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ARIMA Forecasting (ASO)

*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: Fri, 24 Dec 2010 12:55:35 +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/24/t1293195335a7hxdwkpse1cfsk.htm/, Retrieved Fri, 24 Dec 2010 13:55:35 +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/24/t1293195335a7hxdwkpse1cfsk.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 «

4940 3924 3927 4535 3446 3016 4934 2743 3242 6662 3262 3381 7144 3803 3684 6759 3386 3066 5538 2940 3215 7023 3443 3712 7475 4137 3491 7019 3908 3402 5604 3222 3636 7123 4368 4092 8377 4595 4188 6988 4218 3655 6211 3622 3841 8510 4627 4582 8967 4928 4809 7917 4790 4065 7290 4670 3561 5149 6880 6981 8454 4960 4670 7638 4560 3980 6825 3939 4079 8117 5121 5167 7960 4670 4397 7191 4293 3747 6425 3709 3840 7642 4821 4865

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[72])
60	6981	-	-	-	-	-	-	-
61	8454	-	-	-	-	-	-	-
62	4960	-	-	-	-	-	-	-
63	4670	-	-	-	-	-	-	-
64	7638	-	-	-	-	-	-	-
65	4560	-	-	-	-	-	-	-
66	3980	-	-	-	-	-	-	-
67	6825.00000000001	-	-	-	-	-	-	-
68	3939	-	-	-	-	-	-	-
69	4079	-	-	-	-	-	-	-
70	8117.00000000001	-	-	-	-	-	-	-
71	5121	-	-	-	-	-	-	-
72	5167	-	-	-	-	-	-	-
73	7960	9618.2929	7764.285	11861.643	0.0737	0.9999	0.8455	0.9999
74	4670	5442.6443	4336.8451	6796.0326	0.1316	1e-04	0.7577	0.6551
75	4397	4771.1069	3723.0485	6077.6024	0.2873	0.5603	0.5603	0.2763
76	7191	8050.0166	6335.9966	10170.6127	0.2136	0.9996	0.6483	0.9961
77	4293	5005.9594	3835.441	6488.7079	0.173	0.0019	0.7222	0.4157
78	3747	4274.9677	3261.2808	5563.905	0.211	0.4891	0.6731	0.0875
79	6425	7203.7781	5571.8416	9253.9622	0.2283	0.9995	0.6414	0.9742
80	3709	4301.9998	3271.5672	5615.8501	0.1882	8e-04	0.7059	0.0985
81	3840	4279.0492	3243.1033	5603.8497	0.258	0.8005	0.6164	0.0945
82	7642	8015.448	6178.0009	10330.8933	0.376	0.9998	0.4657	0.992
83	4821	5677.5657	4334.1919	7384.7115	0.1627	0.0121	0.7386	0.7211
84	4865	5694.2486	4339.3468	7418.6753	0.173	0.8395	0.7255	0.7255

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
73	0.119	-0.1724	0	2749935.356	0	0
74	0.1269	-0.142	0.1572	596979.2537	1673457.3049	1293.6218
75	0.1397	-0.0784	0.1309	139955.9433	1162290.1843	1078.0956
76	0.1344	-0.1067	0.1249	737909.5176	1056195.0177	1027.7135
77	0.1511	-0.1424	0.1284	508311.0401	946618.2221	972.9431
78	0.1538	-0.1235	0.1276	278749.8451	835306.826	913.9512
79	0.1452	-0.1081	0.1248	606495.3125	802619.4669	895.8903
80	0.1558	-0.1378	0.1264	351648.7615	746248.1287	863.8565
81	0.158	-0.1026	0.1238	192764.2375	684749.9186	827.4962
82	0.1474	-0.0466	0.1161	139463.4269	630221.2694	793.8648
83	0.1534	-0.1509	0.1192	733704.7283	639628.8566	799.768
84	0.1545	-0.1456	0.1214	687653.2479	643630.8892	802.2661

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293195335a7hxdwkpse1cfsk/1ah5x1293195331.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293195335a7hxdwkpse1cfsk/1ah5x1293195331.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293195335a7hxdwkpse1cfsk/2oqlo1293195331.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293195335a7hxdwkpse1cfsk/2oqlo1293195331.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 0.1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 0.1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; 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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