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Forecast ARIMA 2

*The author of this computation has been verified*

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

Title produced by software: ARIMA Forecasting

Date of computation: Tue, 07 Dec 2010 22:40:23 +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/07/t1291761500ycguq6w64ycv3ck.htm/, Retrieved Tue, 07 Dec 2010 23:38:20 +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/07/t1291761500ycguq6w64ycv3ck.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 «

431 465 511 540 552 512 413 542 544 491 458 529 525 483 528 502 563 537 465 528 505 493 456 488 488 468 542 499 477 534 528 598 474 537 376 447 545 425 458 510 472 541 507 472 540 496 432 452 420 435 509 441 416 490 396 463 403 448 398 387 426 428 510 437 453 451 434

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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

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[55])
43	507	-	-	-	-	-	-	-
44	472	-	-	-	-	-	-	-
45	540	-	-	-	-	-	-	-
46	496	-	-	-	-	-	-	-
47	432	-	-	-	-	-	-	-
48	452	-	-	-	-	-	-	-
49	420	-	-	-	-	-	-	-
50	435	-	-	-	-	-	-	-
51	509	-	-	-	-	-	-	-
52	441	-	-	-	-	-	-	-
53	416	-	-	-	-	-	-	-
54	490	-	-	-	-	-	-	-
55	396	-	-	-	-	-	-	-
56	463	506.7083	419.0176	602.7242	0.1861	0.9881	0.7607	0.9881
57	403	528.0069	435.7827	629.0764	0.0077	0.8963	0.408	0.9948
58	448	497.4463	406.7946	597.209	0.1657	0.9682	0.5113	0.9769
59	398	429.5841	345.0782	523.3361	0.2545	0.3501	0.4799	0.7587
60	387	460.9324	372.9297	558.2487	0.0682	0.8975	0.5714	0.9045
61	426	472.9564	383.8085	571.4056	0.1749	0.9565	0.8541	0.9373
62	428	441.7877	355.7038	537.191	0.3885	0.6272	0.5555	0.8266
63	510	503.9435	411.6425	605.5733	0.4535	0.9285	0.4612	0.9813
64	437	477.6629	387.9024	576.757	0.2106	0.2612	0.7658	0.9469
65	453	461.445	373.2904	558.9355	0.4326	0.6884	0.8195	0.9059
66	451	514.2675	420.9382	616.934	0.1136	0.8789	0.6784	0.988
67	434	449.5839	362.622	545.8837	0.3756	0.4885	0.8623	0.8623

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
56	0.0967	-0.0863	0	1910.4117	0	0
57	0.0977	-0.2368	0.1615	15626.7323	8768.572	93.6407
58	0.1023	-0.0994	0.1408	2444.9401	6660.6947	81.6131
59	0.1113	-0.0735	0.124	997.5537	5244.9094	72.4217
60	0.1077	-0.1604	0.1313	5466.0032	5289.1282	72.7264
61	0.1062	-0.0993	0.1259	2204.9055	4775.0911	69.102
62	0.1102	-0.0312	0.1124	190.0998	4120.0923	64.1879
63	0.1029	0.012	0.0999	36.6811	3609.6659	60.0805
64	0.1058	-0.0851	0.0982	1653.4736	3392.3112	58.2436
65	0.1078	-0.0183	0.0902	71.3178	3060.2119	55.3192
66	0.1019	-0.123	0.0932	4002.7775	3145.8997	56.0883
67	0.1093	-0.0347	0.0883	242.8593	2903.9796	53.8886

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291761500ycguq6w64ycv3ck/1gfh61291761619.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291761500ycguq6w64ycv3ck/1gfh61291761619.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291761500ycguq6w64ycv3ck/2u7xf1291761619.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291761500ycguq6w64ycv3ck/2u7xf1291761619.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 0.5 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 0.5 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; 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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