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Workshop 8 (Triple Smoothing model)

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 10 Dec 2010 15:51:42 +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/Dec/10/t1291996240g3bu39mppisxvs0.htm/, Retrieved Fri, 10 Dec 2010 16:50:40 +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/2010/Dec/10/t1291996240g3bu39mppisxvs0.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 «

37 30 47 35 30 43 82 40 47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 3

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.350759329200033
beta	0
gamma	0.714202236422672

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	80	63.3541666666667	16.6458333333333
14	42	27.5678480006422	14.4321519993578
15	54	40.7967266215166	13.2032733784834
16	66	53.302897934998	12.6971020650019
17	81	71.7981916047691	9.20180839523086
18	63	61.1924784115742	1.80752158842579
19	137	103.368150138112	33.6318498618883
20	72	70.8731685687572	1.12683143124282
21	107	77.4767485390348	29.5232514609652
22	58	58.2489710839535	-0.248971083953485
23	36	87.744975486889	-51.7449754868891
24	52	150.636609262302	-98.6366092623024
25	79	64.6323904901925	14.3676095098075
26	77	27.0205035721521	49.9794964278479
27	54	52.1481272098814	1.85187279011862
28	84	60.4379827269411	23.5620172730589
29	48	81.1235170544008	-33.1235170544008
30	96	52.2431506148959	43.7568493851041
31	83	123.889535798133	-40.8895357981334
32	66	50.1832589723158	15.8167410276842
33	61	75.1065733346721	-14.1065733346721
34	53	26.7701715613457	26.2298284386543
35	30	41.6757239761287	-11.6757239761287
36	74	96.8788802384768	-22.8788802384768
37	69	89.8462205932832	-20.8462205932832
38	59	56.3955994351144	2.6044005648856
39	42	42.5897098574903	-0.589709857490305
40	65	60.0899156870922	4.91008431290784
41	70	47.9486439116022	22.0513560883978
42	100	74.069969889459	25.9300301105410
43	63	100.213822431864	-37.2138224318639
44	105	54.0909210414992	50.9090789585008
45	82	77.4480844419703	4.55191555802971
46	81	54.3598731276625	26.6401268723375
47	75	51.8329485809399	23.1670514190601
48	102	114.062751486308	-12.0627514863078
49	121	111.766472107652	9.23352789234812
50	98	99.7404016861067	-1.74040168610671
51	76	82.9294578735977	-6.92945787359767
52	77	100.756132765662	-23.756132765662
53	63	86.5081394689932	-23.5081394689932
54	37	98.447546364477	-61.447546364477
55	35	64.6637801729412	-29.6637801729412
56	23	62.0507588180824	-39.0507588180824
57	40	32.3583566785795	7.64164332142052
58	29	20.5959598897179	8.40404011028209
59	37	10.0621304162760	26.937869583724
60	51	57.2789059931065	-6.2789059931065
61	20	66.886217830153	-46.886217830153
62	28	30.0871310857474	-2.08713108574736
63	13	10.7484597054850	2.25154029451503
64	22	23.9931089624076	-1.99310896240757
65	25	17.4936910945581	7.50630890544188
66	13	22.7196141774821	-9.7196141774821
67	16	21.8176899622591	-5.81768996225912
68	13	23.2162671673847	-10.2162671673847
69	16	25.2885917259022	-9.28859172590225
70	17	7.94127215929363	9.05872784070637
71	9	6.23101594707102	2.76898405292898
72	17	29.5680713779749	-12.5680713779749
73	25	18.140230318059	6.85976968194101
74	14	20.9659000638613	-6.96590006386126
75	8	1.92774974650005	6.07225025349995
76	7	14.5443509061419	-7.54435090614195
77	10	10.5025600306134	-0.502560030613406
78	7	4.93182417400826	2.06817582599174
79	10	9.97385715319611	0.0261428468038893
80	3	11.3826407570439	-8.38264075704385

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
81	14.5282799120459	-35.3287020636707	64.3852618877625
82	8.94647336236186	-43.8885704524202	61.7815171771439
83	1.14229796745304	-54.5116781536917	56.7962740885977
84	16.3964803808856	-41.9403712763298	74.733332038101
85	18.38548650175	-42.5161675353856	79.2871405388856
86	12.3942151340628	-50.9685078790935	75.7569381472191
87	1.8450679459928	-63.8866433570379	67.5767792490235
88	6.01790061131881	-62.0003401334107	74.0361413560483
89	7.887563147406	-62.3428026297348	78.1179289245468
90	3.68512720612633	-68.6897819846561	76.0600363969087
91	7.05485970586599	-67.4028509999904	81.5125704117224
92	4.5554118324795	-71.928402708507	81.039226373466

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996240g3bu39mppisxvs0/11b0y1291996298.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996240g3bu39mppisxvs0/11b0y1291996298.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996240g3bu39mppisxvs0/2ckz11291996298.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996240g3bu39mppisxvs0/2ckz11291996298.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996240g3bu39mppisxvs0/3ckz11291996298.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996240g3bu39mppisxvs0/3ckz11291996298.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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