 56 4.721667e-03 -0.005977784 0.0173891486 1.101385e-02 -0.0019124699
#> 57 1.709322e-03 -0.005889132 0.0119495097 8.920746e-05 -0.0106736913
#> 58 9.746160e-04 -0.008984865 0.0072646621 -1.372613e-04 -0.0118865873
#> 59 -1.781916e-04 -0.010615824 0.0074447835 -3.901340e-05 -0.0133612240
#> 60 6.678902e-05 -0.008761431 0.0085477156 -1.277754e-03 -0.0151986538
#> 61 -4.841937e-03 -0.017410557 0.0056675671 -1.157421e-02 -0.0270426419
#> 62 2.941957e-05 -0.008471371 0.0081122626 1.264995e-03 -0.0145358445
#> 63 1.149815e-04 -0.006709209 0.0104192958 4.721448e-04 -0.0153188099
#> 64 4.073129e-03 -0.007307608 0.0130011518 1.085270e-02 -0.0075142759
#> 65 1.147408e-03 -0.008740510 0.0097168562 -8.856616e-05 -0.0124021493
#> 66 -1.001838e-03 -0.009059477 0.0098878220 -3.526684e-04 -0.0140078387
#> 67 6.723539e-04 -0.012184918 0.0067666617 7.586188e-04 -0.0136334111
#> 68 3.569192e-04 -0.008135038 0.0105372298 5.748017e-04 -0.0113707583
#> 69 1.005147e-03 -0.008737079 0.0122866965 5.294160e-05 -0.0107879717
#> 70 7.981015e-04 -0.008908788 0.0079584070 -1.502983e-04 -0.0163507689
#> 71 -5.197125e-03 -0.016167787 0.0067391074 -1.001373e-02 -0.0236285867
#> 72 -1.319954e-03 -0.012061057 0.0072890648 -1.203162e-03 -0.0121762221
#> 73 5.000077e-03 -0.003319000 0.0189186901 1.294360e-02 -0.0041692429
#> 74 9.746264e-04 -0.009422390 0.0093764627 -6.916854e-04 -0.0169736627
#> 75 -3.213426e-04 -0.007857709 0.0093347903 -2.514891e-03 -0.0178639544
#> BOVESPA.Upper
#> 1 0.0069112882
#> 2 0.0127247655
#> 3 0.0085813528
#> 4 0.0135006118
#> 5 0.0261883947
#> 6 0.0327027453
#> 7 0.0061854090
#> 8 0.0057430959
#> 9 0.0286613493
#> 10 0.0253318967
#> 11 0.0213992447
#> 12 0.0105579879
#> 13 0.0133864689
#> 14 0.0318381876
#> 15 0.0051635699
#> 16 0.0061503690
#> 17 0.0149891341
#> 18 0.0068627458
#> 19 0.0047469395
#> 20 0.0032650879
#> 21 0.0315701713
#> 22 0.0086470544
#> 23 0.0292742476
#> 24 0.0062790790
#> 25 0.0141293800
#> 26 0.0104565775
#> 27 0.0075945742
#> 28 0.0138482948
#> 29 0.0260162279
#> 30 0.0100497732
#> 31 0.0253081838
#> 32 0.0078838688
#> 33 0.0128200159
#> 34 0.0265797171
#> 35 0.0113868199
#> 36 0.0001382463
#> 37 0.0144892913
#> 38 0.0130919426
#> 39 0.0031965361
#> 40 0.0056136980
#> 41 0.0135713182
#> 42 0.0122815306
#> 43 0.0052025579
#> 44 0.0306654355
#> 45 0.0097448696
#> 46 0.0137797940
#> 47 0.0287113588
#> 48 0.0150071368
#> 49 0.0134553808
#> 50 0.0296804114
#> 51 0.0027777879
#> 52 0.0129028476
#> 53 0.0279155694
#> 54 0.0147676329
#> 55 0.0082618697
#> 56 0.0305006054
#> 57 0.0127641001
#> 58 0.0140579092
#> 59 0.0098344777
#> 60 0.0093437064
#> 61 0.0048446013
#> 62 0.0128008714
#> 63 0.0119252103
#> 64 0.0246314918
#> 65 0.0150731266
#> 66 0.0141652645
#> 67 0.0157094404
#> 68 0.0144187180
#> 69 0.0158370433
#> 70 0.0131338738
#> 71 0.0068578224
#> 72 0.0122402815
#> 73 0.0277608532
#> 74 0.0118053529
#> 75 0.0092429002
with(p1,cbind(LS,ES,APE,CR))
#> Log.Score Energy.Score COLCAP.APE BOVESPA.APE COLCAP.CR BOVESPA.CR
#> 1 -4.0920422 0.030983028 174.45838 150.104833 0 0
#> 2 -3.8778849 0.019039855 104.65317 99.835123 0 1
#> 3 -7.3717426 0.009651395 27.27730 3.850268 1 1
#> 4 -6.9240341 0.012010943 159.32618 108.831168 1 1
#> 5 -3.9207816 0.019343196 75.34518 289.975915 0 1
#> 6 -3.8821196 0.021687393 79.45890 317.922765 0 1
#> 7 -5.9173746 0.018099816 115.63123 304.201550 1 1
#> 8 -5.1999188 0.019080544 621.88571 64.244684 1 0
#> 9 -4.4669319 0.027305140 158.00737 167.785160 0 0
#> 10 -6.7645853 0.011430950 345.10625 55.398570 1 1
#> 11 -3.7754866 0.022798574 84.21192 20.784539 0 1
#> 12 -7.2484786 0.008717577 114.32337 Inf 1 1
#> 13 -7.7401074 0.008021218 76.00997 Inf 1 1
#> 14 -6.3321618 0.015976088 251.46619 560.008053 1 1
