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Exponential Smoothing consumptieprijs koffie

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 04 Jan 2011 13:48:53 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149107z8io3nl8sx8ntho.htm/, Retrieved Tue, 04 Jan 2011 14:51:48 +0100

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/2011/Jan/04/t1294149107z8io3nl8sx8ntho.htm/},
    year = {2011},
}
@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 = {2011},
    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:

KDGP2W102 - Natasha Van Linden

Dataseries X:

» Textbox « » Textfile « » CSV «

97 100,7 101,4 101,5 101,8 101,5 102,2 101,8 98,5 98,4 97,5 97,7 98,3 99,6 99,4 96,7 96,9 96,1 97,9 99,2 97,8 94,9 93,3 91,5 89,1 92,3 91,8 92,1 94,4 92,8 92,6 92,3 92,1 89,8 87,4 87,7 86,3 89,1 90,4 87,1 86,7 84,4 88,4 88,9 88,5 87,2 86,2 83,4 87,5 85,7 87,4 86,8 87,9 85,9 87,7 87 86,8 86,2 86,1 87,5 85,7 88,9 89,8 91,4 95,2 94,1 96,8 96,1 96,6 94,2 93,9 96,5 93,4 95 95,2 94 97 96,9 96,3 96,3 97,3 95,7 96,4 95,1 94,6 95,9 96,2 94,3 98,3 95,9 92,1 94,6 94,7 96,7 97,5 96,2 97,1 95,9 94,5 99,4 101,3 101,4 100,9 101,4 103,1 102,4 101,1 102 103,9 101,7 101,2 101,9 101,1 103,1 103,3 101,4 102,8 103 102,6 102,2

