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
)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.
Value
A list containing the forecast summaries and, when requested, measures of predictive accuracy.
ypred | a matrix with the results of the forecasting, |
summary | a matrix with the mean and credible intervals of the forecasting, |
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 -9.119200e-03 -0.020218118 0.003196054 -0.0093164562 -0.027218142
#> 2 -2.664497e-03 -0.011267664 0.006229670 -0.0006761955 -0.013485503
#> 3 -6.587927e-03 -0.021137706 0.005140867 -0.0117876924 -0.024955870
#> 4 -1.073913e-04 -0.007797341 0.011448158 0.0016883439 -0.015436279
#> 5 4.666936e-03 -0.007531809 0.012785618 0.0134608508 -0.004212121
#> 6 6.047212e-03 -0.004435982 0.016182084 0.0121165468 -0.009552941
#> 7 -3.271040e-03 -0.011604025 0.010942304 -0.0104893103 -0.025987160
#> 8 -6.411293e-03 -0.019362595 0.005220886 -0.0116646015 -0.025875003
#> 9 3.318408e-03 -0.006507357 0.013595637 0.0090676091 -0.005156385
#> 10 6.430529e-03 -0.005055116 0.017028160 0.0119790098 -0.002839060
#> 11 6.057967e-03 -0.006219791 0.014824740 0.0096567244 -0.007690585
#> 12 1.229968e-03 -0.011130793 0.008702659 -0.0007006007 -0.011646989
#> 13 -1.077635e-04 -0.009079931 0.008527622 0.0006054791 -0.014761890
#> 14 5.847992e-03 -0.006115111 0.016126954 0.0119124403 -0.007136843
#> 15 -2.382484e-03 -0.015646459 0.010035236 -0.0115670228 -0.026909869
#> 16 -5.067109e-03 -0.019577348 0.008217248 -0.0109817063 -0.025412390
#> 17 -1.667002e-03 -0.011100289 0.006579376 -0.0006734276 -0.013697149
#> 18 -4.921430e-03 -0.014570563 0.010538884 -0.0099583691 -0.023454192
#> 19 -7.001995e-03 -0.017898983 0.006926236 -0.0108826043 -0.025759549
#> 20 -6.227362e-03 -0.020243522 0.007097130 -0.0119971496 -0.028617380
#> 21 3.450765e-03 -0.008045159 0.014230363 0.0130470548 -0.002357175
#> 22 -5.377296e-03 -0.019245767 0.005324078 -0.0119012384 -0.027409706
#> 23 2.419334e-03 -0.007538300 0.013285131 0.0092493713 -0.008295293
#> 24 -5.103992e-03 -0.018876318 0.005246330 -0.0116805514 -0.028761234
#> 25 -7.866375e-04 -0.010702683 0.007785626 -0.0008808668 -0.014103874
#> 26 -5.175548e-04 -0.009415350 0.008802612 -0.0002420705 -0.014714575
#> 27 -4.764730e-03 -0.019137436 0.007515525 -0.0117545361 -0.025049039
#> 28 -2.217715e-04 -0.007951204 0.009729626 0.0019813172 -0.012714625
#> 29 4.116633e-03 -0.005669910 0.015204177 0.0111083968 -0.006475880
#> 30 -3.339907e-03 -0.014284229 0.009962956 -0.0115285067 -0.031475969
#> 31 1.977460e-03 -0.009307230 0.010800672 0.0096180384 -0.003472748
#> 32 -3.816349e-03 -0.015161514 0.007482543 -0.0099228219 -0.023323541
#> 33 -1.208415e-03 -0.009410451 0.011185368 0.0008337572 -0.013496371
#> 34 4.850552e-03 -0.007179417 0.015699862 0.0103175462 -0.005953625
#> 35 1.520162e-03 -0.007928478 0.009974940 -0.0016738363 -0.017174284
#> 36 -5.640307e-03 -0.016338081 0.006704145 -0.0105009923 -0.028215301
#> 37 -1.539077e-04 -0.011807382 0.009989458 0.0018448281 -0.010320530
#> 38 -1.073559e-04 -0.009799198 0.009958559 -0.0017532305 -0.014193079
#> 39 -6.417168e-03 -0.021365512 0.005036071 -0.0105191714 -0.029683637
#> 40 -9.065928e-03 -0.021936474 0.003208881 -0.0134475913 -0.026397060
#> 41 -1.606611e-03 -0.010079614 0.007414171 0.0001217155 -0.010483577
#> 42 -4.426209e-04 -0.008451545 0.009217851 -0.0009054159 -0.012396130
#> 43 -4.764593e-03 -0.017815523 0.006656262 -0.0104582669 -0.025151818
#> 44 3.242181e-03 -0.007023263 0.013737259 0.0106915803 -0.007987678
#> 45 8.439489e-04 -0.008437626 0.010628142 -0.0005510613 -0.015697844
#> 46 -4.208510e-05 -0.008602152 0.008610744 0.0001522652 -0.011426542
#> 47 4.192628e-03 -0.007117624 0.013528045 0.0120715490 -0.001314261
#> 48 2.063570e-03 -0.009268310 0.010319118 -0.0013323502 -0.013867037
#> 49 -8.272815e-04 -0.009982088 0.007463956 -0.0016159426 -0.014443668
#> 50 4.181235e-03 -0.006979476 0.012579722 0.0088485782 -0.008801746
#> 51 -3.981734e-03 -0.019143014 0.008648682 -0.0116811209 -0.026917911
#> 52 -1.100118e-03 -0.009625490 0.007515320 -0.0010803908 -0.015608315
#> 53 4.690374e-03 -0.005732271 0.014258696 0.0104749868 -0.004800889
#> 54 1.502601e-03 -0.007378198 0.010354536 -0.0005896692 -0.012817044
#> 55 -5.623347e-03 -0.018867263 0.006874492 -0.0122634576 -0.026218728
