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Exponential smoothing - Verkoop witte wijn - Innes De Jonghe

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 03 Jun 2010 12:36:19 +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/03/t12755686999wwjcya5cs75h4f.htm/, Retrieved Thu, 03 Jun 2010 14:38:24 +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/03/t12755686999wwjcya5cs75h4f.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 «

1954 2302 3054 2414 2226 2725 2589 3470 2400 3180 4009 3924 2072 2434 2956 2828 2687 2629 3150 4119 3030 3055 3821 4001 2529 2472 3134 2789 2758 2993 3282 3437 2804 3076 3782 3889 2271 2452 3084 2522 2769 3438 2839 3746 2632 2851 3871 3618 2389 2344 2678 2492 2858 2246 2800 3869 3007 3023 3907 4209 2353 2570 2903 2910 3782 2759 2931 3641 2794 3070 3576 4106 2452 2206 2488 2416 2534 2521 3093 3903 2907 3025 3812 4209 2138 2419 2622 2912 2708 2798 3254 2895 3263 3736 4077 4097 2175 3138 2823 2498 2822 2738 4137 3515 3785 3632 4504 4451 2550 2867 3458 2961 3163 2880 3331 3062 3534 3622 4464 5411 2564 2820 3508 3088 3299 2939 3320 3418 3604 3495 4163 4882 2211 3260 2992 2425 2707 3244 3965 3315 3333 3583 4021 4904 2252 2952 3573 3048 3059 2731 3563 3092 3478 3478 4308 5029 2075 3264 3308 3688 3136 2824 3644 4694 2914 3686 4358 5587 2265 3685 3754 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	0.125193707172277
beta	0.0321269389080147
gamma	0.396056119292007

