R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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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(41130
+ ,43144
+ ,46195
+ ,40033
+ ,31710
+ ,42297
+ ,33889
+ ,23495
+ ,27060
+ ,31160
+ ,22214
+ ,16905
+ ,34388
+ ,29982
+ ,36374
+ ,37630
+ ,31023
+ ,39875
+ ,28866
+ ,20205
+ ,26082
+ ,28209
+ ,22813
+ ,15296
+ ,27796
+ ,31813
+ ,42513
+ ,41222
+ ,29094
+ ,28948
+ ,23230
+ ,21308
+ ,20649
+ ,23666
+ ,19206
+ ,16361
+ ,30472
+ ,25051
+ ,39393
+ ,32091
+ ,31007
+ ,32998
+ ,22809
+ ,20439
+ ,19900
+ ,29161
+ ,22149
+ ,15485
+ ,36181
+ ,39545
+ ,37955
+ ,31854
+ ,29788
+ ,31435
+ ,22504
+ ,19540
+ ,21893
+ ,29556
+ ,21811
+ ,13729
+ ,31332
+ ,31434
+ ,38812
+ ,36154
+ ,32820
+ ,32301
+ ,30358
+ ,20724
+ ,21056
+ ,30077
+ ,22411
+ ,16758
+ ,37243
+ ,41795
+ ,37755
+ ,42557
+ ,21507
+ ,43211
+ ,31476
+ ,21440
+ ,25307
+ ,34050
+ ,21970
+ ,17327
+ ,33607
+ ,34259
+ ,43309
+ ,40189
+ ,32663
+ ,36262
+ ,35718
+ ,25002
+ ,28764
+ ,33085
+ ,25403
+ ,17468
+ ,39457
+ ,39408
+ ,49419
+ ,37128
+ ,34698
+ ,40939
+ ,32695
+ ,27523
+ ,26875
+ ,28460
+ ,26511
+ ,19576
+ ,40659
+ ,35685
+ ,44559
+ ,37584
+ ,34670
+ ,42953
+ ,24058
+ ,35359
+ ,30919
+ ,35346
+ ,28309
+ ,17417
+ ,45465
+ ,44651
+ ,47947
+ ,43458
+ ,37744
+ ,39730
+ ,29903
+ ,24284
+ ,37981
+ ,32001
+ ,32273
+ ,23314
+ ,43522
+ ,33000
+ ,43685
+ ,45838
+ ,39741
+ ,42522
+ ,37318
+ ,26920
+ ,28651
+ ,35646
+ ,26312
+ ,20442
+ ,46402
+ ,45329
+ ,42185
+ ,49341
+ ,50472
+ ,33020
+ ,29567
+ ,22870
+ ,25730
+ ,32609
+ ,23536
+ ,15135
+ ,36776
+ ,29982
+ ,38062
+ ,34226
+ ,24906
+ ,30233
+ ,27405
+ ,20784
+ ,22886
+ ,25425
+ ,20838
+ ,15655
+ ,37158
+ ,36364
+ ,43213
+ ,31635
+ ,30113
+ ,29985
+ ,20919
+ ,19429
+ ,21427
+ ,26064
+ ,20109
+ ,15369
+ ,35466
+ ,25954
+ ,33504
+ ,28115
+ ,28501
+ ,28618
+ ,21434
+ ,20177
+ ,21484
+ ,25642
+ ,23515
+ ,12941
+ ,36190
+ ,37785
+ ,38407
+ ,33326
+ ,30304
+ ,27576
+ ,27048
+ ,17291
+ ,21018
+ ,26792
+ ,19426
+ ,13927
+ ,35647
+ ,31746
+ ,31277
+ ,31583
+ ,25607
+ ,28151
+ ,24947
+ ,18077
+ ,23429
+ ,26313
+ ,18862
+ ,14753
+ ,36409
+ ,33163
+ ,34122
+ ,35225
+ ,28249
+ ,30374
+ ,26311
+ ,22069
+ ,23651
+ ,28628
+ ,23187
+ ,14727
+ ,43080
+ ,32519
+ ,39657
+ ,33614
+ ,28671
+ ,34243
+ ,27336
+ ,22916
+ ,24537
+ ,26128
+ ,22602
+ ,15744
+ ,41086
+ ,39690
+ ,43129
+ ,37863
+ ,35953
+ ,29133
+ ,24693
+ ,22205
+ ,21725
+ ,27192
+ ,21790
+ ,13253
+ ,37702
+ ,30364
+ ,32609
+ ,30212
+ ,29965
+ ,28352
+ ,25814
+ ,22414
+ ,20506
+ ,28806
+ ,22228
+ ,13971
+ ,36845
+ ,35338
+ ,35022
+ ,34777
+ ,26887
+ ,23970
+ ,22780
+ ,17351
+ ,21382
+ ,24561
+ ,17409
+ ,11514
+ ,31514
+ ,27071
+ ,29462
+ ,26105
+ ,22397
+ ,23843
+ ,21705
+ ,18089
+ ,20764
+ ,25316
+ ,17704
+ ,15548
+ ,28029
+ ,29383
+ ,36438
+ ,32034
+ ,22679
