R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: i686-pc-linux-gnu (32-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

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Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(1356.876334
+ ,1267.205322
+ ,1296.765977
+ ,1088.768988
+ ,974.9813884
+ ,901.3596576
+ ,697.4384802
+ ,619.518781
+ ,446.3076104
+ ,279.7073872
+ ,388.5496968
+ ,290.3616669
+ ,278.7900756
+ ,433.3678289
+ ,436.029714
+ ,642.0796877
+ ,800.8666721
+ ,1005.060868
+ ,986.1196671
+ ,1320.620732
+ ,1293.652614
+ ,1315.564345
+ ,1438.509653
+ ,1311.68492
+ ,1281.851742
+ ,1229.184547
+ ,1157.483378
+ ,1049.930474
+ ,720.8534348
+ ,756.8141819
+ ,587.8054359
+ ,440.0632504
+ ,476.8424862
+ ,376.9041092
+ ,408.9909215
+ ,335.6074609
+ ,510.7385144
+ ,784.0262709
+ ,868.9048671
+ ,930.5891366
+ ,1232.387738
+ ,1433.973937
+ ,1441.341759
+ ,1560.894767
+ ,1570.121112
+ ,1539.736335
+ ,1509.516021
+ ,1264.261299
+ ,1280.1511
+ ,1104.198071
+ ,867.0732077
+ ,832.9038416
+ ,551.1656185
+ ,578.9382082
+ ,548.7690841
+ ,526.7505509
+ ,543.7872669
+ ,387.4285031
+ ,583.0257696
+ ,858.5103593
+ ,835.2939603
+ ,1234.576103
+ ,1307.198241
+ ,1550.368145
+ ,1513.93417
+ ,1607.433912
+ ,1768.513076
+ ,1778.655313
+ ,1668.394241
+ ,1383.577733
+ ,1271.618447
+ ,1140.579064
+ ,998.7028247
+ ,804.5968421
+ ,743.1134557
+ ,661.133487
+ ,635.0605076
+ ,334.5931783
+ ,502.1494165
+ ,450.8321675
+ ,700.3681247
+ ,799.3587889
+ ,1068.293463
+ ,1229.161035
+ ,1369.983001
+ ,1586.670588
+ ,1649.664042
+ ,1871.680788
+ ,1816.035687
+ ,1919.694672
+ ,1817.473725
+ ,1707.303794
+ ,1606.456459
+ ,1446.737592
+ ,1005.045182
+ ,913.67958
+ ,694.7422417
+ ,647.2193014
+ ,603.2233095
+ ,561.3616255
+ ,477.9286605
+ ,648.8516322
+ ,676.4550378
+ ,1016.256499
+ ,1139.927185
+ ,1269.321991
+ ,1546.025319
+ ,1753.304467
+ ,1958.22963
+ ,2094.065774
+ ,1977.440699
+ ,2027.739055
+ ,1842.633768
+ ,1852.639287
+ ,1706.985147
+ ,1471.71997
+ ,1159.935346
+ ,888.3265125
+ ,747.4889418
+ ,573.6363
+ ,696.6030203
+ ,736.0360216
+ ,625.9859074
+ ,668.0129992
+ ,878.1341576
+ ,925.7355157
+ ,1384.068603
+ ,1504.264376
+ ,1677.525248
+ ,1935.129054
+ ,1995.385689
+ ,2158.635275
+ ,2278.786793
+ ,2004.468115
+ ,2055.40499
+ ,1967.431468
+ ,1770.334016
+ ,1699.341376
+ ,1476.810831
+ ,970.7915825
+ ,997.474492
+ ,652.0843291
+ ,708.677725
+ ,656.5517255
+ ,770.8461221
+ ,901.3881145
+ ,832.0016083
+ ,1028.128263
+ ,1296.071512
+ ,1785.233557
+ ,1804.294853
+ ,2165.319782
+ ,2274.425758
+ ,2444.192672
+ ,2254.896853
+ ,2475.21364
+ ,2096.602738
+ ,2180.683121
+ ,2069.506046
+ ,1776.663609
+ ,1612.449679
+ ,1322.927331
+ ,914.8881288
+ ,749.3597793
+ ,985.6467572
+ ,880.7232311
+ ,819.4581121
+ ,760.5542696
+ ,985.0475722
+ ,1295.758114
+ ,1683.545809
+ ,1787.214405
+ ,1972.790239
+ ,2134.412385
+ ,2263.189757
+ ,2432.266646
+ ,2369.774565
+ ,2360.715385