#> 15 -6.9391821 0.011513611 139.01051 50.873768 1 1
#> 16 -5.4783014 0.021103754 67.27727 66.716001 0 0
#> 17 -6.0193372 0.013470242 104.91257 103.067319 0 1
#> 18 -7.0192951 0.010467790 46.11795 25.328453 1 1
#> 19 -5.7044730 0.019713564 67.01440 61.634825 0 0
#> 20 -7.0002080 0.012150659 19.68304 492.088199 1 1
#> 21 -2.4384916 0.041798593 120.68516 148.442407 0 0
#> 22 -4.5146269 0.019809977 121.30960 30.826330 0 1
#> 23 -3.2229546 0.024421587 89.67721 23.688315 0 1
#> 24 -5.0053585 0.021724346 85.51268 58.854540 0 1
#> 25 -3.3847589 0.024425654 94.57763 95.662960 0 0
#> 26 -4.1055329 0.019004019 98.64630 117.462636 0 1
#> 27 -5.9782171 0.015209058 176.13282 2.153685 0 1
#> 28 -5.3831668 0.014679888 109.88012 81.557634 0 1
#> 29 -4.4613843 0.018271396 78.14695 49.270446 0 1
#> 30 -6.0082729 0.013367442 81.68958 Inf 1 1
#> 31 -6.7648509 0.012297441 41.24717 Inf 1 1
#> 32 -4.0468002 0.031681769 155.17745 147.763806 1 0
#> 33 -6.2550228 0.013442819 115.10239 106.509236 0 1
#> 34 -4.1355872 0.030144004 37.09874 73.867234 1 0
#> 35 -7.6160963 0.007512946 48.42702 97.792151 1 1
#> 36 -3.2686599 0.036710845 68.35586 79.779470 1 0
#> 37 -3.9813936 0.026292696 110.67360 101.259633 0 0
#> 38 -3.6734260 0.029006195 88.44231 103.062183 1 0
#> 39 -6.6311021 0.012716019 192.32465 101.960667 1 1
#> 40 -6.8910674 0.013453443 240.06921 Inf 1 1
#> 41 -7.5767423 0.008925092 153.82647 Inf 1 1
#> 42 -7.7559973 0.007624641 126.26752 Inf 1 1
#> 43 -5.9080226 0.015576250 180.68069 60.221845 1 0
#> 44 -7.2363148 0.010536022 64.62324 11.433046 1 1
#> 45 -7.4280010 0.008833612 101.61118 107.586599 1 1
#> 46 -4.4178948 0.020682207 103.53821 99.559135 0 0
#> 47 -3.9081412 0.021149675 80.30505 32.918491 0 1
#> 48 -7.6970493 0.008172726 94.82022 64.570872 1 1
#> 49 -7.8423579 0.007292363 118.71715 139.940507 1 1
#> 50 -4.3290176 0.026400278 312.41721 71.900275 1 0
#> 51 -7.2004536 0.010727048 31.87459 29.022587 1 1
#> 52 -7.0751514 0.011099407 150.47308 106.745061 1 1
#> 53 -5.9097261 0.015775973 40.09133 345.683054 1 0
#> 54 -7.2275287 0.010603432 70.37956 131.862064 1 1
#> 55 -3.0494647 0.035501834 106.59089 137.705104 1 0
#> 56 -6.1422835 0.018559177 48.09711 63.958875 1 0
#> 57 -4.5980292 0.020350262 89.73875 99.485504 0 0
#> 58 -0.6412836 0.048495849 93.33317 100.274735 0 0
#> 59 -2.1861248 0.036181332 59.51158 100.099278 1 0
#> 60 -6.7152085 0.010946461 99.29413 138.963807 0 1
#> 61 -6.7155680 0.011827060 49.77012 295.353662 1 1
#> 62 -7.1252340 0.010549599 97.67612 114.148750 1 1
#> 63 -5.8465650 0.016281125 95.30724 97.440432 1 0
#> 64 -7.0683523 0.011075991 62.56025 696.724538 1 1
#> 65 -6.3402289 0.014919405 135.27923 99.434490 1 0
#> 66 -2.6824647 0.033380557 90.15012 99.025749 0 0
#> 67 -6.6221932 0.012750401 191.90290 94.317512 1 1
#> 68 0.9201778 0.060143203 95.99239 99.100094 1 0
#> 69 -6.3550861 0.011054104 90.59236 102.716466 1 1
#> 70 -7.4564175 0.008925763 85.25744 103.913488 1 1
#> 71 -5.3974671 0.017473141 265.97879 61.809839 1 0
#> 72 -3.7602582 0.024433581 88.91699 105.266880 1 0
#> 73 -6.5919004 0.012666585 213.06841 108.384216 0 1
#> 74 -5.6392862 0.014241992 93.65580 137.704284 0 1
#> 75 -3.4787180 0.022579340 102.58633 89.328648 0 0
plot(p1,last=100)
###### Example 2: Rainfall and two river flows in Colombia
data(riverflows)
fit2 <- mtar(~ Bedon + LaPlata | Rainfall, data=riverflows, row.names=Date,
subset={Date<="2009-02-13"}, dist="Laplace",
ars=ars(nregim=3,p=5), n.burnin=1000, n.sim=2000, n.thin=2)
p2 <- predict(fit2, newdata=subset(riverflows,Date>"2009-02-13"), n.ahead=60,
credible=0.8, out.of.sample=TRUE)
with(p2,summary)
#> Bedon.Mean Bedon.Lower Bedon.Upper LaPlata.Mean LaPlata.Lower LaPlata.Upper
#> 1 13.501455 7.989354 19.002033 30.35685 8.255682 50.55831
