R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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
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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(280.2
+ ,299.9
+ ,339.2
+ ,374.2
+ ,393.5
+ ,389.2
+ ,381.7
+ ,375.2
+ ,369
+ ,357.4
+ ,352.1
+ ,346.5
+ ,342.9
+ ,340.3
+ ,328.3
+ ,322.9
+ ,314.3
+ ,308.9
+ ,294
+ ,285.6
+ ,281.2
+ ,280.3
+ ,278.8
+ ,274.5
+ ,270.4
+ ,263.4
+ ,259.9
+ ,258
+ ,262.7
+ ,284.7
+ ,311.3
+ ,322.1
+ ,327
+ ,331.3
+ ,333.3
+ ,321.4
+ ,327
+ ,320
+ ,314.7
+ ,316.7
+ ,314.4
+ ,321.3
+ ,318.2
+ ,307.2
+ ,301.3
+ ,287.5
+ ,277.7
+ ,274.4
+ ,258.8
+ ,253.3
+ ,251
+ ,248.4
+ ,249.5
+ ,246.1
+ ,244.5
+ ,243.6
+ ,244
+ ,240.8
+ ,249.8
+ ,248
+ ,259.4
+ ,260.5
+ ,260.8
+ ,261.3
+ ,259.5
+ ,256.6
+ ,257.9
+ ,256.5
+ ,254.2
+ ,253.3
+ ,253.8
+ ,255.5
+ ,257.1
+ ,257.3
+ ,253.2
+ ,252.8
+ ,252
+ ,250.7
+ ,252.2
+ ,250
+ ,251
+ ,253.4
+ ,251.2
+ ,255.6
+ ,261.1
+ ,258.9
+ ,259.9
+ ,261.2
+ ,264.7
+ ,267.1
+ ,266.4
+ ,267.7
+ ,268.6
+ ,267.5
+ ,268.5
+ ,268.5
+ ,270.5
+ ,270.9
+ ,270.1
+ ,269.3
+ ,269.8
+ ,270.1
+ ,264.9
+ ,263.7
+ ,264.8
+ ,263.7
+ ,255.9
+ ,276.2
+ ,360.1
+ ,380.5
+ ,373.7
+ ,369.8
+ ,366.6
+ ,359.3
+ ,345.8
+ ,326.2
+ ,324.5
+ ,328.1
+ ,327.5
+ ,324.4
+ ,316.5
+ ,310.9
+ ,301.5
+ ,291.7
+ ,290.4
+ ,287.4
+ ,277.7
+ ,281.6
+ ,288
+ ,276
+ ,272.9
+ ,283
+ ,283.3
+ ,276.8
+ ,284.5
+ ,282.7
+ ,281.2
+ ,287.4
+ ,283.1
+ ,284
+ ,285.5
+ ,289.2
+ ,292.5
+ ,296.4
+ ,305.2
+ ,303.9
+ ,311.5
+ ,316.3
+ ,316.7
+ ,322.5
+ ,317.1
+ ,309.8
+ ,303.8
+ ,290.3
+ ,293.7
+ ,291.7
+ ,296.5
+ ,289.1
+ ,288.5
+ ,293.8
+ ,297.7
+ ,305.4
+ ,302.7
+ ,302.5
+ ,303
+ ,294.5
+ ,294.1
+ ,294.5
+ ,297.1
+ ,289.4
+ ,292.4
+ ,287.9
+ ,286.6
+ ,280.5
+ ,272.4
+ ,269.2
+ ,270.6
+ ,267.3
+ ,262.5
+ ,266.8
+ ,268.8
+ ,263.1
+ ,261.2
+ ,266
+ ,262.5
+ ,265.2
+ ,261.3
+ ,253.7
+ ,249.2
+ ,239.1
+ ,236.4
+ ,235.2
+ ,245.2
+ ,246.2
+ ,247.7
+ ,251.4
+ ,253.3
+ ,254.8
+ ,250
+ ,249.3
+ ,241.5
+ ,243.3
+ ,248
+ ,253
+ ,252.9
+ ,251.5
+ ,251.6
+ ,253.5
+ ,259.8
+ ,334.1
+ ,448
+ ,445.8
+ ,445
+ ,448.2
+ ,438.2
+ ,439.8
+ ,423.4
+ ,410.8
+ ,408.4
+ ,406.7
+ ,405.9
+ ,402.7
+ ,405.1
+ ,399.6
+ ,386.5
+ ,381.4
+ ,375.2
+ ,357.7
+ ,359
+ ,355
+ ,352.7
+ ,344.4
+ ,343.8
+ ,338
+ ,339
+ ,333.3
+ ,334.4
+ ,328.3
+ ,330.7
+ ,330
+ ,331.6
+ ,351.2
+ ,389.4
+ ,410.9
+ ,442.8
+ ,462.8
+ ,466.9
+ ,461.7
+ ,439.2
+ ,430.3
+ ,416.1
+ ,402.5
+ ,397.3
+ ,403.3
+ ,395.9
+ ,387.8
+ ,378.6
+ ,377.1
+ ,370.4
+ ,362
+ ,350.3
+ ,348.2
+ ,344.6
