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TIJDREEKS A - STAP 32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 12 Aug 2010 09:23:07 +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/Aug/12/t1281604990xfuy8et1afuse1v.htm/, Retrieved Thu, 12 Aug 2010 11:23:11 +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/Aug/12/t1281604990xfuy8et1afuse1v.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:

Hoes Isabelle

Dataseries X:

» Textbox « » Textfile « » CSV «

698 697 696 694 714 713 698 688 689 689 690 692 688 679 677 673 694 690 673 659 657 654 644 643 638 626 621 615 640 633 620 610 601 595 585 584 580 574 560 550 580 569 551 536 535 526 517 512 510 501 496 491 524 514 495 479 479 467 451 459 461 460 452 449 483 470 442 419 419 406 393 396 390 389 373 371 407 391 357 327 321 317 300 304 296 296 283 279 319 295 255 227 228 233 210 219 212 209 201 198 245 216 173 144 143 152 127 141 129 127 113 117 174 143 103 81 92 104 81 89

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.390729284726388
beta	0.122141405310284
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	688	698.392361111112	-10.3923611111115
14	679	684.902081797484	-5.90208179748402
15	677	680.176280501588	-3.17628050158783
16	673	674.613944074414	-1.61394407441389
17	694	695.168367346843	-1.1683673468433
18	690	691.424464403764	-1.42446440376432
19	673	670.762515382625	2.23748461737478
20	659	659.596512633478	-0.596512633478483
21	657	658.669716063091	-1.66971606309073
22	654	656.368901580986	-2.36890158098629
23	644	654.723507518725	-10.7235075187252
24	643	650.38528651341	-7.38528651340994
25	638	634.875521192174	3.12447880782577
26	626	627.938899260585	-1.93889926058478
27	621	625.14795665825	-4.14795665824988
28	615	618.837047553824	-3.83704755382394
29	640	637.367423977055	2.63257602294527
30	633	633.70713348529	-0.707133485290683
31	620	614.345324025832	5.65467597416762
32	610	601.739668350308	8.26033164969238
33	601	602.994136681446	-1.99413668144632
34	595	599.49959347137	-4.49959347136951
35	585	591.188798507169	-6.18879850716928
36	584	590.130056430245	-6.13005643024474
37	580	581.047698397987	-1.04769839798746
38	574	568.730462656111	5.26953734388906
39	560	567.088716376729	-7.08871637672928
40	550	559.3564116933	-9.35641169329995
41	580	578.946773278093	1.05322672190709
42	569	571.834034522757	-2.83403452275684
43	551	554.615179000695	-3.61517900069487
44	536	538.630604842518	-2.63060484251844
45	535	527.517692225214	7.48230777478591
46	526	524.787402018121	1.21259798187907
47	517	516.539984367657	0.460015632343129
48	512	517.29286799924	-5.29286799923955
49	510	510.852059573827	-0.852059573827432
50	501	501.687412756266	-0.687412756266042
51	496	489.131539088154	6.86846091184623
52	491	485.080116957271	5.91988304272934
53	524	517.319756412685	6.68024358731498
54	514	510.643902818448	3.3560971815524
55	495	496.269843131521	-1.2698431315207
56	479	482.815520472513	-3.8155204725125
57	479	478.358566834588	0.641433165412195
58	467	469.766359294742	-2.76635929474162
59	451	459.946790759489	-8.9467907594888
60	459	453.511234230465	5.48876576953495
61	461	454.495463583324	6.50453641667639
62	460	449.163339775758	10.8366602242417
63	452	447.121579930579	4.8784200694206
64	449	443.027425168988	5.97257483101197
65	483	477.066208257756	5.93379174224356
66	470	469.353055170431	0.646944829568554
67	442	452.25237432666	-10.2523743266601
68	419	434.458996661324	-15.4589966613245
69	419	428.334101003334	-9.33410100333401
70	406	413.457831128752	-7.45783112875159
71	393	397.505653553361	-4.50565355336096
72	396	401.278533359715	-5.27853335971474
73	390	397.838674058958	-7.8386740589578
74	389	388.021286588662	0.978713411337651
75	373	376.5067066705	-3.5067066704998
76	371	367.41184979845	3.58815020155026
77	407	397.99052015082	9.00947984918042
78	391	385.899973499283	5.10002650071704
79	357	361.753091982011	-4.75309198201086
80	327	341.053137330405	-14.0531373304053
81	321	337.393300057954	-16.3933000579545
82	317	318.74908429431	-1.74908429430985
83	300	304.945735761255	-4.94573576125543
84	304	306.17434607908	-2.17434607907967
85	296	300.634286378242	-4.63428637824171
86	296	295.840771379659	0.159228620340798
87	283	279.633698772397	3.366301227603
88	279	276.235563968202	2.76443603179825
89	319	308.44467943157	10.55532056843
90	295	293.299233596488	1.7007664035122
91	255	260.381729032973	-5.38172903297345
92	227	232.300684944992	-5.30068494499199
93	228	229.583381261816	-1.58338126181627
94	233	225.303404918218	7.69659508178216
95	210	213.349200152569	-3.34920015256853
96	219	217.072410030458	1.92758996954242
97	212	212.014348766512	-0.0143487665121427
98	209	212.54503141966	-3.54503141966003
99	201	197.266292843594	3.7337071564063
100	198	194.084271105343	3.91572889465706
101	245	231.984188406698	13.0158115933016
102	216	213.01693315193	2.98306684806994
103	173	176.958125888556	-3.95812588855557
104	144	150.223465408778	-6.22346540877811
105	143	150.10717204787	-7.10717204786951
106	152	149.75601147652	2.24398852348037
107	127	129.114317441323	-2.11431744132344
108	141	136.766843022859	4.23315697714131
109	129	131.768316473222	-2.76831647322248
110	127	129.282219346418	-2.28221934641766
111	113	119.202305010908	-6.20230501090795
112	117	112.045388714387	4.95461128561318
113	174	155.741717394231	18.2582826057694
114	143	132.806460091939	10.1935399080613
115	103	95.776313147972	7.22368685202804
116	81	73.0045354692792	7.99546453072082
117	92	79.5581913904612	12.4418086095388
118	104	95.1283518023456	8.87164819765435
119	81	77.3227636768203	3.67723632317968
120	89	94.283819984435	-5.28381998443496

