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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 10 Mar 2008 11:56:43 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Mar/10/t1205171842e0ry9c7xankjola.htm/, Retrieved Mon, 10 Mar 2008 18:57:26 +0100

User-defined keywords:

Dataseries X:

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13328 12873 14000 13477 14237 13674 13529 14058 12975 14326 14008 16193 14483 14011 15057 14884 15414 14440 14900 15074 14442 15307 14938 17193 15528 14765 15838 15723 16150 15486 15986 15983 15692 16490 15686 18897 16316 15636 17163 16534 16518 16375 16290 16352 15943 16362 16393 19051 16747 16320 17910 16961 17480 17049 16879 17473 16998 17307 17418 20169 17871 17226 19062 17804 19100 18522 18060 18869 18127 18871 18890 21263 19547 18450 20254 19240 20216 19420 19415 20018 18652 19978 19509 21971

Text written by user:

Output produced by software:

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.422989536624582
beta	0.000514955626444454
gamma	0.94620902518207

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	14483	13944.8804166667	538.119583333326
14	14011	13686.0979965736	324.902003426432
15	15057	14851.1975415833	205.802458416676
16	14884	14748.4223866353	135.577613364725
17	15414	15341.3473886490	72.6526113509572
18	14440	14402.8799318052	37.1200681947994
19	14900	14878.5989998545	21.4010001455226
20	15074	15071.9237281773	2.07627182270880
21	14442	14462.0747508767	-20.0747508767181
22	15307	15336.3100833830	-29.3100833829540
23	14938	14974.5075825248	-36.5075825247623
24	17193	17225.0276627274	-32.027662727367
25	15528	15776.9425577243	-248.942557724304
26	14765	15068.9243948347	-303.924394834674
27	15838	15902.9691486429	-64.9691486428728
28	15723	15647.2178955276	75.7821044724187
29	16150	16180.3799702807	-30.3799702807264
30	15486	15178.7938436343	307.206156365735
31	15986	15760.0959782035	225.904021796508
32	15983	16029.3387757661	-46.3387757660985
33	15692	15386.8725459578	305.127454042171
34	16490	16393.6492620558	96.3507379441799
35	15686	16081.1241999454	-395.124199945367
36	18897	18182.3748650146	714.625134985403
37	16316	16931.8248968647	-615.824896864662
38	15636	16038.6592424093	-402.659242409331
39	17163	16961.440147934	201.559852066006
40	16534	16895.3692076351	-361.369207635129
41	16518	17185.6590761955	-667.65907619552
42	16375	16098.6842863866	276.315713613410
43	16290	16622.3856142795	-332.385614279458
44	16352	16506.5733049799	-154.573304979949
45	15943	16009.9249756602	-66.9249756602021
46	16362	16744.9690936872	-382.969093687232
47	16393	15960.8885818412	432.111418158844
48	19051	19017.6477028062	33.3522971937673
49	16747	16752.0927339026	-5.09273390255112
50	16320	16233.3314332216	86.6685667783695
51	17910	17692.7749344060	217.225065593975
52	16961	17325.7848750970	-364.784875097022
53	17480	17447.2018104917	32.7981895083321
54	17049	17171.8476788322	-122.847678832197
55	16879	17194.2362119124	-315.236211912375
56	17473	17182.6256225956	290.374377404431
57	16998	16922.0030740834	75.9969259165773
58	17307	17544.9453812475	-237.945381247519
59	17418	17267.2466428405	150.753357159461
60	20169	19987.2481541018	181.751845898201
61	17871	17763.4724595371	107.527540462852
62	17226	17342.4697830918	-116.469783091849
63	19062	18787.2461782215	274.753821778475
64	17804	18126.8193160791	-322.819316079116
65	19100	18483.0563700456	616.94362995437
66	18522	18369.9382247645	152.061775235463
67	18060	18403.7585538249	-343.758553824875
68	18869	18710.9106552419	158.089344758126
69	18127	18277.4405233282	-150.440523328172
70	18871	18633.3007632566	237.699236743370
71	18890	18769.2196251411	120.780374858885
72	21263	21493.6667510483	-230.666751048338
73	19547	19055.0275915991	491.97240840091
74	18450	18674.5381477947	-224.538147794676
75	20254	20287.3700052764	-33.370005276367
76	19240	19170.4542847762	69.5457152238196
77	20216	20205.9306407428	10.0693592572279
78	19420	19582.3543934525	-162.354393452457
79	19415	19212.4632947279	202.536705272050
80	20018	20024.794315328	-6.79431532801027
81	18652	19353.2019642645	-701.201964264452
82	19978	19687.9602181886	290.039781811422
83	19509	19782.1462019758	-273.146201975789
84	21971	22147.9623367409	-176.962336740871

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	20126.4686927122	19570.7333770256	20682.2040083988
86	19146.4658363608	18543.0118806555	19749.9197920661
87	20958.4772741945	20310.7670249181	21606.1875234708
88	19911.7028825152	19222.5313207893	20600.874444241
89	20885.1115365913	20156.7961314371	21613.4269417456
90	20162.9570968649	19397.4597030063	20928.4544907235
91	20060.8157501976	19259.8249495913	20861.8065508039
92	20672.9977986942	19837.9868007746	21508.0087966138
93	19624.9642834964	18757.2329879429	20492.6955790499
94	20797.4795072627	19898.1858978828	21696.7731166425
95	20461.3995910396	19531.5837061900	21391.2154758892
96	22995.2289112622	22035.8315055273	23954.6263169972

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171842e0ry9c7xankjola/16zpi1205171800.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171842e0ry9c7xankjola/16zpi1205171800.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171842e0ry9c7xankjola/2mt551205171800.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171842e0ry9c7xankjola/2mt551205171800.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171842e0ry9c7xankjola/3xxer1205171800.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Mar/10/t1205171842e0ry9c7xankjola/3xxer1205171800.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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