Home » date » 2011 » Jan » 16 »

10/2 eigen reeks addi triple

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Jan 2011 15:15:54 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/16/t1295190889q75olqunhqh68kc.htm/, Retrieved Sun, 16 Jan 2011 16:14:53 +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/2011/Jan/16/t1295190889q75olqunhqh68kc.htm/},
    year = {2011},
}
@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 = {2011},
    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 «

100,4 97,7 97 96,5 98,4 106,3 103,1 102,4 95 98,1 106,1 99,1 101,2 95,5 99,8 97,1 97,5 96,8 97,7 100,9 94,3 99,5 100,8 97 99,2 101 102,3 97 91,2 97,6 95,7 100,5 94,4 102,9 105,1 98,8 100,7 99,6 107,7 102,9 101,6 102,7 110,5 109,8 94,3 102,5 105 102,3 107,7 100,3 99,5 95 97,7 96,3 97,8 106,4 96,1 106,2 114,7 111,9 121 117,7 115,4 114,3 109,5 108,1 108,2 99,1 101,2 98,1 95,5 97,9 98,2 98,7 95,6 95,8 94,4 96,5 103,3 104,3 104,5 102,3 103,8 103,1 102,2 106,3 102,1 94 102,6 102,6 106,7 107,9 109,3 105,9 109,1 108,5 111,7 109,8 109,1 108,5 108,5 106,2 117,1 109,8 115,2 115,9 119,2 121 118,6 117,6 114,6 110,6 102,5 101,6 107,4 105,8 102,8 104 100,4 100,6

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	'Herman Ole Andreas Wold' @ www.yougetit.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.645519343176284
beta	0
gamma	0.630222883115812

