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)

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> x <- c(235.1
+ ,280.7
+ ,264.6
+ ,240.7
+ ,201.4
+ ,240.8
+ ,241.1
+ ,223.8
+ ,206.1
+ ,174.7
+ ,203.3
+ ,220.5
+ ,299.5
+ ,347.4
+ ,338.3
+ ,327.7
+ ,351.6
+ ,396.6
+ ,438.8
+ ,395.6
+ ,363.5
+ ,378.8
+ ,357
+ ,369
+ ,464.8
+ ,479.1
+ ,431.3
+ ,366.5
+ ,326.3
+ ,355.1
+ ,331.6
+ ,261.3
+ ,249
+ ,205.5
+ ,235.6
+ ,240.9
+ ,264.9
+ ,253.8
+ ,232.3
+ ,193.8
+ ,177
+ ,213.2
+ ,207.2
+ ,180.6
+ ,188.6
+ ,175.4
+ ,199
+ ,179.6
+ ,225.8
+ ,234
+ ,200.2
+ ,183.6
+ ,178.2
+ ,203.2
+ ,208.5
+ ,191.8
+ ,172.8
+ ,148
+ ,159.4
+ ,154.5
+ ,213.2
+ ,196.4
+ ,182.8
+ ,176.4
+ ,153.6
+ ,173.2
+ ,171
+ ,151.2
+ ,161.9
+ ,157.2
+ ,201.7
+ ,236.4
+ ,356.1
+ ,398.3
+ ,403.7
+ ,384.6
+ ,365.8
+ ,368.1
+ ,367.9
+ ,347
+ ,343.3
+ ,292.9
+ ,311.5
+ ,300.9
+ ,366.9
+ ,356.9
+ ,329.7
+ ,316.2
+ ,269
+ ,289.3
+ ,266.2
+ ,253.6
+ ,233.8
+ ,228.4
+ ,253.6
+ ,260.1
+ ,306.6
+ ,309.2
+ ,309.5
+ ,271
+ ,279.9
+ ,317.9
+ ,298.4
+ ,246.7
+ ,227.3
+ ,209.1
+ ,259.9
+ ,266
+ ,320.6
+ ,308.5
+ ,282.2
+ ,262.7
+ ,263.5
+ ,313.1
+ ,284.3
+ ,252.6
+ ,250.3
+ ,246.5
+ ,312.7
+ ,333.2
+ ,446.4
+ ,511.6
+ ,515.5
+ ,506.4
+ ,483.2
+ ,522.3
+ ,509.8
+ ,460.7
+ ,405.8
+ ,375
+ ,378.5
+ ,406.8
+ ,467.8
+ ,469.8
+ ,429.8
+ ,355.8
+ ,332.7
+ ,378
+ ,360.5
+ ,334.7
+ ,319.5
+ ,323.1
+ ,363.6
+ ,352.1
+ ,411.9
+ ,388.6
+ ,416.4
+ ,360.7
+ ,338
+ ,417.2
+ ,388.4
+ ,371.1
+ ,331.5
+ ,353.7
+ ,396.7
+ ,447
+ ,533.5
+ ,565.4
+ ,542.3
+ ,488.7
+ ,467.1
+ ,531.3
+ ,496.1
+ ,444
+ ,403.4
+ ,386.3
+ ,394.1
+ ,404.1
+ ,462.1
+ ,448.1
+ ,432.3
+ ,386.3
+ ,395.2
+ ,421.9
+ ,382.9
+ ,384.2
+ ,345.5
+ ,323.4
+ ,372.6
+ ,376
+ ,462.7
+ ,487
+ ,444.2
+ ,399.3
+ ,394.9
+ ,455.4
+ ,414
+ ,375.5
+ ,347
+ ,339.4
+ ,385.8
+ ,378.8
+ ,451.8
+ ,446.1
+ ,422.5
+ ,383.1
+ ,352.8
+ ,445.3
+ ,367.5
+ ,355.1
+ ,326.2
+ ,319.8
+ ,331.8
+ ,340.9
+ ,394.1
+ ,417.2
+ ,369.9
+ ,349.2
+ ,321.4
+ ,405.7
+ ,342.9
+ ,316.5
+ ,284.2
+ ,270.9
+ ,288.8
+ ,278.8
+ ,324.4
+ ,310.9
+ ,299
+ ,273
+ ,279.3
+ ,359.2
+ ,305
+ ,282.1
+ ,250.3
+ ,246.5
+ ,257.9
+ ,266.5
+ ,315.9
+ ,318.4
+ ,295.4
+ ,266.4
+ ,245.8
+ ,362.8
+ ,324.9
+ ,294.2
+ ,289.5
+ ,295.2
+ ,290.3
+ ,272
+ ,307.4
+ ,328.7
+ ,292.9
+ ,249.1
+ ,230.4
+ ,361.5
+ ,321.7
+ ,277.2
+ ,260.7
+ ,251
+ ,257.6
+ ,241.8
+ ,287.5
+ ,292.3
+ ,274.7
+ ,254.2
+ ,230
+ ,339
+ ,318.2
+ ,287
+ ,295.8
+ ,284
+ ,271
+ ,262.7
+ ,340.6
+ ,379.4
+ ,373.3
+ ,355.2
+ ,338.4
+ ,466.9
+ ,451
+ ,422
+ ,429.2
+ ,425.9
+ ,460.7
+ ,463.6
+ ,541.4
+ ,544.2
+ ,517.5
+ ,469.4
+ ,439.4
+ ,549
+ ,533
+ ,506.1
+ ,484
+ ,457