+ ,24319
+ ,18004
+ ,17537
+ ,20366
+ ,22782
+ ,19169
+ ,13807
+ ,29743
+ ,25591
+ ,29096
+ ,26482
+ ,22405
+ ,27044
+ ,17970
+ ,18730
+ ,19684
+ ,19785
+ ,18479
+ ,10698
+ ,31956
+ ,29506
+ ,34506
+ ,27165
+ ,26736
+ ,23691
+ ,18157
+ ,17328
+ ,18205
+ ,20995
+ ,17382
+ ,9367
+ ,31124
+ ,26551
+ ,30651
+ ,25859
+ ,25100
+ ,25778
+ ,20418
+ ,18688
+ ,20424
+ ,24776
+ ,19814
+ ,12738)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '0.5'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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      ma1     sma1
      0.9851  -0.7663  -0.8841
s.e.  0.0132   0.0399   0.0346

sigma^2 estimated as 89.93:  log likelihood = -1153.18,  aic = 2314.36
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 325 
End = 336 
Frequency = 1 
 [1] 172.0811 163.7929 175.0184 165.3674 152.8632 155.0568 138.5517 127.9886
 [9] 134.7408 146.7992 130.0674 104.4396

$se
Time Series:
Start = 325 
End = 336 
Frequency = 1 
 [1]  9.484673  9.708955  9.921736 10.123926 10.316326 10.499645 10.674512
 [8] 10.841490 11.001086 11.153760 11.299926 11.439965

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 325 
End = 336 
Frequency = 1 
 [1] 153.49109 144.76335 155.57176 145.52446 132.64322 134.47753 117.62965
 [8] 106.73926 113.17868 124.93780 107.91957  82.01726
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 325 
End = 336 
Frequency = 1 
 [1] 190.6710 182.8225 194.4650 185.2102 173.0832 175.6361 159.4737 149.2379
 [9] 156.3029 168.6605 152.2153 126.8619
> 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] 41130.00 43144.00 46195.00 40033.00 31710.00 42297.00 33889.00 23495.00
  [9] 27060.00 31160.00 22214.00 16905.00 34388.00 29982.00 36374.00 37630.00
 [17] 31023.00 39875.00 28866.00 20205.00 26082.00 28209.00 22813.00 15296.00
 [25] 27796.00 31813.00 42513.00 41222.00 29094.00 28948.00 23230.00 21308.00
 [33] 20649.00 23666.00 19206.00 16361.00 30472.00 25051.00 39393.00 32091.00
 [41] 31007.00 32998.00 22809.00 20439.00 19900.00 29161.00 22149.00 15485.00
 [49] 36181.00 39545.00 37955.00 31854.00 29788.00 31435.00 22504.00 19540.00
 [57] 21893.00 29556.00 21811.00 13729.00 31332.00 31434.00 38812.00 36154.00
 [65] 32820.00 32301.00 30358.00 20724.00 21056.00 30077.00 22411.00 16758.00
 [73] 37243.00 41795.00 37755.00 42557.00 21507.00 43211.00 31476.00 21440.00
 [81] 25307.00 34050.00 21970.00 17327.00 33607.00 34259.00 43309.00 40189.00
 [89] 32663.00 36262.00 35718.00 25002.00 28764.00 33085.00 25403.00 17468.00
 [97] 39457.00 39408.00 49419.00 37128.00 34698.00 40939.00 32695.00 27523.00
[105] 26875.00 28460.00 26511.00 19576.00 40659.00 35685.00 44559.00 37584.00
[113] 34670.00 42953.00 24058.00 35359.00 30919.00 35346.00 28309.00 17417.00
[121] 45465.00 44651.00 47947.00 43458.00 37744.00 39730.00 29903.00 24284.00
