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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: Wed, 02 Jun 2010 19:54:41 +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/Jun/02/t1275508496kzp6u5qllal319o.htm/, Retrieved Wed, 02 Jun 2010 21:54:56 +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/2010/Jun/02/t1275508496kzp6u5qllal319o.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

464 675 703 887 1139 1077 1318 1260 1120 963 996 960 530 883 894 1045 1199 1287 1565 1577 1076 918 1008 1063 544 635 804 980 1018 1064 1404 1286 1104 999 996 1015 615 722 832 977 1270 1437 1520 1708 1151 934 1159 1209 699 830 996 1124 1458 1270 1753 2258 1208 1241 1265 1828 809 997 1164 1205 1538 1513 1378 2083 1357 1536 1526 1376 779 1005 1193 1522 1539 1546 2116 2326 1596 1356 1553 1613 814 1150 1225 1691 1759 1754 2100 2062 2012 1897 1964 2186 966 1549 1538 1612 2078 2137 2907 2249 1883 1739 1828 1868 1138 1430 1809 1763 2200 2067 2503 2141 2103 1972 2181 2344 970 1199 1718 1683 2025 2051 2439 2353 2230 1852 2147 2286 1007 1665 1642 1518 1831 2207 2822 2393 2306 1785 2047 2171 1212 1335 2011 1860 1954 2152 2835 2224 2182 1992 2389 2724 891 1247 2017 2257 2255 2255 3057 3330 1896 2096 2374 2535 1041 1728 2201 2455 2204 2660 3670 2665 etc...

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.129074112205745
beta	0.000500934054976076
gamma	0.322462326005777