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2072	2006.68440258248	65.3155974175247
14	2434	2346.39287836549	87.607121634514
15	2956	2836.39858085195	119.601419148053
16	2828	2731.91362651944	96.0863734805648
17	2687	2640.20233475900	46.797665241003
18	2629	2614.57841515656	14.4215848434351
19	3150	2782.61972645414	367.380273545858
20	4119	3810.03975875582	308.960241244179
21	3030	2684.05701703421	345.942982965794
22	3055	3630.00274378242	-575.002743782422
23	3821	4467.44341770354	-646.443417703535
24	4001	4305.61930252181	-304.61930252181
25	2529	2281.31173021894	247.688269781060
26	2472	2696.56519508368	-224.565195083681
27	3134	3214.07376951865	-80.073769518654
28	2789	3060.17379420265	-271.173794202645
29	2758	2891.23054258321	-133.230542583205
30	2993	2824.7088875317	168.291112468299
31	3282	3153.18331542525	128.816684574754
32	3437	4192.97405227788	-755.974052277884
33	2804	2896.73829938057	-92.7382993805713
34	3076	3463.36294829674	-387.362948296744
35	3782	4299.54189011614	-517.54189011614
36	3889	4261.80826900495	-372.808269004947
37	2271	2390.40331232745	-119.403312327445
38	2452	2585.69124967042	-133.691249670419
39	3084	3150.80546676277	-66.8054667627653
40	2522	2925.53219914797	-403.532199147966
41	2769	2781.15196243472	-12.1519624347188
42	3438	2825.12146833713	612.878531662873
43	2839	3188.20831564264	-349.208315642635
44	3746	3830.04672401753	-84.0467240175308
45	2632	2845.84390966825	-213.843909668252
46	2851	3280.28633671994	-429.286336719936
47	3871	4040.14534565316	-169.145345653155
48	3618	4085.64321439013	-467.643214390134
49	2389	2309.93304647181	79.0669535281886
50	2344	2518.89393328109	-174.893933281093
51	2678	3089.89421314685	-411.894213146855
52	2492	2704.73420274229	-212.734202742291
53	2858	2713.21286269809	144.787137301912
54	2246	2978.05763015226	-732.057630152264
55	2800	2831.22238017626	-31.2223801762616
56	3869	3542.86747186579	326.132528134206
57	3007	2612.72235820797	394.277641792029
58	3023	3028.77128534522	-5.7712853452158
59	3907	3911.20909719863	-4.20909719862857
60	4209	3867.06883554976	341.931164450237
61	2353	2363.01615714814	-10.0161571481431
62	2570	2471.30432488283	98.6956751171679
63	2903	3001.04715244328	-98.0471524432819
64	2910	2715.17584035319	194.824159646811
65	3782	2908.34781678921	873.652183210786
66	2759	2951.50445293781	-192.504452937806
67	2931	3142.95957301546	-211.959573015459
68	3641	4051.84652003429	-410.846520034286
69	2794	2976.25565874145	-182.255658741448
70	3070	3195.6641803373	-125.664180337298
71	3576	4109.96752865424	-533.967528654239
72	4106	4120.10908941213	-14.1090894121326
73	2452	2411.09343463825	40.9065653617513
74	2206	2565.83325039367	-359.833250393674
75	2488	2967.17985017809	-479.179850178092
76	2416	2732.91512682599	-316.915126825987
77	2534	3063.25844701153	-529.258447011527
78	2521	2592.80590968855	-71.8059096885477
79	3093	2761.03069836954	331.969301630463
80	3903	3587.54827993655	315.451720063454
81	2907	2731.51055778802	175.489442211976
82	3025	2996.81882502637	28.1811749736344
83	3812	3745.12475709111	66.8752429088913
84	4209	3998.77225601464	210.227743985358
85	2138	2370.78136571911	-232.781365719107
86	2419	2346.49111561055	72.5088843894537
87	2622	2748.24707257249	-126.247072572492
88	2912	2612.28682428414	299.713175715859
89	2708	2951.40556406562	-243.405564065621
90	2798	2668.29987289974	129.700127100261
91	3254	3019.19011307488	234.809886925117
92	2895	3865.68067176837	-970.680671768369
93	3263	2796.88139101464	466.11860898536
94	3736	3050.67837743679	685.32162256321
95	4077	3930.09579268135	146.904207318653
96	4097	4260.61214200891	-163.612142008913
97	2175	2370.09476451141	-195.094764511410
98	3138	2462.10353020859	675.896469791409
99	2823	2897.51364926012	-74.5136492601241
100	2498	2921.0046531891	-423.004653189102
101	2822	2987.33156401831	-165.331564018306
102	2738	2839.60962813127	-101.609628131268
103	4137	3211.91206070021	925.087939299788
104	3515	3745.42172085299	-230.421720852994
105	3785	3229.25825010295	555.741749897047
106	3632	3595.60006447554	36.3999355244632
107	4504	4252.58830194226	251.411698057742
108	4451	4508.37179926193	-57.371799261935
109	2550	2479.88389683950	70.1161031604966
110	2867	2942.10319674560	-75.1031967456047
111	3458	3030.20757497546	427.792425024544
112	2961	2989.72167044481	-28.721670444806
113	3163	3220.0325901477	-57.0325901477031
114	2880	3102.55515167413	-222.555151674134
115	3331	3884.91532425601	-553.915324256011
116	3062	3833.51846524582	-771.518465245816
117	3534	3510.45687256395	23.5431274360490
118	3622	3627.27895277377	-5.27895277376638
119	4464	4351.11716344243	112.882836557567
120	5411	4477.1798134772	933.820186522797
121	2564	2566.22711446184	-2.22711446184394
122	2820	2976.15993397383	-156.159933973829
123	3508	3228.6427094204	279.357290579596
124	3088	3006.72945785923	81.2705421407677
125	3299	3242.10418447513	56.8958155248692
126	2939	3076.46546889192	-137.465468891921
127	3320	3764.05441973576	-444.054419735764
128	3418	3641.60513083321	-223.605130833205
129	3604	3665.57747841546	-61.5774784154555
130	3495	3766.41245680783	-271.412456807835
131	4163	4520.02156947913	-357.021569479127
132	4882	4867.27442517698	14.7255748230182
133	2211	2536.96871678841	-325.968716788407
134	3260	2838.13414611879	421.865853881208
135	2992	3307.93248574866	-315.932485748664
136	2425	2946.79597039393	-521.795970393925
137	2707	3078.9868118905	-371.986811890501
138	3244	2801.0461047987	442.953895201298
139	3965	3414.55101211349	550.448987886507
140	3315	3488.27560299426	-173.275602994259
141	3333	3568.63999532627	-235.639995326266
142	3583	3568.62463576879	14.3753642312063
143	4021	4308.7316226438	-287.731622643799
144	4904	4779.49838278938	124.501617210616
145	2252	2380.83043525035	-128.830435250346
146	2952	2956.79252418115	-4.79252418114993
147	3573	3108.42207819868	464.577921801324
148	3048	2768.10331782691	279.896682173094
149	3059	3062.74851001720	-3.74851001720481
150	2731	3117.22529966795	-386.225299667947
151	3563	3672.98295548228	-109.982955482281
152	3092	3412.31752853798	-320.317528537983
153	3478	3448.96268315430	29.0373168456954
154	3478	3567.29143929519	-89.2914392951898
155	4308	4183.54837152876	124.451628471235
156	5029	4852.26900531843	176.730994681573
157	2075	2353.25703410054	-278.257034100538
158	3264	2952.15085465155	311.849145348455
159	3308	3307.36968573034	0.630314269658811
160	3688	2845.26743863561	842.73256136439
161	3136	3115.79939388806	20.2006061119350
162	2824	3038.10125461901	-214.101254619015
163	3644	3731.10337236326	-87.1033723632554
164	4694	3392.18642699610	1301.81357300390
165	2914	3779.56839876408	-865.568398764083
166	3686	3754.58016790621	-68.5801679062129
167	4358	4497.78163549096	-139.781635490962
168	5587	5195.1997465914	391.800253408599
169	2265	2399.6679296203	-134.667929620299
170	3685	3285.41328892342	399.586711076584
171	3754	3565.51555948623	188.484440513767
172	3708	3399.09318361850	308.906816381505
173	3210	3314.01229927252	-104.012299272516
174	3517	3132.59718815175	384.40281184825
175	3905	4014.20649785714	-109.206497857137

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
176	4150.79235735269	3825.37189971189	4476.21281499348
177	3596.6904443016	3262.27826021848	3931.10262838472
178	3984.29295923712	3633.16360364715	4335.4223148271
179	4767.63269205472	4388.79309947495	5146.47228463448
180	5740.43268725371	5322.21488395201	6158.65049055542
181	2512.61125442570	2164.26115469042	2860.96135416099
182	3684.40927969676	3287.08795951662	4081.73059987691
183	3852.98020094208	3435.38101169249	4270.57939019167
184	3697.09423311585	3273.3896330304	4120.79883320131
185	3419.1203184623	2996.20803643922	3842.03260048538
186	3418.72856826715	2982.3654334957	3855.0917030386
187	4101.1979852377	3727.29819122541	4475.09777925

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/03/t12755686999wwjcya5cs75h4f/1wi9l1275568577.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/03/t12755686999wwjcya5cs75h4f/1wi9l1275568577.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/03/t12755686999wwjcya5cs75h4f/269q61275568577.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/03/t12755686999wwjcya5cs75h4f/269q61275568577.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/03/t12755686999wwjcya5cs75h4f/369q61275568577.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/03/t12755686999wwjcya5cs75h4f/369q61275568577.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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