Home » date » 2008 » Dec » 15 »

Gilliam Schoorel

*Unverified author*

R Software Module: rwasp_arimaforecasting.wasp (opens new window with default values)

Title produced by software: ARIMA Forecasting

Date of computation: Mon, 15 Dec 2008 13:58:10 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/15/t1229374760xtga7jav95oyzno.htm/, Retrieved Mon, 15 Dec 2008 21:59:22 +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/2008/Dec/15/t1229374760xtga7jav95oyzno.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

467 460 448 443 436 431 484 510 513 503 471 471 476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514

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	1 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[34])
22	519	-	-	-	-	-	-	-
23	509	-	-	-	-	-	-	-
24	512	-	-	-	-	-	-	-
25	519	-	-	-	-	-	-	-
26	517	-	-	-	-	-	-	-
27	510	-	-	-	-	-	-	-
28	509	-	-	-	-	-	-	-
29	501	-	-	-	-	-	-	-
30	507	-	-	-	-	-	-	-
31	569	-	-	-	-	-	-	-
32	580	-	-	-	-	-	-	-
33	578	-	-	-	-	-	-	-
34	565	-	-	-	-	-	-	-
35	547	556.1203	544.0685	568.1721	0.069	0.0744	1	0.0744
36	555	560.26	540.687	579.8329	0.2992	0.9079	1	0.3175
37	562	568.4567	543.185	593.7284	0.3083	0.8517	0.9999	0.6057
38	561	564.5419	537.4849	591.5988	0.3988	0.573	0.9997	0.4868
39	555	557.6536	527.8601	587.4472	0.4307	0.4129	0.9991	0.3144
40	544	557.5268	524.2789	590.7747	0.2126	0.5592	0.9979	0.3298
41	537	549.4481	513.6652	585.2311	0.2477	0.6173	0.996	0.1971
42	543	554.8696	517.1801	592.5591	0.2685	0.8236	0.9936	0.2992
43	594	617.0445	577.1374	656.9516	0.1289	0.9999	0.9909	0.9947
44	611	628.3475	586.1611	670.5339	0.2101	0.9447	0.9877	0.9984
45	613	626.2011	582.1011	670.3011	0.2787	0.7504	0.9839	0.9967
46	611	613.0385	567.1654	658.9115	0.4653	0.5007	0.9799	0.9799
47	594	604.2755	551.9209	656.6302	0.3502	0.4006	0.984	0.9293
48	595	608.493	548.8184	668.1675	0.3288	0.683	0.9605	0.9234
49	591	616.6073	550.3167	682.8979	0.2245	0.7385	0.9468	0.9365
50	589	612.6588	542.6291	682.6885	0.2539	0.7278	0.9259	0.9089
51	584	605.8258	531.2705	680.381	0.2831	0.6709	0.9093	0.8584
52	573	605.7101	526.1358	685.2845	0.2102	0.7036	0.9357	0.842
53	567	597.5964	513.8274	681.3655	0.237	0.7175	0.9219	0.7772
54	569	603.0169	515.6452	690.3886	0.2227	0.7904	0.9109	0.8031
55	621	665.213	574.006	756.4201	0.171	0.9807	0.937	0.9844
56	629	676.5132	581.4801	771.5462	0.1636	0.8739	0.9117	0.9893
57	628	674.3545	575.872	772.8369	0.1781	0.8166	0.889	0.9852
58	612	661.1955	559.4291	762.962	0.1717	0.7387	0.8332	0.968
59	595	652.4394	543.7183	761.1606	0.1502	0.767	0.854	0.9425
60	597	656.6535	540.2293	773.0776	0.1576	0.8504	0.8504	0.9386
61	593	664.7642	541.0394	788.489	0.1278	0.8585	0.8787	0.943
62	590	660.8184	532.0758	789.5609	0.1405	0.8491	0.8629	0.9277
63	580	653.9871	519.5837	788.3905	0.1403	0.8246	0.8463	0.9028
64	574	653.8696	513.4035	794.3357	0.1325	0.8487	0.8704	0.8925
65	573	645.7551	499.9257	791.5845	0.1641	0.8326	0.8551	0.8611
66	573	651.1768	500.5169	801.8367	0.1546	0.8454	0.8575	0.8689
67	620	713.3732	557.7013	869.0451	0.1199	0.9614	0.8776	0.9691
68	626	724.6726	564.0172	885.3279	0.1143	0.8992	0.8784	0.9743
69	620	722.5138	557.2285	887.7992	0.1121	0.8738	0.8688	0.9691
70	588	709.3554	539.6097	879.1011	0.0806	0.8489	0.8695	0.9522
71	566	700.5992	523.2788	877.9197	0.0684	0.8934	0.8784	0.933
72	557	704.813	519.2603	890.3658	0.0592	0.9287	0.8726	0.9301
73	561	712.9239	519.4245	906.4232	0.0619	0.9429	0.8878	0.933
74	549	708.9781	509.4677	908.4885	0.058	0.927	0.8788	0.9214
75	532	702.1468	496.0698	908.2237	0.0528	0.9274	0.8773	0.904
76	526	702.0292	489.0368	915.0216	0.0526	0.9412	0.8806	0.8963
77	511	693.9148	474.6198	913.2098	0.051	0.9333	0.8601	0.8754
78	499	699.3365	474.2218	924.4512	0.0406	0.9495	0.8643	0.8789
79	555	761.5329	530.4465	992.6193	0.0399	0.987	0.885	0.9522
80	565	772.8322	535.8093	1009.8551	0.0428	0.9642	0.8877	0.9572
81	542	770.6735	528.0438	1013.3032	0.0324	0.9517	0.8882	0.9517
82	527	757.5151	509.445	1005.5852	0.0343	0.9557	0.9098	0.9359
83	510	748.7589	492.4946	1005.0232	0.0339	0.9551	0.9189	0.9201
84	514	752.9727	487.9249	1018.0204	0.0386	0.9638	0.9264	0.9177