+ ,2432.992026
+ ,2437.706015
+ ,1921.308588
+ ,1960.743986
+ ,1481.140265
+ ,1436.91711
+ ,1299.84893
+ ,985.736701
+ ,805.8439046
+ ,736.9963963
+ ,898.3310247
+ ,1065.843227
+ ,1113.559476
+ ,1211.918524
+ ,1462.155718
+ ,1801.38398
+ ,2045.731198
+ ,2405.387519
+ ,2376.281401
+ ,2542.194732
+ ,2535.172687
+ ,2518.76254
+ ,2467.712934
+ ,2483.547793
+ ,2111.5245
+ ,1987.469819
+ ,1900.284914
+ ,1545.174509
+ ,1241.063215
+ ,1244.17204
+ ,1001.510714
+ ,1004.787213
+ ,1064.602774
+ ,1250.752996
+ ,1244.505238
+ ,1565.513983
+ ,1904.45973
+ ,2200.393469
+ ,2489.302736
+ ,2382.022655
+ ,2740.656964
+ ,2692.201467
+ ,2707.985974
+ ,2793.734301
+ ,2909.368555
+ ,2611.616903
+ ,2367.927913
+ ,2036.392713
+ ,1794.090508
+ ,1658.074271
+ ,1450.206111
+ ,1159.117531
+ ,1144.297116
+ ,1188.107289
+ ,1082.864685
+ ,1152.30001
+ ,1370.470201
+ ,1560.414285
+ ,1878.82661
+ ,2213.171169
+ ,2306.794427
+ ,2878.274067
+ ,3043.563683
+ ,3163.511145
+ ,3218.690493
+ ,3177.601319
+ ,2941.518453
+ ,2922.823356
+ ,2325.88093
+ ,2414.009426
+ ,1874.014382
+ ,1866.949762
+ ,1330.453111
+ ,1413.735476
+ ,988.2221384
+ ,1046.533458
+ ,1398.652585
+ ,1444.958119
+ ,1637.387943
+ ,1926.364707
+ ,2088.421239
+ ,2250.892557
+ ,2803.393628
+ ,2920.006864
+ ,3028.392467
+ ,3284.085805
+ ,3116.539112
+ ,3120.244711
+ ,2946.135624
+ ,2740.67997
+ ,2810.140837
+ ,2233.823039
+ ,2114.011418
+ ,2076.542437
+ ,1571.481405
+ ,1567.958655
+ ,1217.444043
+ ,1136.643661
+ ,1481.287919
+ ,1528.477337
+ ,1797.720002
+ ,1819.469046
+ ,2395.358987
+ ,2707.314708
+ ,2921.060577
+ ,3246.433366
+ ,3051.477548
+ ,3444.481052
+ ,3432.580153
+ ,3421.04804
+ ,3381.830601
+ ,3169.679136
+ ,2872.11508
+ ,2601.76563
+ ,2143.011809
+ ,2159.598897
+ ,1645.12941
+ ,1622.54215
+ ,1350.064447
+ ,1372.486802
+ ,1475.078831
+ ,1356.08523
+ ,1974.230192
+ ,1835.493872
+ ,2495.225532
+ ,2813.660064
+ ,3199.803837
+ ,3128.428211
+ ,3614.588977
+ ,3741.816099
+ ,3711.62971
+ ,3501.116488
+ ,3620.888016
+ ,3348.935195)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '2'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '0.5'
> par1 = '12'
> par1 <- as.numeric(par1) #cut off periods
> par2 <- as.numeric(par2) #lambda
> par3 <- as.numeric(par3) #degree of non-seasonal differencing
> par4 <- as.numeric(par4) #degree of seasonal differencing
> par5 <- as.numeric(par5) #seasonal period
> par6 <- as.numeric(par6) #p
> par7 <- as.numeric(par7) #q
> par8 <- as.numeric(par8) #P
> par9 <- as.numeric(par9) #Q
> if (par10 == 'TRUE') par10 <- TRUE
> if (par10 == 'FALSE') par10 <- FALSE
> if (par2 == 0) x <- log(x)
> if (par2 != 0) x <- x^par2
> lx <- length(x)
> first <- lx - 2*par1
> nx <- lx - par1
> nx1 <- nx + 1
> fx <- lx - nx
> if (fx < 1) {
+ fx <- par5
+ nx1 <- lx + fx - 1
+ first <- lx - 2*fx
+ }
> first <- 1
> if (fx < 3) fx <- round(lx/10,0)
> (arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))

