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workshop 9 Arima

*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: Wed, 08 Dec 2010 15:58:11 +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/08/t1291823768q5yppcla369oqc0.htm/, Retrieved Wed, 08 Dec 2010 16:56:10 +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/08/t1291823768q5yppcla369oqc0.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 «

655362 873127 1107897 1555964 1671159 1493308 2957796 2638691 1305669 1280496 921900 867888 652586 913831 1108544 1555827 1699283 1509458 3268975 2425016 1312703 1365498 934453 775019 651142 843192 1146766 1652601 1465906 1652734 2922334 2702805 1458956 1410363 1019279 936574 708917 885295 1099663 1576220 1487870 1488635 2882530 2677026 1404398 1344370 936865 872705 628151 953712 1160384 1400618 1661511 1495347 2918786 2775677 1407026 1370199 964526 850851 683118 847224 1073256 1514326 1503734 1507712 2865698 2788128 1391596 1366378 946295 859626

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

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[60])
48	872705	-	-	-	-	-	-	-
49	628151	-	-	-	-	-	-	-
50	953712	-	-	-	-	-	-	-
51	1160384	-	-	-	-	-	-	-
52	1400618	-	-	-	-	-	-	-
53	1661511	-	-	-	-	-	-	-
54	1495347	-	-	-	-	-	-	-
55	2918786	-	-	-	-	-	-	-
56	2775677	-	-	-	-	-	-	-
57	1407026	-	-	-	-	-	-	-
58	1370199	-	-	-	-	-	-	-
59	964526	-	-	-	-	-	-	-
60	850851	-	-	-	-	-	-	-
61	683118	649109.9609	466849.8269	831370.095	0.3573	0.015	0.5892	0.015
62	847224	901493.1547	712544.115	1090442.1945	0.2867	0.9883	0.294	0.7003
63	1073256	1145123.4804	955683.9552	1334563.0057	0.2286	0.999	0.4373	0.9988
64	1514326	1523618.9431	1334142.8069	1713095.0794	0.4617	1	0.8984	1
65	1503734	1559821.3463	1370342.4737	1749300.2188	0.2809	0.681	0.1464	1
66	1507712	1552768.0842	1363289.0072	1742247.1613	0.3206	0.694	0.7237	1
67	2865698	2914064.3622	2724585.2698	3103543.4545	0.3084	1	0.4805	1
68	2788128	2732136.6112	2542657.5177	2921615.7047	0.2812	0.0836	0.3262	1
69	1391596	1425902.7096	1236423.616	1615381.8031	0.3613	0	0.5774	1
70	1366378	1380833.9026	1191354.809	1570312.9962	0.4406	0.4557	0.5438	1
71	946295	980281.8174	790802.7238	1169760.911	0.3626	0	0.5647	0.9097
72	859626	886375.6492	696896.5556	1075854.7428	0.391	0.2677	0.6434	0.6434

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
61	0.1433	0.0524	0	1156546722.3911	0	0
62	0.1069	-0.0602	0.0563	2945141154.0172	2050843938.2041	45286.2445
63	0.0844	-0.0628	0.0585	5164934743.8013	3088874206.7365	55577.6412
64	0.0634	-0.0061	0.0454	86358792.0562	2338245353.0664	48355.4067
65	0.062	-0.036	0.0435	3145790411.9989	2499754364.8529	49997.5436
66	0.0623	-0.029	0.0411	2030050724.4532	2421470424.7863	49208.4386
67	0.0332	-0.0166	0.0376	2339304989.5895	2409732505.4725	49089.0263
68	0.0354	0.0205	0.0354	3135035618.1087	2500395394.552	50003.9538
69	0.0678	-0.0241	0.0342	1176950320.6369	2353345941.8948	48511.2971
70	0.07	-0.0105	0.0318	208973119.5882	2138908659.6641	46248.3368
71	0.0986	-0.0347	0.0321	1155103756.2301	2049471850.261	45271.0929
72	0.1091	-0.0302	0.0319	715543733.8426	1938311173.8928	44026.2555

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823768q5yppcla369oqc0/1f9on1291823887.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823768q5yppcla369oqc0/1f9on1291823887.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823768q5yppcla369oqc0/24t4h1291823887.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291823768q5yppcla369oqc0/24t4h1291823887.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 1.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 2 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 1.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 2 ; par9 = 0 ; 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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