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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 07:29:24 +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/t1275463925j4jw2fi9kpfmuzn.htm/, Retrieved Wed, 02 Jun 2010 09:32:10 +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/t1275463925j4jw2fi9kpfmuzn.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:

eline.horemans@student.kdg.be

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.128930926063059
beta	0
gamma	0.318961787795789

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	530	488.836959000463	41.163040999537
14	883	814.755238932399	68.2447610676013
15	894	834.618524038149	59.3814759618515
16	1045	999.136032009435	45.8639679905651
17	1199	1167.51744281064	31.4825571893605
18	1287	1265.76789251402	21.2321074859849
19	1565	1471.54411690622	93.455883093782
20	1577	1416.67395034438	160.326049655620
21	1076	1269.32628721628	-193.326287216280
22	918	1065.59758763115	-147.597587631153
23	1008	1084.10736657534	-76.1073665753388
24	1063	1034.95187934666	28.0481206533357
25	544	581.982552876668	-37.9825528766681
26	635	950.01704297118	-315.01704297118
27	804	917.750504008918	-113.750504008918
28	980	1063.42543153307	-83.425431533069
29	1018	1216.09603740948	-198.096037409481
30	1064	1282.55780968998	-218.557809689982
31	1404	1474.02347356884	-70.0234735688375
32	1286	1417.91458147561	-131.914581475614
33	1104	1148.84690724577	-44.8469072457747
34	999	983.319274434603	15.6807255653965
35	996	1041.62335100716	-45.6233510071575
36	1015	1025.6617778338	-10.6617778338000
37	615	559.411247840276	55.5887521597242
38	722	858.653333515306	-136.653333515306
39	832	906.056318391442	-74.0563183914425
40	977	1069.55862086221	-92.55862086221
41	1270	1191.23602602605	78.763973973949
42	1437	1290.50915889255	146.490841107447
43	1520	1593.93855847723	-73.9385584772338
44	1708	1512.02680738275	195.973192617247
45	1151	1278.88506606664	-127.885066066642
46	934	1101.55325635512	-167.553256355115
47	1159	1121.70002051595	37.2999794840518
48	1209	1125.00450634841	83.9954936515919
49	699	638.412885070315	60.5871149296852
50	830	909.400985151356	-79.4009851513558
51	996	990.093850771444	5.90614922855627
52	1124	1179.04487730169	-55.0448773016915
53	1458	1375.82991843031	82.1700815696906
54	1270	1506.27911116513	-236.279111165128
55	1753	1718.3139041886	34.6860958114012
56	2258	1723.10131469524	534.898685304756
57	1208	1397.79915781362	-189.79915781362
58	1241	1178.68476644003	62.315233559967
59	1265	1298.32903611964	-33.3290361196437
60	1828	1305.30176605923	522.698233940772
61	809	774.561182046733	34.4388179532666
62	997	1040.77010167051	-43.7701016705096
63	1164	1168.75073612202	-4.75073612201572
64	1205	1367.6983549032	-162.698354903199
65	1538	1626.18580375515	-88.1858037551515
66	1513	1647.32610180479	-134.326101804787
67	1378	1994.8473981759	-616.847398175902
68	2083	2061.21782094053	21.7821790594703
69	1357	1428.82192211012	-71.8219221101172
70	1536	1284.72546884146	251.274531158535
71	1526	1409.0793621541	116.920637845899
72	1376	1598.65940088826	-222.659400888261
73	779	810.73714273177	-31.7371427317696
74	1005	1051.93266238057	-46.9326623805705
75	1193	1193.37607240147	-0.376072401467354
76	1522	1351.58581532867	170.414184671327
77	1539	1689.45800268104	-150.458002681038
78	1546	1689.68549575826	-143.685495758261
79	2116	1905.13461397824	210.865386021764
80	2326	2288.75654810251	37.2434518974892
81	1596	1559.59203705080	36.4079629492023
82	1356	1510.71249582125	-154.712495821247
83	1553	1548.27143626205	4.72856373794889
84	1613	1632.16622149008	-19.1662214900787
85	814	866.034135880236	-52.0341358802364
86	1150	1118.27300435748	31.7269956425243
87	1225	1295.90142116044	-70.9014211604406
88	1691	1506.94089288937	184.059107110634
89	1759	1773.46513372946	-14.4651337294576
90	1754	1793.43097722004	-39.4309772200411
91	2100	2150.52505344624	-50.5250534462384
92	2062	2474.58202317727	-412.58202317727
93	2012	1649.13461538531	362.865384614687
94	1897	1579.57425173296	317.42574826704
95	1964	1733.10680944281	230.893190557190
96	2186	1848.41951486649	337.580485133513
97	966	990.716000674308	-24.7160006743081
98	1549	1316.00081055352	232.999189446478
99	1538	1516.72552640784	21.2744735921622
100	1612	1865.30779150913	-253.307791509130
101	2078	2048.08749988090	29.9125001190969
102	2137	2067.22079795441	69.7792020455922
103	2907	2493.16925096456	413.830749035440
104	2249	2815.31344148217	-566.313441482172
105	1883	2074.7657014799	-191.765701479898
106	1739	1898.77284610264	-159.772846102645
107	1828	1973.17415285422	-145.174152854216
108	1868	2074.50887478492	-206.508874784916
109	1138	1014.42752648855	123.572473511449
110	1430	1448.76169452102	-18.7616945210216
