R version 2.15.2 (2012-10-26) -- "Trick or Treat"
Copyright (C) 2012 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
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.

R is a collaborative project with many contributors.
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(41
+ ,48
+ ,52
+ ,53
+ ,65
+ ,68
+ ,64
+ ,57
+ ,55
+ ,54
+ ,59
+ ,66
+ ,83
+ ,100
+ ,101
+ ,98
+ ,92
+ ,85
+ ,92
+ ,94
+ ,90
+ ,99
+ ,108
+ ,106
+ ,99
+ ,100
+ ,99
+ ,93
+ ,92
+ ,93
+ ,98
+ ,95
+ ,86
+ ,85
+ ,83
+ ,85
+ ,80
+ ,84
+ ,86
+ ,87
+ ,85
+ ,83
+ ,76
+ ,70
+ ,78
+ ,83
+ ,88
+ ,90
+ ,90
+ ,97
+ ,102
+ ,101
+ ,98
+ ,98
+ ,100
+ ,102
+ ,108
+ ,112
+ ,110
+ ,110
+ ,117
+ ,120
+ ,119
+ ,113
+ ,123
+ ,120
+ ,129
+ ,132
+ ,136
+ ,141
+ ,122
+ ,137
+ ,145
+ ,155
+ ,148
+ ,153
+ ,172
+ ,169
+ ,180
+ ,190
+ ,233
+ ,231
+ ,245
+ ,299
+ ,385
+ ,381
+ ,322
+ ,317
+ ,323
+ ,393
+ ,372
+ ,387
+ ,413
+ ,405
+ ,407
+ ,392
+ ,363
+ ,358
+ ,375
+ ,370
+ ,386
+ ,353
+ ,347
+ ,363
+ ,350
+ ,347
+ ,333
+ ,327
+ ,328
+ ,309
+ ,286
+ ,319
+ ,285
+ ,301
+ ,315
+ ,388
+ ,383
+ ,417
+ ,423
+ ,430
+ ,486
+ ,394
+ ,411
+ ,431
+ ,447
+ ,432
+ ,457
+ ,453
+ ,441
+ ,416
+ ,451
+ ,432
+ ,436
+ ,429
+ ,421
+ ,425
+ ,437
+ ,432
+ ,413
+ ,419
+ ,436
+ ,421
+ ,424
+ ,402
+ ,403
+ ,400
+ ,426
+ ,418
+ ,403
+ ,405
+ ,394
+ ,400
+ ,376
+ ,367
+ ,354
+ ,348
+ ,364
+ ,329
+ ,348
+ ,330
+ ,351
+ ,336
+ ,332
+ ,349
+ ,384
+ ,370
+ ,346
+ ,338
+ ,335
+ ,338
+ ,347
+ ,372
+ ,376
+ ,373
+ ,392
+ ,374
+ ,385
+ ,372
+ ,372
+ ,352
+ ,353
+ ,330
+ ,348
+ ,346
+ ,361
+ ,364
+ ,375
+ ,369
+ ,342
+ ,338
+ ,337
+ ,333
+ ,336
+ ,322
+ ,329
+ ,322
+ ,325
+ ,331
+ ,311
+ ,318
+ ,312
+ ,315
+ ,333
+ ,311
+ ,321
+ ,316
+ ,284
+ ,281
+ ,280
+ ,266
+ ,268
+ ,278
+ ,292
+ ,263
+ ,265
+ ,266
+ ,251
+ ,256
+ ,280
+ ,283
+ ,289
+ ,308
+ ,293
+ ,281
+ ,274
+ ,277
+ ,278
+ ,250
+ ,265
+ ,269
+ ,262
+ ,258
+ ,251
+ ,243
+ ,247
+ ,224
+ ,241
+ ,255
+ ,261
+ ,267
+ ,264
+ ,270
+ ,275
+ ,281
+ ,301
+ ,321
+ ,355
+ ,319
+ ,299
+ ,319
+ ,328
+ ,348
+ ,335
+ ,333
+ ,331
+ ,318
+ ,325
+ ,318
+ ,313
+ ,313
+ ,315
+ ,298
+ ,311
+ ,309
+ ,297
+ ,294
+ ,291
+ ,292
+ ,290
+ ,287
+ ,281
+ ,295
+ ,289
+ ,286
+ ,295
+ ,291
+ ,315
+ ,306
+ ,304
+ ,309
+ ,307
+ ,299
+ ,294
+ ,295
+ ,296
+ ,294
+ ,292
+ ,290
+ ,289
+ ,310
+ ,297
+ ,301
+ ,302
+ ,297
+ ,305
+ ,298
+ ,299
+ ,273
+ ,267
+ ,266
+ ,284
+ ,276
+ ,284
+ ,285
+ ,267
+ ,273
+ ,262
+ ,246
+ ,251
+ ,248
+ ,255
+ ,245
+ ,251
+ ,261
+ ,259
+ ,271
+ ,258
+ ,253
+ ,239
+ ,241
+ ,281
+ ,285
+ ,289
+ ,290
+ ,290
+ ,305
+ ,289
+ ,302
+ ,294
+ ,301
+ ,299
+ ,312
+ ,310
+ ,312
+ ,309
+ ,292
+ ,284
+ ,290
+ ,292
+ ,297
+ ,316
+ ,320
+ ,304
+ ,301
+ ,322
+ ,309
+ ,308
+ ,311
+ ,328
+ ,343
+ ,345
+ ,342
+ ,350
+ ,322
+ ,311
+ ,319
+ ,328
+ ,320
+ ,321
+ ,331
+ ,342
+ ,322
+ ,307
+ ,302
+ ,307
+ ,301
+ ,315
+ ,342
+ ,333
+ ,332
+ ,332
+ ,330
+ ,322
+ ,319
+ ,345
+ ,324
+ ,322
+ ,325
+ ,325
+ ,335
+ ,335
+ ,335
+ ,341
+ ,320
+ ,324
+ ,328
+ ,329
+ ,338
+ ,336
+ ,361
+ ,353
+ ,352
+ ,393
+ ,393
+ ,420
+ ,435
+ ,468
+ ,466
+ ,481
+ ,511
+ ,508
+ ,480
+ ,496
+ ,487
+ ,473
+ ,473
+ ,488
+ ,479
+ ,501
+ ,503
+ ,497
+ ,496
+ ,490
+ ,482
+ ,486
+ ,493
+ ,522
+ ,546
+ ,534
+ ,570
+ ,624
+ ,640
+ ,589
+ ,559
+ ,570
+ ,590
+ ,588
+ ,566
+ ,630
+ ,576
+ ,642
+ ,626
+ ,718
+ ,750
+ ,690
+ ,667
+ ,689
+ ,666
+ ,662
+ ,666
+ ,681
+ ,705
+ ,783
+ ,758
+ ,776
+ ,812
+ ,824
+ ,887
