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B58A,steven,coomans,thesis,Arima

*Unverified author*

R Software Module: Patrick.Wessa/rwasp_demand_forecasting_croston.wasp (opens new window with default values)

Title produced by software: Croston Forecasting

Date of computation: Thu, 13 May 2010 12:13:51 +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/May/13/t12737528707gigi53l7kssute.htm/, Retrieved Thu, 13 May 2010 14:14:32 +0200

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/May/13/t12737528707gigi53l7kssute.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:

B58A,steven,coomans,thesis,Arima

Dataseries X:

» Textbox « » Textfile « » CSV «

797 642.25 726.275 652.75 678.75 602.25 689.775 393 580.525 462.25 725.65 501 675 691 769.025 688.25 518.8 386.275 491.35 269.5 379 375.25 337.5 296 375 399.525 336 483.5 370.25 625.5 736.75 496.05 740.5 690.525 568.75 341.1 519.75 408.75 278.35 217 266 319.025 454.75 378.3 509.575 453.75 252 187.525 401.5 403.75

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	4 seconds
R Server	wessa.org @ wessa.org

Demand Forecast
Point	Forecast	95% LB	80% LB	80% UB	95% UB
51	338.070445003524	118.734910570406	194.654647698306	481.486242308743	557.405979436643
52	311.888275965091	35.6817126687886	131.286511647908	492.490040282275	588.094839261394
53	332.639555111514	-15.3591285773044	105.095446440801	560.183663782226	680.638238800331
54	360.098882353676	-29.1476289950759	105.584268852331	614.61349585502	749.345393702428
55	422.869420052317	-17.5964247786097	134.864284516897	710.874555587737	863.335264883244
56	388.053178826374	-87.4338899288302	77.1488958058652	698.957461846883	863.540247581579
57	449.220121174636	-67.4469692004157	111.389669310029	787.050573039243	965.887211549688
58	423.788356304916	-124.171290867880	65.4968013433286	782.079911266503	971.748003477712
59	326.707888973003	-256.342433124503	-54.5282250419647	707.94400298797	909.758211070508
60	296.837601229282	-314.860080839313	-103.130014644524	696.805217103088	908.535283297877
61	398.040188818173	-244.630075863431	-22.1793102788732	818.25968791522	1040.71045349978
62	399.720461040223	-269.547740904814	-37.890494435145	837.331416515591	1068.98866298526
63	367.91878462912	-365.530429874777	-111.657879283664	847.495448541904	1101.36799913302
64	355.889288218968	-425.011764950192	-154.714465277663	866.493041715598	1136.79034138813
65	365.397566926991	-469.471171992877	-180.49375955985	911.288893413832	1200.26630584686
66	378.79643389878	-499.297889418914	-195.358583040319	952.951450837878	1256.89075721647
67	408.422015168179	-516.903169316534	-196.615601935033	1013.45963227139	1333.74719965289
68	392.070747311511	-573.26604295554	-239.129052584229	1023.27054720725	1357.40753757856
69	421.007431793546	-586.76284110123	-237.938131045809	1079.9529946329	1428.77770468832
70	409.062260225559	-636.128327699261	-274.35113145565	1092.47565190677	1454.25284815038
71	362.679219705706	-721.343319746871	-346.125020310519	1071.48345972193	1446.70175915828
72	348.573722283442	-770.704651909711	-383.283068985131	1080.43051355202	1467.85209647659
73	396.673252518131	-758.624371122333	-358.735260048921	1152.08176508518	1551.97087615860
74	397.561924698866	-791.141531846723	-379.689487939602	1174.81333733733	1586.26538124446

