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Exponential smoothing double

*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: Sat, 18 Dec 2010 12:59:24 +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/18/t12926770215x6b6a0z7txnly9.htm/, Retrieved Sat, 18 Dec 2010 13:57:01 +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/18/t12926770215x6b6a0z7txnly9.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	0.458869668369215
beta	0.0711214003368765
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	47	23	24
4	35	27.7961229221380	7.20387707786197
5	30	25.1201162836829	4.87988371631707
6	43	21.5369567996790	21.4630432003210
7	82	26.2637623545111	55.7362376454889
8	40	48.5364746639713	-8.53647466397128
9	47	41.0377970698181	5.96220293018186
10	19	40.3867020508952	-21.3867020508952
11	52	26.4880593551706	25.5119406448294
12	136	34.9423750299138	101.057624970086
13	80	81.3603752267783	-1.36037522677834
14	42	80.7374651759678	-38.7374651759678
15	54	61.6991275165035	-7.69912751650345
16	66	56.6520770483874	9.34792295161262
17	81	59.7324746789973	21.2675253210027
18	63	68.9764916272027	-5.9764916272027
19	137	65.5240100394252	71.4759899605748
20	72	99.9447743308188	-27.9447743308188
21	107	87.832375102736	19.1676248972640
22	58	97.963971013387	-39.9639710133869
23	36	79.6576288052268	-43.6576288052268
24	52	58.231592561216	-6.23159256121597
25	79	53.7758583083132	25.2241416916868
26	77	64.5774077007445	12.4225922992555
27	54	69.910131300781	-15.910131300781
28	84	61.7225930700318	22.2774069299682
29	48	71.7851911184991	-23.7851911184991
30	96	59.9348195802041	36.0651804197959
31	83	76.7249716959281	6.27502830407185
32	66	80.0501149833582	-14.0501149833582
33	61	73.5901346383135	-12.5901346383135
34	53	67.3892102379062	-14.3892102379062
35	30	59.8931462137544	-29.8931462137544
36	74	44.3072198501116	29.6927801498884
37	69	57.0325050989245	11.9674949010755
38	59	62.0147592058625	-3.01475920586248
39	42	60.023723305792	-18.023723305792
40	65	50.5573166448234	14.4426833551766
41	70	56.4601027609279	13.5398972390721
42	100	62.3905083965314	37.6094916034686
43	63	80.5931236260234	-17.5931236260234
44	105	72.8907735460244	32.1092264539756
45	82	89.0432235276216	-7.04322352762159
46	81	86.9999429771944	-5.99994297719438
47	75	85.2395813676036	-10.2395813676036
48	102	81.1996049153803	20.8003950846197
49	121	92.0817624881826	28.9182375118174
50	98	107.632711515764	-9.63271151576438
51	76	105.179431440083	-29.1794314400825
52	77	92.8044705004144	-15.8044705004144
53	63	86.0510873912678	-23.0510873912678
54	37	75.2201689045499	-38.2201689045499
55	35	56.1812864736566	-21.1812864736566
56	23	44.2697694858315	-21.2697694858315
57	40	31.6235017569562	8.37649824304384
58	29	32.8543778871680	-3.85437788716804
59	37	28.3470865737739	8.6529134262261
60	51	29.8614036303334	21.1385963696666
61	20	37.7948895549917	-17.7948895549917
62	28	27.2822354163540	0.717764583645952
63	13	25.2879013155591	-12.2879013155591
64	22	16.9246403860728	5.07535961392715
65	25	16.6944899032083	8.30551009679168
66	13	18.2176115888137	-5.21761158881375
67	16	13.3651037914331	2.63489620856690
68	13	12.2018646752962	0.798135324703777
69	16	10.2218392096930	5.77816079030695
70	17	10.7155692750934	6.28443072490658
71	9	11.6467065034724	-2.64670650347244
72	17	8.39323928698331	8.60676071301669
73	25	10.5845323781871	14.4154676218129
74	14	15.911720203901	-1.91172020390099
75	8	13.6844669110252	-5.68446691102515
76	7	9.54049943290813	-2.54049943290813
77	10	6.75629291801707	3.24370708198293
78	7	6.73214317966675	0.267856820333247
79	10	5.35120764741106	4.64879235258894
80	3	6.13226599611504	-3.13226599611504

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
81	3.24060975987728	-43.5153135754138	49.9965330951684
82	1.78625538252099	-50.3120403950252	53.8845511600672
83	0.331901005164704	-57.242482346862	57.9062843571914
84	-1.12245337219158	-64.3087232375479	62.0638164931648
85	-2.57680774954787	-71.5113739159997	66.357758416904
86	-4.03116212690416	-78.85011362839	70.7877893745816
87	-5.48551650426044	-86.324026630373	75.3529936218522
88	-6.93987088161673	-93.9318176679625	80.052075904729
89	-8.39422525897302	-101.671953087355	84.8835025694094
90	-9.8485796363293	-109.542754867831	89.8455955951728
91	-11.3029340136856	-117.542464089393	94.9365960620216
92	-12.7572883910419	-125.669284130717	100.154707348633

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926770215x6b6a0z7txnly9/1e3hl1292677160.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926770215x6b6a0z7txnly9/1e3hl1292677160.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926770215x6b6a0z7txnly9/2e3hl1292677160.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926770215x6b6a0z7txnly9/2e3hl1292677160.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926770215x6b6a0z7txnly9/3e3hl1292677160.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926770215x6b6a0z7txnly9/3e3hl1292677160.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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