#> 2 15.265672 8.757578 21.772893 35.91165 13.237111 58.68436
#> 3 12.926787 8.566590 18.499977 29.57690 15.371273 47.38782
#> 4 11.288721 7.410766 15.405806 24.78058 13.555100 35.54616
#> 5 11.117279 6.867805 15.853844 24.49393 14.179204 36.93192
#> 6 10.168799 6.694966 14.287128 22.47161 12.022664 31.62910
#> 7 9.520005 5.824334 12.669107 21.11879 12.073384 29.55184
#> 8 8.936109 5.532213 12.067328 19.89678 11.294555 28.20266
#> 9 8.375637 5.037146 11.428044 18.72746 10.306594 26.12041
#> 10 7.954628 4.704687 10.995714 18.03046 9.352619 25.08063
#> 11 7.704590 4.932103 10.964335 17.23194 9.426795 23.96495
#> 12 7.403089 4.578809 10.379184 16.61485 9.797654 24.35154
#> 13 7.197758 4.098751 9.892007 16.32486 9.425076 23.91195
#> 14 8.041580 3.929093 11.743820 18.33107 8.939828 27.43289
#> 15 7.544271 4.298864 10.967150 17.12028 8.352303 24.92580
#> 16 8.239683 3.877416 12.371440 19.06873 9.786731 30.02317
#> 17 8.413851 4.591510 13.476292 20.05996 8.463784 29.74293
#> 18 12.049246 6.466860 18.834601 29.32089 8.184178 53.48126
#> 19 14.534213 7.887396 22.091615 35.43031 11.526782 60.39484
#> 20 12.816345 7.441717 19.367954 30.08302 14.500552 48.36309
#> 21 11.741378 6.020794 16.800055 27.53833 13.380515 41.68418
#> 22 10.265105 5.466062 14.163213 23.51925 12.604410 34.52243
#> 23 9.519027 5.799869 13.243130 21.39965 11.780273 30.57434
#> 24 9.070295 5.626025 12.852304 20.65624 11.558753 29.89974
#> 25 8.579058 5.282735 12.018842 19.58388 10.335465 27.54129
#> 26 8.197857 4.792286 11.484575 18.72621 9.665226 26.30586
#> 27 8.837458 4.212756 12.745147 20.37970 11.222673 31.53113
#> 28 8.215030 4.506003 11.555021 18.83383 10.710434 28.01961
#> 29 7.796039 4.398508 10.876729 17.52301 9.553069 25.03141
#> 30 8.344620 4.640917 12.722382 19.40167 9.942099 30.02066
#> 31 8.794186 3.945462 13.173544 20.37601 10.308366 31.30006
#> 32 9.149795 4.795709 14.162211 20.82145 10.655285 32.23714
#> 33 12.796211 6.302876 18.689489 31.26652 10.208118 54.79187
#> 34 14.979526 8.239432 22.133030 36.47233 11.250672 59.96011
#> 35 13.309487 7.142568 19.290854 30.88055 13.724211 47.19745
#> 36 15.338190 8.025659 22.658448 34.61642 11.179457 60.29772
#> 37 16.616361 8.918776 24.278144 38.39987 11.691493 65.14720
#> 38 18.098893 9.552530 25.535805 40.77195 14.250164 67.89504
#> 39 15.909198 8.453796 21.916510 34.44541 16.640897 53.99288
#> 40 14.709292 8.656947 20.637360 31.55910 15.083463 45.10905
#> 41 17.012504 9.959624 24.166761 37.45742 10.848521 62.63834
#> 42 15.596989 9.126953 22.260445 32.88393 14.845282 51.64647
#> 43 18.139420 10.721946 25.626647 39.24173 14.703989 64.97089
#> 44 19.243480 11.484786 26.750324 42.08758 17.006789 69.10101
#> 45 17.036016 10.410451 23.965908 35.42811 18.237983 54.27070
#> 46 14.529143 9.318495 20.181342 30.15588 17.797651 44.60006
#> 47 12.823312 7.791087 16.672056 26.63391 14.472269 36.32432
#> 48 11.680873 7.916694 15.956407 24.37061 14.316303 34.29856
#> 49 10.967702 7.244314 14.858732 23.23655 14.273037 32.61994
#> 50 10.276467 6.418444 13.890036 22.12461 13.098068 30.50458
#> 51 9.608892 6.107081 13.157449 20.67521 11.353034 28.16579
#> 52 13.661853 8.219688 19.796683 32.54316 10.495731 54.42887
#> 53 15.882468 9.216545 22.885191 37.82593 14.721622 63.46319
#> 54 14.148074 7.990652 19.950420 31.69943 15.292989 49.59329
#> 55 12.726591 7.199533 18.371830 28.59630 14.388540 42.21108
#> 56 12.134518 6.720269 17.355505 27.25265 15.322659 40.72352
#> 57 15.325149 9.335060 22.260779 35.63692 13.779081 59.29138
#> 58 14.126188 7.828054 19.803182 31.13434 14.970778 48.54342
#> 59 12.097998 7.429437 16.969705 26.16860 14.789686 38.49918
#> 60 10.869430 7.078000 15.317335 23.69886 14.204530 34.31835
with(p2,cbind(LS,ES,APE,CR))
