Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Jan » 12 »

*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, 12 Jan 2010 04:30:52 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/12/t1263295928d8jmc1teuy95n8o.htm/, Retrieved Tue, 12 Jan 2010 12:32:11 +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/Jan/12/t1263295928d8jmc1teuy95n8o.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 «

90.2 90 88.8 85.8 84.2 80 77.8 76.8 86.4 89.2 86.2 84.6 83.2 83.2 82.6 79.8 77.2 74.8 73 73 83.6 85.6 84.8 84.2 83.4 84.6 84.6 83.8 81.2 79.6 78 78.2 88.8 92 91 91.2 90.4 91.8 92.2 90.2 88.6 87.8 86 87.2 97.6 101.2 100.4 100.2 100.2 103 104.2 104 102.4 101.8 101 102.2 114 118.4 118.8 117.2 117.2 118.4 118.8 117.2 114.4 112.6 111 110.8 120.2 124.4 123.4 121.2 119 119.8 120 118.4 115 113.4 111 111 121.6 126.2 125.8 124.8 122 123.2 124.2 120.8 116.8 114.8 111 109 119.8 124 121.6 118 115.8 116 115.8 114.4 112 110.2 107.4 108.2 117.6 121.4 119.8 115.6 112.6 113.2 112.2 110.8 108 105.2 102.4 101 110.8 116.8 113.8 108 104.4 105.2 105.4 103.2 100.6 97.8 95.8 95 104.8 110.4 106.4 102.2 98.4 98.4 98.6 96.2 92.4 91.4 88.4 87.8 97.6 104.2 100.2 97 92.8 92 93.4 92 89.6 88.6 87.2 86.2 96.8 102 102.6 100.6 94.2 94.2 95.2 95 94 92.2 91 91.2 103.4 105 104.6 103. etc...

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	'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[229])
223	102.2	-	-	-	-	-	-	-
224	99.8	-	-	-	-	-	-	-
225	111	-	-	-	-	-	-	-
226	113	-	-	-	-	-	-	-
227	108.4	-	-	-	-	-	-	-
228	105.4	-	-	-	-	-	-	-
229	102	-	-	-	-	-	-	-
230	102.8	99.9621	97.5582	102.3659	0.0103	0.0483	0.5526	0.0483
231	103.4	101.3332	97.8146	104.8518	0.1248	0.2069	0	0.3552
232	101.6	99.2659	94.8227	103.709	0.1516	0.0341	0	0.1139
233	98.6	95.4194	90.1473	100.6915	0.1185	0.0108	0	0.0072
234	98	94.702	88.6624	100.7415	0.1422	0.1029	3e-04	0.0089
235	93.8	91.9344	85.1728	98.6961	0.2943	0.0394	0.0018	0.0018
236	95.6	89.5895	81.959	97.2201	0.0613	0.1397	3e-04	7e-04
237	105.6	100.6081	92.1557	109.0605	0.1235	0.8772	0.2587	0.3734
238	106.8	102.5515	93.3158	111.7872	0.1836	0.2588	0.58	0.5466
239	103.6	97.9993	88.0135	107.9851	0.1358	0.042	0.4531	0.2162
240	101.2	95.0776	84.3709	105.7842	0.1312	0.0594	0.2963	0.1025
241	100.4	91.715	80.3138	103.1163	0.0677	0.0515	0.36	0.0385
242	103.2	89.6903	76.6512	102.7293	0.0211	0.0537	0.1872	0.0321
243	105.6	91.297	76.7134	105.8806	0.0273	0.0548	0.0273	0.0752
244	106.6	89.3355	73.2824	105.3887	0.0175	0.0235	0.0165	0.061
245	107.2	85.4863	68.027	102.9455	0.0074	0.0089	0.021	0.0319
246	107.4	84.7304	65.9207	103.5402	0.0091	0.0096	0.0431	0.036
247	104.8	81.9594	61.8488	102.0699	0.013	0.0066	0.0361	0.0254
248	107.2	79.6303	58.1051	101.1556	0.006	0.011	0.0159	0.0208
249	117.4	90.4436	67.5507	113.3365	0.0105	0.0757	0.0972	0.1612
250	119.4	92.3052	68.0883	116.5222	0.0142	0.0211	0.1236	0.2163
251	116.2	87.7746	62.2743	113.2749	0.0145	0.0075	0.0677	0.1371
252	112.8	84.9067	58.1611	111.6523	0.0205	0.0109	0.0496	0.1052
253	111.6	81.5618	53.6067	109.5169	0.0176	0.0143	0.0516	0.0759

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
230	0.0123	0.0284	0	8.0539	0	0
231	0.0177	0.0204	0.0244	4.2717	6.1628	2.4825
232	0.0228	0.0235	0.0241	5.4482	5.9246	2.434
233	0.0282	0.0333	0.0264	10.1161	6.9725	2.6405
234	0.0325	0.0348	0.0281	10.8771	7.7534	2.7845
235	0.0375	0.0203	0.0268	3.4804	7.0412	2.6535
236	0.0435	0.0671	0.0325	36.1257	11.1962	3.3461
237	0.0429	0.0496	0.0347	24.9192	12.9115	3.5933
238	0.0459	0.0414	0.0354	18.0496	13.4824	3.6718
239	0.052	0.0572	0.0376	31.368	15.271	3.9078
240	0.0575	0.0644	0.04	37.4841	17.2904	4.1582
241	0.0634	0.0947	0.0446	75.4285	22.1352	4.7048
242	0.0742	0.1506	0.0528	182.5125	34.4719	5.8713
243	0.0815	0.1567	0.0602	204.576	46.6222	6.828
244	0.0917	0.1933	0.069	298.0626	63.3849	7.9615
245	0.1042	0.254	0.0806	471.4859	88.8912	9.4282
246	0.1133	0.2675	0.0916	513.9096	113.8923	10.672
247	0.1252	0.2787	0.102	521.6952	136.548	11.6854
248	0.1379	0.3462	0.1148	760.0862	169.3658	13.0141
249	0.1291	0.298	0.124	726.6479	197.2299	14.0439
250	0.1339	0.2935	0.1321	734.1255	222.7964	14.9264
251	0.1482	0.3238	0.1408	808.0059	249.3968	15.7923
252	0.1607	0.3285	0.149	778.0356	272.3811	16.504
253	0.1749	0.3683	0.1581	902.293	298.6274	17.2808

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263295928d8jmc1teuy95n8o/1yrxu1263295849.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263295928d8jmc1teuy95n8o/1yrxu1263295849.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263295928d8jmc1teuy95n8o/2ekry1263295849.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263295928d8jmc1teuy95n8o/2ekry1263295849.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 6 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 6 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; 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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by