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*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 17 Aug 2010 08:38:17 +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/17/t1282034269efn9dnf9b0jytil.htm/, Retrieved Tue, 17 Aug 2010 10:37:50 +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/17/t1282034269efn9dnf9b0jytil.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 «

93 92 91 89 87 86 87 89 90 90 91 93 93 87 89 92 98 92 92 87 92 98 101 102 102 90 87 92 105 90 88 83 98 109 118 118 115 107 101 111 128 115 111 105 120 132 135 142 139 127 113 130 143 139 137 134 139 157 152 153 147 132 117 123 139 134 134 128 118 144 140 151 144 135 122 124 146 146 147 148 132 161 159 173

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.980528379652785
beta	0.0160501661027114
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	91	91	0
4	89	90	-1
5	87	88.0037339769854	-1.00373397698537
6	86	85.9880102762076	0.0119897237923539
7	87	84.9684211799255	2.03157882007453
8	89	85.9610687707171	3.03893122928288
9	90	87.9892796029368	2.0107203970632
10	90	89.0409445344081	0.95905546559193
11	91	89.0765154275679	1.92348457243213
12	93	90.0880075443606	2.91199245563938
13	93	92.1145875928878	0.88541240711217
14	87	92.1679826948873	-5.16798269488729
15	89	86.2045202375728	2.79547976242723
16	92	88.093452983481	3.90654701651901
17	98	91.1332985474514	6.86670145254864
18	92	97.1837252426364	-5.18372524263637
19	92	91.3367869571125	0.663213042887463
20	87	91.233375004965	-4.23337500496511
21	92	86.2620961623845	5.73790383761552
22	98	91.1582402906265	6.84175970937348
23	101	97.2444196024472	3.75558039755281
24	102	100.363616499244	1.63638350075617
25	102	101.430633516597	0.569366483402618
26	90	101.460370553521	-11.4603705535213
27	87	89.5142498014151	-2.51424980141513
28	92	86.3004859678525	5.69951403214748
29	105	91.2302475960375	13.7697524039625
30	90	104.289810430865	-14.2898104308645
31	88	89.6112876452237	-1.61128764522371
32	83	87.3390583926643	-4.3390583926643
33	98	82.3238859555427	15.6761140444573
34	109	97.1808632087944	11.8191367912056
35	118	108.441970165222	9.55802983477753
36	118	117.636418446224	0.363581553775873
37	115	117.82117116928	-2.82117116928018
38	107	114.838784879478	-7.83878487947842
39	101	106.813121947869	-5.81312194786888
40	111	100.682194168279	10.3178058317213
41	128	110.530476815163	17.4695231848374
42	115	127.666150415617	-12.6661504156166
43	111	115.053605452864	-4.05360545286376
44	105	110.822111050179	-5.8221110501789
45	120	104.764920412431	15.2350795875691
46	132	119.594667039892	12.4053329601077
47	135	131.844997497812	3.15500250218773
48	142	135.07476872476	6.92523127523967
49	139	142.110343081477	-3.11034308147734
50	127	139.256802505168	-12.2568025051683
51	113	127.242005704005	-14.2420057040047
52	130	113.056525220477	16.9434747795226
53	143	129.715943747547	13.2840562524527
54	139	142.996258295498	-3.99625829549785
55	137	139.26984233202	-2.26984233201961
56	134	137.200504246708	-3.20050424670845
57	139	134.16825734777	4.83174265222991
58	157	139.087896728296	17.9121032717041
59	152	157.11509520546	-5.11509520545954
60	153	152.482972527761	0.517027472238595
61	147	153.381442767199	-6.3814427671987
62	132	147.415338290273	-15.4153382902734
63	117	132.34864177784	-15.3486417778405
64	123	117.105791638283	5.89420836171654
65	139	122.78491987437	16.2150801256297
66	134	138.839142925832	-4.83914292583214
67	134	134.172946058252	-0.172946058251995
68	128	134.079365880996	-6.07936588099551
69	118	128.098698553294	-10.0986985532939
70	144	118.018031756888	25.9819682431125
71	140	143.724377661203	-3.72437766120251
72	151	140.244195423178	10.7558045768224
73	144	151.13151382858	-7.13151382858004
74	135	144.367575680335	-9.36757568033548
75	122	135.263691862564	-13.2636918625635
76	124	122.130816305498	1.869183694502
77	146	123.865571244251	22.134428755749
78	146	145.819317831951	0.180682168048605
79	147	146.249636362229	0.750363637771358
80	148	147.250352696254	0.74964730374569
81	132	148.262164326352	-16.262164326352
82	161	132.337483721372	28.6625162786283
83	159	160.913807855458	-1.91380785545789
84	173	159.479059605118	13.5209403948821

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	173.391307784884	154.584681314348	192.19793425542
86	174.045890187874	147.498913051365	200.592867324384
87	174.700472590865	142.035915484475	207.365029697255
88	175.355054993855	137.400367725492	213.309742262218
89	176.009637396846	133.281752146574	218.737522647117
90	176.664219799836	129.520925825548	223.807513774124
91	177.318802202826	126.023700576816	228.613903828837
92	177.973384605817	122.729025355153	233.217743856481
93	178.627967008807	119.594750086864	237.66118393075
94	179.282549411798	116.590388314421	241.974710509174
95	179.937131814788	113.693086674405	246.18117695517
96	180.591714217778	110.885220549797	250.29820788576

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282034269efn9dnf9b0jytil/12wc21282034293.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282034269efn9dnf9b0jytil/12wc21282034293.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282034269efn9dnf9b0jytil/2v5tn1282034293.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282034269efn9dnf9b0jytil/2v5tn1282034293.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282034269efn9dnf9b0jytil/3v5tn1282034293.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282034269efn9dnf9b0jytil/3v5tn1282034293.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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