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
35	0.0111	-0.0164	3e-04	83.1804	1.6636	1.2898
36	0.0178	-0.0094	2e-04	27.6674	0.5533	0.7439
37	0.0227	-0.0114	2e-04	41.6892	0.8338	0.9131
38	0.0245	-0.0063	1e-04	12.5448	0.2509	0.5009
39	0.0273	-0.0048	1e-04	7.0417	0.1408	0.3753
40	0.0304	-0.0243	5e-04	182.9748	3.6595	1.913
41	0.0332	-0.0227	5e-04	154.9557	3.0991	1.7604
42	0.0347	-0.0214	4e-04	140.8867	2.8177	1.6786
43	0.033	-0.0373	7e-04	531.0488	10.621	3.259
44	0.0343	-0.0276	6e-04	300.9353	6.0187	2.4533
45	0.0359	-0.0211	4e-04	174.2692	3.4854	1.8669
46	0.0382	-0.0033	1e-04	4.1553	0.0831	0.2883
47	0.0442	-0.017	3e-04	105.5869	2.1117	1.4532
48	0.05	-0.0222	4e-04	182.06	3.6412	1.9082
49	0.0549	-0.0415	8e-04	655.7319	13.1146	3.6214
50	0.0583	-0.0386	8e-04	559.7388	11.1948	3.3459
51	0.0628	-0.036	7e-04	476.3651	9.5273	3.0866
52	0.067	-0.054	0.0011	1069.9525	21.3991	4.6259
53	0.0715	-0.0512	0.001	936.1402	18.7228	4.327
54	0.0739	-0.0564	0.0011	1157.1464	23.1429	4.8107
55	0.07	-0.0665	0.0013	1954.792	39.0958	6.2527
56	0.0717	-0.0702	0.0014	2257.4995	45.15	6.7194
57	0.0745	-0.0687	0.0014	2148.7351	42.9747	6.5555
58	0.0785	-0.0744	0.0015	2420.2011	48.404	6.9573
59	0.085	-0.088	0.0018	3299.2888	65.9858	8.1232
60	0.0905	-0.0908	0.0018	3558.5384	71.1708	8.4363
61	0.095	-0.108	0.0022	5150.1066	103.0021	10.149
62	0.0994	-0.1072	0.0021	5015.2432	100.3049	10.0152
63	0.1049	-0.1131	0.0023	5474.0881	109.4818	10.4634
64	0.1096	-0.1221	0.0024	6379.1491	127.583	11.2953
65	0.1152	-0.1127	0.0023	5293.3086	105.8662	10.2891
66	0.118	-0.1201	0.0024	6111.6125	122.2323	11.0559
67	0.1113	-0.1309	0.0026	8718.5572	174.3711	13.205
68	0.1131	-0.1362	0.0027	9736.2737	194.7255	13.9544
69	0.1167	-0.1419	0.0028	10509.0877	210.1818	14.4976
70	0.1221	-0.1711	0.0034	14727.1334	294.5427	17.1622
71	0.1291	-0.1921	0.0038	18116.9528	362.3391	19.0352
72	0.1343	-0.2097	0.0042	21848.6855	436.9737	20.9039
73	0.1385	-0.2131	0.0043	23080.8563	461.6171	21.4853
74	0.1436	-0.2256	0.0045	25593.005	511.8601	22.6243
75	0.1497	-0.2423	0.0048	28949.9206	578.9984	24.0624
76	0.1548	-0.2507	0.005	30986.272	619.7254	24.8943
77	0.1612	-0.2636	0.0053	33457.8203	669.1564	25.8681
78	0.1642	-0.2865	0.0057	40134.7141	802.6943	28.3319
79	0.1548	-0.2712	0.0054	42655.8276	853.1166	29.2082
80	0.1565	-0.2689	0.0054	43194.2236	863.8845	29.3919
81	0.1606	-0.2967	0.0059	52291.5748	1045.8315	32.3393
82	0.1671	-0.3043	0.0061	53137.2003	1062.744	32.5998
83	0.1746	-0.3189	0.0064	57005.8066	1140.1161	33.7656
84	0.1796	-0.3174	0.0063	57107.9351	1142.1587	33.7958

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229374760xtga7jav95oyzno/1sv8w1229374688.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229374760xtga7jav95oyzno/1sv8w1229374688.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229374760xtga7jav95oyzno/242261229374688.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229374760xtga7jav95oyzno/242261229374688.ps (open in new window)

Parameters (Session):

par1 = 50 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 2 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 50 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 2 ; 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,fx))

(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.se <- array(0, dim=fx)

perf.mse <- 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.mape[i] = perf.mape[i] + abs(perf.pe[i])

perf.se[i] = (x[nx+i] - forecast$pred[i])^2

perf.mse[i] = perf.mse[i] + perf.se[i]

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 = perf.mape / fx

perf.mse = perf.mse / fx

perf.rmse = sqrt(perf.mse)

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[1:12] <- 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.mape[i],4))

a<-table.element(a,round(perf.se[i],4))

a<-table.element(a,round(perf.mse[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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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.

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