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Exponential Smoothing eigen reeks

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 21 Dec 2010 17:25:11 +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/21/t1292952204y5mxk0gwe0gxv22.htm/, Retrieved Tue, 21 Dec 2010 18:23:28 +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/21/t1292952204y5mxk0gwe0gxv22.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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

57.7 63.6 78 77.4 74.1 85.9 82 78.4 68.1 70.9 85.2 149.6 57.9 63.7 85 66.1 80.2 83.4 85.7 81.8 69.4 76.4 90.3 157.3 65.3 68.4 72.7 86.6 82.6 84.8 93.4 82.2 75.2 83.9 85.4 166.3 70.4 73.9 82.4 92.3 82.7 95.8 105.8 84.2 82.7 88.4 90.2 176.6 69.5 77.3 98.6 86.4 90.8 101.5 112.2 93.6 93.8 90.8 98.1 187.6 75 83.7 99.7 104.9 98.9 117.3 115.7 102.2 101.9 96.6 110 203.7 82.3 93.3 121.9 100.9 107.7 130 123.2 116.1 105.3 107.7 123.9 205.2 90.3 106.9 122.4 111.3 122.6 124.8 139.5 118.8 111 121.2 120.6 219.1 101.3 105 113.4 133.6 123.9 136.2 151.7 121.9 120.2 132.2 125.2 233.8

