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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: Sat, 25 Dec 2010 16:51:28 +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/25/t1293295767z3izzq93y05blqc.htm/, Retrieved Sat, 25 Dec 2010 17:49:29 +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/25/t1293295767z3izzq93y05blqc.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 «

175.348 154.439 136.186 113.662 106.157 100.546 98.314 118.179 112.295 126.938 130.92 181.279 180.389 146.917 150.597 124.222 101.554 102.138 110.315 111.015 105.017 119.888 127.623 149.415 159.755 139.737 136.283 101.952 104.044 96.712 100.665 103.699 103.765 122.732 127.297 160.278 191.784 155.375 142.616 115.331 102.136 95.205 101.566 105.273 117.394 121.148 116.666 154.841 177.74 154.427 133.159 118.102 101.361 101.345 102.233 108.522 101.939 118.405 125.06 178 167.714 143.582 139.259 104.674 103.722 106.153 106.21 113.986 96.906 107.512 112.616 148.507 130.48 137.436 128.21 97.552 91.55 83.104 84.68 85.98 84.891 89.896 94.835 115.348 131.284 134.701 127.193 87.077 72.744 77.542 78.005 85.329 86.041 96.384 116.678 160.672 152.364 144.936 122.974 94.456 82.491 84.89 85.277 81.206 71.012 87.302 97.427 133.242 137.064 119.042 116.47 96.028 79.281 73.872 80.964 86.739 89.997 96.292 101.355 13 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	6 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[108])
96	160.672	-	-	-	-	-	-	-
97	152.364	-	-	-	-	-	-	-
98	144.936	-	-	-	-	-	-	-
99	122.974	-	-	-	-	-	-	-
100	94.456	-	-	-	-	-	-	-
101	82.491	-	-	-	-	-	-	-
102	84.89	-	-	-	-	-	-	-
103	85.277	-	-	-	-	-	-	-
104	81.206	-	-	-	-	-	-	-
105	71.012	-	-	-	-	-	-	-
106	87.302	-	-	-	-	-	-	-
107	97.427	-	-	-	-	-	-	-
108	133.242	-	-	-	-	-	-	-
109	137.064	138.5079	121.0743	155.9415	0.4355	0.7231	0.0596	0.7231
110	119.042	125.168	105.5713	144.7647	0.27	0.1171	0.024	0.2097
111	116.47	113.817	93.1809	134.4531	0.4005	0.3099	0.1922	0.0325
112	96.028	84.1285	62.7101	105.5468	0.1381	0.0015	0.1723	0
113	79.281	73.9115	51.793	96.0299	0.3171	0.025	0.2235	0
114	73.872	72.7049	49.9231	95.4867	0.46	0.2858	0.1472	0
115	80.964	74.4774	51.0554	97.8995	0.2936	0.5202	0.1831	0
116	86.739	78.6001	54.5559	102.6442	0.2535	0.4236	0.4159	0
117	89.997	74.2908	49.6406	98.941	0.1059	0.1611	0.6028	0
118	96.292	86.4214	61.1796	111.6633	0.2217	0.3906	0.4727	1e-04
119	101.355	94.1849	68.3642	120.0057	0.2931	0.4365	0.4028	0.0015
120	136.543	130.9585	104.5694	157.3476	0.3392	0.9861	0.4327	0.4327

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
109	0.0642	-0.0104	0	2.0848	0	0
110	0.0799	-0.0489	0.0297	37.5277	19.8063	4.4504
111	0.0925	0.0233	0.0276	7.0383	15.5503	3.9434
112	0.1299	0.1414	0.056	141.5987	47.0624	6.8602
113	0.1527	0.0726	0.0594	28.8319	43.4163	6.5891
114	0.1599	0.0161	0.0521	1.3621	36.4073	6.0338
115	0.1605	0.0871	0.0571	42.0754	37.217	6.1006
116	0.1561	0.1035	0.0629	66.2422	40.8452	6.391
117	0.1693	0.2114	0.0794	246.6847	63.7162	7.9822
118	0.149	0.1142	0.0829	97.428	67.0874	8.1907
119	0.1399	0.0761	0.0823	51.4103	65.6622	8.1032
120	0.1028	0.0426	0.079	31.1866	62.7892	7.924

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293295767z3izzq93y05blqc/1qdaa1293295881.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293295767z3izzq93y05blqc/1qdaa1293295881.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293295767z3izzq93y05blqc/24np01293295881.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293295767z3izzq93y05blqc/24np01293295881.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; 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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