111	1809	1560.78133262785	248.218667372145
112	1763	1872.46637985906	-109.466379859062
113	2200	2167.82898868277	32.1710113172339
114	2067	2198.99757413641	-131.997574136406
115	2503	2712.50610912219	-209.506109122188
116	2141	2677.56580949333	-536.565809493326
117	2103	2039.05393585696	63.9460641430412
118	1972	1900.54022236161	71.4597776383923
119	2181	2012.03876025336	168.961239746642
120	2344	2141.73511193062	202.264888069379
121	970	1141.04354334107	-171.043543341066
122	1199	1516.72816114097	-317.728161140968
123	1718	1667.26490517319	50.7350948268104
124	1683	1855.10955042207	-172.109550422071
125	2025	2182.64731643919	-157.647316439192
126	2051	2143.70912748383	-92.709127483828
127	2439	2637.04671442342	-198.046714423419
128	2353	2509.46343944927	-156.463439449273
129	2230	2081.67868386108	148.321316138916
130	1852	1953.33939339838	-101.339393398375
131	2147	2069.79325703407	77.2067429659337
132	2286	2196.18554403938	89.8144559606185
133	1007	1084.64792832794	-77.647928327937
134	1665	1430.19404726694	234.805952733061
135	1642	1769.23922025062	-127.239220250619
136	1518	1875.82278453689	-357.822784536888
137	1831	2191.54539780048	-360.545397800477
138	2207	2144.18528899211	62.8147110078899
139	2822	2637.89742440655	184.102575593454
140	2393	2566.47025484265	-173.470254842647
141	2306	2207.31785414757	98.6821458524314
142	1785	1994.72252902756	-209.722529027564
143	2047	2151.56574794136	-104.565747941355
144	2171	2259.77921774676	-88.7792177467613
145	1212	1070.26508143285	141.734918567153
146	1335	1544.13335047298	-209.133350472983
147	2011	1723.90986670660	287.090133293397
148	1860	1818.52528118570	41.4747188142951
149	1954	2201.59379662456	-247.593796624557
150	2152	2292.73539533376	-140.735395333764
151	2835	2817.79631950020	17.2036804998047
152	2224	2616.82823281669	-392.828232816688
153	2182	2297.14668489135	-115.146684891355
154	1992	1965.49774545083	26.5022545491663
155	2389	2188.10276913204	200.897230867962
156	2724	2345.61843415762	378.381565842381
157	891	1193.66533165030	-302.665331650297
158	1247	1519.99089775425	-272.990897754245
159	2017	1833.60178236905	183.398217630952
160	2257	1846.38991421299	410.610085787007
161	2255	2205.65988299313	49.3401170068732
162	2255	2371.89557184749	-116.895571847493
163	3057	2974.95897107681	82.041028923195
164	3330	2647.35367654457	682.646323455434
165	1896	2520.14220101208	-624.142201012083
166	2096	2137.97226036438	-41.9722603643763
167	2374	2419.71801410648	-45.7180141064846
168	2535	2603.13644850766	-68.1364485076638
169	1041	1148.50094503263	-107.50094503263
170	1728	1528.24102368985	199.758976310149
171	2201	2076.81793642787	124.182063572127
172	2455	2145.67557931209	309.324420687911
173	2204	2408.11543436073	-204.115434360731
174	2660	2502.41008370423	157.589916295772
175	3670	3252.23288577992	417.767114220076
176	2665	3109.720088842	-444.720088841997
177	2639	2442.44363393001	196.556366069986
178	2226	2314.42316529856	-88.423165298559
179	2586	2612.65435638816	-26.6543563881555
180	2684	2806.99681258423	-122.996812584234
181	1185	1211.47427616192	-26.4742761619227
182	1749	1730.07097698978	18.9290230102185
183	2459	2271.6238317361	187.376168263900
184	2618	2405.78894534087	212.211054659133
185	2585	2517.28777215465	67.7122278453548
186	3310	2764.81400431412	545.185995685879
187	3923	3717.08072903676	205.919270963237

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
188	3262.85177136476	3097.72152904186	3427.98201368767
189	2779.90302837335	2608.90564984184	2950.90040690486
190	2522.42600214271	2346.03073013678	2698.82127414865
191	2882.93206219248	2693.71910196576	3072.14502241921
192	3070.84778100358	2870.96264867985	3270.73291332731
193	1340.56310847030	1166.82838026070	1514.29783667991
194	1936.53683464634	1739.11931027989	2133.95435901279
195	2587.65967758135	2357.76423752611	2817.55511763658
196	2714.66020854532	2473.43565412471	2955.88476296592
197	2761.51980800167	2512.87939827370	3010.16021772965
198	3159.45509988435	2884.32834292068	3434.58185684802
199	3991.41730230635	3706.1359745955	4276.69863001720

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275463925j4jw2fi9kpfmuzn/1ceuj1275463761.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275463925j4jw2fi9kpfmuzn/1ceuj1275463761.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275463925j4jw2fi9kpfmuzn/2ceuj1275463761.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275463925j4jw2fi9kpfmuzn/2ceuj1275463761.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275463925j4jw2fi9kpfmuzn/3ceuj1275463761.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275463925j4jw2fi9kpfmuzn/3ceuj1275463761.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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