#> Log.Score Energy.Score Bedon.APE LaPlata.APE Bedon.CR LaPlata.CR
#> 1 6.720491 10.477652 18.8508344 18.241706 1 1
#> 2 8.269662 25.041256 7.7602913 44.175888 1 0
#> 3 5.760879 7.492268 11.4378219 9.578421 1 1
#> 4 4.590936 5.090994 1.5964208 7.801094 1 1
#> 5 6.790677 10.732445 3.1287441 32.893354 1 1
#> 6 4.628800 4.975723 7.3879894 13.136416 1 1
#> 7 5.278370 7.007633 10.1038287 26.645394 1 1
#> 8 4.741045 5.259700 19.2763388 18.722299 1 1
#> 9 4.334467 3.816486 4.0451793 7.564342 1 1
#> 10 4.833618 4.871628 0.6660064 19.935803 1 1
#> 11 4.964254 4.334381 15.9631213 16.023671 1 1
#> 12 4.910398 3.821955 33.5333436 5.704607 1 1
#> 13 5.309914 4.314515 31.1783852 14.841620 1 1
#> 14 6.320366 6.536398 48.0954008 22.260094 1 1
#> 15 4.318744 3.894103 0.1629142 6.954974 1 1
#> 16 4.673221 4.955213 6.2636475 13.979232 1 1
#> 17 5.212284 5.618511 23.5104422 10.406623 1 1
#> 18 8.413858 32.066878 39.6934621 54.939461 0 0
#> 19 6.802840 12.372289 17.1169426 18.250322 1 1
#> 20 5.661318 8.403159 24.4305301 20.235891 1 1
#> 21 5.432889 7.487734 20.7587941 23.103854 1 1
#> 22 4.977150 5.566834 7.7135923 17.127762 1 1
#> 23 4.783891 5.005822 3.9195098 21.175849 1 1
#> 24 4.811010 5.143221 2.3273356 26.337884 1 1
#> 25 4.334030 3.980949 0.7283261 3.290530 1 1
#> 26 5.133537 6.308714 9.7748549 26.187577 1 1
#> 27 5.048323 5.041116 20.5327003 5.078234 1 1
#> 28 6.856842 6.921846 42.3255439 25.469608 1 1
#> 29 4.391759 3.991020 1.4887574 11.320807 1 1
#> 30 4.635884 4.855631 10.1395694 8.049055 1 1
#> 31 4.876024 5.056597 9.2175481 4.517291 1 1
#> 32 6.026179 6.102273 65.0395886 5.997986 1 1
#> 33 6.723043 16.010294 17.0692756 34.807099 1 1
#> 34 6.238298 11.052731 17.1486414 5.743497 1 1
#> 35 5.568589 8.237441 5.9065537 19.091993 1 1
#> 36 7.494783 13.509394 32.4308804 16.368250 0 1
#> 37 6.022236 11.832082 8.0953489 7.397045 1 1
#> 38 6.370478 14.798582 18.2208705 22.970053 1 1
#> 39 5.980578 10.511154 8.6203429 20.869713 1 1
#> 40 6.731908 10.343095 10.0994923 24.155017 1 1
#> 41 6.406752 11.406098 18.2244871 4.489356 1 1
#> 42 7.010686 11.860296 8.9175201 25.500828 1 1
#> 43 7.612993 20.968200 6.2077570 36.910395 1 1
#> 44 6.351249 12.133140 22.4139960 12.203628 1 1
#> 45 6.126329 8.690318 24.5322841 4.822872 1 1
#> 46 5.311350 6.738316 1.3806465 12.560782 1 1
#> 47 5.635609 7.739708 3.1471902 23.112260 1 1
#> 48 5.211093 5.669109 2.8245899 16.194606 1 1
#> 49 4.659819 4.542936 0.1120000 9.161277 1 1
#> 50 5.054455 5.513449 0.2284776 18.808781 1 1
#> 51 4.338645 3.948926 1.6168820 5.485763 1 1
#> 52 5.993946 11.027678 31.3639742 28.832777 1 1
#> 53 6.715459 11.296844 19.9582194 10.534686 1 1
#> 54 6.052322 8.147042 24.5429066 5.233394 1 1
#> 55 5.695696 7.081976 13.9354626 11.739820 1 1
#> 56 5.202480 6.052848 14.5846851 8.274323 1 1
#> 57 7.282101 11.883393 33.7273053 16.599763 1 1
#> 58 5.623967 7.723646 13.4926459 6.369452 1 1
#> 59 5.048340 5.522780 5.5671751 4.424412 1 1
#> 60 4.751571 4.780066 1.8118320 8.215107 1 1
plot(p2,last=100)
###### Example 3: Temperature, precipitation, and two river flows in Iceland
data(iceland.rf)
fit3 <- mtar(~ Jokulsa + Vatnsdalsa | Temperature | Precipitation,
data=iceland.rf, subset={Date<="1974-11-06"}, row.names=Date,
ars=ars(nregim=2,p=15,q=4,d=2), n.burnin=1000, n.sim=2000,
n.thin=2, dist="Slash")
p3 <- predict(fit3, newdata=subset(iceland.rf,Date>"1974-11-06"), n.ahead=55,
credible=0.8, out.of.sample=TRUE)
with(p3,summary)
#> Jokulsa.Mean Jokulsa.Lower Jokulsa.Upper Vatnsdalsa.Mean Vatnsdalsa.Lower
#> 1 25.339131 25.353610 28.61864 6.6143681 6.8190044
#> 2 27.002598 23.570123 29.49816 6.7669800 4.9593423
#> 3 27.013603 22.766854 31.80299 8.4442479 4.2337470
#> 4 -187.636991 21.798205 33.81715 3.8999376 2.9745988
#> 5 -159.862953 19.872514 34.25589 18.7169203 1.5417062