#> 56 4.246698e-03 -0.007705642 0.013338111 0.0099306937 -0.002457072
#> 57 1.330818e-03 -0.008541273 0.009615044 -0.0003240183 -0.014293341
#> 58 2.435684e-05 -0.008478329 0.009978547 -0.0008638059 -0.015270544
#> 59 -1.487630e-04 -0.007261069 0.008935325 -0.0004694735 -0.013025305
#> 60 6.618727e-04 -0.009175960 0.008087943 -0.0011039872 -0.013777961
#> 61 -5.290375e-03 -0.016186062 0.009751810 -0.0117737384 -0.027044276
#> 62 -1.828084e-04 -0.010366280 0.008551094 0.0020483186 -0.012427980
#> 63 6.388967e-04 -0.008226260 0.012434155 -0.0006411711 -0.012979234
#> 64 5.559824e-03 -0.005902789 0.015590718 0.0124097453 -0.004484497
#> 65 1.899343e-03 -0.008737329 0.009581668 0.0004089558 -0.011186304
#> 66 9.719537e-04 -0.008009784 0.008240353 -0.0006522036 -0.012032323
#> 67 8.405352e-05 -0.010535725 0.010096088 0.0018693778 -0.011069274
#> 68 1.198370e-03 -0.006828932 0.011583671 0.0026172945 -0.013506795
#> 69 3.998314e-04 -0.007331674 0.009338798 -0.0007161397 -0.013817964
#> 70 1.276110e-03 -0.007662388 0.008764574 0.0009281796 -0.015254749
#> 71 -5.093055e-03 -0.017447466 0.007030388 -0.0107537875 -0.027423481
#> 72 -2.036028e-03 -0.012148116 0.006462556 -0.0006273929 -0.016855026
#> 73 4.534326e-03 -0.004310562 0.014703996 0.0123442357 -0.003227678
#> 74 1.108805e-03 -0.007817731 0.010375070 -0.0014657652 -0.012508284
#> 75 -1.305028e-03 -0.009394148 0.007708242 -0.0017468491 -0.012350453
#> BOVESPA.Upper
#> 1 0.002718051
#> 2 0.010083453
#> 3 0.004223443
#> 4 0.014476350
#> 5 0.029532807
#> 6 0.027705937
#> 7 0.006885372
#> 8 0.009338028
#> 9 0.025021237
#> 10 0.033229442
#> 11 0.023981968
#> 12 0.013350131
#> 13 0.013806420
#> 14 0.024562834
#> 15 0.008168155
#> 16 0.008694124
#> 17 0.014226703
#> 18 0.010096171
#> 19 0.002640522
#> 20 0.003873722
#> 21 0.030075828
#> 22 0.006136615
#> 23 0.024391878
#> 24 0.003030029
#> 25 0.011129211
#> 26 0.011007828
#> 27 0.006604331
#> 28 0.018161771
#> 29 0.030479237
#> 30 0.002778527
#> 31 0.029031442
#> 32 0.008817542
#> 33 0.014552087
#> 34 0.026197397
#> 35 0.010624893
#> 36 0.005628481
#> 37 0.021443579
#> 38 0.013366657
#> 39 0.002973933
#> 40 0.004472476
#> 41 0.013922644
#> 42 0.013155984
#> 43 0.005354685
#> 44 0.024324364
#> 45 0.014526892
#> 46 0.013102125
#> 47 0.032986144
#> 48 0.012255024
#> 49 0.010342653
#> 50 0.023230574
#> 51 0.004916274
#> 52 0.008795181
#> 53 0.025190963
#> 54 0.014586778
#> 55 0.007164780
#> 56 0.027706287
#> 57 0.011392521
#> 58 0.012262881
#> 59 0.012708436
#> 60 0.012754292
#> 61 0.003939105
#> 62 0.018190289
#> 63 0.016380542
#> 64 0.027621207
#> 65 0.017145427
#> 66 0.013447508
#> 67 0.015577426
#> 68 0.013385976
#> 69 0.013314495
#> 70 0.015343549
#> 71 0.004728221
#> 72 0.012235852
#> 73 0.026021742
#> 74 0.012047978
#> 75 0.013493617
with(p1,cbind(LS,ES,APE,CR))
#> Log.Score Energy.Score COLCAP.APE BOVESPA.APE COLCAP.CoverageRate
#> 1 -4.0340084 0.032386673 189.46687963 148.052822 0
#> 2 -4.0455824 0.020254902 115.81882031 93.501973 0
#> 3 -7.3566405 0.009935567 37.03243721 45.577046 1
#> 4 -6.7799086 0.013031755 81.38717650 114.742266 1
#> 5 -3.8052409 0.021807580 81.18532603 381.926217 0
#> 6 -3.9199414 0.020962700 76.36524931 279.807197 0
#> 7 -5.8180960 0.018853724 133.54681008 292.758334 1
#> 8 -5.2068126 0.018832515 750.18208482 61.503716 1
#> 9 -5.0743354 0.024460308 143.21634193 155.573552 0
#> 10 -6.8605802 0.012374022 386.08247735 92.567994 1
#> 11 -3.7763885 0.021178442 78.52228250 22.553466 0
#> 12 -7.2462230 0.008944686 122.78672541 Inf 1
#> 13 -7.8071015 0.007910194 95.12530783 Inf 1
#> 14 -6.5080552 0.015840515 269.43472962 571.760825 1
#> 15 -6.9056132 0.011888868 150.22319446 65.516323 1
#> 16 -5.6019380 0.021175817 75.89601830 61.173011 0
#> 17 -5.9812135 0.014139781 114.92345526 110.231614 0
#> 18 -7.1008029 0.011471746 57.26304801 35.126193 1
#> 19 -5.7477963 0.018816734 66.83080079 58.392188 0
#> 20 -6.9610656 0.012033348 7.38619893 491.110817 1
#> 21 -2.6005740 0.041520854 119.73265565 147.585687 0
#> 22 -4.5723299 0.020636062 133.62221443 18.005744 0
#> 23 -3.0578289 0.025598103 91.58047223 34.713892 0
#> 24 -5.1498676 0.019926611 77.56762721 51.027490 0
#> 25 -3.5345049 0.024372140 96.50726247 94.667299 0
#> 26 -4.1080581 0.019277133 102.60923124 107.681626 0
