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

Title produced by software: ARIMA Forecasting

Date of computation: Mon, 22 Dec 2008 07:20:27 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/22/t1229955655y0224ggyav66i9n.htm/, Retrieved Mon, 22 Dec 2008 15:20:57 +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/2008/Dec/22/t1229955655y0224ggyav66i9n.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

130,3 130,9 104,7 115,2 124,5 112,3 127,5 120,6 117,5 117,7 120,4 125 131,6 121,1 114,2 112,1 127 116,8 112 129,7 113,6 115,7 119,5 125,8 129,6 128 112,8 101,6 123,9 118,8 109,1 130,6 112,4 111 116,2 119,8 117,2 127,3 107,7 97,5 120,1 110,6 111,3 119,8 105,5 108,7 128,7 119,5 121,1 128,4 108,8 107,5 125,6 102,9 107,5 120,4 104,3 100,6 121,9 112,7 124,9 123,9 102,2 104,9 109,8 98,9 107,3 112,6 104 110,6 100,8 103,8 117 108,4 95,5 96,9 103,9 101,1 100,6 104,3 98 99,5 97,4 105,6 117,5 107,4 97,8 91,5 107,7 100,1 96,6 106,8 98 98,6

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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

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[82])
70	110.6	-	-	-	-	-	-	-
71	100.8	-	-	-	-	-	-	-
72	103.8	-	-	-	-	-	-	-
73	117	-	-	-	-	-	-	-
74	108.4	-	-	-	-	-	-	-
75	95.5	-	-	-	-	-	-	-
76	96.9	-	-	-	-	-	-	-
77	103.9	-	-	-	-	-	-	-
78	101.1	-	-	-	-	-	-	-
79	100.6	-	-	-	-	-	-	-
80	104.3	-	-	-	-	-	-	-
81	98	-	-	-	-	-	-	-
82	99.5	-	-	-	-	-	-	-
83	97.4	100.333	91.718	108.9479	0.2523	0.5752	0.4577	0.5752
84	105.6	106.1833	97.5238	114.8428	0.4475	0.9766	0.7052	0.9348
85	117.5	106.9574	98.0784	115.8365	0.01	0.6178	0.0133	0.9501
86	107.4	108.0633	97.3653	118.7612	0.4516	0.0419	0.4754	0.9417
87	97.8	93.931	83.1024	104.7597	0.2419	0.0074	0.3882	0.1567
88	91.5	87.8308	76.6234	99.0382	0.2605	0.0406	0.0564	0.0206
89	107.7	108.6066	96.4941	120.719	0.4417	0.9972	0.7769	0.9297
90	100.1	98.0199	85.7022	110.3376	0.3703	0.0617	0.312	0.4069
91	96.6	95.8338	83.1031	108.5644	0.453	0.2556	0.2315	0.2862
92	106.8	108.5585	95.2597	121.8574	0.3978	0.961	0.7349	0.9091
93	98	93.7004	80.1525	107.2483	0.267	0.029	0.267	0.2007
94	98.6	92.1343	78.1909	106.0778	0.1817	0.2048	0.1502	0.1502

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
83	0.0438	-0.0292	0.0024	8.6022	0.7169	0.8467
84	0.0416	-0.0055	5e-04	0.3402	0.0284	0.1684
85	0.0424	0.0986	0.0082	111.1455	9.2621	3.0434
86	0.0505	-0.0061	5e-04	0.4399	0.0367	0.1915
87	0.0588	0.0412	0.0034	14.969	1.2474	1.1169
88	0.0651	0.0418	0.0035	13.4629	1.1219	1.0592
89	0.0569	-0.0083	7e-04	0.8219	0.0685	0.2617
90	0.0641	0.0212	0.0018	4.3266	0.3606	0.6005
91	0.0678	0.008	7e-04	0.5871	0.0489	0.2212
92	0.0625	-0.0162	0.0013	3.0924	0.2577	0.5076
93	0.0738	0.0459	0.0038	18.4863	1.5405	1.2412
94	0.0772	0.0702	0.0058	41.8047	3.4837	1.8665

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t1229955655y0224ggyav66i9n/17d4w1229955621.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t1229955655y0224ggyav66i9n/17d4w1229955621.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t1229955655y0224ggyav66i9n/2nd4e1229955622.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t1229955655y0224ggyav66i9n/2nd4e1229955622.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; 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,fx))

(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.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)

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[1:12] <- 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.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='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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