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Tijdreeks B Stap 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 20 Aug 2010 07:49:05 +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/Aug/20/t1282290529aviw0rmst0356i8.htm/, Retrieved Fri, 20 Aug 2010 09:48:57 +0200

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/Aug/20/t1282290529aviw0rmst0356i8.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 «

76 75 74 72 70 69 70 72 73 73 74 76 74 67 66 58 55 58 64 68 66 76 75 88 85 83 77 66 65 65 63 62 57 68 69 79 74 76 82 75 75 76 78 77 67 74 68 87 76 88 95 96 96 105 108 113 101 107 102 116 105 121 134 140 131 141 131 128 123 129 125 144 135 141 156 159 146 154 145 133 126 127 122 148

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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.853661782423506
beta	0.00329071622036451
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	74	80.240411948487	-6.24041194848706
14	67	67.632330326825	-0.632330326824984
15	66	65.933156926383	0.0668430736170222
16	58	57.5982141158911	0.401785884108882
17	55	54.2994049601402	0.700595039859763
18	58	56.8974964663567	1.10250353364327
19	64	64.0993687803489	-0.0993687803488683
20	68	65.613765208217	2.38623479178297
21	66	68.6120576315391	-2.6120576315391
22	76	66.6105113770921	9.38948862290788
23	75	76.3382818181108	-1.33828181811079
24	88	77.7949401853773	10.2050598146227
25	85	83.4641937638682	1.53580623613183
26	83	77.5192595660054	5.48074043399458
27	77	81.1128249630908	-4.11282496309083
28	66	67.940679940157	-1.94067994015697
29	65	62.2884206493315	2.71157935066854
30	65	67.1641148449105	-2.16411484491054
31	63	72.2921996125122	-9.29219961251218
32	62	66.3506539610196	-4.35065396101965
33	57	62.7932770504556	-5.79327705045564
34	68	59.3743307284742	8.62566927152582
35	69	66.7775677006701	2.22243229932992
36	79	72.4109737723475	6.58902622765245
37	74	74.133741985889	-0.133741985889046
38	76	68.080486284877	7.91951371512306
39	82	72.5157337133069	9.4842662866931
40	75	70.8758988708582	4.12410112914178
41	75	70.7485461494082	4.25145385059177
42	76	76.6013714626525	-0.601371462652509
43	78	82.9872341082717	-4.98723410827175
44	77	82.2958932680294	-5.29589326802939
45	67	77.8421144404391	-10.8421144404391
46	74	72.9929300807638	1.00706991923616
47	68	72.96481777294	-4.96481777294001
48	87	73.0358018133258	13.9641981866742
49	76	79.7902153235534	-3.79021532355343
50	88	71.5708447577251	16.4291552422749
51	95	83.1985295593372	11.8014704406628
52	96	81.3869300133229	14.6130699866771
53	96	89.4650022378298	6.53499776217018
54	105	97.159000803315	7.840999196685
55	108	112.637161530114	-4.63716153011377
56	113	113.843811412907	-0.843811412907115
57	101	112.092463834908	-11.0924638349082
58	107	112.4920597365	-5.4920597365
59	102	105.567425895142	-3.56742589514207
60	116	113.246851925026	2.75314807497436
61	105	105.542226559521	-0.542226559521424
62	121	102.063570859471	18.9364291405286
63	134	114.134263135505	19.8657368644951
64	140	115.143217379642	24.8567826203578
65	131	128.645488103100	2.35451189690014
66	141	133.947840405514	7.05215959448597
67	131	149.461821142014	-18.4618211420136
68	128	140.975067209160	-12.9750672091596
69	123	126.940551140281	-3.94055114028126
70	129	136.807948893198	-7.80794889319833
71	125	127.933651460175	-2.93365146017474
72	144	139.965838476658	4.03416152334179
73	135	130.588732565777	4.41126743422339
74	141	133.898933040652	7.10106695934772
75	156	135.082653727691	20.9173462723091
76	159	135.031675942176	23.968324057824
77	146	143.338992827662	2.66100717233786
78	154	150.068516765705	3.93148323429509
79	145	159.416466608536	-14.4164666085359
80	133	156.097421860839	-23.0974218608394
81	126	134.677514939105	-8.67751493910461
82	127	140.353222925781	-13.3532229257807
83	122	127.461348104025	-5.46134810402451
84	148	138.064666867936	9.93533313206424

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	133.561981257641	115.204119823497	151.919842691785
86	133.459104619344	109.269193710852	157.649015527836
87	130.386347762239	101.857488712259	158.915206812219
88	115.302111327558	85.1568190588556	145.447403596261
89	104.059160926535	72.2682384314985	135.850083421571
90	107.183074713933	70.797189837427	143.568959590438
91	109.170517656469	68.7855548293011	149.555480483636
92	114.452346313391	69.1826047770838	159.722087849698
93	114.654033344408	66.4320877355408	162.875978953275
94	125.723730040039	70.4490874561326	180.998372623946
95	125.365066058023	67.7519959965753	182.978136119471
96	143.320112510630	48.2934173403048	238.346807680956

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282290529aviw0rmst0356i8/12jqw1282290539.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282290529aviw0rmst0356i8/12jqw1282290539.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282290529aviw0rmst0356i8/2vsph1282290539.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282290529aviw0rmst0356i8/2vsph1282290539.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282290529aviw0rmst0356i8/3vsph1282290539.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282290529aviw0rmst0356i8/3vsph1282290539.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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