#> 27 -5.9016365 0.014065772 158.29585322 8.113490 0
#> 28 -5.4392124 0.014480414 101.60238105 4.228083 0
#> 29 -4.4054916 0.019514066 82.53688019 33.939971 0
#> 30 -6.0497778 0.014648273 68.89653596 Inf 1
#> 31 -6.7958463 0.011909384 67.89896310 Inf 1
#> 32 -3.9654904 0.030998637 161.80906384 142.829537 1
#> 33 -6.3805797 0.013405028 111.75375741 87.352348 1
#> 34 -4.0317400 0.031053263 41.54218630 77.043524 1
#> 35 -7.5721300 0.008819403 68.19532875 141.310707 1
#> 36 -3.3634189 0.036190374 55.73663785 78.946145 1
#> 37 -4.7793602 0.024053198 101.21265535 92.735097 0
#> 38 -3.6040180 0.029819127 101.57600344 105.716802 1
#> 39 -6.5468714 0.013647745 219.88609668 86.458472 0
#> 40 -6.7760810 0.015009245 408.22176547 Inf 1
#> 41 -7.5143042 0.007822652 148.97455495 Inf 1
#> 42 -7.7488526 0.007620602 115.07248715 Inf 1
#> 43 -5.9431800 0.016002536 199.21262754 60.623779 1
#> 44 -7.1881382 0.009844192 62.90099223 13.631963 1
#> 45 -7.3880261 0.010064862 20.08448686 107.728923 1
#> 46 -4.3660870 0.020408030 99.48778466 99.278249 1
#> 47 -3.7839785 0.022314599 84.71018148 27.038594 0
#> 48 -7.7875332 0.007796143 0.08968133 63.858791 1
#> 49 -7.8450623 0.006981180 6.46164845 201.989656 1
#> 50 -4.1602073 0.028113279 258.78767921 77.827680 1
#> 51 -7.2553828 0.010212407 26.94187080 29.844055 1
#> 52 -7.1437167 0.010122777 8.03051942 89.526766 1
#> 53 -5.8899425 0.015373895 51.55980975 323.636938 1
#> 54 -7.2317492 0.009163192 71.47575927 91.651524 1
#> 55 -2.9839700 0.036693413 179.02207557 143.088901 1
#> 56 -5.9371655 0.018870270 53.31820479 67.503350 1
#> 57 -4.5200705 0.021324029 92.01095649 101.868746 0
#> 58 -0.6478011 0.049122683 99.83338795 101.728951 0
#> 59 -2.1445444 0.036547777 66.19829995 101.194680 1
#> 60 -6.6709302 0.011146413 93.00487479 133.664960 0
#> 61 -6.6970086 0.012228028 45.11805424 302.169222 1
#> 62 -6.9760509 0.011735368 114.44019272 122.910090 1
#> 63 -5.7647875 0.017420240 73.92458949 103.475885 1
#> 64 -7.1485925 0.012339536 121.89483640 811.031547 1
#> 65 -6.3886322 0.015604606 158.39890634 102.611252 1
#> 66 -2.7788006 0.033949517 109.55605694 98.198278 0
#> 67 -6.7790955 0.011716864 111.48913200 85.997295 1
#> 68 -0.4590200 0.057862467 86.54429747 95.902380 1
#> 69 -6.4031679 0.011633020 96.25779163 63.254434 0
#> 70 -7.3961465 0.008543407 76.42764130 75.831937 1
#> 71 -5.4325171 0.017114236 262.65515638 58.987420 1
#> 72 -3.7371081 0.023360189 82.90446971 102.746433 1
#> 73 -6.6951249 0.011915435 202.53621737 98.734736 0
#> 74 -5.5926080 0.013846293 92.78238200 179.899951 0
#> 75 -3.4295880 0.023417377 110.50352422 92.587653 0
#> BOVESPA.CoverageRate
#> 1 0
#> 2 1
#> 3 1
#> 4 1
#> 5 1
#> 6 1
#> 7 1
#> 8 0
#> 9 0
#> 10 1
#> 11 1
#> 12 1
#> 13 1
#> 14 1
#> 15 1
#> 16 0
#> 17 1
#> 18 1
#> 19 0
#> 20 1
#> 21 0
#> 22 1
#> 23 1
#> 24 1
#> 25 0
#> 26 1
#> 27 1
#> 28 1
#> 29 1
#> 30 1
#> 31 1
#> 32 0
#> 33 1
#> 34 0
#> 35 1
#> 36 0
#> 37 0
#> 38 0
#> 39 1
#> 40 1
#> 41 1
#> 42 1
#> 43 0
#> 44 1
#> 45 1
#> 46 0
#> 47 1
#> 48 1
#> 49 1
#> 50 0
#> 51 1
#> 52 1
#> 53 1
#> 54 1
#> 55 0
#> 56 0
#> 57 0
#> 58 0
#> 59 0
#> 60 1
#> 61 1
#> 62 1
#> 63 0
#> 64 1
#> 65 0
#> 66 0
#> 67 1
#> 68 0
#> 69 1
#> 70 1
#> 71 1
#> 72 0
#> 73 1
#> 74 1
#> 75 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=100, n.sim=200, 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 13.600612 8.370351 19.58326 32.70210 12.019767 52.71172
#> 2 15.639506 8.320413 21.02139 37.34028 16.865101 61.99265
#> 3 13.071111 7.613268 17.56920 30.41830 19.953969 50.98096
#> 4 11.455297 7.734947 15.45852 25.37616 15.716261 36.92616
#> 5 11.434506 6.730015 15.55541 24.60579 16.435318 36.70618
#> 6 10.065412 6.564491 13.73590 22.15700 13.872644 31.27158
#> 7 9.726586 5.874645 12.89311 21.00559 14.316696 30.35814
#> 8 9.038285 5.999823 12.82590 19.96815 12.766529 28.15206
#> 9 8.677133 6.030699 12.01824 18.98015 11.584352 27.26795
#> 10 8.063550 4.749049 10.54648 17.73212 9.523311 25.77968
#> 11 7.694877 5.772537 11.06389 16.53746 10.233936 25.49616
#> 12 7.535826 4.997557 10.29486 16.03746 10.681229 24.81483
#> 13 7.377500 4.905302 10.03026 16.08374 10.243089 23.56778
#> 14 7.896249 4.252106 12.56558 18.02053 6.574131 26.58953
#> 15 7.483957 4.233460 10.41201 17.11866 7.858977 25.99376
#> 16 7.981971 3.953850 12.94998 17.79346 7.609170 27.89019