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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.78713528221648
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	100.7	97	3.7
3	101.4	99.912400544201	1.48759945579903
4	101.5	101.083342561666	0.416657438333573
5	101.8	101.411308331977	0.388691668023284
6	101.5	101.717261257781	-0.217261257781416
7	102.2	101.546247256323	0.653752743677074
8	101.8	102.060839106717	-0.260839106716986
9	98.5	101.855523442838	-3.35552344283822
10	98.4	99.2142725506757	-0.814272550675739
11	97.5	98.5733298966985	-1.07332989669847
12	97.7	97.7284740655493	-0.0284740655493323
13	98.3	97.7060611239273	0.593938876072684
14	99.6	98.1735713687641	1.42642863123586
15	99.4	99.2963636719736	0.103636328026369
16	96.7	99.3779394822826	-2.67793948228255
17	96.9	97.2700388321374	-0.370038832137425
18	96.1	96.9787682115719	-0.878768211571895
19	97.9	96.2870587473534	1.61294125264664
20	99.2	97.556661715454	1.64333828454602
21	97.8	98.8501912598373	-1.05019125983726
22	94.9	98.023548666144	-3.12354866614398
23	93.3	95.5648933053018	-2.26489330530184
24	91.5	93.7821158742429	-2.28211587424286
25	89.1	91.98578195152	-2.88578195152
26	92.3	89.714281160695	2.58571883930492
27	91.8	91.7495916890038	0.0504083109961755
28	92.1	91.7892698491058	0.310730150894145
29	94.4	92.033856514123	2.36614348587692
30	92.8	93.8963315346435	-1.0963315346435
31	92.6	93.033370302719	-0.433370302719069
32	92.3	92.692249247184	-0.392249247184054
33	92.1	92.3834960253026	-0.28349602530264
34	89.8	92.1603463014188	-2.36034630141879
35	87.4	90.3024344493229	-2.90243444932288
36	87.7	88.0178258899403	-0.317825889940295
37	86.3	87.7676539183664	-1.46765391836644
38	89.1	86.612411737137	2.48758826286304
39	90.4	88.570480226464	1.82951977353595
40	87.1	90.0105597897269	-2.9105597897269
41	86.7	87.7195554882323	-1.01955548823227
42	84.4	86.9170273912672	-2.51702739126721
43	88.4	84.9357863252955	3.46421367470451
44	88.9	87.6625911337922	1.23740886620779
45	88.5	88.6365993109119	-0.136599310911862
46	87.2	88.5290771737667	-1.32907717376668
47	86.2	87.4829136375064	-1.28291363750637
48	83.4	86.4730870493884	-3.07308704938842
49	87.5	84.0541518074923	3.44584819250774
50	85.7	86.766500496977	-1.06650049697699
51	87.4	85.927020327305	1.47297967269502
52	86.8	87.086454597671	-0.286454597670925
53	87.9	86.860976077091	1.039023922909
54	85.9	87.6788284658797	-1.77882846587966
55	87.7	86.2786498193748	1.42135018062523
56	87	87.3974446949297	-0.397444694929661
57	86.8	87.0846019528208	-0.284601952820765
58	86.2	86.8605817143678	-0.660581714367822
59	86.1	86.3406145402019	-0.240614540201875
60	87.5	86.1512183461947	1.34878165380532
61	85.7	87.2128919739111	-1.51289197391114
62	88.9	86.0220413230635	2.87795867693646
63	89.8	88.2873841384413	1.5126158615587
64	91.4	89.4780174515144	1.92198254848557
65	95.2	90.9908777272318	4.20912227276823
66	94.1	94.3040263752909	-0.204026375290866
67	96.8	94.1434300167967	2.65656998320331
68	96.1	96.2345099802533	-0.134509980253256
69	96.6	96.1286324289857	0.471367571014326
70	94.2	96.4996624750237	-2.29966247502372
71	93.9	94.6895170037433	-0.78951700374327
72	96.5	94.0680603141871	2.43193968581289
73	93.4	95.982325845113	-2.58232584511289
74	95	93.949686062245	1.05031393775495
75	95.2	94.7764252200557	0.423574779944303
76	94	95.109835874007	-1.10983587400695
77	97	94.2362449001065	2.76375509989349
78	96.9	96.4116940506384	0.488305949361603
79	96.3	96.7960568918971	-0.49605689189714
80	96.3	96.4055930102982	-0.10559301029825
81	97.3	96.322477026337	0.977522973662957
82	95.7	97.0919198480843	-1.39191984808431
83	96.4	95.9962906256398	0.403709374360247
84	95.1	96.3140645179602	-1.21406451796025
85	94.6	95.3584315009866	-0.758431500986589
86	95.9	94.7614433074156	1.13855669258437
87	96.2	95.6576414509525	0.542358549047506
88	94.3	96.0845510005195	-1.78455100051953
89	98.3	94.6798679450959	3.6201320549041
90	95.9	97.5294016117938	-1.62940161179375
91	92.1	96.2468421142505	-4.1468421142505
92	94.6	92.9827163763428	1.61728362365724
93	94.7	94.2557373778743	0.44426262212572
94	96.7	94.6054321623194	2.09456783768056
95	97.5	96.2541404083537	1.24585959164631
96	96.2	97.2348004496263	-1.03480044962632
97	97.1	96.420272505672	0.67972749432802
98	95.9	96.9553099987502	-1.05530999875016
99	94.5	96.124638265058	-1.62463826505808
100	99.4	94.845828165792	4.55417183420811
101	101.3	98.4305774977736	2.86942250222636
102	101.4	100.689201188862	0.710798811138105
103	100.9	101.248696011666	-0.34869601166622
104	101.4	100.974225078116	0.425774921884425
105	103.1	101.309367541414	1.79063245858622
106	102.4	102.718837527049	-0.318837527049027
107	101.1	102.467869260214	-1.36786926021409
108	102	101.39117110404	0.608828895959775
109	103.9	101.870401808883	2.02959819111693
110	101.7	103.467970153834	-1.76797015383396
111	101.2	102.076338467846	-0.876338467845557
112	101.9	101.386541540641	0.513458459359214
113	101.1	101.790702809955	-0.690702809954956
114	103.1	101.247026258713	1.85297374128665
115	103.3	102.705567267501	0.594432732499257
116	101.4	103.173466244155	-1.77346624415524
117	102.8	101.777508391561	1.02249160843928
118	103	102.582347612334	0.41765238766645
119	102.6	102.911096542368	-0.311096542367778
120	102.2	102.666221477695	-0.466221477694532

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	102.299242103274	98.8707257081588	105.727758498389
122	102.299242103274	97.9360162399012	106.662467966647
123	102.299242103274	97.168866366738	107.42961783981
124	102.299242103274	96.5023661807388	108.096118025809
125	102.299242103274	95.904964526839	108.693519679709
126	102.299242103274	95.3587953606117	109.239688845936
127	102.299242103274	94.8525773296345	109.745906876914
128	102.299242103274	94.3786467017783	110.21983750477
129	102.299242103274	93.9315156033562	110.666968603192
130	102.299242103274	93.5070943542505	111.091389852298
131	102.299242103274	93.1022383898959	111.496245816652
132	102.299242103274	92.7144681066102	111.884016099938

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149107z8io3nl8sx8ntho/1runv1294148928.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149107z8io3nl8sx8ntho/1runv1294148928.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149107z8io3nl8sx8ntho/2nem61294148928.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149107z8io3nl8sx8ntho/2nem61294148928.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149107z8io3nl8sx8ntho/31d0u1294148928.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149107z8io3nl8sx8ntho/31d0u1294148928.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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