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Paper

*Unverified author*

R Software Module: /rwasp_arimaforecasting.wasp (opens new window with default values)

Title produced by software: ARIMA Forecasting

Date of computation: Wed, 29 Dec 2010 19:50:34 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293652108sxyst439mhuqkg2.htm/, Retrieved Wed, 29 Dec 2010 20:48:30 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293652108sxyst439mhuqkg2.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596 194581 185686 178106 172608 167302 168053 202300 202388 182516 173476 166444 171297 169701 164182 161914 159612 151001 158114 186530 187069 174330 169362 166827 178037 186413 189226 191563 188906 186005 195309 223532 226899 214126 206903 204442 220375 214320 212588 205816 202196 195722 198563 229139 229527 211868 203555 195770

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

Univariate ARIMA Extrapolation Forecast
time	Y[t]	F[t]	95% LB	95% UB	p-value (H0: Y[t] = F[t])	P(F[t]>Y[t-1])	P(F[t]>Y[t-s])	P(F[t]>Y[59])
47	166827	-	-	-	-	-	-	-
48	178037	-	-	-	-	-	-	-
49	186413	-	-	-	-	-	-	-
50	189226	-	-	-	-	-	-	-
51	191563	-	-	-	-	-	-	-
52	188906	-	-	-	-	-	-	-
53	186005	-	-	-	-	-	-	-
54	195309	-	-	-	-	-	-	-
55	223532	-	-	-	-	-	-	-
56	226899	-	-	-	-	-	-	-
57	214126	-	-	-	-	-	-	-
58	206903	-	-	-	-	-	-	-
59	204442	-	-	-	-	-	-	-
60	220375	211582.0919	201700.7415	221463.4423	0.0406	0.9217	1	0.9217
61	214320	215037.1765	200472.4584	229601.8946	0.4616	0.2363	0.9999	0.923
62	212588	213820.1627	193330.3168	234310.0086	0.4531	0.4809	0.9907	0.8152
63	205816	213007.7007	187599.1494	238416.2519	0.2895	0.5129	0.951	0.7456
64	202196	210498.1642	180224.1116	240772.2167	0.2955	0.6191	0.9189	0.6525
65	195722	205877.7455	171251.634	240503.8569	0.2827	0.5825	0.8697	0.5324
66	198563	212274.2	173536.9044	251011.4956	0.2439	0.7988	0.8047	0.6541
67	229139	242095.8849	199571.862	284619.9079	0.2752	0.9776	0.8039	0.9587
68	229527	244466.1452	198381.048	290551.2425	0.2626	0.7428	0.7725	0.9556
69	211868	230678.5868	181258.6676	280098.506	0.2278	0.5182	0.7442	0.851
70	203555	222483.7044	169910.6255	275056.7832	0.2402	0.6539	0.7193	0.7494
71	195770	218034.5679	162475.0637	273594.0722	0.2161	0.6953	0.6842	0.6842

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
60	0.0238	0.0416	0	77315232.9213	0	0
61	0.0346	-0.0033	0.0224	514342.0972	38914787.5093	6238.1718
62	0.0489	-0.0058	0.0169	1518224.871	26449266.6298	5142.885
63	0.0609	-0.0338	0.0211	51720558.7753	32767089.6662	5724.2545
64	0.0734	-0.0394	0.0248	68925929.6135	39998857.6557	6324.465
65	0.0858	-0.0493	0.0289	103139165.7366	50522242.3358	7107.9
66	0.0931	-0.0646	0.034	187997004.6852	70161494.1	8376.2458
67	0.0896	-0.0535	0.0364	167880866.9241	82376415.703	9076.1454
68	0.0962	-0.0611	0.0392	223178059.7557	98021042.82	9900.5577
69	0.1093	-0.0815	0.0434	353838175.6565	123602756.1036	11117.6776
70	0.1206	-0.0851	0.0472	358295849.9295	144938491.906	12039.0403
71	0.13	-0.1021	0.0518	495710985.7269	174169533.0577	13197.3305

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293652108sxyst439mhuqkg2/1xgmo1293652233.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293652108sxyst439mhuqkg2/1xgmo1293652233.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293652108sxyst439mhuqkg2/2tq2x1293652233.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293652108sxyst439mhuqkg2/2tq2x1293652233.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

R code (references can be found in the software module):

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'))

(forecast <- predict(arima.out,par1))

(lb <- forecast$pred - 1.96 * forecast$se)

(ub <- forecast$pred + 1.96 * forecast$se)

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))

(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)

bitmap(file='test1.png')

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()

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)

bitmap(file='test2.png')

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()

load(file='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='mytable.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='mytable1.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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