+ ,481.5
+ ,469.5
+ ,544.7
+ ,541.2
+ ,521.5
+ ,469.7
+ ,434.4
+ ,542.6
+ ,517.3
+ ,485.7
+ ,465.8
+ ,447
+ ,426.6
+ ,411.6
+ ,467.5
+ ,484.5
+ ,451.2
+ ,417.4
+ ,379.9
+ ,484.7
+ ,455
+ ,420.8
+ ,416.5
+ ,376.3
+ ,405.6
+ ,405.8
+ ,500.8
+ ,514
+ ,475.5
+ ,430.1
+ ,414.4
+ ,538
+ ,526
+ ,488.5
+ ,520.2
+ ,504.4
+ ,568.5
+ ,610.6
+ ,818
+ ,830.9
+ ,835.9
+ ,782
+ ,762.3
+ ,856.9
+ ,820.9
+ ,769.6
+ ,752.2
+ ,724.4
+ ,723.1
+ ,719.5
+ ,817.4
+ ,803.3
+ ,752.5
+ ,689
+ ,630.4
+ ,765.5
+ ,757.7
+ ,732.2
+ ,702.6
+ ,683.3
+ ,709.5
+ ,702.2
+ ,784.8
+ ,810.9
+ ,755.6
+ ,656.8
+ ,615.1
+ ,745.3
+ ,694.1
+ ,675.7
+ ,643.7
+ ,622.1
+ ,634.6
+ ,588
+ ,689.7
+ ,673.9
+ ,647.9
+ ,568.8
+ ,545.7)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '0'
> par3 = '0'
> par2 = '1'
> par1 = '12'
> par10 <- 'FALSE'
> par9 <- '0'
> par8 <- '0'
> par7 <- '0'
> par6 <- '0'
> par5 <- '12'
> par4 <- '0'
> par3 <- '0'
> par2 <- '1'
> par1 <- '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa P., (2009), ARIMA Forecasting (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/
> #Source of accompanying publication: 
> #Technical description: 
> 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")


sigma^2 estimated as 166931:  log likelihood = -2623.36,  aic = 5248.72
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 354 
End = 365 
Frequency = 1 
 [1] 0 0 0 0 0 0 0 0 0 0 0 0

$se
Time Series:
Start = 354 
End = 365 
Frequency = 1 
 [1] 408.5724 408.5724 408.5724 408.5724 408.5724 408.5724 408.5724 408.5724
 [9] 408.5724 408.5724 408.5724 408.5724

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 354 
End = 365 
Frequency = 1 
 [1] -800.8019 -800.8019 -800.8019 -800.8019 -800.8019 -800.8019 -800.8019
 [8] -800.8019 -800.8019 -800.8019 -800.8019 -800.8019
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 354 
End = 365 
Frequency = 1 
 [1] 800.8019 800.8019 800.8019 800.8019 800.8019 800.8019 800.8019 800.8019
 [9] 800.8019 800.8019 800.8019 800.8019
> 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] 235.1 280.7 264.6 240.7 201.4 240.8 241.1 223.8 206.1 174.7 203.3 220.5
 [13] 299.5 347.4 338.3 327.7 351.6 396.6 438.8 395.6 363.5 378.8 357.0 369.0
 [25] 464.8 479.1 431.3 366.5 326.3 355.1 331.6 261.3 249.0 205.5 235.6 240.9
 [37] 264.9 253.8 232.3 193.8 177.0 213.2 207.2 180.6 188.6 175.4 199.0 179.6
 [49] 225.8 234.0 200.2 183.6 178.2 203.2 208.5 191.8 172.8 148.0 159.4 154.5
 [61] 213.2 196.4 182.8 176.4 153.6 173.2 171.0 151.2 161.9 157.2 201.7 236.4
 [73] 356.1 398.3 403.7 384.6 365.8 368.1 367.9 347.0 343.3 292.9 311.5 300.9
 [85] 366.9 356.9 329.7 316.2 269.0 289.3 266.2 253.6 233.8 228.4 253.6 260.1
