| ws9 | *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: Sat, 04 Dec 2010 15:44:00 +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/04/t1291477310ykvyllga12f7vq7.htm/, Retrieved Sat, 04 Dec 2010 16:41:50 +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/04/t1291477310ykvyllga12f7vq7.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 « | 7945
7833
7889
7957
8038
8106
8180
7951
7908
7895
7988
7982
7964
8007
7976
7951
7982
7995
7933
8050
8119
8224
8143
8174
8211
8261
8162
8156
8168
8218
8267
8267
8162
8162
8249
8404
8391
8354
8360
8360
8391
8459
8428
8478
8540
8633
8552
8664
8627
8559
8472
8311
8304
8339
8413
8413
8357
8370
8376
8351
8351
8370
8391
8335
8348
8342
8413
8379
8397
8459
8391
8540
8596
8590
8608
8559
8583
8577
8515
8509
8596
8664
8689
8676
8608
8577
8435
8416
8335
8335
8335
8280
8255
8292
8342
8267
8211
8286
8335
8311
8205
8280
8193
8311
8329
8187
8057
7951
7926
7976
8026
8050
8057
8106
8032
8044
8069
8106
8038
8026
8057
8149
8162
8261
8261
8249
8050
8088
8106
8125
8088
8094
7995
8038
8044
7920
7815
7821
7747
7709
7697
7672
7722
7722
7734
7691
7654
7635
7635
7635
7722
7883
7864
7939
7982
7914
7815
7796
7815
7815
7815
7840
7815
7784
7740
7685
7685
7747
7802
7784
7802 etc... | | Output produced by software: |
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[2970]) | 2963 | 32275 | - | - | - | - | - | - | - | 2964 | 32200 | - | - | - | - | - | - | - | 2965 | 31835 | - | - | - | - | - | - | - | 2966 | 31985 | - | - | - | - | - | - | - | 2967 | 31875 | - | - | - | - | - | - | - | 2968 | 31795 | - | - | - | - | - | - | - | 2969 | 32260 | - | - | - | - | - | - | - | 2970 | 33255 | - | - | - | - | - | - | - | 2971 | 33160 | 33160.9537 | 32158.2474 | 34207.9825 | 0.4993 | 0.4301 | 0.964 | 0.4301 | 2972 | 32195 | 33142.0071 | 31788.7303 | 34577.3324 | 0.098 | 0.4902 | 0.9629 | 0.4387 | 2973 | 33130 | 33113.5251 | 31494.0075 | 34852.0774 | 0.4926 | 0.8498 | 0.8984 | 0.4366 | 2974 | 33950 | 33141.6743 | 31311.22 | 35125.5164 | 0.2123 | 0.5046 | 0.8946 | 0.4554 | 2975 | 34210 | 33122.513 | 31094.7382 | 35340.361 | 0.1683 | 0.2323 | 0.8796 | 0.4534 | 2976 | 33855 | 33136.9905 | 30937.8466 | 35561.3643 | 0.2808 | 0.1928 | 0.7608 | 0.462 | 2977 | 33735 | 33125.5821 | 30765.1893 | 35747.5036 | 0.3244 | 0.2928 | 0.4615 | 0.4615 |
Univariate ARIMA Extrapolation Forecast Performance | time | % S.E. | PE | MAPE | Sq.E | MSE | RMSE | 2971 | 0.0161 | 0 | 0 | 0.9095 | 0 | 0 | 2972 | 0.0221 | -0.0286 | 0.0143 | 896822.406 | 448411.6577 | 669.6355 | 2973 | 0.0268 | 5e-04 | 0.0097 | 271.4222 | 299031.5792 | 546.8378 | 2974 | 0.0305 | 0.0244 | 0.0134 | 653390.4317 | 387621.2923 | 622.5924 | 2975 | 0.0342 | 0.0328 | 0.0173 | 1182627.9428 | 546622.6224 | 739.3393 | 2976 | 0.0373 | 0.0217 | 0.018 | 515537.6762 | 541441.7981 | 735.8273 | 2977 | 0.0404 | 0.0184 | 0.0181 | 371390.2181 | 517148.7152 | 719.1305 |
| | Charts produced by software: | | http://www.freestatistics.org/blog/date/2010/Dec/04/t1291477310ykvyllga12f7vq7/135bt1291477432.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/04/t1291477310ykvyllga12f7vq7/135bt1291477432.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/04/t1291477310ykvyllga12f7vq7/2zwqk1291477432.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/04/t1291477310ykvyllga12f7vq7/2zwqk1291477432.ps (open in new window) |
| | Parameters (Session): | par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ; | | Parameters (R input): | par1 = 7 ; par2 = -0.4 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; 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 <- 7 #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')
| |
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This work is licensed under a
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Software written by Ed van Stee & Patrick Wessa
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