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	0.111001096231486
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	63.6	57.7	5.9
3	78	58.3549064677658	19.6450935322342
4	77.4	60.5355333854138	16.8644666145862
5	74.1	62.4075076669922	11.6924923330078
6	85.9	63.7053871336343	22.1946128663657
7	82	66.1690134922343	15.8309865077657
8	78.4	67.9262703490222	10.4737296509778
9	68.1	69.088865821913	-0.988865821912952
10	70.9	68.9791006316548	1.92089936834525
11	85.2	69.1923225672915	16.0076774327085
12	149.6	70.9691923104421	78.6308076895579
13	57.9	79.6972981615502	-21.7972981615502
14	63.7	77.2777741707336	-13.5777741707336
15	85	75.7706263533986	9.22937364660142
16	66.1	76.7950969457013	-10.6950969457013
17	80.2	75.6079294604265	4.59207053957354
18	83.4	76.1176543242914	7.28234567570857
19	85.7	76.9260026774317	8.77399732256829
20	81.8	77.8999259985689	3.90007400143108
21	69.4	78.3328384881117	-8.93283848811167
22	76.4	77.3412836234725	-0.941283623472458
23	90.3	77.2368001094023	13.0631998905977
24	157.3	78.6868296175496	78.6131703824504
25	65.3	87.4129777082342	-22.1129777082342
26	68.4	84.9584129416778	-16.5584129416778
27	72.7	83.1204109532979	-10.4204109532979
28	86.6	81.9637339142993	4.63626608570071
29	82.6	82.478364532233	0.121635467767078
30	84.8	82.4918662024957	2.30813379750431
31	93.4	82.7480715842676	10.6519284157324
32	82.2	83.9304473153932	-1.73044731539321
33	75.2	83.7383657664137	-8.53836576641373
34	83.9	82.7905978063164	1.10940219368358
35	85.4	82.9137426659769	2.48625733402309
36	166.3	83.189719955567	83.110280044433
37	70.4	92.4150521486049	-22.0150521486049
38	73.9	89.9713572265164	-16.0713572265164
39	82.4	88.1874189564453	-5.78741895644529
40	92.3	87.545009107929	4.75499089207101
41	82.7	88.0728183095196	-5.3728183095196
42	95.8	87.4764295873103	8.32357041268968
43	105.8	88.4003550276788	17.3996449723212
44	84.2	90.3317346936452	-6.13173469364516
45	82.7	89.65110542085	-6.95110542084991
46	88.4	88.879525099115	-0.479525099114937
47	90.2	88.8262972874427	1.37370271255733
48	176.6	88.9787797944327	87.6212202055673
49	69.5	98.704831290391	-29.2048312903911
50	77.3	95.463063001902	-18.1630630019021
51	98.6	93.4469430977694	5.15305690223059
52	86.4	94.0189380628602	-7.6189380628602
53	90.8	93.173227585763	-2.37322758576293
54	101.5	92.9097967221364	8.59020327786357
55	112.2	93.8633187028306	18.3366812971694
56	93.6	95.8987104280638	-2.2987104280638
57	93.8	95.64355105063	-1.84355105062997
58	90.8	95.4389148630513	-4.63891486305134
59	98.1	94.9239902279281	3.17600977207189
60	187.6	95.27653079427	92.32346920573
61	75	105.524537084000	-30.5245370839998
62	83.7	102.136280005717	-18.4362800057172
63	99.7	100.089832714652	-0.389832714651973
64	104.9	100.046560855979	4.85343914402129
65	98.9	100.585297921458	-1.68529792145787
66	117.3	100.398228004699	16.9017719953006
67	115.7	102.274343224432	13.4256567755676
68	102.2	103.764605844148	-1.56460584414809
69	101.9	103.590932880277	-1.69093288027746
70	96.6	103.403237476913	-6.80323747691281
71	110	102.648070659052	7.35192934094765
72	203.7	103.464142875314	100.235857124686
73	82.3	114.590432897857	-32.2904328978567
74	93.3	111.006159448405	-17.7061594484054
75	121.9	109.040756339583	12.8592436604171
76	100.9	110.468146482597	-9.56814648259696
77	107.7	109.406071734125	-1.70607173412526
78	130	109.216695901388	20.7833040986122
79	123.2	111.523665439646	11.6763345603539
80	116.1	112.819751375811	3.28024862418903
81	105.3	113.183862569008	-7.88386256900777
82	107.7	112.308745181310	-4.60874518130953
83	123.9	111.797169413933	12.1028305860674
84	205.2	113.14059687649	92.05940312351
85	90.3	123.359291541616	-33.0592915416159
86	106.9	119.689673939860	-12.7896739398603
87	122.4	118.270006112093	4.12999388790749
88	111.3	118.728439961080	-7.42843996107958
89	122.6	117.90387498211	4.69612501789004
90	124.8	118.425150007136	6.37484999286414
91	139.5	119.132765344655	20.3672346553449
92	118.8	121.393550718602	-2.59355071860224
93	111	121.105663745705	-10.1056637457054
94	121.2	119.983923991785	1.21607600821466
95	120.6	120.118909761798	0.481090238202015
96	219.1	120.172311305625	98.9276886943753
97	101.3	131.153393198348	-29.8533931983475
98	105	127.839633827101	-22.8396338271014
99	113.4	125.304409434767	-11.9044094347674
100	133.6	123.983006937520	9.61699306248023
101	123.9	125.050503709906	-1.15050370990565
102	136.2	124.922796536888	11.2772034631122
103	151.7	126.174578483719	25.5254215162813
104	121.9	129.007928253797	-7.10792825379667
105	120.2	128.218940425691	-8.0189404256905
106	132.2	127.328829247824	4.87117075217611
107	125.2	127.869534541246	-2.66953454124616
108	233.8	127.57321328074	106.22678671926

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	139.364503055726	83.4956249755803	195.233381135872
110	139.364503055726	83.1524916752866	195.576514436166
111	139.364503055726	82.8114402833605	195.917565828092
112	139.364503055726	82.4724333584864	196.256572752966
113	139.364503055726	82.1354345683215	196.593571543131
114	139.364503055726	81.8004086440487	196.928597467404
115	139.364503055726	81.4673213372955	197.261684774157
116	139.364503055726	81.1361393792717	197.592866732181
117	139.364503055726	80.8068304419866	197.922175669466
118	139.364503055726	80.4793631014188	198.249643010033
119	139.364503055726	80.1537068025189	198.575299308933
120	139.364503055726	79.8298318259353	198.899174285517

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292952204y5mxk0gwe0gxv22/1ceb11292952308.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292952204y5mxk0gwe0gxv22/1ceb11292952308.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292952204y5mxk0gwe0gxv22/2ar0a1292952308.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292952204y5mxk0gwe0gxv22/2ar0a1292952308.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292952204y5mxk0gwe0gxv22/3ar0a1292952308.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292952204y5mxk0gwe0gxv22/3ar0a1292952308.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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