#> 6 -73.226021 19.836837 36.15158 7.2724687 -0.1540777
#> 7 -53.011453 17.036575 34.69734 5.4819255 -0.6584208
#> 8 -41.135414 15.448743 35.29546 5.0780691 -1.3974717
#> 9 -30.359860 15.231763 37.18139 6.3413222 -3.0121590
#> 10 -666.867566 16.310505 38.91471 -144.8614829 -3.5288706
#> 11 -589.638504 16.203049 40.85031 -134.0230453 -3.9159423
#> 12 -457.454057 12.686292 37.78426 -108.6353570 -4.3964113
#> 13 -349.967994 13.215064 39.36333 -72.3371223 -6.8679810
#> 14 -272.212531 11.640911 38.13309 -51.2663937 -4.9836105
#> 15 -198.030278 10.933819 37.95909 -34.4210958 -6.6851991
#> 16 -158.735448 13.495525 41.31291 -33.5510176 -6.2102751
#> 17 -134.446697 13.085062 41.44992 -17.6700975 -7.5289064
#> 18 -113.200169 13.785933 42.92194 -4.2782541 -8.8073471
#> 19 -96.645838 9.697880 39.19277 -5.1973223 -10.0935378
#> 20 -83.646266 9.776235 39.32782 5.3188686 -9.4871900
#> 21 -66.242191 9.710060 40.03321 10.5927513 -10.3623815
#> 22 -61.121261 10.188352 39.91153 7.1665847 -12.1179944
#> 23 -42.141521 9.706105 39.96764 19.8606779 -12.0693272
#> 24 -36.587424 11.120871 40.75396 27.9304570 -10.9794438
#> 25 -23.357208 10.105260 40.32454 25.3623195 -10.3710478
#> 26 -18.220187 11.529278 44.41073 16.1423543 -11.9499377
#> 27 -3.231586 9.479286 43.31186 22.4622440 -12.7940910
#> 28 3.260770 11.421725 45.90956 19.7518799 -14.8255347
#> 29 8.576058 7.863118 42.14305 18.3645236 -14.7726559
#> 30 19.676362 7.633864 42.22607 13.8685260 -16.7940979
#> 31 27.518624 7.219054 41.40026 6.6983183 -12.3902090
#> 32 28.163312 7.794921 42.75799 3.6430914 -14.4399503
#> 33 28.740295 9.842258 47.23630 -3.9138159 -17.4650094
#> 34 21.765108 9.826302 45.57978 -5.1988049 -16.8028744
#> 35 26.292940 6.194154 41.59957 -5.7591754 -17.4819785
#> 36 30.820318 9.530639 44.10572 -6.2595339 -12.6827792
#> 37 25.903857 9.514188 43.60149 -4.5047049 -13.1514757
#> 38 21.463134 7.160920 43.85108 -6.5550584 -13.5384821
#> 39 23.404700 7.884026 42.92710 -4.7057812 -13.4889031
#> 40 14.670758 10.143344 45.89183 0.7663577 -16.4385537
#> 41 20.981075 6.672537 44.67700 4.2067500 -16.4633398
#> 42 25.491041 6.490574 44.53224 5.6742480 -18.1067003
#> 43 26.869898 9.276865 46.64245 3.8440303 -16.0244748
#> 44 24.948241 4.553324 43.01574 17.2490595 -19.7457618
#> 45 28.153508 7.839154 48.30550 15.1686906 -15.2670315
#> 46 29.397051 8.146278 48.26700 14.5491936 -18.3870964
#> 47 33.507095 7.059934 46.23943 17.1782558 -16.5236687
#> 48 33.897500 6.344495 43.92205 11.9450188 -21.9842322
#> 49 30.812167 7.642792 46.49500 7.7898953 -20.7106349
#> 50 30.426397 6.610076 43.75327 4.0285141 -20.3857583
#> 51 -2.127945 7.379379 45.61777 24.5284069 -18.9408338
#> 52 16.350446 7.385427 46.52833 29.6249932 -18.7791642
#> 53 10.486376 8.456797 47.55017 21.3448470 -17.5946809
#> 54 11.241271 6.013528 44.96582 18.7552760 -18.5597927
#> 55 14.825362 4.363356 43.34902 16.3487525 -20.9769686
#> Vatnsdalsa.Upper
#> 1 8.905219
#> 2 9.334984
#> 3 11.653091
#> 4 12.852128
#> 5 14.344995
#> 6 14.331724
#> 7 14.942303
#> 8 16.276342
#> 9 16.890521
#> 10 17.757770
#> 11 18.152068
#> 12 18.400967
#> 13 17.274415
#> 14 21.069311
#> 15 18.884856
#> 16 21.371205
#> 17 21.368490
#> 18 21.308198
#> 19 20.956803
#> 20 22.163175
#> 21 22.544516
#> 22 20.501425
#> 23 21.919793
#> 24 23.682807
#> 25 24.788119
#> 26 25.241742
#> 27 27.107322
#> 28 24.701794
#> 29 25.307765
#> 30 23.872798
#> 31 28.089711
#> 32 26.553929
#> 33 24.964807
#> 34 25.822750
#> 35 25.692511
#> 36 30.750241
#> 37 30.142044
#> 38 30.643491
#> 39 29.659612
#> 40 29.267769
#> 41 29.983249
#> 42 28.332545
#> 43 30.827779
#> 44 28.469633
#> 45 34.341049
#> 46 30.551721
#> 47 32.186273
#> 48 26.543183
#> 49 27.791885
#> 50 28.179666
#> 51 28.225296