#> 17 8.498426 4.104346 13.25315 20.17048 10.270490 30.54149
#> 18 12.250136 5.585419 16.56463 30.86235 1.025427 50.27033
#> 19 14.332078 9.043677 21.00984 33.84199 13.369384 57.58570
#> 20 12.415709 7.504847 18.40567 28.37740 8.331245 42.46313
#> 21 11.517357 5.766874 15.25045 26.89389 10.504445 40.81995
#> 22 10.053920 5.835094 14.03314 23.53292 9.442761 32.81884
#> 23 9.147763 5.827650 12.73526 21.19551 11.237127 28.54419
#> 24 8.920684 5.253213 11.65842 20.30939 11.254465 27.08856
#> 25 8.513038 5.608953 11.24197 19.23483 11.700230 27.31201
#> 26 8.209635 5.704889 10.92460 18.18665 11.765834 27.53330
#> 27 8.839982 5.289704 12.61447 20.24896 13.865209 33.24601
#> 28 8.082814 4.883632 11.43973 18.93271 11.181256 27.61170
#> 29 7.776990 5.350614 11.34818 18.19157 10.154976 24.67614
#> 30 8.544304 3.666108 12.22619 19.48819 6.600532 25.52995
#> 31 9.020855 4.698460 14.17872 19.93985 8.623182 30.13205
#> 32 9.295921 3.709125 13.31571 21.52828 9.298662 33.38876
#> 33 12.478127 6.279820 17.45066 29.85827 14.348492 54.24131
#> 34 14.814281 8.718132 20.43903 35.69869 12.613112 60.35547
#> 35 12.975698 8.085636 19.49082 30.65988 11.453560 43.81294
#> 36 15.340494 9.843871 22.18214 34.37556 13.634761 54.39340
#> 37 16.718981 6.523753 22.06894 38.91171 22.043381 71.87777
#> 38 18.189116 9.501143 24.56438 40.44000 20.897491 77.21784
#> 39 15.866228 10.674864 22.70573 34.82181 11.325114 51.41905
#> 40 14.954478 8.973840 19.66979 32.43639 17.843271 51.30648
#> 41 17.737736 10.325194 23.90607 39.85531 15.918159 68.18486
#> 42 15.885792 10.466387 23.02448 33.91958 15.077434 51.67711
#> 43 18.128835 10.450099 24.80430 38.91297 17.638592 62.65088
#> 44 19.358724 12.120724 27.02147 44.74477 23.291093 72.43133
#> 45 17.090377 10.865110 23.62776 37.31569 20.583146 59.46026
#> 46 14.570531 10.281987 19.41220 31.02806 16.284437 42.03868
#> 47 12.715396 9.880634 17.48493 27.01873 14.375559 37.25470
#> 48 11.578451 8.041935 15.23678 24.88483 14.239685 33.72087
#> 49 10.800725 7.217400 14.64410 23.30656 15.321748 32.52502
#> 50 9.881388 6.385587 13.86039 21.88644 12.076523 30.30434
#> 51 9.515730 6.024255 12.50404 20.40700 13.441891 28.93124
#> 52 13.983584 9.018974 21.59810 31.55447 5.665685 54.70465
#> 53 16.139350 9.161141 22.90236 36.38694 14.272273 55.87670
#> 54 13.714659 9.890035 21.75844 30.86929 14.723866 48.34407
#> 55 12.594584 6.042706 17.53953 28.04724 12.100186 39.90278
#> 56 12.095762 7.143659 17.71045 26.95736 14.427970 39.35038
#> 57 15.204674 9.103763 21.32725 34.76964 11.539408 57.95369
#> 58 13.388582 7.125364 19.86217 29.71128 14.978341 49.59961
#> 59 11.654936 7.133315 15.86450 25.41148 12.545893 38.14560
#> 60 10.387964 6.306573 14.48000 23.05517 13.374506 33.34826
with(p2,cbind(LS,ES,APE,CR))
#> Log.Score Energy.Score Bedon.APE LaPlata.APE Bedon.CoverageRate
#> 1 6.709284 11.019354 19.7236931 11.925410 1
#> 2 8.306796 23.488671 5.5014766 41.955114 1
#> 3 5.727137 7.197744 12.6819883 7.006108 1
#> 4 4.545639 4.975518 0.1443775 5.585169 1
#> 5 6.840247 10.732768 6.0714885 32.586883 1
#> 6 4.804493 4.783810 8.3295798 14.352547 1
#> 7 5.382802 6.850931 8.1531103 27.038580 1
#> 8 4.554505 5.071374 18.3533437 18.430743 1
#> 9 4.413226 3.885057 7.7904706 6.317146 1
#> 10 4.955208 5.198558 2.0444153 21.260565 1
#> 11 5.107795 4.540914 15.8169317 19.408106 1
#> 12 5.203755 3.977834 35.9276007 8.981485 1
#> 13 5.587254 4.342498 34.4541699 16.099410 1
#> 14 6.449882 6.523648 45.4189453 23.577064 1
#> 15 4.162623 4.290599 0.6378531 6.963796 1
#> 16 4.749924 4.868709 2.9400439 6.356590 1
#> 17 5.206486 5.721415 22.7415773 9.912975 1
#> 18 8.435983 30.734077 38.6880081 52.570542 0
#> 19 6.766649 12.263657 15.4881411 21.915115 1
#> 20 5.605234 8.142533 20.5408667 13.418862 1
#> 21 5.438197 7.215498 18.4547679 20.223043 1
#> 22 4.803616 5.638187 5.4975833 17.195793 1
#> 23 4.739282 4.667731 0.1335901 20.019848 1
#> 24 4.648340 4.726562 0.6394896 24.216458 1
#> 25 4.337864 3.713491 1.4922752 1.449543 1
#> 26 4.963386 6.357525 9.6452229 28.314333 1
#> 27 5.000582 4.757561 20.5671237 5.687212 1
#> 28 6.722702 6.681936 40.0348998 25.078317 1
#> 29 4.424035 3.760227 1.2407727 7.937381 1
#> 30 4.686688 4.734018 7.9892364 7.638993 1
#> 31 4.862405 5.276573 12.0326186 6.561168 1
#> 32 6.061961 6.237445 67.6753371 2.806871 1
