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*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 29 Dec 2010 09:10:57 +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/Dec/29/t1293613722ngk2nxpmeeidirr.htm/, Retrieved Wed, 29 Dec 2010 10:08:43 +0100

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/Dec/29/t1293613722ngk2nxpmeeidirr.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 «

1775 2197 2920 4240 5415 6136 6719 6234 7152 3646 2165 2803 1615 2350 3350 3536 5834 6767 5993 7276 5641 3477 2247 2466 1567 2237 2598 3729 5715 5776 5852 6878 5488 3583 2054 2282 1552 2261 2446 3519 5161 5085 5711 6057 5224 3363 1899 2115 1491 2061 2419 3430 4778 4862 6176 5664 5529 3418 1941 2402 1579 2146 2462 3695 4831 5134 6250 5760 6249 2917 1741 2359 1511 2059 2635 2867 4403 5720 4502 5749 5627 2846 1762 2429 1169 2154 2249 2687 4359 5382 4459 6398 4596 3024 1887 2070 1351 2218 2461 3028 4784 4975 4607 6249 4809 3157 1910 2228 1594 2467 2222 3607 4685 4962 5770 5480 5000 3228 1993 2288 1588 2105 2191 3591 4668 4885 5822 5599 5340 3082 2010 2301

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0531970593633077
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1615	1538.19070512821	76.8092948717931
14	2350	2260.40115099657	89.5988490034279
15	3350	3281.00029686864	68.9997031313578
16	3536	3536.96196208825	-0.96196208825495
17	5834	5834.82687245003	-0.826872450025803
18	6767	6774.6989691833	-7.69896918329869
19	5993	6672.4554905787	-679.455490578703
20	7276	6147.89320709441	1128.10679290559
21	5641	7097.90458837418	-1456.90458837418
22	3477	3522.10929908251	-45.1092990825127
23	2247	2046.87570093747	200.124299062532
24	2466	2648.06280907082	-182.062809070821
25	1567	1523.35028651109	43.6497134889078
26	2237	2255.90592762143	-18.9059276214339
27	2598	3251.22960656391	-653.229606563909
28	3729	3402.53088595997	326.469114040027
29	5715	5717.94206998266	-2.9420699826569
30	5776	6651.19512303182	-875.195123031818
31	5852	5866.78235018446	-14.7823501844578
32	6878	7088.98400859382	-210.984008593817
33	5488	5520.26331963836	-32.2633196383595
34	3583	3356.94668796943	226.05331203057
35	2054	2128.32603521152	-74.3260352115221
36	2282	2353.05731476613	-71.0573147661262
37	1552	1447.95523817465	104.044761825346
38	2261	2124.49585329991	136.504146700086
39	2446	2527.50736665351	-81.5073666535072
40	3519	3636.80421759122	-117.80421759122
41	5161	5616.69388910629	-455.693889106289
42	5085	5700.01012115041	-615.010121150406
43	5711	5744.07976878683	-33.0797687868253
44	6057	6779.54375119282	-722.543751192821
45	5224	5352.82286209809	-128.822862098089
46	3363	3428.94449319634	-65.9444931963435
47	1899	1900.39036658448	-1.3903665844814
48	2115	2132.09644336256	-17.0964433625609
49	1491	1395.65208747884	95.3479125211634
50	2061	2102.46269684605	-41.4626968460502
51	2419	2289.59295552298	129.407044477019
52	3430	3375.7438677065	54.2561322934962
53	4778	5044.87170926723	-266.871709267229
54	4862	4987.39164903083	-125.391649030826
55	6176	5608.48092845755	567.519071542454
56	5664	6023.10847702099	-359.108477020991
57	5529	5177.85795949342	351.142040506578
58	3418	3339.04573658645	78.9542634135478
59	1941	1879.31983463798	61.6801653620196
60	2402	2099.51051856874	302.489481431258
61	1579	1486.52984090666	92.4701590933391
62	2146	2063.65467499477	82.3453250052339
63	2462	2419.15112991029	42.8488700897142
64	3695	3429.54429710566	265.455702894341
65	4831	4805.86255005113	25.1374499488666
66	5134	4897.87025546546	236.129744534538
67	6250	6194.24131776426	55.7586822357443
68	5760	5704.31103066312	55.6889693368776
69	6249	5553.59379609704	695.406203902963
70	2917	3475.38722656988	-558.387226569878
71	1741	1965.40146471203	-224.401464712025
72	2359	2398.37241577205	-39.3724157720517
73	1511	1568.35877849033	-57.3587784903261
74	2059	2127.92693100338	-68.9269310033751
75	2635	2437.98078707724	197.019212922755