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	84.0250195442005	71.7670244199028	96.283014668498
122	85.772945679727	72.3884639900133	99.1574273694406
123	77.1614812301571	62.5101756071824	91.8127868531318
124	82.4866830495328	66.4401220078042	98.5332440912614
125	135.377295911256	117.818170014486	152.936421808027
126	102.54767755106	83.3685858841437	121.726769217976
127	61.3919889699537	40.4941291817852	82.2898487581222
128	37.5899993995408	14.8819321179643	60.2980666811172
129	44.6691156478565	20.0656739634916	69.2725573322214
130	53.549422460061	26.9707830928549	80.1280618272672
131	29.0359455833193	0.406852669208423	57.6650384974302
132	38.8483225783051	8.09744499950508	69.5992001571051

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/12/t1281604990xfuy8et1afuse1v/19jow1281604981.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/12/t1281604990xfuy8et1afuse1v/19jow1281604981.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/12/t1281604990xfuy8et1afuse1v/29jow1281604981.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/12/t1281604990xfuy8et1afuse1v/29jow1281604981.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/12/t1281604990xfuy8et1afuse1v/32t6h1281604981.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/12/t1281604990xfuy8et1afuse1v/32t6h1281604981.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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

par1 <- as.numeric(par1)

if (par2 == 'Single') K <- 1

if (par2 == 'Double') K <- 2

if (par2 == 'Triple') K <- par1

nx <- length(x)

nxmK <- nx - K

x <- ts(x, frequency = par1)

if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)

if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)

if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)

fit

myresid <- x - fit$fitted[,'xhat']

bitmap(file='test1.png')

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

plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')

plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')

par(op)

dev.off()

bitmap(file='test2.png')

p <- predict(fit, par1, prediction.interval=TRUE)

np <- length(p[,1])

plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')

dev.off()

bitmap(file='test3.png')

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

acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')

spectrum(myresid,main='Residals Periodogram')

cpgram(myresid,main='Residal Cumulative Periodogram')

qqnorm(myresid,main='Residual Normal QQ Plot')

qqline(myresid)

par(op)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

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

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

a<-table.row.end(a)

a<-table.row.start(a)

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

a<-table.element(a,fit$alpha)

a<-table.row.end(a)

a<-table.row.start(a)

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

a<-table.element(a,fit$beta)

a<-table.row.end(a)

a<-table.row.start(a)

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

a<-table.element(a,fit$gamma)

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,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'t',header=TRUE)

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

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

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

a<-table.row.end(a)

for (i in 1:nxmK) {

a<-table.row.start(a)

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

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

a<-table.element(a,fit$fitted[i,'xhat'])

a<-table.element(a,myresid[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,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'t',header=TRUE)

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

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

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

a<-table.row.end(a)

for (i in 1:np) {

a<-table.row.start(a)

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

a<-table.element(a,p[i,'fit'])

a<-table.element(a,p[i,'lwr'])

a<-table.element(a,p[i,'upr'])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable2.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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