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Paper exponential smoothinh

*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: Mon, 20 Dec 2010 20:29:05 +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/20/t1292876823lqipq8x0ccrlmz1.htm/, Retrieved Mon, 20 Dec 2010 21:27:06 +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/20/t1292876823lqipq8x0ccrlmz1.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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.458869668359626
beta	0.0711214003445339
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	47	23	24
4	35	27.7961229219759	7.20387707802414
5	30	25.1201162836198	4.87988371638025
6	43	21.5369567997076	21.4630432002924
7	82	26.2637623544902	55.7362376455098
8	40	48.5364746637534	-8.53647466375342
9	47	41.0377970700929	5.96220292990706
10	19	40.3867020513055	-21.3867020513055
11	52	26.4880593558425	25.5119406441575
12	136	34.9423750303279	101.057624969672
13	80	81.3603752266012	-1.36037522660121
14	42	80.7374651764547	-38.7374651764547
15	54	61.6991275175825	-7.6991275175825
16	66	56.6520770494322	9.3479229505678
17	81	59.7324746798525	21.2675253201475
18	63	68.9764916278734	-5.97649162787336
19	137	65.5240100402184	71.4759899597816
20	72	99.9447743311122	-27.9447743311122
21	107	87.8323751036235	19.1676248963765
22	58	97.9639710141695	-39.9639710141695
23	36	79.6576288063808	-43.6576288063808
24	52	58.2315925624452	-6.23159256244519
25	79	53.7758583091664	25.2241416908336
26	77	64.5774077011363	12.4225922988637
27	54	69.9101313010682	-15.9101313010682
28	84	61.7225930704797	22.2774069295203
29	48	71.7851911187162	-23.7851911187162
30	96	59.9348195806636	36.0651804193364
31	83	76.724971696032	6.27502830396799
32	66	80.0501149835696	-14.0501149835696
33	61	73.5901346387314	-12.5901346387314
34	53	67.3892102383725	-14.3892102383725
35	30	59.8931462142082	-29.8931462142082
36	74	44.3072198506079	29.6927801493921
37	69	57.0325050989402	11.9674949010598
38	59	62.0147592058215	-3.01475920582153
39	42	60.0237233058568	-18.0237233058568
40	65	50.5573166450362	14.4426833549638
41	70	56.4601027609435	13.5398972390565
42	100	62.3905083964867	37.6094916035133
43	63	80.5931236258233	-17.5931236258233
44	105	72.8907735462262	32.1092264537738
45	82	89.0432235276487	-7.04322352764866
46	81	86.9999429774815	-5.99994297748148
47	75	85.2395813679951	-10.2395813679951
48	102	81.1996049158271	20.8003950841729
49	121	92.081762488406	28.9182375115939
50	98	107.632711515864	-9.63271151586369
51	76	105.179431440454	-29.1794314404538
52	77	92.8044705010255	-15.8044705010255
53	63	86.0510873918158	-23.0510873918158
54	37	75.22016890505	-38.22016890505
55	35	56.1812864741518	-21.1812864741518
56	23	44.2697694860844	-21.2697694860844
57	40	31.6235017570103	8.37649824298966
58	29	32.8543778868524	-3.85437788685239
59	37	28.3470865733748	8.65291342662523
60	51	29.8614036298067	21.1385963701933
61	20	37.7948895543533	-17.7948895543533
62	28	27.282235415999	0.717764584001024
63	13	25.2879013151935	-12.2879013151935
64	22	16.9246403858033	5.07535961419669
65	25	16.6944899028475	8.30551009715252
66	13	18.2176115884078	-5.21761158840782
67	16	13.3651037911309	2.63489620886909
68	13	12.2018646749922	0.798135325007793
69	16	10.2218392094178	5.77816079058217
70	17	10.7155692748114	6.28443072518861
71	9	11.6467065032089	-2.64670650320886
72	17	8.39323928681646	8.60676071318354
73	25	10.5845323779945	14.4154676220055
74	14	15.9117202036859	-1.91172020368588
75	8	13.6844669109560	-5.68446691095602
76	7	9.54049943294032	-2.54049943294032
77	10	6.7562929180657	3.2437070819343
78	7	6.73214317967641	0.267856820323587
79	10	5.35120764742861	4.64879235257139
80	3	6.13226599610745	-3.13226599610745

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
81	3.24060975992207	-43.515313575402	49.9965330952461
82	1.78625538258464	-50.3120403948589	53.8845511600282
83	0.331901005247214	-57.2424823466158	57.9062843571102
84	-1.12245337209021	-64.3087232372839	62.0638164931035
85	-2.57680774942764	-71.5113739157706	66.3577584169154
86	-4.03116212676506	-78.8501136282416	70.7877893747115
87	-5.48551650410249	-86.3240266303458	75.3529936221408
88	-6.93987088143991	-93.9318176680923	80.0520759052125
89	-8.39422525877734	-101.671953087675	84.8835025701201
90	-9.84857963611477	-109.542754868370	89.8455955961403
91	-11.3029340134522	-117.542464090177	94.936596063273
92	-12.7572883907896	-125.669284131773	100.154707350194

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876823lqipq8x0ccrlmz1/1lxy61292876942.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876823lqipq8x0ccrlmz1/1lxy61292876942.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876823lqipq8x0ccrlmz1/2lxy61292876942.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876823lqipq8x0ccrlmz1/2lxy61292876942.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876823lqipq8x0ccrlmz1/3lxy61292876942.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292876823lqipq8x0ccrlmz1/3lxy61292876942.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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