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Tijdreeks 1 - 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, 05 Aug 2010 13:42:52 +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/05/t128101586740z6c0le8djopyn.htm/, Retrieved Thu, 05 Aug 2010 15:44:31 +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/05/t128101586740z6c0le8djopyn.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:

Mathias Goossenaerts

Dataseries X:

» Textbox « » Textfile « » CSV «

36 35 34 32 52 51 36 26 27 27 28 30 28 29 25 28 55 53 42 32 37 41 37 38 39 32 36 39 83 83 66 53 72 77 69 72 81 71 63 66 114 116 109 97 111 120 110 106 115 110 103 112 163 166 156 140 166 176 163 162 171 167 163 168 222 216 197 178 204 220 196 195 213 218 216 225 280 272 252 230 248 259 240 237 252 250 255 255 313 291 271 247 268 283 259 259 267 270 279 269 334 326 301 276 301 313 291 287 289 298 320 312 385 380 351 322 350 363 344 345

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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.601667916362739
beta	0.0534961536760316
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	28	28.6610576923077	-0.661057692307701
14	29	29.0120022848353	-0.0120022848352548
15	25	24.5864097087405	0.413590291259538
16	28	27.0968613951253	0.90313860487474
17	55	53.9725945113945	1.02740548860555
18	53	52.2061640422371	0.793835957762909
19	42	38.6164200807209	3.38357991927913
20	32	31.6937489863031	0.306251013696908
21	37	33.9710717646357	3.02892823536429
22	41	36.9007006092486	4.09929939075144
23	37	41.1062812553989	-4.10628125539889
24	38	40.9926587481785	-2.99265874817853
25	39	37.0644222208437	1.93557777915627
26	32	39.5188411962294	-7.51884119622937
27	36	30.7871521894391	5.21284781056087
28	39	36.5756397798799	2.42436022012006
29	83	64.6605798923608	18.3394201076392
30	83	74.0188526368362	8.98114736316384
31	66	67.4519113967683	-1.45191139676832
32	53	57.3036239330653	-4.30362393306527
33	72	58.6530273257272	13.3469726742728
34	77	69.3103264827397	7.68967351726033
35	69	73.6164079359505	-4.61640793595049
36	72	74.8318646627762	-2.83186466277621
37	81	74.1610374859409	6.83896251405915
38	71	77.1550821602728	-6.15508216027283
39	63	75.7146734558376	-12.7146734558376
40	66	70.428280962221	-4.42828096222098
41	114	101.331398644255	12.6686013557446
42	116	103.969208164141	12.0307918358593
43	109	95.5986635451229	13.4013364548771
44	97	94.2465958812676	2.75340411873236
45	111	108.095355264368	2.90464473563188
46	120	111.102820303519	8.89717969648059
47	110	112.158841656803	-2.15884165680269
48	106	116.568208733904	-10.568208733904
49	115	115.85029392439	-0.850293924389959
50	110	109.549942977455	0.450057022545423
51	103	110.191266184242	-7.19126618424195
52	112	112.427175337348	-0.427175337347634
53	163	153.574958639764	9.42504136023553
54	166	154.929853955165	11.0701460448349
55	156	147.419023024574	8.58097697542607
56	140	139.661905667139	0.338094332861033
57	166	152.776572277290	13.2234277227102
58	176	165.370544391567	10.6294556084333
59	163	164.111616664646	-1.11161666464602
60	162	166.881815760854	-4.88181576085424
61	171	174.719676939564	-3.71967693956404
62	167	168.382023717026	-1.38202371702567
63	163	165.989431415208	-2.98943141520823
64	168	174.695221143629	-6.69522114362937
65	222	217.04184431105	4.95815568894989
66	216	217.266348439443	-1.26634843944308
67	197	201.846347553377	-4.8463475533766
68	178	182.79966987299	-4.79966987298999
69	204	197.863016161036	6.13698383896426
70	220	204.839215099513	15.1607849004873
71	196	201.454821641072	-5.4548216410721
72	195	199.795292596558	-4.79529259655803
73	213	207.836144289016	5.16385571098436
74	218	207.748538597498	10.2514614025021
75	216	212.063553709084	3.93644629091582
76	225	224.031604287978	0.968395712021987
77	280	276.449079319361	3.55092068063914
78	272	274.120166637217	-2.12016663721715
79	252	257.505631495046	-5.50563149504649
80	230	238.804865984211	-8.80486598421086
81	248	256.40990835776	-8.40990835775995
82	259	258.355032835679	0.644967164320974
83	240	237.684714980032	2.3152850199684
84	237	240.872652118435	-3.8726521184347
85	252	253.375102955871	-1.37510295587134
86	250	251.108730943252	-1.10873094325166
87	255	245.436518813986	9.56348118601386
88	255	259.152332045134	-4.1523320451343
89	313	308.897137640297	4.10286235970273
90	291	304.038705444525	-13.0387054445246
91	271	278.552233324085	-7.55223332408542
92	247	256.285965185278	-9.2859651852782
93	268	272.723447776690	-4.72344777668951
94	283	279.576678431684	3.42332156831594
95	259	260.416008828737	-1.41600882873661
96	259	257.946653779799	1.05334622020098
97	267	273.618887948337	-6.61888794833737
98	270	267.345936192573	2.65406380742729
99	279	267.352207134476	11.6477928655236
100	269	276.089168638958	-7.08916863895843
101	334	326.491288216854	7.50871178314645
102	326	316.099639276183	9.9003607238173
103	301	306.584272393367	-5.58427239336697
104	276	284.858772003442	-8.85877200344248
105	301	303.431739945875	-2.43173994587499
106	313	315.043760152929	-2.04376015292894
107	291	290.624916671927	0.375083328072833
108	287	290.233331739831	-3.23333173983139
109	289	300.148841420857	-11.1488414208574
110	298	294.576800076805	3.42319992319545
111	320	298.385806384765	21.6141936152353
112	312	305.733966288152	6.26603371184842
113	385	370.494417326095	14.5055826739048
114	380	365.998569903826	14.0014300961735
115	351	353.647997782839	-2.64799778283901
116	322	333.344670072757	-11.3446700727569
117	350	353.861881279653	-3.86188127965318
118	363	365.601779590946	-2.60177959094551
119	344	342.626539215838	1.37346078416221
120	345	342.246275704166	2.75372429583427

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	353.651685569883	339.688594721905	367.614776417862
122	361.991584982937	345.459781017536	378.523388948339
123	372.276364865005	353.308218648937	391.244511081073
124	361.099945830178	339.7729215597	382.426970100656
125	425.764370218070	402.124177852895	449.404562583244
126	412.265237017782	386.337554205881	438.192919829682
127	384.332867497281	356.129958788011	412.535776206552
128	361.71823756373	331.242991236539	392.19348389092
129	391.966603668744	359.215138880941	424.718068456546
130	406.581109077463	371.544535994063	441.617682160862
131	386.887583162421	349.55323390625	424.221932418592
132	386.319389504836	346.671704058641	425.967074951032

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/05/t128101586740z6c0le8djopyn/1jjb31281015770.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t128101586740z6c0le8djopyn/1jjb31281015770.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t128101586740z6c0le8djopyn/2uss61281015770.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t128101586740z6c0le8djopyn/2uss61281015770.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t128101586740z6c0le8djopyn/3uss61281015770.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t128101586740z6c0le8djopyn/3uss61281015770.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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