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exponential Smoothing - maandelijkse bezoekers - mattias debbaut

*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 19:19:58 +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/t1281986473kj0hff1h37nkuiz.htm/, Retrieved Mon, 16 Aug 2010 21:21:17 +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/t1281986473kj0hff1h37nkuiz.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:

mattias debbaut

Dataseries X:

» Textbox « » Textfile « » CSV «

900 899 898 896 916 915 900 890 891 891 892 894 896 889 878 883 901 897 881 866 867 866 862 871 865 856 847 859 870 872 856 839 829 825 822 827 822 812 810 816 820 823 810 793 777 772 765 765 753 742 736 740 742 742 728 707 699 696 689 692 673 653 642 648 654 653 630 609 598 601 592 591 568 538 523 530 529 534 513 491 480 478 462 461 437 411 400 405 395 407 385 366 349 343 332 327 306 276 269 268 260 274 247 226 212 199 188 179 155 124 117 116 105 112 86 64 53 42 32 24

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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.474509737981929
beta	0.109980424057153
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	896	903.770888491585	-7.77088849158486
14	889	892.83650764698	-3.83650764697927
15	878	879.78255457044	-1.78255457043906
16	883	883.677270637965	-0.67727063796508
17	901	901.309957990233	-0.309957990232760
18	897	897.00751071256	-0.00751071256001978
19	881	879.980847886478	1.01915211352241
20	866	868.959308324936	-2.95930832493616
21	867	867.292335495294	-0.292335495294196
22	866	866.018077851283	-0.0180778512832376
23	862	865.638398416371	-3.63839841637139
24	871	864.508303861816	6.49169613818378
25	865	864.747970495067	0.252029504932693
26	856	859.49110324043	-3.49110324042977
27	847	847.675768997403	-0.675768997402656
28	859	852.18301658722	6.8169834127807
29	870	873.09086321796	-3.09086321795951
30	872	867.702182693535	4.29781730646539
31	856	853.929924601814	2.07007539818596
32	839	841.943201446102	-2.94320144610219
33	829	841.875940892999	-12.8759408929988
34	825	834.360315607434	-9.36031560743447
35	822	826.784407948278	-4.78440794827816
36	827	829.129726468095	-2.12972646809533
37	822	820.8222892973	1.17771070270044
38	812	812.980619331017	-0.98061933101701
39	810	802.98271971499	7.01728028501054
40	816	813.744545521368	2.25545447863203
41	820	825.489205821766	-5.48920582176584
42	823	821.550235460297	1.44976453970332
43	810	804.81289967523	5.18710032477054
44	793	791.334395475885	1.66560452411511
45	777	787.418860610278	-10.4188606102782
46	772	781.961988489794	-9.96198848979361
47	765	775.565519365578	-10.5655193655775
48	765	774.860936287358	-9.8609362873583
49	753	763.250970817308	-10.2509708173083
50	742	747.229430873978	-5.22943087397778
51	736	737.245218203866	-1.24521820386576
52	740	738.077159387358	1.92284061264218
53	742	741.84727992547	0.152720074530293
54	742	741.138820216192	0.861179783808097
55	728	724.742528087708	3.25747191229209
56	707	707.43442221544	-0.434422215440236
57	699	694.351514289071	4.64848571092864
58	696	694.029509792166	1.97049020783356
59	689	691.465648497205	-2.46564849720528
60	692	693.16948672136	-1.16948672135993
61	673	685.220962762477	-12.2209627624771
62	653	670.655439264295	-17.6554392642953
63	642	655.642040473916	-13.6420404739156
64	648	649.334880788702	-1.33488078870209
65	654	647.614826081217	6.38517391878338
66	653	647.81878267693	5.18121732306997
67	630	634.439669594048	-4.43966959404827
68	609	611.689698128818	-2.68969812881812
69	598	598.880552017984	-0.880552017983973
70	601	592.076117776483	8.92388222351747
71	592	588.680000442368	3.31999955763217
72	591	590.918539714358	0.0814602856419242
73	568	577.322600841805	-9.3226008418053
74	538	560.646388107491	-22.6463881074912
75	523	543.286387955832	-20.2863879558323
76	530	535.807350992743	-5.80735099274261
77	529	531.738635342179	-2.73863534217855
78	534	523.34537266301	10.6546273369898
79	513	507.611186916838	5.38881308316201
80	491	490.855512628605	0.144487371395201
81	480	479.163899090739	0.83610090926146
82	478	475.328874264389	2.67112573561121
83	462	464.709057863621	-2.70905786362118
84	461	458.722747891583	2.27725210841652
85	437	441.589932636353	-4.5899326363529
86	411	420.786323599084	-9.78632359908397
87	400	408.6521977364	-8.65219773639961
88	405	409.14032888495	-4.14032888494961
89	395	404.366251105912	-9.36625110591217
90	407	396.222544225601	10.7774557743990
91	385	380.187005195887	4.81299480411258
92	366	362.649125684918	3.35087431508248
93	349	352.563721873452	-3.56372187345175
94	343	344.895839178019	-1.89583917801906
95	332	329.556847173016	2.44315282698352
96	327	325.512386146091	1.48761385390941
97	306	307.07581436036	-1.0758143603598
98	276	288.009108495393	-12.0091084953934
99	269	273.570104211447	-4.57010421144713
100	268	271.955898722831	-3.95589872283085
101	260	261.930948891483	-1.93094889148279
102	274	261.061240606169	12.9387593938314
103	247	247.179743554591	-0.179743554591198
104	226	229.589440102179	-3.58944010217937
105	212	213.634612075621	-1.63461207562054
106	199	204.857537420710	-5.85753742071049
107	188	189.584014525368	-1.58401452536751
108	179	179.806136301810	-0.80613630181034
109	155	162.297327857733	-7.29732785773254
110	124	139.9346030249	-15.9346030249000
111	117	122.761255042656	-5.76125504265616
112	116	112.228438846279	3.77156115372080
113	105	102.732210176703	2.26778982329726
114	112	97.8092187494058	14.1907812505942
115	86	85.9549356576072	0.0450643423927772
116	64	70.8606110124776	-6.86061101247756
117	53	54.5112363119745	-1.51123631197454
118	42	41.4597795297662	0.540220470233834
119	32	29.3769736230244	2.62302637697558
120	24	18.4665542885328	5.53344571146723

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	8.25680434010511	-4.38872952575427	20.9023382059645
122	-3.16451383997611	-17.1980547115194	10.8690270315672
123	-14.7319763741312	-30.8682055540182	1.40425280575568
124	-28.4686487311091	-47.3327159661397	-9.60458149607852
125	-41.3210877826505	-62.3723405562992	-20.2698350090018
126	-61.510553324487	-87.0604936165888	-35.9606130323852
127	-66.7573082191459	-92.0681891928197	-41.4464272454722
128	-72.5503927618333	-98.293345006633	-46.8074405170336
129	-86.623910827988	-115.29354711593	-57.9542745400462
130	-101.048454177377	-132.755180217567	-69.3417281371869
131	-118.243073530658	-153.736302072643	-82.749844988674
132	-144.966165330087	-184.780290439648	-105.152040220525

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281986473kj0hff1h37nkuiz/1s31b1281986396.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281986473kj0hff1h37nkuiz/1s31b1281986396.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281986473kj0hff1h37nkuiz/2s31b1281986396.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281986473kj0hff1h37nkuiz/2s31b1281986396.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281986473kj0hff1h37nkuiz/3lu1e1281986396.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281986473kj0hff1h37nkuiz/3lu1e1281986396.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 12 ;

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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