#> 52 28.522941
#> 53 32.878352
#> 54 32.421732
#> 55 29.637647
with(p3,cbind(LS,ES,APE,CR))
#> Log.Score Energy.Score Jokulsa.APE Vatnsdalsa.APE Jokulsa.CR Vatnsdalsa.CR
#> 1 5.207869 5.786823 12.623686 4.139593 0 1
#> 2 5.754766 9.099345 10.587423 7.301644 0 1
#> 3 4.268312 11.020779 4.881681 34.035681 1 1
#> 4 5.500519 123.025414 774.953206 24.419815 1 1
#> 5 4.083707 112.480599 662.897721 206.834759 1 1
#> 6 3.851538 122.722656 374.254760 31.747622 1 1
#> 7 4.636393 105.795668 294.181145 9.858226 1 1
#> 8 4.548883 89.263610 250.679173 4.905073 1 1
#> 9 4.048425 76.911622 213.707339 18.751353 1 1
#> 10 4.265174 396.071349 2645.296053 2812.761852 1 1
#> 11 4.196855 353.879004 2350.528642 2697.345840 1 1
#> 12 3.922593 282.642619 1846.007852 2002.545656 1 1
#> 13 3.953818 225.924664 1435.755702 1410.455114 1 1
#> 14 4.157994 186.963371 1159.192728 1028.739016 1 1
#> 15 4.656990 147.953253 905.001130 767.075500 1 1
#> 16 4.571435 127.350276 745.266047 796.079203 1 1
#> 17 4.073351 117.874305 613.155334 420.110462 1 1
#> 18 4.115897 114.044604 523.970670 170.135313 1 1
#> 19 4.159000 108.743809 461.969432 188.090209 1 1
#> 20 4.119922 122.852918 413.281894 6.849937 1 1
#> 21 4.276756 115.666382 352.832788 91.897669 1 1
#> 22 4.479139 106.947973 333.287254 38.887301 1 1
#> 23 4.446614 89.702641 263.974789 298.009577 1 1
#> 24 4.860939 83.283461 242.363517 523.447701 1 1
#> 25 4.419641 70.466107 194.947999 426.189202 1 1
#> 26 4.503421 64.029953 172.302330 212.836324 1 1
#> 27 4.401795 67.736583 112.574266 335.314806 1 1
#> 28 4.468975 64.567548 87.060438 282.788370 1 1
#> 29 4.439908 61.158215 66.630124 255.901620 1 1
#> 30 4.456178 61.819413 24.899381 168.769884 1 1
#> 31 4.577683 63.187943 9.200889 38.969258 1 1
#> 32 4.708405 60.013128 7.493559 21.653947 1 1
#> 33 4.939657 58.080762 14.048789 202.455913 1 1
#> 34 4.988199 54.071526 13.630525 225.574997 1 1
#> 35 4.565759 54.723159 4.337065 223.853234 1 1
#> 36 4.825325 55.411946 25.285844 234.613632 1 1
#> 37 4.891902 52.719973 5.300231 204.517515 1 1
#> 38 5.114067 53.181853 12.751489 252.089521 1 1
#> 39 4.679173 49.523054 4.858943 191.197310 1 1
#> 40 4.870874 50.891092 40.362774 85.148106 1 1
#> 41 4.927411 52.287174 14.711076 18.473838 1 1
#> 42 4.649240 49.464543 3.622119 9.966046 1 1
#> 43 4.855889 46.879371 9.227227 25.503289 1 1
#> 44 4.862104 55.161166 1.415612 245.672535 1 1
#> 45 4.898178 58.612286 14.445156 226.208401 1 1
#> 46 4.988252 55.991709 19.500208 181.961117 1 1
#> 47 5.121413 54.722640 36.207705 232.911935 1 1
#> 48 5.034113 61.427503 37.794715 131.492612 1 1
#> 49 5.321079 57.765882 25.252711 50.966962 1 1
#> 50 5.221961 53.336799 23.684539 21.928021 1 1
#> 51 5.372540 72.195911 108.650183 375.356724 1 1
#> 52 5.105944 72.775575 33.534773 474.127774 1 1
#> 53 5.137304 71.410345 57.372454 313.659825 1 1
#> 54 4.962329 65.847602 54.303778 251.222397 1 1
#> 55 4.731579 59.677874 42.313765 206.156415 1 1
plot(p3,last=100)
###### Example 4: U.S. stock returns
data(US.returns)
fit4 <- mtar(~ CCR | dVIX, data=US.returns, subset={Date<="2025-11-28"},
row.names=Date, ars=ars(nregim=2,p=3,d=3), n.burnin=1000,
n.sim=2000, n.thin=2, dist="Student-t")
p4 <- predict(fit4, newdata=subset(US.returns,Date>"2025-11-28"),n.ahead=100,
credible=0.8, out.of.sample=TRUE)
with(p4,summary)
#> CCR.Mean CCR.Lower CCR.Upper
#> 1 0.0701043761 -0.9704474 1.1400940
#> 2 0.0869978936 -1.0323462 1.0558001
#> 3 0.0766240518 -1.0380363 1.0481784
#> 4 0.0634913590 -1.0055895 0.9596353
#> 5 0.1284548931 -0.8854098 1.1811781
#> 6 0.0768642443 -1.0295697 1.1321729
#> 7 -0.0539273644 -1.4842047 1.7042178
#> 8 0.0369715397 -0.9289614 1.1217112
#> 9 0.0719905427 -0.9271710 1.1285411
#> 10 0.1637056616 -0.9527240 1.2448021