#> 33 6.736315 16.260826 19.1307412 37.743383 1
#> 34 6.283200 11.490113 18.0626049 7.742813 1
#> 35 5.343234 7.583759 3.2505204 18.240964 1
#> 36 7.664518 12.797815 32.4207300 16.950145 0
#> 37 6.008310 11.527554 7.5277618 6.162708 1
#> 38 6.377347 15.701803 17.8132031 23.597209 1
#> 39 5.919801 10.793453 8.8671560 20.005031 1
#> 40 6.665248 10.764288 11.9347187 22.046648 1
#> 41 6.430336 11.690086 23.2643201 1.624872 1
#> 42 6.612543 11.299803 10.9343049 23.154545 1
#> 43 7.554686 21.271972 6.2624850 37.438951 1
#> 44 6.356236 13.045520 23.1470990 19.287574 1
#> 45 6.179983 8.817961 24.9296554 10.407763 1
#> 46 5.328156 6.380425 1.0997207 10.031820 1
#> 47 5.633836 7.737192 3.9622624 22.001346 1
#> 48 5.164761 5.542128 1.9229858 14.426313 1
#> 49 4.511033 4.605459 1.6327416 8.887565 1
#> 50 5.149830 5.588284 4.0641982 19.682777 1
#> 51 4.384608 3.667116 0.6316608 4.117353 1
#> 52 6.012259 11.678314 34.4575348 24.918741 1
#> 53 6.773181 11.249595 21.8984129 13.938185 1
#> 54 6.298688 8.245609 20.7276308 7.715132 1
#> 55 5.732426 7.617427 12.7536584 13.434454 1
#> 56 5.187564 6.210565 14.2187143 7.101141 1
#> 57 7.278872 12.467681 32.6760397 18.629443 1
#> 58 5.589403 8.120713 7.5665697 1.507634 1
#> 59 4.967638 6.128023 1.7010082 7.189612 1
#> 60 4.960140 5.059908 6.1611158 10.708085 1
#> LaPlata.CoverageRate
#> 1 1
#> 2 0
#> 3 1
#> 4 1
#> 5 1
#> 6 1
#> 7 1
#> 8 1
#> 9 1
#> 10 1
#> 11 1
#> 12 1
#> 13 1
#> 14 1
#> 15 1
#> 16 1
#> 17 1
#> 18 0
#> 19 1
#> 20 1
#> 21 1
#> 22 1
#> 23 1
#> 24 1
#> 25 1
#> 26 1
#> 27 1
#> 28 1
#> 29 1
#> 30 1
#> 31 1
#> 32 1
#> 33 1
#> 34 1
#> 35 1
#> 36 1
#> 37 1
#> 38 1
#> 39 1
#> 40 1
#> 41 1
#> 42 1
#> 43 1
#> 44 1
#> 45 1
#> 46 1
#> 47 1
#> 48 1
#> 49 1
#> 50 1
#> 51 1
#> 52 1
#> 53 1
#> 54 1
#> 55 1
#> 56 1
#> 57 1
#> 58 1
#> 59 1
#> 60 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=100, n.sim=200,
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 26.740793 25.376119 28.38160 7.895348 6.8727785
#> 2 26.570813 24.208473 29.19941 7.369298 5.0343127
#> 3 25.918248 22.600451 29.78008 4.249852 4.4799864
#> 4 10.476583 23.019408 31.54190 -16.045929 3.8540736
#> 5 9.625698 22.195901 31.80397 -17.386045 3.1008940
#> 6 10.673384 22.003413 33.73273 -15.378834 0.5621175
#> 7 11.935468 20.114374 32.66816 -12.050314 0.8397593
#> 8 39.447416 19.473753 33.69771 -3.942799 -0.3538601
#> 9 39.393566 17.567637 35.79781 -1.735296 -1.7597392
#> 10 36.315005 20.105252 36.76161 -1.411381 -0.5578702
#> 11 32.429148 17.393019 36.75101 -2.297637 -0.9695667
#> 12 30.309777 14.520347 33.42045 -3.244199 -4.0932041
#> 13 29.834413 17.098988 36.47697 -2.916472 -1.9767787
#> 14 39.620597 17.891487 37.21390 2.280644 -1.1425278
#> 15 38.227125 16.418807 37.69439 12.609517 -2.8729247
#> 16 28.201171 13.729900 36.52374 11.037737 -3.4332529
#> 17 25.875828 10.340917 34.33019 9.719362 -3.8664006
#> 18 23.937981 13.306545 41.69255 8.763713 -2.9593093
#> 19 26.835556 12.461579 38.37944 8.729192 -2.5857613
#> 20 28.512351 12.473061 37.11909 10.371451 -2.4381428
#> 21 27.809135 17.063687 40.63036 11.911441 -5.4073190
#> 22 22.111566 18.866657 43.81853 14.255267 -6.8107579
#> 23 -25.095164 18.270656 41.67944 7.288849 -6.3660928
#> 24 -18.182399 17.270405 38.06013 12.323524 -6.5203397
#> 25 -4.326606 17.267485 42.02112 12.659742 -14.9189001
#> 26 91.501977 10.663583 36.27705 -31.530543 -13.2409997
#> 27 71.890093 10.034176 38.71286 -51.820631 -13.4786741
#> 28 52.877026 14.231481 45.13752 -52.350671 -15.5829143
#> 29 43.299457 8.323787 39.75578 -48.249218 -9.2138649
#> 30 31.326490 13.843753 45.61805 -42.842594 -12.5304671
#> 31 -17.079902 15.789726 45.05250 -125.169103 -10.2326127
#> 32 -7.827270 11.813777 46.29082 -116.292535 -13.4239050
#> 33 -5.721844 13.873089 46.83837 -95.082711 -10.6170496
#> 34 -5.429371 10.814378 41.06405 -73.682793 -12.1469881
#> 35 -8.269561 14.421131 43.60202 -57.860959 -9.4561275
#> 36 -5.739094 15.327989 42.82230 -49.387799 -8.3381755
#> 37 -196.907032 15.935979 47.16701 -195.070241 -13.5031846
#> 38 -212.895624 12.637042 46.26781 -195.413805 -14.1181844
#> 39 -177.316387 13.452230 47.08655 -161.078320 -15.0314710
#> 40 -141.614640 13.237774 45.76033 -132.963535 -12.0299649
#> 41 -115.481217 7.945655 42.25419 -111.859731 -10.4341944
#> 42 -84.991905 5.916290 46.27207 -90.661017 -9.6377323
