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Datareeks - Aardolie - Silke van den Berg

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 01 Jun 2009 09:25:49 -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/01/t1243869991wd0it4hwgesshmj.htm/, Retrieved Mon, 01 Jun 2009 17:26:35 +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/01/t1243869991wd0it4hwgesshmj.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

493395.00 487190.00 519493.00 519453.00 538588.00 438224.00 542034.00 512027.00 619880.00 533737.00 573789.00 589213.00 532168.00 551102.00 593789.00 527106.00 547327.00 601305.00 610872.00 601325.00 642143.00 614216.00 657979.00 673098.00 602297.00 615381.00 703671.00 733852.00 716596.00 745798.00 742027.10 679181.20 739022.70 645410.60 729382.10 671052.70 744954.80 677639.30 778207.20 763316.20 658531.60 831700.10 664156.30 621402.10 683588.70 600023.80 643273.80 653615.90 620177.50 574128.80 599828.00 599369.40 596617.70 616114.60 510226.90 493960.10 634503.30 588556.20 603239.00 617458.20 646543.50 680125.60 731595.80 759600.30 785031.70 849573.30 762342.00 815346.60 929603.20 784057.50 944667.70 1007258.30 664292.70 873207.40 1146510.00 1417266.80 1089387.90 1373379.70 1009397.60 818175.10 1003458.10 961142.70 1121906.60 1141713.30 1042352.60 992223.60 920525.30 1076093.40 967880.40 1236416.10

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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.496602762806755
beta	0
gamma	0.507424910716124

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	532168	498335.787126069	33832.2128739315
14	551102	533020.214649824	18081.7853501763
15	593789	585576.561349895	8212.43865010526
16	527106	524229.221544946	2876.77845505386
17	547327	544555.88647907	2771.11352092994
18	601305	598445.16124831	2859.83875169035
19	610872	606472.455545609	4399.54445439111
20	601325	579909.996948779	21415.0030512213
21	642143	698177.337101558	-56034.3371015583
22	614216	586331.245956908	27884.7540430925
23	657979	645086.148993589	12892.8510064112
24	673098	665291.864895856	7806.13510414364
25	602297	616640.353841763	-14343.3538417629
26	615381	623377.430933972	-7996.43093397166
27	703671	660462.27399216	43208.7260078394
28	733852	615131.265888698	118720.734111302
29	716596	692959.368596563	23636.6314034375
30	745798	757233.180838146	-11435.1808381460
31	742027.1	758554.825637675	-16527.7256376750
32	679181.2	725946.192650208	-46764.9926502083
33	739022.7	790571.785827685	-51549.0858276851
34	645410.6	702389.064842577	-56978.4648425775
35	729382.1	715171.182706234	14210.9172937659
36	671052.7	734732.122088612	-63679.422088612
37	744954.8	644922.902369835	100031.897630165
38	677639.3	710080.279831851	-32440.9798318512
39	778207.2	748105.548106556	30101.6518934442
40	763316.2	715554.038600451	47762.1613995489
41	658531.6	733855.98684741	-75324.3868474098
42	831700.1	740026.870127488	91673.2298725117
43	664156.3	791251.615762852	-127095.315762852
44	621402.1	696011.11649086	-74609.0164908601
45	683588.7	745587.259450212	-61998.5594502125
46	600023.8	650828.440517532	-50804.6405175315
47	643273.8	684860.848837695	-41587.0488376948
48	653615.9	656816.344127681	-3200.44412768132
49	620177.5	638858.965428205	-18681.4654282050
50	574128.8	611224.57739083	-37095.7773908296
51	599828	662913.918661127	-63085.9186611273
52	599369.4	588596.339329835	10773.0606701651
53	596617.7	557088.625726115	39529.0742738849
54	616114.6	662953.308129673	-46838.7081296729
55	510226.9	589511.215225406	-79284.3152254063
56	493960.1	531420.696901841	-37460.5969018411
57	634503.3	602666.01612729	31837.2838727098
58	588556.2	557365.66945289	31190.53054711
59	603239	634471.613757007	-31232.6137570074
60	617458.2	621374.482320561	-3916.28232056089
61	646543.5	599107.201624384	47436.2983756161
62	680125.6	599603.394082108	80522.2059178918
63	731595.8	703063.32534512	28532.4746548806
64	759600.3	693109.957523074	66490.342476926
65	785031.7	696616.929664801	88414.7703351992
66	849573.3	804696.917178626	44876.3828213738
67	762342	768513.006064364	-6171.00606436364
68	815346.6	757414.054851035	57932.5451489652
69	929603.2	893733.066105559	35870.1338944414
70	784057.5	850270.239618636	-66212.7396186361
71	944667.7	863060.313952883	81607.386047117
72	1007258.3	912977.420755102	94280.879244898
73	664292.7	952592.434904953	-288299.734904953
74	873207.4	794812.527404886	78394.8725951145
75	1146510	883935.954567406	262574.045432594
76	1417266.8	999904.094646863	417362.705353137
77	1089387.9	1183255.54627635	-93867.6462763508
78	1373379.7	1189692.29755638	183687.40244362
79	1009397.6	1209402.96624799	-200005.366247988
80	818175.1	1118419.71005999	-300244.610059994
81	1003458.1	1071231.41580464	-67773.3158046413
82	961142.7	950223.29453691	10919.4054630904
83	1121906.6	1039076.03091024	82830.569089763
84	1141713.3	1092837.84397776	48875.4560222351
85	1042352.6	1012179.42369121	30173.1763087875
86	992223.6	1106221.15686581	-113997.556865809
87	920525.3	1146848.01811857	-226322.718118569
88	1076093.4	1059567.31697501	16526.0830249907
89	967880.4	913275.40600643	54604.9939935703
90	1236416.1	1064341.71482013	172074.385179875

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
91	980276.266597313	783146.717752625	1177405.815442
92	963011.486496802	742912.632707672	1183110.34028593
93	1124307.10194291	883419.261131322	1365194.94275449
94	1057056.37395933	797036.378069696	1317076.36984897
95	1158855.22484304	881017.422026317	1436693.02765976
96	1162809.78007093	868229.9248778	1457389.63526405
97	1053102.43219356	742682.172711057	1363522.69167605
98	1095333.64426866	769842.962514543	1420824.32602278
99	1163880.08383610	823986.526497422	1503773.64117477
100	1251024.2685674	897313.826635135	1604734.71049966
101	1106252.19516516	739244.670523637	1473259.71980668
102	1260207.45952770	880368.059840048	1640046.85921535

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243869991wd0it4hwgesshmj/15t4r1243869947.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243869991wd0it4hwgesshmj/15t4r1243869947.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243869991wd0it4hwgesshmj/25xlz1243869947.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243869991wd0it4hwgesshmj/25xlz1243869947.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243869991wd0it4hwgesshmj/308u61243869947.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243869991wd0it4hwgesshmj/308u61243869947.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=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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