+ ,343.5
+ ,342.8
+ ,347.6
+ ,346.6
+ ,349.5
+ ,342.1
+ ,342
+ ,342.8
+ ,339.3
+ ,348.2
+ ,333.7
+ ,334.7
+ ,354
+ ,367.7
+ ,363.3
+ ,358.4
+ ,353.1
+ ,343.1
+ ,344.6
+ ,344.4
+ ,333.9
+ ,331.7
+ ,324.3
+ ,321.2
+ ,322.4
+ ,321.7
+ ,320.5
+ ,312.8
+ ,309.7
+ ,315.6
+ ,309.7
+ ,304.6
+ ,302.5
+ ,301.5
+ ,298.8
+ ,291.3
+ ,293.6
+ ,294.6
+ ,285.9
+ ,297.6
+ ,301.1
+ ,293.8
+ ,297.7
+ ,292.9
+ ,292.1
+ ,287.2
+ ,288.2
+ ,283.8
+ ,299.9
+ ,292.4
+ ,293.3
+ ,300.8
+ ,293.7
+ ,293.1
+ ,294.4
+ ,292.1
+ ,291.9
+ ,282.5
+ ,277.9
+ ,287.5
+ ,289.2
+ ,285.6
+ ,293.2
+ ,290.8
+ ,283.1
+ ,275
+ ,287.8
+ ,287.8
+ ,287.4
+ ,284
+ ,277.8
+ ,277.6
+ ,304.9
+ ,294
+ ,300.9
+ ,324
+ ,332.9
+ ,341.6
+ ,333.4
+ ,348.2
+ ,344.7
+ ,344.7
+ ,329.3
+ ,323.5
+ ,323.2
+ ,317.4
+ ,330.1
+ ,329.2
+ ,334.9
+ ,315.8
+ ,315.4
+ ,319.6
+ ,317.3
+ ,313.8
+ ,315.8
+ ,311.3)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> par1 <- as.numeric(par1) #cut off periods
> par1 <- 28
> 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
> par6 <- 3
> par7 <- as.numeric(par7) #q
> par7 <- 3
> 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      ma1    ma2     ma3
      1.2495  -0.706  -0.059  -0.7195  0.139  0.4351
s.e.     NaN     NaN     NaN      NaN    NaN     NaN

sigma^2 estimated as 106.2:  log likelihood = -1238.23,  aic = 2490.45
Warning messages:
1: In arima(x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8,  :
  possible convergence problem: optim gave code=1
2: In sqrt(diag(x$var.coef)) : NaNs produced
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 332 
End = 359 
Frequency = 1 
 [1] 284.2960 285.5797 286.5592 287.0835 286.9713 286.4031 285.7415 285.3225
 [9] 285.2997 285.6060 286.0296 286.3440 286.4196 286.2672 286.0047 285.7800
[17] 285.6935 285.7595 285.9164 286.0709 286.1493 286.1289 286.0389 285.9363
[25] 285.8728 285.8712 285.9201 285.9861

$se
Time Series:
Start = 332 
End = 359 
Frequency = 1 
 [1] 10.30464 18.83519 25.20416 30.96754 36.08974 40.45148 44.07051 47.11629
 [9] 49.82450 52.40851 55.00230 57.63801 60.26284 62.79065 65.15856 67.35611
[17] 69.41927 71.40452 73.36133 75.31429 77.25951 79.17449 81.03478 82.82772
[25] 84.55692 86.23775 87.88842 89.52185

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 332 
End = 359 
Frequency = 1 
 [1] 264.0989 248.6627 237.1590 226.3871 216.2354 207.1182 199.3633 192.9746
 [9] 187.6436 182.8853 178.2251 173.3735 168.3044 163.1975 158.2940 153.7620
[17] 149.6317 145.8066 142.1282 138.4549 134.7206 130.9469 127.2108 123.5940