#> 11 0.1569008262 -0.9288041 1.0651366
#> 12 0.0728681292 -1.0271811 0.9683613
#> 13 -0.0217104365 -0.9551291 1.0342994
#> 14 0.2818649410 -1.2348089 1.7291236
#> 15 0.0449383950 -1.0855646 1.0028971
#> 16 0.0317383130 -0.9203402 1.1491541
#> 17 0.2068788820 -0.7649928 1.3319735
#> 18 0.1117551644 -1.0178441 1.0549904
#> 19 0.0570800181 -0.9435774 1.1667403
#> 20 0.0409211974 -0.9853378 1.0980559
#> 21 0.1098926293 -0.9916107 1.0404661
#> 22 0.0697385890 -0.9437401 1.1304039
#> 23 0.1185279470 -0.9493896 1.2135799
#> 24 0.0814730297 -1.0951384 1.0165484
#> 25 0.0743582897 -0.9212533 1.0774167
#> 26 0.0906494710 -1.1374614 0.9696480
#> 27 0.0848786801 -0.8776950 1.1550925
#> 28 0.0508434495 -0.9061195 1.0545380
#> 29 0.0524988660 -0.9682303 1.1283123
#> 30 0.1366144661 -0.8497017 1.1889986
#> 31 0.0593225591 -1.0277820 1.0548563
#> 32 0.0302368299 -1.0961422 0.9994821
#> 33 0.0466537036 -0.9086729 1.1439851
#> 34 0.1405064919 -0.8305787 1.2485476
#> 35 0.1010015324 -1.5025959 1.7186173
#> 36 -0.1183814247 -1.1510745 0.9273367
#> 37 0.0614958160 -0.8398117 1.1398453
#> 38 0.2714461950 -0.6933243 1.4480600
#> 39 -0.0009445086 -1.0487921 1.0779864
#> 40 0.0436529842 -0.9223114 1.1075327
#> 41 0.0990324795 -0.9220119 1.1655743
#> 42 0.0611119778 -0.8587965 1.0921572
#> 43 0.0554413073 -0.9375631 1.1083550
#> 44 0.0428704076 -0.9605631 1.0894107
#> 45 0.0829172558 -1.4457253 1.5969937
#> 46 0.0739681712 -1.0887161 1.0625654
#> 47 -0.0353609479 -1.4999716 1.5122040
#> 48 -0.0173228881 -1.0235583 1.0961593
#> 49 0.2998108562 -0.9040761 1.1811992
#> 50 0.2159583043 -0.9071144 1.1825349
#> 51 -0.0067538648 -0.9913596 1.0510124
#> 52 0.0312012071 -1.4057767 1.5131064
#> 53 -0.0672791816 -1.1103790 0.9471805
#> 54 0.0430566802 -1.0244708 1.0432755
#> 55 0.1348370398 -0.9018776 1.1874719
#> 56 0.1047127641 -0.8475987 1.1296451
#> 57 0.0865090753 -0.8568783 1.1286480
#> 58 0.0237012479 -1.6318207 1.4848093
#> 59 0.0660375252 -0.9695613 1.1167400
#> 60 0.0447712836 -0.9793054 1.0580995
#> 61 0.2312714750 -0.9032599 1.2101105
#> 62 -0.0273483084 -1.6828260 1.4129526
#> 63 0.0002733227 -1.7143798 1.4289589
#> 64 0.0858909534 -1.4103979 1.6771128
#> 65 -0.0127815236 -1.0283895 1.0114120
#> 66 0.0477002404 -1.5226168 1.7159421
#> 67 0.1767217509 -1.3128562 1.8403543
#> 68 -0.2583547596 -1.3018237 0.7939929
#> 69 0.1059795278 -0.8725025 1.1410988
#> 70 0.2887895929 -0.8731611 1.2199444
#> 71 -0.1699399582 -1.7984027 1.3842870
#> 72 -0.0679537687 -1.0278891 1.0468290
#> 73 0.0176694961 -1.0369365 0.9313396
#> 74 0.2725877043 -0.7996631 1.2431894
#> 75 0.0144815600 -1.4936019 1.5938152
#> 76 -0.0668645843 -1.0613867 0.9541710
#> 77 0.0449101347 -1.6909555 1.4180803
#> 78 0.0723657910 -0.8944583 1.0779425
#> 79 0.0276405105 -0.8441875 1.1618245
#> 80 0.1709720753 -0.9111563 1.1041167
#> 81 -0.0612429160 -1.6411851 1.4917741
#> 82 0.1151374730 -1.4256831 1.7545225
#> 83 -0.1232081710 -1.1553328 0.8768577
#> 84 0.0369808600 -0.9220609 1.0920441
#> 85 0.3900046620 -0.7541871 1.3078576
#> 86 0.2903668076 -0.8236809 1.2606166
#> 87 0.0239008228 -0.9531384 1.1457454
#> 88 0.0495130293 -1.6683164 1.4886805
#> 89 0.0081549312 -1.1209990 0.9931845
#> 90 0.1967041082 -0.8088877 1.3218740
#> 91 0.2763682591 -0.7798588 1.2982923
#> 92 -0.0034111178 -0.9776309 1.0745639
#> 93 0.0640373460 -1.0427102 0.9783209
#> 94 0.1708625200 -0.9068444 1.1382774
#> 95 0.1468100650 -0.8146346 1.1989405
#> 96 0.0654439175 -0.9397118 1.1300273
#> 97 -0.0218308518 -1.6783436 1.5907265
#> 98 0.0167782479 -0.9911371 1.0228888
#> 99 0.0783676410 -1.0109278 1.0401455
#> 100 0.0957279883 -1.0208458 1.1526204
with(p4,cbind(LS,ES,APE,CR))
#> Log.Score Energy.Score CCR.APE CCR.CR
#> 1 1.0925579 0.6555916 113.13418 1