+ ,984
+ ,1016
+ ,897
+ ,980
+ ,957
+ ,969
+ ,1063
+ ,1048
+ ,968
+ ,1022
+ ,1014
+ ,1035
+ ,1069
+ ,1038
+ ,1133
+ ,1260
+ ,1207
+ ,1235
+ ,1297
+ ,1179
+ ,1332
+ ,1323
+ ,1248
+ ,1248
+ ,1260
+ ,1260
+ ,1317
+ ,1308
+ ,1380
+ ,1327
+ ,1327)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '0.3'
> 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:
         sma1
      -0.9980
s.e.   0.1732

sigma^2 estimated as 0.008587:  log likelihood = 414.25,  aic = -824.5
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 468 
End = 479 
Frequency = 1 
 [1] 8.582260 8.627144 8.635053 8.628615 8.636332 8.660635 8.657734 8.655700
 [9] 8.675549 8.703497 8.696458 8.730950

$se
Time Series:
Start = 468 
End = 479 
Frequency = 1 
 [1] 0.09378535 0.13263252 0.16242323 0.18753994 0.20966914 0.22967601
 [7] 0.24807457 0.26519976 0.28128425 0.29649747 0.31096732 0.32479315

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 468 
End = 479 
Frequency = 1 
 [1] 8.398441 8.367184 8.316704 8.261036 8.225380 8.210470 8.171508 8.135908
 [9] 8.124232 8.122362 8.086962 8.094355
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 468 
End = 479 
Frequency = 1 
 [1] 8.766079 8.887104 8.953403 8.996193 9.047283 9.110800 9.143960 9.175491
 [9] 9.226867 9.284632 9.305954 9.367544
> 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]   41.000   48.000   52.000   53.000   65.000   68.000   64.000   57.000
  [9]   55.000   54.000   59.000   66.000   83.000  100.000  101.000   98.000
 [17]   92.000   85.000   92.000   94.000   90.000   99.000  108.000  106.000
 [25]   99.000  100.000   99.000   93.000   92.000   93.000   98.000   95.000
 [33]   86.000   85.000   83.000   85.000   80.000   84.000   86.000   87.000
 [41]   85.000   83.000   76.000   70.000   78.000   83.000   88.000   90.000
 [49]   90.000   97.000  102.000  101.000   98.000   98.000  100.000  102.000
 [57]  108.000  112.000  110.000  110.000  117.000  120.000  119.000  113.000
 [65]  123.000  120.000  129.000  132.000  136.000  141.000  122.000  137.000
 [73]  145.000  155.000  148.000  153.000  172.000  169.000  180.000  190.000
 [81]  233.000  231.000  245.000  299.000  385.000  381.000  322.000  317.000
 [89]  323.000  393.000  372.000  387.000  413.000  405.000  407.000  392.000
 [97]  363.000  358.000  375.000  370.000  386.000  353.000  347.000  363.000
[105]  350.000  347.000  333.000  327.000  328.000  309.000  286.000  319.000
[113]  285.000  301.000  315.000  388.000  383.000  417.000  423.000  430.000
[121]  486.000  394.000  411.000  431.000  447.000  432.000  457.000  453.000
[129]  441.000  416.000  451.000  432.000  436.000  429.000  421.000  425.000
[137]  437.000  432.000  413.000  419.000  436.000  421.000  424.000  402.000
[145]  403.000  400.000  426.000  418.000  403.000  405.000  394.000  400.000
[153]  376.000  367.000  354.000  348.000  364.000  329.000  348.000  330.000
[161]  351.000  336.000  332.000  349.000  384.000  370.000  346.000  338.000
[169]  335.000  338.000  347.000  372.000  376.000  373.000  392.000  374.000
[177]  385.000  372.000  372.000  352.000  353.000  330.000  348.000  346.000
[185]  361.000  364.000  375.000  369.000  342.000  338.000  337.000  333.000
[193]  336.000  322.000  329.000  322.000  325.000  331.000  311.000  318.000
[201]  312.000  315.000  333.000  311.000  321.000  316.000  284.000  281.000