Actuals and Interpolation
Time	Actual	Forecast
1	797	796.20300065502
2	642.25	762.952337247724
3	726.275	704.410416896747
4	652.75	665.581080920744
5	678.75	704.818827828887
6	602.25	631.816961296255
7	689.775	654.598278915382
8	393	606.863336282914
9	580.525	509.418190174305
10	462.25	465.80488389292
11	725.65	584.551182892532
12	501	584.24363832272
13	675	643.519082911609
14	691	520.449547068052
15	769.025	758.07019155421
16	688.25	708.310127515555
17	518.8	727.053151603044
18	386.275	508.80532190237
19	491.35	434.2318942773
20	269.5	331.248437042921
21	379	389.269640545343
22	375.25	299.1481893675
23	337.5	502.876183618978
24	296	267.453582131041
25	375	340.713876999818
26	399.525	407.070535873498
27	336	417.641465716004
28	483.5	332.898922218684
29	370.25	337.338283908306
30	625.5	355.134629732789
31	736.75	571.23916170188
32	496.05	681.062633873284
33	740.5	549.057121163136
34	690.525	693.072231556067
35	568.75	712.003500002354
36	341.1	548.996333351918
37	519.75	427.493775297068
38	408.75	468.264830665661
39	278.35	446.239032991459
40	217	330.312869791279
41	266	205.218731892318
42	319.025	337.419117389042
43	454.75	419.036160167183
44	378.3	291.687302641049
45	509.575	515.635322954833
46	453.75	469.396122015109
47	252	413.361749776128
48	187.525	166.430760748899
49	401.5	248.202334497077
50	403.75	333.451042483504

What is next?

Simulate Time Series

Generate Forecasts

Forecast Analysis

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/13/t12737528707gigi53l7kssute/11zcp1273752825.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/13/t12737528707gigi53l7kssute/11zcp1273752825.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/13/t12737528707gigi53l7kssute/2crts1273752825.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/13/t12737528707gigi53l7kssute/2crts1273752825.ps (open in new window)

Parameters (Session):

par1 = Input box ; par2 = ARIMA ; par3 = NA ; par4 = NA ; par5 = ZZZ ; par6 = 12 ; par7 = dum ; par8 = dumresult ; par9 = 3 ; par10 = 0.1 ;

Parameters (R input):

par1 = Input box ; par2 = ARIMA ; par3 = NA ; par4 = NA ; par5 = ZZZ ; par6 = 12 ; par7 = dum ; par8 = dumresult ; par9 = 3 ; par10 = 0.1 ;

R code (references can be found in the software module):

par10 <- '0.1'

par9 <- '3'

par8 <- 'dumresult'

par7 <- 'dum'

par6 <- '12'

par5 <- 'ZZZ'

par4 <- 'NA'

par3 <- 'NA'

par2 <- 'ETS'

par1 <- 'Input box'

if(par3!='NA') par3 <- as.numeric(par3) else par3 <- NA

if(par4!='NA') par4 <- as.numeric(par4) else par4 <- NA

par6 <- as.numeric(par6) #Seasonal Period

par9 <- as.numeric(par9) #Forecast Horizon

par10 <- as.numeric(par10) #Alpha

library(forecast)

if (par1 == 'CSV') {

xarr <- read.csv(file=paste('tmp/',par7,'.csv',sep=''),header=T)

numseries <- length(xarr[1,])-1

n <- length(xarr[,1])

nmh <- n - par9

nmhp1 <- nmh + 1

rarr <- array(NA,dim=c(n,numseries))

farr <- array(NA,dim=c(n,numseries))

parr <- array(NA,dim=c(numseries,8))

colnames(parr) = list('ME','RMSE','MAE','MPE','MAPE','MASE','ACF1','TheilU')

for(i in 1:numseries) {

sindex <- i+1

x <- xarr[,sindex]

if(par2=='Croston') {

if (i==1) m <- croston(x,alpha=par10)

if (i==1) mydemand <- m$model$demand[]

fit <- croston(x[1:nmh],h=par9,alpha=par10)

}

if(par2=='ARIMA') {

m <- auto.arima(ts(x,freq=par6),d=par3,D=par4)

mydemand <- forecast(m)

fit <- auto.arima(ts(x[1:nmh],freq=par6),d=par3,D=par4)