#> 2 0.5673139 0.4862141 64.55123 1
#> 3 0.6361471 0.5032892 74.24701 1
#> 4 0.5113026 0.4260904 41.19826 1
#> 5 0.5130369 0.4339806 33.60819 1
#> 6 0.8501629 0.5701043 122.06653 1
#> 7 0.9202928 0.6932145 38.49126 1
#> 8 1.1443003 0.6563130 94.50386 1
#> 9 0.5613701 0.4606733 65.34280 1
#> 10 2.2130060 1.1412344 115.26972 0
#> 11 0.6880383 0.4981456 198.19917 1
#> 12 0.6543341 0.4796441 130.53009 1
#> 13 2.1424698 1.0581645 98.13803 0
#> 14 1.3015782 0.9191440 64.33449 1
#> 15 1.4892405 0.8010184 94.88137 1
#> 16 1.0203557 0.6255901 95.05313 1
#> 17 0.6344617 0.5066999 54.43292 1
#> 18 0.5683415 0.4701269 65.25391 1
#> 19 0.5258966 0.4643682 287.49825 1
#> 20 0.8431657 0.5624182 111.69777 1
#> 21 0.6026231 0.5139244 179.82819 1
#> 22 1.4259069 0.7701627 109.44349 1
#> 23 0.5363778 0.4930696 37.38231 1
#> 24 1.0433973 0.6252334 87.13736 1
#> 25 0.9837378 0.5867749 87.96322 1
#> 26 0.8388315 0.5627402 126.30644 1
#> 27 0.5133891 0.4695412 1008.41867 1
#> 28 1.0588807 0.6049867 92.12296 1
#> 29 0.5243357 0.4711161 66.69607 1
#> 30 0.6998558 0.4932192 170.38223 1
#> 31 1.1236956 0.6560715 111.09328 1
#> 32 0.6143604 0.5076642 88.26477 1
#> 33 0.5321731 0.4564385 172.61910 1
#> 34 3.7522188 2.0078365 106.74135 0
#> 35 1.7303430 1.0976615 91.23333 1
#> 36 1.1654894 0.7091658 121.63204 1
#> 37 0.5344202 0.4544571 88.14672 1
#> 38 0.6035668 0.4809570 45.64093 1
#> 39 0.7565606 0.5281581 100.23186 1
#> 40 0.5121819 0.4458243 634.42855 1
#> 41 0.5875404 0.4866180 176.56373 1
#> 42 0.9534513 0.5643920 114.17523 1
#> 43 0.8931330 0.5681201 89.68872 1
#> 44 1.6212013 0.8428297 105.07973 1
#> 45 1.1497027 0.8106287 116.30521 1
#> 46 2.3250283 1.1653811 106.00068 0
#> 47 2.7427100 1.7601378 101.81298 0
#> 48 0.9131883 0.5738949 103.70138 1
#> 49 0.9552226 0.6610496 190.59876 1
#> 50 0.6295177 0.4940362 4509.13177 1
#> 51 2.8306670 1.4124975 99.57213 0
#> 52 0.9132329 0.6589653 37.46523 1
#> 53 0.5469473 0.4549575 165.27220 1
#> 54 0.9762023 0.5901031 92.24296 1
#> 55 0.8556207 0.5674659 147.71090 1
#> 56 1.0580195 0.6088836 84.85893 1
#> 57 2.0196750 1.0216710 108.28632 0
#> 58 1.3559187 0.8836219 96.89063 1
#> 59 1.3718853 0.7395880 91.85067 1
#> 60 1.1198674 0.6466065 108.32176 1
#> 61 1.1761236 0.6806003 153.18055 1
#> 62 0.9252006 0.6803580 168.67270 1
#> 63 1.5577876 1.0053944 100.02880 1
#> 64 1.2492726 0.8292328 88.88303 1
#> 65 1.0199670 0.6110969 97.74286 1
#> 66 2.0509999 1.3516514 103.56885 1
#> 67 1.2558044 0.8521265 78.63057 1
#> 68 0.5330200 0.4632379 20.87535 1
#> 69 0.6385590 0.4743885 226.47835 1
#> 70 3.2267507 1.6766109 118.81996 0
#> 71 1.0870105 0.7543259 72.03794 1
#> 72 1.8597015 0.9731432 106.74150 1
#> 73 0.6252306 0.4671085 92.90711 1
#> 74 2.9576468 1.4942526 119.89538 0
#> 75 0.9808534 0.7093237 105.26107 1
#> 76 2.6260035 1.3099508 95.61656 0
#> 77 1.7455726 1.1145692 96.05640 1
#> 78 0.8383488 0.5517218 119.29953 1
#> 79 0.9435010 0.6136509 94.88567 1
#> 80 3.2744735 1.7319806 109.73674 0
#> 81 2.4066618 1.4660413 96.36826 0
#> 82 1.1405490 0.7754904 129.12239 1
#> 83 4.6878638 2.7892034 104.29074 0
#> 84 1.1721286 0.6825963 94.82276 1
#> 85 0.6412249 0.4890768 248.14686 1
#> 86 0.6110558 0.4984032 34.26142 1
#> 87 0.5188506 0.4608955 68.50833 1
#> 88 3.3133465 2.1774711 98.00125 0
#> 89 1.1162135 0.6811072 98.67422 1
#> 90 0.7387067 0.5381643 272.67366 1
#> 91 1.3239718 0.7197563 72.69591 1
#> 92 2.0633407 1.0548788 100.29120 0
#> 93 1.3294335 0.7241094 91.93901 1
#> 94 0.5516590 0.4630936 34.45040 1
#> 95 1.9825557 0.9971560 87.73364 1
#> 96 0.6916404 0.5014648 127.52975 1
#> 97 1.2516061 0.8448070 96.57200 1
#> 98 1.8154758 0.9417822 98.38760 0
#> 99 0.8480363 0.5652572 118.92284 1
#> 100 1.1281451 0.6682326 87.09853 1
plot(p4,last=100)
# }