[209]  280.000  266.000  268.000  278.000  292.000  263.000  265.000  266.000
[217]  251.000  256.000  280.000  283.000  289.000  308.000  293.000  281.000
[225]  274.000  277.000  278.000  250.000  265.000  269.000  262.000  258.000
[233]  251.000  243.000  247.000  224.000  241.000  255.000  261.000  267.000
[241]  264.000  270.000  275.000  281.000  301.000  321.000  355.000  319.000
[249]  299.000  319.000  328.000  348.000  335.000  333.000  331.000  318.000
[257]  325.000  318.000  313.000  313.000  315.000  298.000  311.000  309.000
[265]  297.000  294.000  291.000  292.000  290.000  287.000  281.000  295.000
[273]  289.000  286.000  295.000  291.000  315.000  306.000  304.000  309.000
[281]  307.000  299.000  294.000  295.000  296.000  294.000  292.000  290.000
[289]  289.000  310.000  297.000  301.000  302.000  297.000  305.000  298.000
[297]  299.000  273.000  267.000  266.000  284.000  276.000  284.000  285.000
[305]  267.000  273.000  262.000  246.000  251.000  248.000  255.000  245.000
[313]  251.000  261.000  259.000  271.000  258.000  253.000  239.000  241.000
[321]  281.000  285.000  289.000  290.000  290.000  305.000  289.000  302.000
[329]  294.000  301.000  299.000  312.000  310.000  312.000  309.000  292.000
[337]  284.000  290.000  292.000  297.000  316.000  320.000  304.000  301.000
[345]  322.000  309.000  308.000  311.000  328.000  343.000  345.000  342.000
[353]  350.000  322.000  311.000  319.000  328.000  320.000  321.000  331.000
[361]  342.000  322.000  307.000  302.000  307.000  301.000  315.000  342.000
[369]  333.000  332.000  332.000  330.000  322.000  319.000  345.000  324.000
[377]  322.000  325.000  325.000  335.000  335.000  335.000  341.000  320.000
[385]  324.000  328.000  329.000  338.000  336.000  361.000  353.000  352.000
[393]  393.000  393.000  420.000  435.000  468.000  466.000  481.000  511.000
[401]  508.000  480.000  496.000  487.000  473.000  473.000  488.000  479.000
[409]  501.000  503.000  497.000  496.000  490.000  482.000  486.000  493.000
[417]  522.000  546.000  534.000  570.000  624.000  640.000  589.000  559.000
[425]  570.000  590.000  588.000  566.000  630.000  576.000  642.000  626.000
[433]  718.000  750.000  690.000  667.000  689.000  666.000  662.000  666.000
[441]  681.000  705.000  783.000  758.000  776.000  812.000  824.000  887.000
[449]  984.000 1016.000  897.000  980.000  957.000  969.000 1063.000 1048.000
[457]  968.000 1022.000 1014.000 1035.000 1069.000 1038.000 1133.000 1260.000
[465] 1207.000 1235.000 1297.000 1294.212 1316.912 1320.941 1317.661 1321.593
[473] 1334.031 1332.542 1331.498 1341.704 1356.165 1352.513 1370.477
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 468 
End = 479 
Frequency = 1 
 [1] 0.03734496 0.05307195 0.06544030 0.07611795 0.08551315 0.09388342
 [7] 0.10192669 0.10947629 0.11631567 0.12266465 0.12924443 0.13489263
> postscript(file="/var/wessaorg/rcomp/tmp/1v1fb1356122649.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2ml841356122649.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/3gtg01356122649.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/4rura1356122649.tab") 
> 
> try(system("convert tmp/1v1fb1356122649.ps tmp/1v1fb1356122649.png",intern=TRUE))
character(0)
> try(system("convert tmp/2ml841356122649.ps tmp/2ml841356122649.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.888   0.278   2.287