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Exponential_Smoothing_Reeks_A_Jeroen_Kinne

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 16 Aug 2010 14:20:22 +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/16/t1281968478dc0cvsounltxsx0.htm/, Retrieved Mon, 16 Aug 2010 16:21:22 +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/16/t1281968478dc0cvsounltxsx0.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:

Jeroen_Kinne

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.124791631525621
beta	0.0903911823166393
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	28	28.7814054374197	-0.781405437419746
14	29	29.4996210015149	-0.499621001514875
15	25	25.0751391320068	-0.0751391320067611
16	28	27.4842187019420	0.515781298057966
17	55	53.088556297424	1.91144370257596
18	53	50.8091947650192	2.19080523498079
19	42	37.6399610034024	4.36003899659757
20	32	28.3268226177709	3.67317738222907
21	37	30.7891925673153	6.21080743268472
22	41	32.4984223435561	8.5015776564439
23	37	35.369013088035	1.63098691196502
24	38	38.4449775716736	-0.444977571673597
25	39	35.1359330833744	3.86406691662564
26	32	37.2471740287663	-5.24717402876632
27	36	31.7529292396107	4.24707076038930
28	39	36.3376900300889	2.66230996991113
29	83	72.258367045599	10.7416329544010
30	83	71.1414813594441	11.8585186405559
31	66	57.2583315437538	8.74166845624622
32	53	44.1541972389296	8.84580276107038
33	72	51.5274890875057	20.4725109124943
34	77	58.6441304201867	18.3558695798133
35	69	55.2326034175893	13.7673965824107
36	72	59.237437293985	12.7625627060150
37	81	62.3636404614659	18.6363595385341
38	71	54.7488926594172	16.2511073405828
39	63	63.8486403153705	-0.848640315370545
40	66	69.4028479886932	-3.40284798869324
41	114	145.936784916613	-31.9367849166129
42	116	140.301520865075	-24.3015208650754
43	109	107.719421940463	1.28057805953746
44	97	84.8715482805097	12.1284517194903
45	111	112.196601480667	-1.19660148066666
46	120	115.319786486398	4.68021351360176
47	110	100.509132171797	9.49086782820338
48	106	103.002307624348	2.99769237565154
49	115	111.615143906972	3.38485609302802
50	110	94.1087000038788	15.8912999961212
51	103	84.834953366099	18.1650466339010
52	112	91.3936470896508	20.6063529103492
53	163	166.495244554399	-3.49524455439897
54	166	172.614676298980	-6.61467629898044
55	156	161.279978360779	-5.27997836077907
56	140	140.462656150105	-0.462656150105460
57	166	160.724789786533	5.27521021346718
58	176	173.487466319285	2.51253368071482
59	163	157.340503206209	5.65949679379102
60	162	151.564791538878	10.4352084611216
61	171	165.084861457369	5.91513854263061
62	167	155.225053585998	11.7749464140016
63	163	142.697405308208	20.3025946917918
64	168	153.304117435719	14.6958825642812
65	222	225.738019612001	-3.73801961200067
66	216	229.909230344462	-13.9092303444623
67	197	214.720204210965	-17.7202042109653
68	178	190.210088540833	-12.2100885408333
69	204	222.047100034280	-18.0471000342803
70	220	231.616305991051	-11.6163059910511
71	196	211.21750758362	-15.2175075836199
72	195	205.135795250163	-10.1357952501627
73	213	212.894166393789	0.105833606210808
74	218	204.671053964642	13.3289460353577
75	216	196.662389520552	19.3376104794482
76	225	201.499312273073	23.5006877269274
77	280	269.156390093195	10.8436099068049
78	272	263.876973335896	8.12302666410437
79	252	243.122942803387	8.87705719661264
80	230	221.825958166675	8.17404183332474
81	248	257.536031178919	-9.53603117891947
82	259	277.802840768603	-18.8028407686027
83	240	247.255624673105	-7.25562467310519
84	237	246.344461665583	-9.34446166558308
85	252	267.536872966414	-15.5368729664141
86	250	269.242449940353	-19.2424499403534
87	255	260.480463680905	-5.4804636809053
88	255	265.746466884705	-10.7464668847052
89	313	325.740518194468	-12.7405181944683
90	291	311.916455303031	-20.9164553030314
91	271	283.436620072139	-12.4366200721386
92	247	254.309660286664	-7.30966028666396
93	268	272.464183474588	-4.46418347458797
94	283	284.370560790463	-1.37056079046289
95	259	262.656050995746	-3.65605099574577
96	259	258.591586167305	0.40841383269526
97	267	275.497912500129	-8.49791250012868
98	270	273.299518289933	-3.29951828993308
99	279	277.832748497263	1.16725150273680
100	269	278.235774979787	-9.23577497978715
101	334	340.411527037191	-6.41152703719052
102	326	317.220722934781	8.77927706521916
103	301	297.262378337408	3.73762166259178
104	276	271.766073686691	4.23392631330893
105	301	295.57049447262	5.42950552738017
106	313	312.628474228203	0.371525771796712
107	291	286.323624215527	4.67637578447273
108	287	286.611160698901	0.388839301098983
109	289	296.411979002331	-7.41197900233067
110	298	299.032979654439	-1.03297965443949
111	320	308.504261027379	11.4957389726211
112	312	299.981123420088	12.0188765799124
113	385	375.377297595348	9.6227024046521
114	380	366.617703744161	13.3822962558390
115	351	339.836774110095	11.1632258899053
116	322	312.637839513514	9.36216048648572
117	350	341.879056634634	8.1209433653662
118	363	356.969997265305	6.03000273469485
119	344	332.375301479536	11.6246985204639
120	345	329.701855701650	15.2981442983503

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	335.636009681172	314.261896244569	357.010123117774
122	347.004585361403	325.424263598509	368.584907124297
123	371.717489459965	349.853301219648	393.581677700281
124	361.26754001249	339.187271515152	383.347808509828
125	444.974623900517	422.121586314335	467.8276614867
126	437.671737480202	414.513484180969	460.829990779434
127	402.894824386870	379.669632770995	426.120016002746
128	368.356574187279	345.101706443548	391.611441931009
129	399.218236369251	375.215519815881	423.22095292262
130	413.09177712158	388.451803952472	437.731750290688
131	389.625832274864	364.893737164886	414.357927384841
132	388.234357368062	372.560490417341	403.908224318783

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281968478dc0cvsounltxsx0/18wca1281968419.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281968478dc0cvsounltxsx0/18wca1281968419.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281968478dc0cvsounltxsx0/28wca1281968419.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281968478dc0cvsounltxsx0/28wca1281968419.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281968478dc0cvsounltxsx0/3j5cu1281968419.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281968478dc0cvsounltxsx0/3j5cu1281968419.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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