}

if(par2=='ETS') {

m <- ets(ts(x,freq=par6),model=par5)

mydemand <- forecast(m)

fit <- ets(ts(x[1:nmh],freq=par6),model=par5)

}

try(rarr[,i] <- mydemand$resid,silent=T)

try(farr[,i] <- mydemand$mean,silent=T)

if (par2!='Croston') parr[i,] <- accuracy(forecast(fit,par9),x[nmhp1:n])

if (par2=='Croston') parr[i,] <- accuracy(fit,x[nmhp1:n])

}

write.csv(farr,file=paste('tmp/',par8,'_f.csv',sep=''))

write.csv(rarr,file=paste('tmp/',par8,'_r.csv',sep=''))

write.csv(parr,file=paste('tmp/',par8,'_p.csv',sep=''))

}

if (par1 == 'Input box') {

numseries <- 1

n <- length(x)

if(par2=='Croston') {

m <- croston(x)

mydemand <- m$model$demand[]

}

if(par2=='ARIMA') {

m <- auto.arima(ts(x,freq=par6),d=par3,D=par4)

mydemand <- forecast(m)

}

if(par2=='ETS') {

m <- ets(ts(x,freq=par6),model=par5)

mydemand <- forecast(m)

}

summary(m)

}

bitmap(file='test1.png')

op <- par(mfrow=c(2,1))

if (par2=='Croston') plot(m)

if ((par2=='ARIMA') | par2=='ETS') plot(forecast(m))

plot(mydemand$resid,type='l',main='Residuals', ylab='residual value', xlab='time')

par(op)

dev.off()

bitmap(file='pic2.png')

op <- par(mfrow=c(2,2))

acf(mydemand$resid, lag.max=n/3, main='Residual ACF', ylab='autocorrelation', xlab='time lag')

pacf(mydemand$resid,lag.max=n/3, main='Residual PACF', ylab='partial autocorrelation', xlab='time lag')

cpgram(mydemand$resid, main='Cumulative Periodogram of Residuals')

qqnorm(mydemand$resid); qqline(mydemand$resid, col=2)

par(op)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Demand Forecast',6,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Point',header=TRUE)

a<-table.element(a,'Forecast',header=TRUE)

a<-table.element(a,'95% LB',header=TRUE)

a<-table.element(a,'80% LB',header=TRUE)

a<-table.element(a,'80% UB',header=TRUE)

a<-table.element(a,'95% UB',header=TRUE)

a<-table.row.end(a)

for (i in 1:length(mydemand$mean)) {

a<-table.row.start(a)

a<-table.element(a,i+n,header=TRUE)

a<-table.element(a,as.numeric(mydemand$mean[i]))

a<-table.element(a,as.numeric(mydemand$lower[i,2]))

a<-table.element(a,as.numeric(mydemand$lower[i,1]))

a<-table.element(a,as.numeric(mydemand$upper[i,1]))

a<-table.element(a,as.numeric(mydemand$upper[i,2]))

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,'Actuals and Interpolation',3,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time',header=TRUE)

a<-table.element(a,'Actual',header=TRUE)

a<-table.element(a,'Forecast',header=TRUE)

a<-table.row.end(a)

for (i in 1:n) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,x[i])

a<-table.element(a,x[i] - as.numeric(m$resid[i]))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'What is next?',1,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,hyperlink(paste('http://www.wessa.net/Patrick.Wessa/rwasp_demand_forecasting_simulate.wasp',sep=''),'Simulate Time Series','',target=''))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,hyperlink(paste('http://www.wessa.net/Patrick.Wessa/rwasp_demand_forecasting_croston.wasp',sep=''),'Generate Forecasts','',target=''))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,hyperlink(paste('http://www.wessa.net/Patrick.Wessa/rwasp_demand_forecasting_analysis.wasp',sep=''),'Forecast Analysis','',target=''))

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable0.tab')

-SERVER-wessa.org

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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