Call:
arima(x = x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8, 
    par4, par9), period = par5), include.mean = par10, method = "ML")

Coefficients:
          ar1     ar2     ar3     sar1    sar2
      -0.1343  0.2691  0.1743  -0.2968  0.2636
s.e.   0.0698  0.0676  0.0587   0.0688  0.0612

sigma^2 estimated as 5.054:  log likelihood = -668.52,  aic = 1349.03
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 301 
End = 312 
Frequency = 1 
 [1] 39.28247 39.94320 41.69361 42.69624 45.74199 46.56305 48.86713 49.73423
 [9] 50.34023 51.16368 50.73849 51.18496

$se
Time Series:
Start = 301 
End = 312 
Frequency = 1 
 [1]  2.248038  2.973353  3.944189  4.845879  5.650571  6.429144  7.141270
 [8]  7.810022  8.437950  9.028445  9.587861 10.118998

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 301 
End = 312 
Frequency = 1 
 [1] 34.87632 34.11543 33.96300 33.19832 34.66687 33.96192 34.87024 34.42658
 [9] 33.80184 33.46793 31.94628 31.35172
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 301 
End = 312 
Frequency = 1 
 [1] 43.68863 45.77097 49.42422 52.19417 56.81710 59.16417 62.86402 65.04187
 [9] 66.87861 68.85943 69.53069 71.01819
> if (par2 == 0) {
+ x <- exp(x)
+ forecast$pred <- exp(forecast$pred)
+ lb <- exp(lb)
+ ub <- exp(ub)
+ }
> if (par2 != 0) {
+ x <- x^(1/par2)
+ forecast$pred <- forecast$pred^(1/par2)
+ lb <- lb^(1/par2)
+ ub <- ub^(1/par2)
+ }
> if (par2 < 0) {
+ olb <- lb
+ lb <- ub
+ ub <- olb
+ }
> (actandfor <- c(x[1:nx], forecast$pred))
  [1] 1356.8763 1267.2053 1296.7660 1088.7690  974.9814  901.3597  697.4385
  [8]  619.5188  446.3076  279.7074  388.5497  290.3617  278.7901  433.3678
 [15]  436.0297  642.0797  800.8667 1005.0609  986.1197 1320.6207 1293.6526
 [22] 1315.5643 1438.5097 1311.6849 1281.8517 1229.1845 1157.4834 1049.9305
 [29]  720.8534  756.8142  587.8054  440.0633  476.8425  376.9041  408.9909
 [36]  335.6075  510.7385  784.0263  868.9049  930.5891 1232.3877 1433.9739
 [43] 1441.3418 1560.8948 1570.1211 1539.7363 1509.5160 1264.2613 1280.1511
 [50] 1104.1981  867.0732  832.9038  551.1656  578.9382  548.7691  526.7506
 [57]  543.7873  387.4285  583.0258  858.5104  835.2940 1234.5761 1307.1982
 [64] 1550.3681 1513.9342 1607.4339 1768.5131 1778.6553 1668.3942 1383.5777
 [71] 1271.6184 1140.5791  998.7028  804.5968  743.1135  661.1335  635.0605
 [78]  334.5932  502.1494  450.8322  700.3681  799.3588 1068.2935 1229.1610
 [85] 1369.9830 1586.6706 1649.6640 1871.6808 1816.0357 1919.6947 1817.4737
 [92] 1707.3038 1606.4565 1446.7376 1005.0452  913.6796  694.7422  647.2193
 [99]  603.2233  561.3616  477.9287  648.8516  676.4550 1016.2565 1139.9272
[106] 1269.3220 1546.0253 1753.3045 1958.2296 2094.0658 1977.4407 2027.7391
[113] 1842.6338 1852.6393 1706.9851 1471.7200 1159.9353  888.3265  747.4889
[120]  573.6363  696.6030  736.0360  625.9859  668.0130  878.1342  925.7355