 [97] 306.6 309.2 309.5 271.0 279.9 317.9 298.4 246.7 227.3 209.1 259.9 266.0
[109] 320.6 308.5 282.2 262.7 263.5 313.1 284.3 252.6 250.3 246.5 312.7 333.2
[121] 446.4 511.6 515.5 506.4 483.2 522.3 509.8 460.7 405.8 375.0 378.5 406.8
[133] 467.8 469.8 429.8 355.8 332.7 378.0 360.5 334.7 319.5 323.1 363.6 352.1
[145] 411.9 388.6 416.4 360.7 338.0 417.2 388.4 371.1 331.5 353.7 396.7 447.0
[157] 533.5 565.4 542.3 488.7 467.1 531.3 496.1 444.0 403.4 386.3 394.1 404.1
[169] 462.1 448.1 432.3 386.3 395.2 421.9 382.9 384.2 345.5 323.4 372.6 376.0
[181] 462.7 487.0 444.2 399.3 394.9 455.4 414.0 375.5 347.0 339.4 385.8 378.8
[193] 451.8 446.1 422.5 383.1 352.8 445.3 367.5 355.1 326.2 319.8 331.8 340.9
[205] 394.1 417.2 369.9 349.2 321.4 405.7 342.9 316.5 284.2 270.9 288.8 278.8
[217] 324.4 310.9 299.0 273.0 279.3 359.2 305.0 282.1 250.3 246.5 257.9 266.5
[229] 315.9 318.4 295.4 266.4 245.8 362.8 324.9 294.2 289.5 295.2 290.3 272.0
[241] 307.4 328.7 292.9 249.1 230.4 361.5 321.7 277.2 260.7 251.0 257.6 241.8
[253] 287.5 292.3 274.7 254.2 230.0 339.0 318.2 287.0 295.8 284.0 271.0 262.7
[265] 340.6 379.4 373.3 355.2 338.4 466.9 451.0 422.0 429.2 425.9 460.7 463.6
[277] 541.4 544.2 517.5 469.4 439.4 549.0 533.0 506.1 484.0 457.0 481.5 469.5
[289] 544.7 541.2 521.5 469.7 434.4 542.6 517.3 485.7 465.8 447.0 426.6 411.6
[301] 467.5 484.5 451.2 417.4 379.9 484.7 455.0 420.8 416.5 376.3 405.6 405.8
[313] 500.8 514.0 475.5 430.1 414.4 538.0 526.0 488.5 520.2 504.4 568.5 610.6
[325] 818.0 830.9 835.9 782.0 762.3 856.9 820.9 769.6 752.2 724.4 723.1 719.5
[337] 817.4 803.3 752.5 689.0 630.4 765.5 757.7 732.2 702.6 683.3 709.5 702.2
[349] 784.8 810.9 755.6 656.8 615.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0
[361]   0.0   0.0   0.0   0.0   0.0
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 354 
End = 365 
Frequency = 1 
 [1] Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
> postscript(file="/var/fisher/rcomp/tmp/19mx71352745233.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/fisher/rcomp/tmp/2jeal1352745233.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/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/fisher/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/fisher/rcomp/tmp/3qizt1352745233.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/fisher/rcomp/tmp/44dlx1352745233.tab") 
> 
> try(system("convert tmp/19mx71352745233.ps tmp/19mx71352745233.png",intern=TRUE))
character(0)
> try(system("convert tmp/2jeal1352745233.ps tmp/2jeal1352745233.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.439   0.305   1.724