Home » date » 2010 » Dec » 21 »

arima forecast

*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, 21 Dec 2010 19:43:55 +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/21/t1292960533ns8rzf1muxzrnap.htm/, Retrieved Tue, 21 Dec 2010 20:42:13 +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/21/t1292960533ns8rzf1muxzrnap.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 «
2350.44 2440.25 2408.64 2472.81 2407.6 2454.62 2448.05 2497.84 2645.64 2756.76 2849.27 2921.44 2981.85 3080.58 3106.22 3119.31 3061.26 3097.31 3161.69 3257.16 3277.01 3295.32 3363.99 3494.17 3667.03 3813.06 3917.96 3895.51 3801.06 3570.12 3701.61 3862.27 3970.1 4138.52 4199.75 4290.89 4443.91 4502.64 4356.98 4591.27 4696.96 4621.4 4562.84 4202.52 4296.49 4435.23 4105.18 4116.68 3844.49 3720.98 3674.4 3857.62 3801.06 3504.37 3032.6 3047.03 2962.34 2197.82 2014.45 1862.83 1905.41 1810.99 1670.07 1864.44 2052.02 2029.6 2070.83 2293.41 2443.27 2513.17 2466.92 2502.66 2539.91
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value
(H0: Y[t] = F[t])
P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[49])
374443.91-------
384502.64-------
394356.98-------
404591.27-------
414696.96-------
424621.4-------
434562.84-------
444202.52-------
454296.49-------
464435.23-------
474105.18-------
484116.68-------
493844.49-------
503720.983795.07813544.57614045.58010.2810.349500.3495
513674.43786.10813398.35384173.86250.28620.6290.0020.384
523857.623784.47983291.62024277.33940.38560.66927e-040.4057
533801.063784.18423204.19994364.16850.47730.4020.0010.4193
543504.373784.13053128.37194439.88910.20150.47980.00620.4284
553032.63784.12083060.45844507.78310.02090.77570.01750.4351
563047.033784.1192998.39614569.8420.0330.96960.14830.4401
572962.343784.11872940.88994627.34750.02810.95670.11680.4442
582197.823784.11862887.06274681.17463e-040.96370.07740.4475
592014.453784.11862836.28754731.94981e-040.99950.25340.4503
601862.833784.11862788.09734780.13991e-040.99980.25640.4527
611905.413784.11862742.13354826.10372e-040.99980.45480.4548
621810.993784.11862698.11334870.12392e-040.99970.54540.4566
631670.073784.11862655.80924912.4281e-040.99970.57560.4582
641864.443784.11862615.03494953.20236e-040.99980.4510.4597
652052.023784.11862575.63564992.60160.00250.99910.4890.461
662029.63784.11862537.48095030.75640.00290.99680.670.4622
672070.833784.11862500.45975067.77760.00440.99630.87440.4633
682293.413784.11862464.47675103.76050.01340.99450.86320.4643
692443.273784.11862429.44925138.78810.02620.98450.88280.4652
702513.173784.11862395.30485172.93250.03640.97080.98740.4661
712466.923784.11862361.97995206.25730.03470.96010.99260.4668
722502.663784.11862329.41835238.81890.04210.9620.99520.4676
732539.913784.11862297.56975270.66750.05050.95440.99340.4683


Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
500.0337-0.019505490.530200
510.0523-0.02950.024512478.71028984.620294.7872
520.06640.01930.02285349.49057772.910388.1641
530.07820.00450.0182284.79315900.88176.8172
540.0884-0.07390.029378265.950420373.8949142.7372
550.0976-0.19860.0576564783.4855111108.8267333.3299
560.1059-0.19480.0772543300.2137172850.4534415.7529
570.1137-0.21720.0947675320.2192235659.1741485.4474
580.1209-0.41920.13072516343.3565489068.5277699.3343
590.1278-0.46770.16443131727.037753334.3786867.9484
600.1343-0.50770.19563691349.96741020426.70491010.1617
610.1405-0.49650.22073529546.08351229519.98641108.8372
620.1464-0.52140.24383893236.55571434421.2611197.6733
630.1521-0.55870.26634469201.57261651191.28331284.9869
640.1576-0.50730.28243685166.00851786789.59831336.7085
650.1629-0.45770.29333000165.63341862625.60051364.7804
660.1681-0.46370.30343078335.5921934137.95291390.7329
670.1731-0.45280.31172935357.89941989761.28331410.589
680.1779-0.39390.3162222212.19322001995.54171414.9189
690.1826-0.35430.31791797875.02491991789.51591411.3077
700.1873-0.33590.31881615310.39761973861.93881404.942
710.1917-0.34810.32011735012.20761963005.13281401.0729
720.1961-0.33860.32091642136.19771949054.30961396.0854
730.2004-0.32880.32121548055.0931932346.00891390.0885
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292960533ns8rzf1muxzrnap/1g0351292960631.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292960533ns8rzf1muxzrnap/1g0351292960631.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292960533ns8rzf1muxzrnap/2gt3u1292960632.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292960533ns8rzf1muxzrnap/2gt3u1292960632.ps (open in new window)


 
Parameters (Session):
par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
 
Parameters (R input):
par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; 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')
 





Copyright

Creative Commons License

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.


Privacy Policy

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