Home » date » 2010 » Jul » 26 »

Kelly Janbroers - 2de zit - Stap 32/A

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 Jul 2010 15:48:44 +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/Jul/26/t1280159334cud36wf2rskay6s.htm/, Retrieved Mon, 26 Jul 2010 17:48:54 +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/Jul/26/t1280159334cud36wf2rskay6s.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 «

33 32 31 29 49 48 33 23 24 24 25 27 24 21 15 21 49 48 35 36 51 50 61 63 61 62 58 65 93 94 86 88 102 107 121 127 125 128 117 127 160 162 153 160 177 178 196 212 212 211 204 216 248 250 240 249 275 277 286 302 290 290 277 285 311 300 291 299 332 337 343 360 353 351 341 348 381 358 353 358 399 409 407 419 418 421 414 424 463 437 430 436 474 489 482 492 502 500 493 504 538 516 502 501 541 571 559 569 576 573 562 570 597 573 562 556 600 630 624 634

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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.116508597215365
beta	0.113960080374117
gamma	0.923119969726914

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	24	26.4444669311186	-2.44446693111864
14	21	22.7999103475503	-1.79991034755028
15	15	15.5071479699010	-0.507147969901043
16	21	20.4863904332728	0.513609566727155
17	49	45.1358407222432	3.86415927775681
18	48	41.8380525166743	6.16194748332573
19	35	36.3824260342733	-1.38242603427332
20	36	26.4011771216597	9.5988228783403
21	51	30.4618799396217	20.5381200603783
22	50	34.9644587202633	15.0355412797367
23	61	39.9088891886615	21.0911108113385
24	63	47.3590795126269	15.6409204873731
25	61	41.7474488407776	19.2525511592224
26	62	39.6124065589765	22.3875934410235
27	58	30.9248103084356	27.0751896915644
28	65	48.8396652611018	16.1603347388982
29	93	120.376007733544	-27.3760077335443
30	94	115.441865223909	-21.4418652239095
31	86	85.4818643154791	0.518135684520871
32	88	84.3868182017308	3.61318179826920
33	102	112.134675530090	-10.1346755300897
34	107	105.140763240839	1.85923675916068
35	121	121.118271453613	-0.118271453613005
36	127	121.077115027069	5.92288497293131
37	125	110.945392624378	14.0546073756224
38	128	106.352336148663	21.6476638513365
39	117	90.9649988625661	26.0350011374339
40	127	101.772867383471	25.2271326165286
41	160	157.892212670898	2.10778732910242
42	162	161.286935759247	0.713064240753056
43	153	144.317225248130	8.68277475187034
44	160	146.834948882523	13.1650511174767
45	177	174.675906040562	2.32409395943776
46	178	181.105546752881	-3.10554675288139
47	196	203.976018348845	-7.97601834884512
48	212	210.472869930212	1.52713006978769
49	212	202.646610211188	9.35338978881151
50	211	202.148783322787	8.85121667721307
51	204	178.105414782944	25.8945852170555
52	216	190.21585649707	25.7841435029301
53	248	244.510236825574	3.48976317442575
54	250	246.450783325021	3.54921667497905
55	240	229.372890883863	10.6271091161367
56	249	236.937563788766	12.0624362112345
57	275	263.042385367727	11.9576146322730
58	277	265.712552142234	11.2874478577659
59	286	294.649798731673	-8.64979873167329
60	302	315.135086901385	-13.1350869013848
61	290	309.893093353792	-19.8930933537925
62	290	303.117698760301	-13.1176987603006
63	277	283.486602623844	-6.4866026238443
64	285	292.823866971079	-7.82386697107933
65	311	334.270974687350	-23.2709746873496
66	300	330.791503884563	-30.7915038845633
67	291	308.866917739733	-17.8669177397330
68	299	313.146783649465	-14.1467836494645
69	332	338.698860574392	-6.69886057439152
70	337	335.098864372296	1.90113562770421
71	343	345.341446975476	-2.34144697547589
72	360	362.791377332174	-2.79137733217431
73	353	348.003837533957	4.99616246604324
74	351	346.945006011618	4.05499398838157
75	341	329.821484837055	11.1785151629454
76	348	339.658970072508	8.34102992749234
77	381	373.841083503257	7.1589164967433
78	358	364.443136986266	-6.4431369862657
79	353	352.952257879794	0.0477421202064647
80	358	363.236019478418	-5.23601947841757
81	399	401.904778684521	-2.90477868452052
82	409	405.775236689811	3.22476331018885
83	407	413.224574255489	-6.22457425548936
84	419	432.469211640472	-13.4692116404721
85	418	420.232241543497	-2.23224154349737
86	421	416.084403274391	4.91559672560919
87	414	401.662335549377	12.3376644506232
88	424	409.493631417327	14.5063685826732
89	463	448.375875034616	14.6241249653841
90	437	424.032348112696	12.9676518873035
91	430	418.531764110505	11.4682358894946
92	436	426.552824927083	9.44717507291728
93	474	476.553445223035	-2.553445223035
94	489	487.009146895982	1.99085310401750
95	482	486.231795117647	-4.23179511764693
96	492	502.246427752703	-10.2464277527030
97	502	499.117353209686	2.88264679031357
98	500	501.693261568068	-1.69326156806761
99	493	490.637377835757	2.36262216424342
100	504	500.247827420412	3.75217257958786
101	538	544.266158879228	-6.26615887922787
102	516	510.539515840027	5.46048415997313
103	502	500.687709295027	1.31229070497284
104	501	505.760629563508	-4.76062956350842
105	541	549.401803617438	-8.40180361743785
106	571	563.886924550248	7.11307544975182
107	559	556.52810803436	2.47189196563954
108	569	569.123138142177	-0.123138142176572
109	576	578.319365692353	-2.31936569235324
110	573	575.369278243249	-2.36927824324903
111	562	565.481496797421	-3.48149679742119
112	570	576.077233259365	-6.07723325936456
113	597	614.63374958803	-17.6337495880302
114	573	584.699471116764	-11.6994711167645
115	562	566.285335599852	-4.28533559985181
116	556	564.350268451656	-8.35026845165567
117	600	608.180435407701	-8.18043540770122
118	630	637.202970029505	-7.20297002950474
119	624	621.356514805579	2.64348519442080
120	634	631.355294228884	2.64470577111581

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	638.301890061408	617.075085764316	659.528694358501
122	633.76228918743	612.33697205899	655.187606315869
123	620.694976661165	599.049663884489	642.340289437841
124	629.116610441239	607.17979435738	651.053426525099
125	660.63537349351	638.280785539932	682.989961447088
126	634.123589831142	611.512970567519	656.734209094764
127	621.106080396055	598.169561865774	644.042598926336
128	615.071615963833	591.747445347015	638.395786580651
129	664.024070526507	639.839811170905	688.20832988211
130	697.4299466292	672.366044308721	722.493848949679
131	689.212738480854	663.625475474793	714.800001486914
132	699.38549502688	682.363862116969	716.40712793679

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/26/t1280159334cud36wf2rskay6s/1p5n61280159319.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jul/26/t1280159334cud36wf2rskay6s/1p5n61280159319.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jul/26/t1280159334cud36wf2rskay6s/2he581280159319.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jul/26/t1280159334cud36wf2rskay6s/2he581280159319.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jul/26/t1280159334cud36wf2rskay6s/3he581280159319.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jul/26/t1280159334cud36wf2rskay6s/3he581280159319.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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