#> 43 -62.458037 7.484483 48.33388 -137.320982 -7.0974955
#> 44 -70.712333 10.548059 48.58128 -138.809309 -16.2412476
#> 45 -64.883758 11.400050 44.51409 -126.950820 -12.7201245
#> 46 -56.892037 11.220759 42.83285 -120.411053 -12.8308017
#> 47 -53.257201 13.829914 43.79207 -113.024580 -11.2560488
#> 48 -47.838474 12.335336 39.38707 -104.946287 -8.8427792
#> 49 -48.038471 9.744195 39.50596 -92.142029 -10.3977064
#> 50 -37.725760 14.928778 40.44581 -74.063117 -12.1129533
#> 51 -14.601032 12.314695 38.70131 -61.610600 -9.6891229
#> 52 -5.824661 13.452408 41.34375 -53.786832 -9.3302759
#> 53 -7.256199 10.796049 37.87863 -55.380212 -10.4049913
#> 54 -6.349377 10.940634 39.77055 -59.251904 -6.1634841
#> 55 -6.136667 10.904510 42.01325 -56.709944 -5.9126173
#> Vatnsdalsa.Upper
#> 1 9.045608
#> 2 9.262123
#> 3 10.905464
#> 4 11.169132
#> 5 11.729537
#> 6 11.744953
#> 7 13.863724
#> 8 13.507141
#> 9 13.800117
#> 10 14.754380
#> 11 14.685216
#> 12 12.972531
#> 13 12.756081
#> 14 12.126985
#> 15 13.703909
#> 16 15.076525
#> 17 16.941431
#> 18 16.136564
#> 19 15.955458
#> 20 17.186277
#> 21 15.008617
#> 22 16.180238
#> 23 18.548213
#> 24 19.423433
#> 25 15.948085
#> 26 20.412088
#> 27 22.862595
#> 28 23.712787
#> 29 28.826289
#> 30 24.806356
#> 31 22.862892
#> 32 18.280917
#> 33 20.627019
#> 34 18.666007
#> 35 22.184900
#> 36 23.138539
#> 37 21.781610
#> 38 22.615386
#> 39 20.320199
#> 40 25.589531
#> 41 25.426104
#> 42 28.102054
#> 43 36.211745
#> 44 24.489211
#> 45 22.312022
#> 46 20.755849
#> 47 22.344241
#> 48 25.977655
#> 49 28.476337
#> 50 25.484106
#> 51 25.893518
#> 52 25.361302
#> 53 22.985524
#> 54 25.844241
#> 55 29.870521
with(p3,cbind(LS,ES,APE,CR))
#> Log.Score Energy.Score Jokulsa.APE Vatnsdalsa.APE Jokulsa.CoverageRate
#> 1 5.300585 3.439013 7.7903702 14.4253363 0
#> 2 5.881536 4.699381 12.0171761 0.9492876 0
#> 3 3.683296 5.480224 8.7385647 32.5420282 1
#> 4 5.923160 30.125798 62.3144495 410.9676092 1
#> 5 4.245695 28.997401 66.1066965 385.0171260 1
#> 6 4.634029 25.620004 60.0247795 378.6020623 1
#> 7 4.837821 22.150768 56.2803366 341.4892549 1
#> 8 4.281791 31.730738 44.4960279 173.8351875 1
#> 9 4.282961 28.402962 47.5414466 132.4961731 1
#> 10 3.795076 24.457853 38.6068882 126.4303518 1
#> 11 4.303347 22.670478 23.7753725 144.5278478 1
#> 12 3.510727 20.854688 15.6861704 156.8160932 1
#> 13 3.667900 18.271599 13.8718060 152.8346404 1
#> 14 3.918800 22.538971 54.1657466 58.6839917 1
#> 15 4.297526 25.868699 55.3948188 144.3704790 1
#> 16 3.911428 29.546815 14.6389063 128.9986951 1
#> 17 4.358525 28.394695 1.2372996 76.0754037 1
#> 18 4.292969 27.713034 10.3446419 43.6674322 1
#> 19 4.715816 25.198515 0.5076996 47.9524092 1
#> 20 4.420864 23.182554 6.7878317 81.6366267 1
#> 21 4.549759 22.154037 6.1417385 115.7869685 1
#> 22 4.313578 23.915594 15.6047116 176.2648611 1
#> 23 3.889152 46.647622 197.6465540 46.0691221 1
#> 24 4.349246 43.185341 170.7486342 175.0786593 1
#> 25 3.873332 41.205486 117.5878292 162.6502513 1
#> 26 4.746838 86.575258 263.1030825 711.0570254 1
#> 27 4.405683 76.747027 179.7279877 1104.2757962 1
#> 28 3.734660 65.746899 109.8294695 1114.5478839 1
#> 29 4.200901 58.408003 68.4803764 1035.0623595 1
#> 30 4.082391 50.128097 19.5667552 930.2828327 1
#> 31 4.202838 95.474175 167.7773896 2696.8693593 1
#> 32 4.451020 109.327631 129.8750749 2600.9147306 1
#> 33 5.110685 96.483065 122.7057295 2589.0762150 1
#> 34 4.244453 83.928879 121.5451222 1879.7776054 1
#> 35 4.640301 75.703094 132.8157177 1344.3216899 1
#> 36 4.500755 68.507679 123.3296492 1162.1032012 1
#> 37 4.107207 187.586580 900.4350894 4625.9916612 1
#> 38 5.055577 191.543170 965.4293671 4633.9629820 1
#> 39 4.217733 161.910103 820.7983212 3221.6728724 1
#> 40 4.723157 138.604280 675.6692669 2676.8126957 1
#> 41 4.702941 122.141067 569.4358423 2267.8242379 1
#> 42 4.848571 102.987355 445.4955468 1856.9964587 1
#> 43 5.677795 118.889635 353.8944612 2761.2593373 1
#> 44 4.282780 115.893253 387.4485091 2881.7496802 1
#> 45 5.671069 105.878337 363.7551128 2830.1251679 1
#> 46 5.039461 96.999931 331.2684412 2433.5475356 1
#> 47 5.651133 91.430492 316.4926887 2290.3988433 1
#> 48 6.039762 86.096662 294.4653399 2133.8427760 1
#> 49 5.231276 82.091500 295.2783377 1885.6982393 1
#> 50 6.020094 71.297506 253.3567485 1535.3317331 1
