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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: Tue, 02 Jun 2009 10:29:01 -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/02/t12439602115tjjqtk39vc23b1.htm/, Retrieved Tue, 02 Jun 2009 18:30:14 +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/02/t12439602115tjjqtk39vc23b1.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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.668837108850633
beta	0
gamma	0.703044343859426

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	532168	499791.708476475	32376.2915235246
14	551102	539103.860765777	11998.1392342234
15	593789	590455.104842513	3333.89515748725
16	527106	527271.974943384	-165.974943384412
17	547327	546140.125967571	1186.87403242872
18	601305	599384.527307553	1920.47269244655
19	610872	608483.732180449	2388.26781955070
20	601325	576989.859138153	24335.140861847
21	642143	716926.628860752	-74783.6288607515
22	614216	576047.110066571	38168.8899334290
23	657979	651719.137024963	6259.86297503684
24	673098	670713.562394768	2384.437605232
25	602297	610728.630374213	-8431.63037421345
26	615381	619039.750355153	-3658.75035515311
27	703671	662212.638258278	41458.361741722
28	733852	612127.883262676	121724.116737324
29	716596	717293.380123523	-697.38012352318
30	745798	784016.794608828	-38218.7946088276
31	742027.1	766974.573905942	-24947.4739059421
32	679181.2	714498.114775428	-35316.9147754284
33	739022.7	804449.728749846	-65427.0287498465
34	645410.6	683691.368821074	-38280.7688210745
35	729382.1	703670.014938122	25712.0850618776
36	671052.7	735545.105597858	-64492.4055978581
37	744954.8	626277.833757071	118676.966242929
38	677639.3	722358.702578015	-44719.4025780149
39	778207.2	754405.332784488	23801.8672155116
40	763316.2	701027.808503255	62288.3914967446
41	658531.6	737651.945883853	-79120.3458838535
42	831700.1	740543.715176659	91156.3848233406
43	664156.3	813401.07946849	-149244.779468491
44	621402.1	676910.5401654	-55508.4401653998
45	683588.7	739212.716908837	-55624.016908837
46	600023.8	635439.675750915	-35415.8757509151
47	643273.8	668950.699031645	-25676.8990316449
48	653615.9	645863.192224382	7752.70777561842
49	620177.5	625701.958769171	-5524.45876917127
50	574128.8	604329.101478896	-30200.3014788956
51	599828	651597.175796715	-51769.1757967147
52	599369.4	569440.119221997	29929.2807780030
53	596617.7	559913.550929166	36704.1490708342
54	616114.6	667475.504536375	-51360.9045363754
55	510226.9	596686.845058719	-86459.9450587189
56	493960.1	527542.88488512	-33582.7848851199
57	634503.3	585770.022328746	48733.2776712541
58	588556.2	563108.582126976	25447.6178730238
59	603239	637365.210952478	-34126.210952478
60	617458.2	616585.308318703	872.891681296634
61	646543.5	590578.10751721	55965.3924827899
62	680125.6	604004.447400742	76121.152599258
63	731595.8	724242.242373012	7353.55762698816
64	759600.3	693397.966404895	66202.3335951052
65	785031.7	701432.916879808	83598.7831201917
66	849573.3	834801.360212398	14771.9397876016
67	762342	779240.207694494	-16898.2076944942
68	815346.6	766455.354583783	48891.2454162168
69	929603.2	955007.951241408	-25404.7512414085
70	784057.5	844729.693556326	-60672.1935563263
71	944667.7	861113.046510262	83554.6534897379
72	1007258.3	929447.667399311	77810.6326006893
73	664292.7	955073.862868592	-290781.162868592
74	873207.4	735038.697237401	138168.702762599
75	1146510	891699.382528233	254810.617471767
76	1417266.8	1026218.64548934	391048.154510665
77	1089387.9	1226540.72989738	-137152.829897380
78	1373379.7	1221902.54560288	151477.154397119
79	1009397.6	1206666.75808575	-197269.158085752
80	818175.1	1091436.31765757	-273261.217657573
81	1003458.1	1063152.38644291	-59694.2864429121
82	961142.7	910505.322475077	50637.3775249226
83	1121906.6	1050042.74597773	71863.8540222712
84	1141713.3	1108996.02422576	32717.2757742386
85	1042352.6	983653.035840164	58699.5641598356
86	992223.6	1124671.42382884	-132447.823828837
87	920525.3	1133535.55347793	-213010.253477934
88	1076093.4	971710.947012389	104382.452987611
89	967880.4	901678.349604884	66202.0503951164
90	1236416.1	1076801.59113149	159614.508868511

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
91	1006991.05379214	831150.775784212	1182831.33180006
92	993605.904937146	776063.716942258	1211148.09293203
93	1232034.45041535	946012.322001396	1518056.57882931
94	1124096.3014259	829296.654736894	1418895.94811490
95	1252228.08112224	904878.522084628	1599577.64015985
96	1253324.27861662	883401.654833915	1623246.90239933
97	1096810.67582455	744412.445743095	1449208.90590600
98	1154287.95037287	764523.035627818	1544052.86511792
99	1235607.78165482	802492.443593142	1668723.11971649
100	1303159.64685823	831648.888221738	1774670.40549472
101	1119269.30958045	691194.06580129	1547344.55335962
102	1292046.43721176	819196.40488035	1764896.46954317

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439602115tjjqtk39vc23b1/19k0i1243960138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439602115tjjqtk39vc23b1/19k0i1243960138.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439602115tjjqtk39vc23b1/2dxmc1243960138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439602115tjjqtk39vc23b1/2dxmc1243960138.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439602115tjjqtk39vc23b1/3zyst1243960138.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439602115tjjqtk39vc23b1/3zyst1243960138.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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