[127] 1384.0686 1504.2644 1677.5252 1935.1291 1995.3857 2158.6353 2278.7868
[134] 2004.4681 2055.4050 1967.4315 1770.3340 1699.3414 1476.8108  970.7916
[141]  997.4745  652.0843  708.6777  656.5517  770.8461  901.3881  832.0016
[148] 1028.1283 1296.0715 1785.2336 1804.2949 2165.3198 2274.4258 2444.1927
[155] 2254.8969 2475.2136 2096.6027 2180.6831 2069.5060 1776.6636 1612.4497
[162] 1322.9273  914.8881  749.3598  985.6468  880.7232  819.4581  760.5543
[169]  985.0476 1295.7581 1683.5458 1787.2144 1972.7902 2134.4124 2263.1898
[176] 2432.2666 2369.7746 2360.7154 2432.9920 2437.7060 1921.3086 1960.7440
[183] 1481.1403 1436.9171 1299.8489  985.7367  805.8439  736.9964  898.3310
[190] 1065.8432 1113.5595 1211.9185 1462.1557 1801.3840 2045.7312 2405.3875
[197] 2376.2814 2542.1947 2535.1727 2518.7625 2467.7129 2483.5478 2111.5245
[204] 1987.4698 1900.2849 1545.1745 1241.0632 1244.1720 1001.5107 1004.7872
[211] 1064.6028 1250.7530 1244.5052 1565.5140 1904.4597 2200.3935 2489.3027
[218] 2382.0227 2740.6570 2692.2015 2707.9860 2793.7343 2909.3686 2611.6169
[225] 2367.9279 2036.3927 1794.0905 1658.0743 1450.2061 1159.1175 1144.2971
[232] 1188.1073 1082.8647 1152.3000 1370.4702 1560.4143 1878.8266 2213.1712
[239] 2306.7944 2878.2741 3043.5637 3163.5111 3218.6905 3177.6013 2941.5185
[246] 2922.8234 2325.8809 2414.0094 1874.0144 1866.9498 1330.4531 1413.7355
[253]  988.2221 1046.5335 1398.6526 1444.9581 1637.3879 1926.3647 2088.4212
[260] 2250.8926 2803.3936 2920.0069 3028.3925 3284.0858 3116.5391 3120.2447
[267] 2946.1356 2740.6800 2810.1408 2233.8230 2114.0114 2076.5424 1571.4814
[274] 1567.9587 1217.4440 1136.6437 1481.2879 1528.4773 1797.7200 1819.4690
[281] 2395.3590 2707.3147 2921.0606 3246.4334 3051.4775 3444.4811 3432.5802
[288] 3421.0480 3381.8306 3169.6791 2872.1151 2601.7656 2143.0118 2159.5989
[295] 1645.1294 1622.5421 1350.0644 1372.4868 1475.0788 1356.0852 1543.1126
[302] 1595.4594 1738.3570 1822.9691 2092.3293 2168.1172 2387.9966 2473.4933
[309] 2534.1384 2617.7219 2574.3939 2619.8998
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 301 
End = 312 
Frequency = 1 
 [1] 0.1208740 0.1597399 0.2067388 0.2522410 0.2769724 0.3135142 0.3341304
 [8] 0.3624040 0.3903049 0.4139561 0.4479206 0.4719926
> postscript(file="/var/wessaorg/rcomp/tmp/1ft8j1386184217.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
> box()
> par(opar)
> dev.off()
null device 
          1 
> prob.dec <- array(NA, dim=fx)
> prob.sdec <- array(NA, dim=fx)
> prob.ldec <- array(NA, dim=fx)
> prob.pval <- array(NA, dim=fx)
> perf.pe <- array(0, dim=fx)
> perf.mape <- array(0, dim=fx)
> perf.mape1 <- array(0, dim=fx)
> perf.se <- array(0, dim=fx)
> perf.mse <- array(0, dim=fx)
> perf.mse1 <- array(0, dim=fx)
> perf.rmse <- array(0, dim=fx)
> for (i in 1:fx) {
+ locSD <- (ub[i] - forecast$pred[i]) / 1.96
+ perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
+ prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
+ prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
+ prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
+ }
> perf.mape[1] = abs(perf.pe[1])
> perf.mse[1] = abs(perf.se[1])
> for (i in 2:fx) {
+ perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
+ perf.mape1[i] = perf.mape[i] / i
+ perf.mse[i] = perf.mse[i-1] + perf.se[i]
+ perf.mse1[i] = perf.mse[i] / i
+ }
> perf.rmse = sqrt(perf.mse1)
> postscript(file="/var/wessaorg/rcomp/tmp/2urmc1386184218.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
> dum <- forecast$pred
> dum[1:par1] <- x[(nx+1):lx]
> lines(dum, lty=1)
> lines(ub,lty=3)
> lines(lb,lty=3)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'time',1,header=TRUE)
> a<-table.element(a,'Y[t]',1,header=TRUE)
> a<-table.element(a,'F[t]',1,header=TRUE)
> a<-table.element(a,'95% LB',1,header=TRUE)
> a<-table.element(a,'95% UB',1,header=TRUE)
> a<-table.element(a,'p-value<br />(H0: Y[t] = F[t])',1,header=TRUE)
> a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
> a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
> mylab <- paste('P(F[t]>Y[',nx,sep='')
> mylab <- paste(mylab,'])',sep='')
> a<-table.element(a,mylab,1,header=TRUE)
> a<-table.row.end(a)
> for (i in (nx-par5):nx) {
+ a<-table.row.start(a)
+ a<-table.element(a,i,header=TRUE)
+ a<-table.element(a,x[i])
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.row.end(a)
+ }
> for (i in 1:fx) {
+ a<-table.row.start(a)
+ a<-table.element(a,nx+i,header=TRUE)
+ a<-table.element(a,round(x[nx+i],4))
+ a<-table.element(a,round(forecast$pred[i],4))
+ a<-table.element(a,round(lb[i],4))
+ a<-table.element(a,round(ub[i],4))
+ a<-table.element(a,round((1-prob.pval[i]),4))
+ a<-table.element(a,round((1-prob.dec[i]),4))
+ a<-table.element(a,round((1-prob.sdec[i]),4))
+ a<-table.element(a,round((1-prob.ldec[i]),4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/3ylnj1386184218.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'time',1,header=TRUE)
> a<-table.element(a,'% S.E.',1,header=TRUE)
> a<-table.element(a,'PE',1,header=TRUE)
> a<-table.element(a,'MAPE',1,header=TRUE)
> a<-table.element(a,'Sq.E',1,header=TRUE)
> a<-table.element(a,'MSE',1,header=TRUE)
> a<-table.element(a,'RMSE',1,header=TRUE)
> a<-table.row.end(a)
> for (i in 1:fx) {
+ a<-table.row.start(a)
+ a<-table.element(a,nx+i,header=TRUE)
+ a<-table.element(a,round(perc.se[i],4))
+ a<-table.element(a,round(perf.pe[i],4))
+ a<-table.element(a,round(perf.mape1[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse1[i],4))
+ a<-table.element(a,round(perf.rmse[i],4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/47btg1386184218.tab") 
> 
> try(system("convert tmp/1ft8j1386184217.ps tmp/1ft8j1386184217.png",intern=TRUE))
character(0)
> try(system("convert tmp/2urmc1386184218.ps tmp/2urmc1386184218.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  5.222   1.394   6.754