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	530	488.836959000463	41.163040999537
14	883	814.769180136285	68.230819863715
15	894	834.649242011631	59.3507579883687
16	1045	999.192165248972	45.8078347510281
17	1199	1167.60153495692	31.3984650430839
18	1287	1265.87492766457	21.1250723354269
19	1565	1471.68364055591	93.3163594440866
20	1577	1416.83455770272	160.165442297285
21	1076	1269.50663614626	-193.506636146263
22	918	1065.72885869940	-147.728858699401
23	1008	1084.2152672451	-76.2152672451004
24	1063	1035.03817558380	27.9618244161961
25	544	582.173549598269	-38.1735495982692
26	635	950.279703272534	-315.279703272534
27	804	917.8820476586	-113.882047658599
28	980	1063.43198202462	-83.4319820246214
29	1018	1215.98034271037	-197.980342710371
30	1064	1282.32424149349	-218.324241493494
31	1404	1473.86706678750	-69.8670667874956
32	1286	1417.88509443065	-131.885094430645
33	1104	1147.80505570157	-43.8050557015699
34	999	982.52338970301	16.4766102969901
35	996	1041.06932055722	-45.0693205572168
36	1015	1025.42181012321	-10.4218101232145
37	615	559.20355897905	55.7964410209495
38	722	857.541913373212	-135.541913373212
39	832	905.609678642965	-73.6096786429654
40	977	1069.12052501393	-92.1205250139342
41	1270	1190.32512746677	79.6748725332277
42	1437	1289.52881127662	147.471188723384
43	1520	1593.65374322978	-73.6537432297798
44	1708	1511.62678785961	196.373212140391
45	1151	1278.03622592088	-127.036225920883
46	934	1101.04125811502	-167.041258115022
47	1159	1121.09214750614	37.9078524938625
48	1209	1124.76644821184	84.2335517881563
49	699	638.42763830089	60.5723616991103
50	830	908.01061953216	-78.0106195321601
51	996	989.483222486196	6.51677751380385
52	1124	1178.42304517839	-54.4230451783903
53	1458	1375.45353777758	82.5464622224167
54	1270	1505.99433837198	-235.994338371978
55	1753	1717.65844816864	35.3415518313609
56	2258	1723.28938701246	534.710612987541
57	1208	1396.55030916633	-188.550309166326
58	1241	1177.62476199254	63.3752380074559
59	1265	1298.02429530364	-33.0242953036384
60	1828	1305.41735025192	522.582649748082
61	809	774.83266094363	34.1673390563706
62	997	1039.36945363520	-42.3694536352036
63	1164	1168.33975232397	-4.33975232396506
64	1205	1367.08090456414	-162.080904564136
65	1538	1626.2868854581	-88.2868854581002
66	1513	1646.33742562572	-133.337425625715
67	1378	1994.69039876606	-616.690398766055
68	2083	2063.16936900672	19.8306309932782
69	1357	1427.09831942623	-70.0983194262324
70	1536	1284.01934919386	251.980650806142
71	1526	1408.61492913749	117.385070862512
72	1376	1600.33223898861	-224.332238988606
73	779	810.845167194428	-31.8451671944277
74	1005	1050.49573693738	-45.4957369373781
75	1193	1192.70937440726	0.290625592740071
76	1522	1350.22596016804	171.774039831964
77	1539	1688.93680276946	-149.936802769462
78	1546	1688.23615636363	-142.236156363628
79	2116	1902.69253111387	213.307468886131
80	2326	2290.59267200516	35.4073279948379
81	1596	1558.17294232762	37.8270576723808
82	1356	1511.12962890956	-155.129628909558
83	1553	1548.21141631436	4.78858368563692
84	1613	1632.52638986099	-19.5263898609867
85	814	866.013219630146	-52.0132196301461
86	1150	1117.02597020484	32.9740297951616
87	1225	1295.3822019996	-70.3822019995996
88	1691	1506.36868386985	184.631316130150
89	1759	1772.35514762486	-13.3551476248631
90	1754	1791.71838832041	-37.718388320415
91	2100	2149.20213814788	-49.202138147878
92	2062	2475.75202043459	-413.75202043459
93	2012	1647.94559089079	364.054409109214
94	1897	1579.19509767656	317.804902323442
95	1964	1733.09269504805	230.907304951946
96	2186	1848.74678049347	337.25321950653
97	966	990.637162874265	-24.6371628742654
98	1549	1315.29531853704	233.704681462955
99	1538	1516.30565950867	21.6943404913313
100	1612	1865.89816072850	-253.898160728497
101	2078	2047.41388426638	30.5861157336158
102	2137	2065.97205856532	71.0279414346755
103	2907	2492.28903847496	414.710961525036
104	2249	2815.40117186052	-566.401171860515
105	1883	2075.63354545762	-192.633545457625
106	1739	1899.78141450023	-160.781414500229
107	1828	1973.93893170057	-145.938931700572
108	1868	2075.68898702426	-207.688987024259
109	1138	1014.12589478372	123.874105216275
110	1430	1448.76050845518	-18.7605084551751
111	1809	1560.14900034589	248.850999654105
112	1763	1871.68832633665	-108.688326336651
113	2200	2167.13957332622	32.8604266737848
114	2067	2197.97278776171	-130.972787761711
115	2503	2712.60059138710	-209.600591387104
116	2141	2675.05191677941	-534.051916779406
117	2103	2038.62262546849	64.377374531513
