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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: Fri, 24 Dec 2010 12:00:28 +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/t1293191904mfxqetd369273iz.htm/, Retrieved Fri, 24 Dec 2010 12:58:28 +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/t1293191904mfxqetd369273iz.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:

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15 14,4 13 13,7 13,6 15,2 12,9 14 14,1 13,2 11,3 13,3 14,4 13,3 11,6 13,2 13,1 14,6 14 14,3 13,8 13,7 11 14,4 15,6 13,7 12,6 13,2 13,3 14,3 14 13,4 13,9 13,7 10,5 14,5 15 13,5 13,5 13,2 13,8 16,2 14,7 13,9 16 14,4 12,3 15,9 15,9 15,5 15,1 14,5 15,1 17,4 16,2 15,6 17,2 14,9 13,8 17,5 16,2 17,5 16,6 16,2 16,6 19,6 15,9 18 18,3 16,3 14,9 18,2 18,4 18,5 16 17,4 17,2 19,6 17,2 18,3 19,3 18,1 16,2 18,4 20,5 19 16,5 18,7 19 19,2 20,5 19,3 20,6 20,1 16,1 20,4 19,7 15,6 14,4 13,7 14,1 15 14,2 13,6 15,4 14,8 12,5 16,2 16,1 16 15,8 15,2 15,7 18,9 17,4 17 19,8 17,7 16 19,6 19,7

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	39 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[109])
97	19.7	-	-	-	-	-	-	-
98	15.6	-	-	-	-	-	-	-
99	14.4	-	-	-	-	-	-	-
100	13.7	-	-	-	-	-	-	-
101	14.1	-	-	-	-	-	-	-
102	15	-	-	-	-	-	-	-
103	14.2	-	-	-	-	-	-	-
104	13.6	-	-	-	-	-	-	-
105	15.4	-	-	-	-	-	-	-
106	14.8	-	-	-	-	-	-	-
107	12.5	-	-	-	-	-	-	-
108	16.2	-	-	-	-	-	-	-
109	16.1	-	-	-	-	-	-	-
110	16	14.0525	12.6428	15.4622	0.0034	0.0022	0.0157	0.0022
111	15.8	13.1314	11.5396	14.7232	5e-04	2e-04	0.0591	1e-04
112	15.2	12.7996	10.8696	14.7296	0.0074	0.0012	0.1802	4e-04
113	15.7	12.9646	10.4974	15.4318	0.0149	0.0379	0.1835	0.0064
114	18.9	14.9509	12.2385	17.6632	0.0022	0.2941	0.4858	0.2032
115	17.4	12.9627	9.8817	16.0437	0.0024	1e-04	0.2156	0.023
116	17	13.1849	9.7546	16.6153	0.0146	0.008	0.4063	0.0479
117	19.8	14.4012	10.7183	18.0841	0.002	0.0833	0.2975	0.183
118	17.7	13.3106	9.3143	17.3068	0.0157	7e-04	0.2325	0.0856
119	16	11.6564	7.3941	15.9187	0.0229	0.0027	0.349	0.0205
120	19.6	14.8234	10.3222	19.3245	0.0188	0.3042	0.2744	0.2891
121	19.7	15.3379	10.577	20.0988	0.0363	0.0397	0.3769	0.3769

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
110	0.0512	0.1386	0	3.7928	0	0
111	0.0618	0.2032	0.1709	7.1215	5.4572	2.3361
112	0.0769	0.1875	0.1765	5.762	5.5588	2.3577
113	0.0971	0.211	0.1851	7.4823	6.0397	2.4576
114	0.0926	0.2641	0.2009	15.5957	7.9509	2.8197
115	0.1213	0.3423	0.2245	19.6899	9.9074	3.1476
116	0.1327	0.2894	0.2337	14.5548	10.5713	3.2514
117	0.1305	0.3749	0.2514	29.1468	12.8932	3.5907
118	0.1532	0.3298	0.2601	19.2669	13.6014	3.688
119	0.1866	0.3726	0.2713	18.8665	14.1279	3.7587
120	0.1549	0.3222	0.276	22.8164	14.9178	3.8624
121	0.1584	0.2844	0.2767	19.0279	15.2603	3.9064

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293191904mfxqetd369273iz/19tkt1293191988.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293191904mfxqetd369273iz/19tkt1293191988.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293191904mfxqetd369273iz/253hk1293191988.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293191904mfxqetd369273iz/253hk1293191988.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; 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,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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