[129] 37981.00 32001.00 32273.00 23314.00 43522.00 33000.00 43685.00 45838.00
[137] 39741.00 42522.00 37318.00 26920.00 28651.00 35646.00 26312.00 20442.00
[145] 46402.00 45329.00 42185.00 49341.00 50472.00 33020.00 29567.00 22870.00
[153] 25730.00 32609.00 23536.00 15135.00 36776.00 29982.00 38062.00 34226.00
[161] 24906.00 30233.00 27405.00 20784.00 22886.00 25425.00 20838.00 15655.00
[169] 37158.00 36364.00 43213.00 31635.00 30113.00 29985.00 20919.00 19429.00
[177] 21427.00 26064.00 20109.00 15369.00 35466.00 25954.00 33504.00 28115.00
[185] 28501.00 28618.00 21434.00 20177.00 21484.00 25642.00 23515.00 12941.00
[193] 36190.00 37785.00 38407.00 33326.00 30304.00 27576.00 27048.00 17291.00
[201] 21018.00 26792.00 19426.00 13927.00 35647.00 31746.00 31277.00 31583.00
[209] 25607.00 28151.00 24947.00 18077.00 23429.00 26313.00 18862.00 14753.00
[217] 36409.00 33163.00 34122.00 35225.00 28249.00 30374.00 26311.00 22069.00
[225] 23651.00 28628.00 23187.00 14727.00 43080.00 32519.00 39657.00 33614.00
[233] 28671.00 34243.00 27336.00 22916.00 24537.00 26128.00 22602.00 15744.00
[241] 41086.00 39690.00 43129.00 37863.00 35953.00 29133.00 24693.00 22205.00
[249] 21725.00 27192.00 21790.00 13253.00 37702.00 30364.00 32609.00 30212.00
[257] 29965.00 28352.00 25814.00 22414.00 20506.00 28806.00 22228.00 13971.00
[265] 36845.00 35338.00 35022.00 34777.00 26887.00 23970.00 22780.00 17351.00
[273] 21382.00 24561.00 17409.00 11514.00 31514.00 27071.00 29462.00 26105.00
[281] 22397.00 23843.00 21705.00 18089.00 20764.00 25316.00 17704.00 15548.00
[289] 28029.00 29383.00 36438.00 32034.00 22679.00 24319.00 18004.00 17537.00
[297] 20366.00 22782.00 19169.00 13807.00 29743.00 25591.00 29096.00 26482.00
[305] 22405.00 27044.00 17970.00 18730.00 19684.00 19785.00 18479.00 10698.00
[313] 31956.00 29506.00 34506.00 27165.00 26736.00 23691.00 18157.00 17328.00
[321] 18205.00 20995.00 17382.00  9367.00 29611.89 26828.12 30631.43 27346.36
[329] 23367.16 24042.62 19196.57 16381.08 18155.09 21550.00 16917.54 10907.63
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 325 
End = 336 
Frequency = 1 
 [1] 0.1161893 0.1254383 0.1196783 0.1297877 0.1439015 0.1444168 0.1657210
 [8] 0.1834768 0.1763582 0.1632744 0.1885484 0.2425900
> postscript(file="/var/www/html/rcomp/tmp/1343b1229432398.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/2po3m1229432398.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[1:12] <- 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/3ouo01229432398.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/4eksb1229432398.tab") 
> 
> system("convert tmp/1343b1229432398.ps tmp/1343b1229432398.png")
> system("convert tmp/2po3m1229432398.ps tmp/2po3m1229432398.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.783   0.423   3.205