#> 51 5.048226 68.471197 159.3537874 1294.0038779 1
#> 52 5.430836 65.836493 123.6774821 1142.3804690 1
#> 53 4.705301 64.243922 129.4967434 1173.2599216 1
#> 54 5.014128 63.694013 125.8104743 1209.5862170 1
#> 55 3.685054 60.093947 123.8780801 1161.9839622 1
#> Vatnsdalsa.CoverageRate
#> 1 1
#> 2 1
#> 3 1
#> 4 1
#> 5 1
#> 6 1
#> 7 1
#> 8 1
#> 9 1
#> 10 1
#> 11 1
#> 12 1
#> 13 1
#> 14 1
#> 15 1
#> 16 1
#> 17 1
#> 18 1
#> 19 1
#> 20 1
#> 21 1
#> 22 1
#> 23 1
#> 24 1
#> 25 1
#> 26 1
#> 27 1
#> 28 1
#> 29 1
#> 30 1
#> 31 1
#> 32 1
#> 33 1
#> 34 1
#> 35 1
#> 36 1
#> 37 1
#> 38 1
#> 39 1
#> 40 1
#> 41 1
#> 42 1
#> 43 1
#> 44 1
#> 45 1
#> 46 1
#> 47 1
#> 48 1
#> 49 1
#> 50 1
#> 51 1
#> 52 1
#> 53 1
#> 54 1
#> 55 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=100,
n.sim=200, 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 0.112586219 -1.1390357 1.0262864
#> 2 0.035599237 -0.9689363 0.8155837
#> 3 0.097336481 -1.0032996 0.7949761
#> 4 -0.013298870 -0.7624546 1.1090434
#> 5 0.189889456 -1.0109540 1.1799783
#> 6 -0.025013733 -0.8620217 1.0030341
#> 7 0.172848190 -0.6510998 1.1227964
#> 8 -0.043812236 -1.0430066 1.0325524
#> 9 -0.042057030 -0.9509143 1.2833571
#> 10 0.202995757 -0.9712202 1.1340758
#> 11 0.213729685 -0.9602116 1.5215730
#> 12 0.015910207 -0.7778474 0.9135868
#> 13 -0.039163455 -1.0259053 1.0440651
#> 14 0.217240167 -0.6976278 1.1545083
#> 15 0.012121369 -1.0307799 0.9570123
#> 16 0.198119154 -0.7297412 0.9029907
#> 17 0.208026267 -0.5853317 1.2721352
#> 18 0.142215373 -0.8143463 1.1375432
#> 19 0.039152554 -1.1556823 0.9613983
#> 20 0.233289169 -0.7779800 1.2653505
#> 21 -0.041057458 -0.9171602 0.7817267
#> 22 0.034901764 -0.9503359 1.0627866
#> 23 0.058845514 -0.9021102 0.9911139
#> 24 0.017608810 -0.7609695 0.9483231
#> 25 0.155193819 -0.8171376 1.3364946
#> 26 0.101354243 -0.7983924 1.2299209
#> 27 -0.046789242 -0.8878021 0.9756678
#> 28 -0.081675342 -0.7773106 1.0838927
#> 29 0.079404222 -0.8004698 1.2198963
#> 30 0.160053684 -0.8650256 1.0601268
#> 31 0.024620333 -0.8801337 0.9464468
#> 32 0.072500218 -0.8358809 1.4039132
#> 33 0.002134313 -1.1292310 0.8822617
#> 34 0.184040727 -0.7389741 0.9887795
#> 35 0.182835700 -0.9124597 1.2145833
#> 36 -0.047512554 -1.5090228 2.0360920
#> 37 0.128730343 -0.9026442 1.0780256
#> 38 0.233261526 -1.1211093 1.2259727
#> 39 -0.008780516 -1.0453155 0.7911265
#> 40 -0.012839121 -0.8766293 1.3541774
#> 41 -0.085600473 -0.7721337 1.3526424
#> 42 0.114550495 -0.9957940 0.9349809
#> 43 0.141991798 -0.6966973 1.4939427
#> 44 0.003238459 -0.7807743 1.0529165
#> 45 0.027519916 -0.7648122 1.1797901
#> 46 0.480292350 -1.5671242 2.3997725
#> 47 0.028033013 -1.0693254 0.9671299
#> 48 0.162664306 -1.7383638 2.3185343
#> 49 0.372387414 -1.1572059 1.3445638
#> 50 0.120140993 -0.9610197 1.1323038
#> 51 0.010966810 -1.0775274 0.8213435
#> 52 0.192661103 -0.6713139 1.2376239
#> 53 0.034508853 -1.4810398 2.2973360
#> 54 0.071052439 -0.8102468 1.1128845
#> 55 0.208515971 -0.7292826 1.3501893
#> 56 -0.090342981 -0.8900475 1.1618030
#> 57 0.015395123 -0.8403066 0.9672527
#> 58 0.249533507 -0.8634791 1.1226054
#> 59 0.632020552 -0.8827043 3.3837886
#> 60 0.083390540 -0.9421312 0.8059986
#> 61 0.256528400 -1.1857627 1.1194832
#> 62 0.052080731 -0.7505654 1.1773129
#> 63 -0.202176238 -1.0370565 1.0994203
#> 64 -0.106435601 -1.0932689 1.0711666
#> 65 -0.065904521 -1.6394671 1.9912239
#> 66 0.329047970 -0.7066354 1.1741708
#> 67 0.325380710 -1.3595375 1.8694325
#> 68 -0.060409587 -1.9610306 2.2933785
#> 69 0.316909497 -0.7748288 1.2576989
#> 70 0.304230930 -0.5442671 1.0874795
#> 71 0.005307201 -0.8825800 1.0403448
#> 72 0.151305022 -2.3762986 2.2294219
#> 73 0.030456128 -0.8687905 1.0880073
#> 74 0.349822610 -0.6986892 1.4989223
#> 75 0.095605779 -0.8765479 1.0676881
#> 76 0.149141682 -1.5383552 2.2304358
#> 77 0.019616029 -1.0125738 1.2522548
#> 78 0.574744804 -1.6129442 2.6834627
#> 79 -0.076903051 -0.8099937 1.3648171
#> 80 0.140221834 -0.8161557 1.1476815
#> 81 0.073639928 -0.8950290 1.1398186
#> 82 0.397730785 -2.0574184 2.2102982
#> 83 -0.285051578 -2.1008092 2.0479705
#> 84 0.212694824 -0.8309488 1.4383083
#> 85 0.454809535 -0.7617805 1.2340245
#> 86 0.152022332 -0.6029416 1.1506120
#> 87 -0.057032173 -1.0005957 0.8570818
#> 88 0.100060521 -0.8076734 1.4652176
#> 89 -0.099506790 -1.2033716 1.0271652
