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Duncan Huysmans Opgave 10 Opdracht 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, 05 Jun 2009 14:19:40 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/05/t124423328496ue81pejg2loi7.htm/, Retrieved Fri, 05 Jun 2009 22:21:28 +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/2009/Jun/05/t124423328496ue81pejg2loi7.htm/},
    year = {2009},
}
@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 = {2009},
    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:

Duncan Huysmans Opgave 10 Opdracht 2

Dataseries X:

» Textbox « » Textfile « » CSV «

1664.81 2397.53 2840.71 3547.29 3752.96 3714.74 4349.61 3566.34 5021.82 6423.48 7600.60 19756.21 2499.81 5198.24 7225.14 4806.03 5900.88 4951.34 6179.12 4752.15 5496.43 5835.10 12600.08 28541.72 4717.02 5702.63 9957.58 5304.78 6492.43 6630.80 7349.62 8176.62 8573.17 9690.50 15151.84 34061.01 5921.10 5814.58 12421.25 6369.77 7609.12 7224.75 8121.22 7979.25 8093.06 8476.70 17914.66 30114.41 4826.64 6470.23 9638.77 8821.17 8722.37 10209.48 11276.55 12552.22 11637.39 13606.89 21822.11 45060.69 7615.03 9849.69 14558.40 11587.33 9332.56 13082.09 16732.78 19888.61 23933.38 25391.35 36024.80 80721.71 10243.24 11266.88 21826.84 17357.33 15997.79 18601.53 26155.15 28586.52 30505.41 30821.33 46634.38 104660.67

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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.488903716392153
beta	0.0465372441384407
gamma	0.947454970073025

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2499.81	2094.39367811309	405.416321886914
14	5198.24	4816.56402005839	381.675979941614
15	7225.14	7085.97950572379	139.160494276210
16	4806.03	4899.7479008483	-93.7179008483026
17	5900.88	5962.72230169536	-61.8423016953557
18	4951.34	4719.27181523893	232.068184761075
19	6179.12	6003.72918904137	175.390810958627
20	4752.15	4985.4572851177	-233.307285117704
21	5496.43	6674.10111646775	-1177.67111646775
22	5835.1	7669.30214520937	-1834.20214520937
23	12600.08	7978.9790636539	4621.10093634609
24	28541.72	26666.7932759403	1874.92672405971
25	4717.02	3807.00257376309	910.017426236914
26	5702.63	8505.38475298753	-2802.75475298753
27	9957.58	9763.6994469637	193.880553036308
28	5304.78	6579.83538265766	-1275.05538265767
29	6492.43	7281.90853964856	-789.47853964856
30	6630.8	5584.4174584067	1046.38254159331
31	7349.62	7446.24219872818	-96.6221987281779
32	8176.62	5789.92577776088	2386.69422223912
33	8573.17	8824.0750751731	-250.905075173094
34	9690.5	10482.5750151408	-792.075015140841
35	15151.84	16708.8825988694	-1557.04259886937
36	34061.01	35009.7735615791	-948.76356157905
37	5921.1	5061.18076645123	859.919233548773
38	5814.58	7994.35792622826	-2179.77792622826
39	12421.25	11745.5899383707	675.660061629298
40	6369.77	7117.20428899281	-747.434288992808
41	7609.12	8660.91093174328	-1051.79093174328
42	7224.75	7530.0624350017	-305.312435001703
43	8121.22	8207.73478065402	-86.5147806540235
44	7979.25	7442.77961440537	536.470385594627
45	8093.06	8175.56306823937	-82.5030682393735
46	8476.7	9464.45362099461	-987.753620994614
47	17914.66	14563.6213425034	3351.03865749662
48	30114.41	36632.6098584899	-6518.19985848985
49	4826.64	5299.83716395774	-473.197163957743
50	6470.23	5755.2482338799	714.981766120101
51	9638.77	12474.7316323203	-2835.96163232033
52	8821.17	5959.14119359385	2862.02880640615
53	8722.37	9342.26261108106	-619.892611081061
54	10209.48	8734.54933144548	1474.93066855452
55	11276.55	10711.2978516089	565.252148391053
56	12552.22	10451.08837869	2101.13162130999
57	11637.39	11791.9475416962	-154.557541696195
58	13606.89	13041.1690625705	565.720937429522
59	21822.11	25293.0891801767	-3470.97918017666
60	45060.69	44001.5136777243	1059.1763222757
61	7615.03	7477.63237666557	137.397623334435
62	9849.69	9550.00943106132	299.680568938678
63	14558.4	16515.8104435388	-1957.41044353881
64	11587.33	11430.1019549011	157.228045098867
65	9332.56	11887.3401339983	-2554.78013399832
66	13082.09	11406.1950948553	1675.89490514472
67	16732.78	13161.6837847215	3571.0962152785
68	19888.61	15070.4473828305	4818.16261716948
69	23933.38	16370.9532991315	7562.4267008685
70	25391.35	23103.3934566428	2287.95654335720
71	36024.8	42162.4754632356	-6137.67546323562
72	80721.71	80109.8347724822	611.875227517798
73	10243.24	13559.8674871677	-3316.6274871677
74	11266.88	15246.5065443697	-3979.62654436974
75	21826.84	20922.411621172	904.428378828004
76	17357.33	16836.9839506788	520.346049321186
77	15997.79	15516.1542990580	481.635700942026
78	18601.53	20488.2313864995	-1886.70138649949
79	26155.15	22071.3148411403	4083.83515885965
80	28586.52	24719.0214976063	3867.49850239369
81	30505.41	26017.3572955989	4488.05270440106
82	30821.33	28590.1039749526	2231.2260250474
83	46634.38	45451.6939866384	1182.68601336162
84	104660.67	102035.051932041	2625.61806795884

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	14994.7405385046	10497.8195356343	19491.6615413749
86	18948.0920930103	13580.8574378648	24315.3267481558
87	35767.0508907713	27310.6753804430	44223.4264010997
88	28159.4264766049	20617.1432447154	35701.7097084944
89	25669.2640583713	18148.2101315721	33190.3179851706
90	31472.7017002141	22232.1081756953	40713.295224733
91	40496.4481569367	28592.1178677006	52400.7784461729
92	41217.9584905466	28690.6622447967	53745.2547362965
93	40537.8498450410	27771.0461339649	53304.6535561172
94	39431.6404596473	26561.5423624458	52301.7385568489
95	58785.1997797297	39615.0155997528	77955.3839597066
96	129819.012363308	87614.241560001	172023.783166615

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124423328496ue81pejg2loi7/1nf5w1244233178.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124423328496ue81pejg2loi7/1nf5w1244233178.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124423328496ue81pejg2loi7/2pwbv1244233178.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124423328496ue81pejg2loi7/2pwbv1244233178.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124423328496ue81pejg2loi7/3attx1244233178.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124423328496ue81pejg2loi7/3attx1244233178.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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=0, beta=0)

if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)

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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