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	101.2	102.525	-1.32500000000003
14	95.5	96.0715808096854	-0.571580809685358
15	99.8	99.9086749469057	-0.108674946905722
16	97.1	96.9237504392867	0.17624956071333
17	97.5	97.4144168793474	0.0855831206526005
18	96.8	96.8923897119053	-0.0923897119053265
19	97.7	101.167977638487	-3.46797763848723
20	100.9	98.1020582638682	2.7979417361318
21	94.3	92.2975777150154	2.00242228498456
22	99.5	96.3629073059075	3.1370926940925
23	100.8	106.214855260675	-5.41485526067517
24	97	95.9671887221368	1.03281127786325
25	99.2	98.8731082390186	0.326891760981354
26	101	93.6543323527597	7.3456676472403
27	102.3	102.70557752661	-0.40557752661033
28	97	99.59264931476	-2.59264931475998
29	91.2	98.2756829235404	-7.07568292354041
30	97.6	93.09116054796	4.50883945204001
31	95.7	99.5828184106473	-3.88281841064732
32	100.5	97.64892909525	2.85107090474993
33	94.4	91.7010239579606	2.69897604203936
34	102.9	96.4694799088498	6.43052009115019
35	105.1	106.53687820285	-1.43687820285
36	98.8	100.29749325132	-1.49749325132005
37	100.7	101.412348544547	-0.712348544546884
38	99.6	97.0907302569181	2.50926974308186
39	107.7	101.288344741201	6.4116552587989
40	102.9	102.08747633793	0.812523662070177
41	101.6	101.967097095834	-0.36709709583387
42	102.7	103.701100037914	-1.00110003791352
43	110.5	104.761273727738	5.73872627226244
44	109.8	110.542640755584	-0.742640755584318
45	94.3	102.240946958373	-7.9409469583727
46	102.5	100.974760540363	1.52523945963662
47	105	106.118114193257	-1.11811419325703
48	102.3	100.070956063586	2.2290439364139
49	107.7	103.766765952236	3.93323404776383
50	100.3	103.163676482069	-2.86367648206925
51	99.5	104.764750280781	-5.26475028078139
52	95	96.7756800451205	-1.7756800451205
53	97.7	94.7210358198958	2.9789641801042
54	96.3	98.4733486269165	-2.17334862691654
55	97.8	100.282502652167	-2.48250265216697
56	106.4	99.3089581844446	7.09104181555536
57	96.1	94.455943297413	1.64405670258699
58	106.2	101.491825435905	4.7081745640951
59	114.7	108.099295245738	6.60070475426187
60	111.9	107.782545276358	4.11745472364193
61	121	113.078080031173	7.92191996882654
62	117.7	113.531322283615	4.16867771638482
63	115.4	119.135512485183	-3.73551248518277
64	114.3	112.913059473067	1.38694052693265
65	109.5	113.962144182978	-4.46214418297819
66	108.1	111.760041540663	-3.6600415406631
67	108.2	112.540440960346	-4.34044096034586
68	99.1	112.506308649066	-13.4063086490663
69	101.2	93.204991157053	7.99500884294704
70	98.1	105.025065261446	-6.92506526144575
71	95.5	104.54584843191	-9.0458484319095
72	97.9	93.5741831466092	4.32581685339082
73	98.2	99.8541441523693	-1.6541441523693
74	98.7	93.2873706271604	5.41262937283958
75	95.6	97.9287451960203	-2.32874519602026
76	95.8	93.7587530141292	2.04124698587081
77	94.4	93.9235090210424	0.476490978957571
78	96.5	95.0885820960125	1.41141790398754
79	103.3	98.990704215611	4.30929578438892
80	104.3	102.514812930829	1.78518706917117
81	104.5	97.8009930880508	6.69900691194917
82	102.3	105.451301144575	-3.15130114457507
83	103.8	106.934335225665	-3.13433522566451
84	103.1	102.76592044436	0.334079555639818
85	102.2	105.133203630046	-2.93320363004567
86	106.3	99.3195025489525	6.98049745104753
87	102.1	103.243529109843	-1.14352910984277
88	94	100.814881051026	-6.81488105102643
89	102.6	94.9132657622475	7.68673423775253
90	102.6	100.941554707846	1.65844529215403
91	106.7	105.650528981918	1.04947101808204
92	107.9	106.506467270344	1.393532729656
93	109.3	102.637583279226	6.66241672077385
94	105.9	108.063694896898	-2.16369489689808
95	109.1	110.188038131494	-1.08803813149372
96	108.5	108.115397886404	0.384602113595903
97	111.7	109.785377345308	1.91462265469212
98	109.8	109.315780783212	0.484219216788134
99	109.1	107.231411753191	1.86858824680893
100	108.5	105.480153357686	3.01984664231378
101	108.5	109.166732300793	-0.666732300792702
102	106.2	108.455966281895	-2.25596628189453
103	117.1	110.502066205659	6.59793379434106
104	109.8	115.016508554146	-5.21650855414576
105	115.2	108.057793336303	7.14220666369683
106	115.9	111.821849230182	4.07815076981788
107	119.2	118.21572826052	0.984271739479709
108	121	117.809794635443	3.19020536455668
109	118.6	121.632654638014	-3.0326546380138
110	117.6	117.649940153837	-0.0499401538369852
111	114.6	115.530031480746	-0.930031480745939
112	110.6	112.229403139543	-1.62940313954277
113	102.5	112.091212966017	-9.59121296601667
114	101.6	105.264484283663	-3.6644842836628
115	107.4	108.379335996946	-0.979335996946219
116	105.8	105.363136185416	0.436863814583987
117	102.8	104.814741677478	-2.0147416774781
118	104	101.983294624632	2.01670537536775
119	100.4	106.355292566911	-5.95529256691141
120	100.6	101.962545538909	-1.36254553890876

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	101.45631850879	93.287596187126	109.625040830454
122	100.09758510356	90.3747628114492	109.820407395671
123	97.813299760208	86.7526251750177	108.873974345398
124	94.956783827072	82.7034670828193	107.210100571325
125	94.0917220798663	80.7519687016926	107.43147545804
126	94.780348875083	80.436211774999	109.124485975167
127	100.860563094627	85.5779089370035	116.14321725225
128	98.7929252301718	82.6261454934083	114.959704966935
129	97.414833546932	80.4098338111915	114.419833282673
130	96.7845738334989	78.980774661186	114.588373005812
131	98.0737905847748	79.5055242703458	116.642056899204
132	98.5513281549718	79.2488474108014	117.853808899142

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295190889q75olqunhqh68kc/1u9sc1295190952.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295190889q75olqunhqh68kc/1u9sc1295190952.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295190889q75olqunhqh68kc/25nik1295190952.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295190889q75olqunhqh68kc/25nik1295190952.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295190889q75olqunhqh68kc/3lj0c1295190952.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295190889q75olqunhqh68kc/3lj0c1295190952.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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