118	1972	1900.48654221681	71.5134577831939
119	2181	2011.98252307719	169.017476922813
120	2344	2141.93416303978	202.065836960222
121	970	1141.29282653254	-171.292826532538
122	1199	1516.61682348787	-317.616823487874
123	1718	1667.41007847986	50.5899215201352
124	1683	1853.85438536200	-170.854385361998
125	2025	2181.80535089781	-156.805350897809
126	2051	2142.05746174646	-91.0574617464604
127	2439	2635.84388087434	-196.84388087434
128	2353	2505.50343662525	-152.503436625251
129	2230	2081.28217536558	148.717824634422
130	1852	1953.21950775809	-101.219507758093
131	2147	2069.86037234918	77.1396276508167
132	2286	2196.40493747476	89.5950625252426
133	1007	1083.99651255359	-76.9965125535855
134	1665	1428.83744025122	236.16255974878
135	1642	1769.46825088515	-127.468250885149
136	1518	1874.24915300942	-356.24915300942
137	1831	2190.2679331991	-359.267933199102
138	2207	2142.48916888812	64.5108311118788
139	2822	2636.13763741813	185.862362581871
140	2393	2562.88994936457	-169.889949364575
141	2306	2207.28049642154	98.7195035784575
142	1785	1994.05865432917	-209.058654329167
143	2047	2151.59126451920	-104.591264519196
144	2171	2259.86660013019	-88.8666001301949
145	1212	1069.36234318583	142.637656814169
146	1335	1543.63471134505	-208.634711345049
147	2011	1723.1722805291	287.827719470902
148	1860	1815.88330158162	44.1166984183819
149	1954	2199.31242062952	-245.312420629516
150	2152	2291.62126002699	-139.621260026993
151	2835	2816.83716572309	18.1628342769109
152	2224	2613.27011602859	-389.270116028592
153	2182	2297.00876454059	-115.008764540588
154	1992	1963.95558691649	28.0444130835087
155	2389	2187.4827704661	201.517229533898
156	2724	2345.20316503874	378.79683496126
157	891	1193.38919948532	-302.389199485323
158	1247	1518.69079291897	-271.690792918967
159	2017	1833.62108883129	183.378911168708
160	2257	1844.12159399804	412.878406001957
161	2255	2202.66838186641	52.3316181335927
162	2255	2370.2214183267	-115.221418326702
163	3057	2973.89042768552	83.1095723144804
164	3330	2643.08637504267	686.91362495733
165	1896	2519.81158383102	-623.81158383102
166	2096	2136.98116213232	-40.9811621323188
167	2374	2419.93500335947	-45.9350033594742
168	2535	2603.90129612003	-68.9012961200287
169	1041	1147.16878251544	-106.168782515444
170	1728	1526.39053984195	201.609460158049
171	2201	2077.77000369211	123.229996307889
172	2455	2145.41238810246	309.587611897541
173	2204	2405.83168961193	-201.831689611933
174	2660	2500.46608959121	159.533910408795
175	3670	3251.46625919908	418.533740800921
176	2665	3108.31874948913	-443.318749489129
177	2639	2439.44977608105	199.550223918949
178	2226	2313.34448108028	-87.3444810802825
179	2586	2612.52680620413	-26.526806204125
180	2684	2807.31910509382	-123.319105093822
181	1185	1210.11578193156	-25.1157819315579
182	1749	1729.34102376120	19.6589762388023
183	2459	2272.62009321613	186.379906783869
184	2618	2406.4619875861	211.538012413898
185	2585	2514.64061854919	70.3593814508117
186	3310	2763.70256109067	546.297438909328
187	3923	3717.7065728895	205.293427110496

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
188	3260.0287353497	3093.57334924266	3426.48412145673
189	2777.93569256481	2605.63435610249	2950.23702902713
190	2520.71421309991	2343.02905372457	2698.39937247526
191	2882.03106413825	2691.53511577736	3072.52701249914
192	3070.01537519007	2868.84272802585	3271.18802235429
193	1339.16689636985	1164.13049948455	1514.20329325516
194	1935.49287653904	1736.78847449315	2134.19727858494
195	2588.33121789624	2357.0350192507	2819.62741654178
196	2715.31191339544	2472.63023185579	2957.99359493509
197	2759.20525137023	2509.19764887846	3009.21285386200
198	3159.38708623222	2882.63787293661	3436.13629952782
199	3991.07026379319	3704.3495951894	4277.79093239699

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275508496kzp6u5qllal319o/1idjo1275508476.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275508496kzp6u5qllal319o/1idjo1275508476.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275508496kzp6u5qllal319o/2bnir1275508476.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275508496kzp6u5qllal319o/2bnir1275508476.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275508496kzp6u5qllal319o/3bnir1275508476.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275508496kzp6u5qllal319o/3bnir1275508476.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=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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