76	2867	3667.34016705761	-800.34016705761
77	4403	4759.42718526263	-356.427185262634
78	5720	5030.90489909207	689.095100907925
79	4502	6180.59653415312	-1678.59653415312
80	5749	5598.33764527104	150.662354728958
81	5627	6058.35887438874	-431.358874388736
82	2846	2733.11640918054	112.883590819461
83	1762	1575.058982302	186.941017697995
84	2429	2205.09819145702	223.901808542976
85	1169	1372.06042760199	-203.060427601994
86	2154	1912.92492002083	241.075079979171
87	2249	2491.26856259593	-242.268562595932
88	2687	2752.95633086746	-65.956330867456
89	4359	4304.40852615203	54.5914738479732
90	5382	5587.65479903709	-205.654799037085
91	4459	4448.01096795875	10.9890320412542
92	6398	5687.58075792026	710.419242079743
93	4596	5626.31999616176	-1030.31999616176
94	3024	2784.50492708077	239.495072919229
95	1887	1703.30064827616	183.699351723842
96	2070	2368.1619957942	-298.161995794199
97	1351	1103.10287202553	247.897127974465
98	2218	2088.46578491772	129.53421508228
99	2461	2203.24459935331	257.75540064669
100	3028	2658.46511155127	369.534888448733
101	4784	4347.21917507387	436.780824926133
102	4975	5404.39486109894	-429.394861098941
103	4607	4457.96773299292	149.032267007082
104	6249	6367.10359675419	-118.10359675419
105	4809	4613.63082670566	195.369173294343
106	3157	3039.28345860385	117.716541396147
107	1910	1898.77336712589	11.226632874108
108	2228	2098.23193237149	129.768067628508
109	1594	1372.94781373574	221.052186264263
110	2467	2244.81630068151	222.183699318486
111	2222	2485.9239907743	-263.923990774304
112	3607	3019.22584117206	587.774158827938
113	4685	4783.2582425191	-98.2582425190994
114	4962	4991.87373687506	-29.8737368750571
115	5770	4614.35646356609	1155.64353643391
116	5480	6324.11606542414	-844.116065424137
117	5000	4828.81850747275	171.181492527252
118	3228	3179.66268565193	48.3373143480749
119	1993	1934.63686477731	58.3631352226917
120	2288	2248.83833234928	39.1616676507169
121	1588	1605.16229163298	-17.1622916329752
122	2105	2465.42978874396	-360.429788743961
123	2191	2215.29596408047	-24.2959640804656
124	3591	3567.7356334176	23.2643665823998
125	4668	4652.20027886796	15.7997211320435
126	4885	4931.62997252489	-46.6299725248882
127	5822	5675.67255729787	146.327442702125
128	5599	5438.36123939567	160.63876060433
129	5340	4957.80039705972	382.199602940284
130	3082	3203.56088904513	-121.560889045125
131	2010	1958.98946004527	51.0105399547347
132	2301	2254.61978520861	46.3802147913898

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	1558.00005969496	787.686993262783	2328.31312612714
134	2094.17386456308	1322.77160325135	2865.57612587481
135	2181.46633840655	1408.97641795609	2953.95625885702
136	3580.22874251642	2806.65269219023	4353.80479284261
137	4656.38824381344	3881.72758644211	5431.04890118476
138	4875.86882122995	4100.12507325664	5651.61256920326
139	5805.08463157405	5028.25930309898	6581.90996004911
140	5573.53912189013	4795.63371671473	6351.44452706553
141	5294.20722692388	4515.22324259442	6073.19121125335
142	3042.67390875467	2262.6128366055	3822.73498090384
143	1967.96029803255	1186.82362322895	2749.09697283614
144	2256.49300699301	1474.28220857359	3038.70380541242

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293613722ngk2nxpmeeidirr/1jux21293613853.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293613722ngk2nxpmeeidirr/1jux21293613853.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293613722ngk2nxpmeeidirr/2cle51293613853.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293613722ngk2nxpmeeidirr/2cle51293613853.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293613722ngk2nxpmeeidirr/3cle51293613853.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293613722ngk2nxpmeeidirr/3cle51293613853.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=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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