[25] 120.1412 116.8452 113.6588 110.5233
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 332 
End = 359 
Frequency = 1 
 [1] 304.4931 322.4967 335.9593 347.7798 357.7072 365.6880 372.1197 377.6704
 [9] 382.9557 388.3267 393.8341 399.3145 404.5348 409.3368 413.7155 417.7980
[17] 421.7552 425.7124 429.7046 433.6869 437.5779 441.3109 444.8671 448.2787
[25] 451.6044 454.8972 458.1814 461.4489
> 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] 280.2000 299.9000 339.2000 374.2000 393.5000 389.2000 381.7000 375.2000
  [9] 369.0000 357.4000 352.1000 346.5000 342.9000 340.3000 328.3000 322.9000
 [17] 314.3000 308.9000 294.0000 285.6000 281.2000 280.3000 278.8000 274.5000
 [25] 270.4000 263.4000 259.9000 258.0000 262.7000 284.7000 311.3000 322.1000
 [33] 327.0000 331.3000 333.3000 321.4000 327.0000 320.0000 314.7000 316.7000
 [41] 314.4000 321.3000 318.2000 307.2000 301.3000 287.5000 277.7000 274.4000
 [49] 258.8000 253.3000 251.0000 248.4000 249.5000 246.1000 244.5000 243.6000
 [57] 244.0000 240.8000 249.8000 248.0000 259.4000 260.5000 260.8000 261.3000
 [65] 259.5000 256.6000 257.9000 256.5000 254.2000 253.3000 253.8000 255.5000
 [73] 257.1000 257.3000 253.2000 252.8000 252.0000 250.7000 252.2000 250.0000
 [81] 251.0000 253.4000 251.2000 255.6000 261.1000 258.9000 259.9000 261.2000
 [89] 264.7000 267.1000 266.4000 267.7000 268.6000 267.5000 268.5000 268.5000
 [97] 270.5000 270.9000 270.1000 269.3000 269.8000 270.1000 264.9000 263.7000
[105] 264.8000 263.7000 255.9000 276.2000 360.1000 380.5000 373.7000 369.8000
[113] 366.6000 359.3000 345.8000 326.2000 324.5000 328.1000 327.5000 324.4000
[121] 316.5000 310.9000 301.5000 291.7000 290.4000 287.4000 277.7000 281.6000
[129] 288.0000 276.0000 272.9000 283.0000 283.3000 276.8000 284.5000 282.7000
[137] 281.2000 287.4000 283.1000 284.0000 285.5000 289.2000 292.5000 296.4000
[145] 305.2000 303.9000 311.5000 316.3000 316.7000 322.5000 317.1000 309.8000
[153] 303.8000 290.3000 293.7000 291.7000 296.5000 289.1000 288.5000 293.8000
[161] 297.7000 305.4000 302.7000 302.5000 303.0000 294.5000 294.1000 294.5000
[169] 297.1000 289.4000 292.4000 287.9000 286.6000 280.5000 272.4000 269.2000
[177] 270.6000 267.3000 262.5000 266.8000 268.8000 263.1000 261.2000 266.0000
[185] 262.5000 265.2000 261.3000 253.7000 249.2000 239.1000 236.4000 235.2000
[193] 245.2000 246.2000 247.7000 251.4000 253.3000 254.8000 250.0000 249.3000
[201] 241.5000 243.3000 248.0000 253.0000 252.9000 251.5000 251.6000 253.5000