#> 90 0.365087460 -0.7764373 1.4141346
#> 91 0.233048851 -0.8076558 1.1551818
#> 92 0.004339078 -1.0977424 1.0317388
#> 93 0.022584949 -0.7953599 1.1988615
#> 94 0.129533717 -0.9107310 1.0192957
#> 95 0.036035708 -0.9716085 1.2244094
#> 96 0.061140186 -1.0157507 1.1056341
#> 97 0.061652417 -0.7749012 1.3714720
#> 98 0.085018414 -0.8985184 1.0391335
#> 99 -0.007997215 -0.8621282 1.0621351
#> 100 0.220846435 -0.8849370 1.0199131
with(p4,cbind(LS,ES,APE,CR))
#> Log.Score Energy.Score CCR.APE CCR.CoverageRate
#> 1 1.0945093 0.6236309 121.09322 1
#> 2 0.5535746 0.4195060 85.49449 1
#> 3 0.6479101 0.4297599 67.28566 1
#> 4 0.5062249 0.4225470 112.31659 1
#> 5 0.5122662 0.4304720 1.85578 1
#> 6 0.8392733 0.5072243 92.81895 1
#> 7 0.5666900 0.4240419 297.14804 1
#> 8 1.1914992 0.7528619 106.51307 1
#> 9 0.5587869 0.4782559 120.24681 1
#> 10 2.2475821 1.1228559 118.93452 0
#> 11 0.6805190 0.6067251 233.76652 1
#> 12 0.6261127 0.4423475 106.66602 1
#> 13 2.1565633 1.1578872 96.64119 0
#> 14 1.2553497 0.7572080 72.51173 1
#> 15 1.5316679 0.7799085 98.61934 1
#> 16 0.9760628 0.5220757 69.12029 1
#> 17 0.6251267 0.4569687 54.18020 1
#> 18 0.5864078 0.4459885 55.78345 1
#> 19 0.5178605 0.4669990 228.60955 1
#> 20 0.8499748 0.5904109 166.68824 1
#> 21 0.5860369 0.4044859 70.17505 1
#> 22 1.3909897 0.7446496 104.72614 1
#> 23 0.5291957 0.4847170 68.91222 1
#> 24 1.0390931 0.5837042 97.21999 1
#> 25 0.9468050 0.6457649 74.87793 1
#> 26 0.8111970 0.6034389 129.41296 1
#> 27 0.5191825 0.4354436 711.01409 1
#> 28 1.0645352 0.6365251 112.65375 1
#> 29 0.5166004 0.4946508 49.62800 1
#> 30 0.7211274 0.5194764 182.45785 1
#> 31 1.0637980 0.6142686 104.60398 1
#> 32 0.6135431 0.4941103 71.86192 1
#> 33 0.5307121 0.4233911 103.32218 1
#> 34 3.7996734 2.0399905 108.83008 0
#> 35 1.9128213 0.8526778 84.13033 1
#> 36 1.2719993 0.9817772 108.68205 1
#> 37 0.5934710 0.4382190 293.85105 1
#> 38 0.6539088 0.5521025 53.28769 1
#> 39 0.7871581 0.5436240 102.15548 1
#> 40 0.5137651 0.4673813 57.18496 1
#> 41 0.5930831 0.6548153 33.82078 1
#> 42 0.9434096 0.6040726 126.57055 1
#> 43 0.9161054 0.5803871 73.59158 1
#> 44 1.6070569 0.8092469 100.38373 0
#> 45 1.1774188 0.6399824 105.41164 1
#> 46 2.0484515 1.5524117 138.96379 1
#> 47 3.3935477 1.7471806 98.56273 0
#> 48 1.2333088 0.9759886 65.24352 1
#> 49 1.1031947 0.7116333 212.53041 1
#> 50 0.5737908 0.4397593 2552.86919 1
#> 51 2.7884324 1.4662478 100.69477 0
#> 52 0.5087479 0.4484861 286.13945 1
#> 53 1.1972100 0.7992162 66.52057 1
#> 54 0.9090366 0.5396111 87.19928 1
#> 55 0.8280512 0.5682685 173.78153 1
#> 56 1.0548854 0.7088356 113.06325 1
#> 57 1.9780651 0.9846394 101.47463 0
#> 58 1.1383737 0.7191717 67.26362 1
#> 59 1.3382062 0.8882639 22.00575 1
#> 60 1.1473738 0.6216681 115.50003 1
#> 61 1.0987663 0.7443868 158.98835 1
#> 62 0.5124698 0.4510207 30.77680 1
#> 63 1.6637010 0.9252929 78.69334 1
#> 64 1.3641714 0.8240754 113.77609 1
#> 65 1.3822773 0.8202662 88.36165 1
#> 66 2.8158622 1.4600220 124.61878 0
#> 67 1.2657799 0.8708421 60.65453 1
#> 68 1.2636159 0.8948299 71.73642 1
#> 69 0.7631659 0.5197850 478.20691 1
#> 70 3.0840978 1.6628653 119.82625 0
#> 71 1.1720548 0.6116519 100.87325 1
#> 72 1.4689006 1.1219075 84.98946 1
#> 73 0.5866188 0.4618063 87.77429 1
#> 74 2.9899973 1.5210654 125.53254 0
#> 75 0.8204880 0.5316537 134.73304 1
#> 76 2.1596920 1.6623199 109.77728 1
#> 77 1.8696183 1.0448584 98.27750 1
#> 78 1.4788644 1.1283114 253.28109 1
#> 79 0.8921611 0.6235932 114.22938 1
#> 80 3.2031725 1.7038080 107.98553 0
#> 81 3.2535728 1.5558866 104.36690 0
#> 82 1.4474407 1.0312004 200.60036 1
#> 83 3.3711185 2.7703618 109.92695 0
#> 84 1.0791189 0.6637545 70.22321 1
#> 85 0.7046353 0.4909200 305.99646 1
#> 86 0.7024990 0.4807924 65.58239 1
#> 87 0.5136464 0.4110922 175.14545 1
#> 88 4.0521820 2.1428382 95.96075 0
#> 89 1.1687991 0.7366656 116.17720 1
#> 90 0.8534895 0.5774012 420.48638 1
#> 91 1.4407340 0.7552922 76.97569 1
#> 92 2.1051550 1.0714234 99.62958 0
#> 93 1.3239771 0.7396557 97.15702 1
#> 94 0.5433949 0.4525251 50.30576 1
#> 95 1.9973538 1.0073641 96.98912 1
#> 96 0.6985609 0.5250258 125.71934 1
#> 97 1.3447276 0.7511561 109.68099 1
#> 98 1.8718254 0.9181893 91.82966 0
#> 99 0.8542266 0.5244090 98.06897 1
#> 100 1.1009380 0.5671691 70.23605 1
plot(p4,last=100)
# }