[209] 259.8000 334.1000 448.0000 445.8000 445.0000 448.2000 438.2000 439.8000
[217] 423.4000 410.8000 408.4000 406.7000 405.9000 402.7000 405.1000 399.6000
[225] 386.5000 381.4000 375.2000 357.7000 359.0000 355.0000 352.7000 344.4000
[233] 343.8000 338.0000 339.0000 333.3000 334.4000 328.3000 330.7000 330.0000
[241] 331.6000 351.2000 389.4000 410.9000 442.8000 462.8000 466.9000 461.7000
[249] 439.2000 430.3000 416.1000 402.5000 397.3000 403.3000 395.9000 387.8000
[257] 378.6000 377.1000 370.4000 362.0000 350.3000 348.2000 344.6000 343.5000
[265] 342.8000 347.6000 346.6000 349.5000 342.1000 342.0000 342.8000 339.3000
[273] 348.2000 333.7000 334.7000 354.0000 367.7000 363.3000 358.4000 353.1000
[281] 343.1000 344.6000 344.4000 333.9000 331.7000 324.3000 321.2000 322.4000
[289] 321.7000 320.5000 312.8000 309.7000 315.6000 309.7000 304.6000 302.5000
[297] 301.5000 298.8000 291.3000 293.6000 294.6000 285.9000 297.6000 301.1000
[305] 293.8000 297.7000 292.9000 292.1000 287.2000 288.2000 283.8000 299.9000
[313] 292.4000 293.3000 300.8000 293.7000 293.1000 294.4000 292.1000 291.9000
[321] 282.5000 277.9000 287.5000 289.2000 285.6000 293.2000 290.8000 283.1000
[329] 275.0000 287.8000 287.8000 284.2960 285.5797 286.5592 287.0835 286.9713
[337] 286.4031 285.7415 285.3225 285.2997 285.6060 286.0296 286.3440 286.4196
[345] 286.2672 286.0047 285.7800 285.6935 285.7595 285.9164 286.0709 286.1493
[353] 286.1289 286.0389 285.9363 285.8728 285.8712 285.9201 285.9861
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 332 
End = 359 
Frequency = 1 
 [1] 0.03624618 0.06595423 0.08795445 0.10786946 0.12576082 0.14123965
 [7] 0.15423211 0.16513344 0.17463919 0.18349933 0.19229584 0.20128943
[13] 0.21040054 0.21934281 0.22782336 0.23569217 0.24298516 0.24987630
[19] 0.25658319 0.26327145 0.26999723 0.27670919 0.28329983 0.28967191
[25] 0.29578511 0.30166645 0.30738805 0.31302869
> postscript(file="/var/www/html/rcomp/tmp/1z2i31260471274.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/www/html/rcomp/tmp/2nilb1260471274.ps",horizontal=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/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/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/www/html/rcomp/tmp/39uyt1260471274.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/www/html/rcomp/tmp/47t2j1260471274.tab") 
> 
> system("convert tmp/1z2i31260471274.ps tmp/1z2i31260471274.png")
> system("convert tmp/2nilb1260471274.ps tmp/2nilb1260471274.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.631   0.338   1.757