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ws 8

*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: Tue, 30 Nov 2010 16:11:48 +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/Nov/30/t12911335699w7tfx8mp473irm.htm/, Retrieved Tue, 30 Nov 2010 17:12:53 +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/Nov/30/t12911335699w7tfx8mp473irm.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 «

2938 2909 3141 2427 3059 2918 2901 2823 2798 2892 2967 2397 3458 3024 3100 2904 3056 2771 2897 2772 2857 3020 2648 2364 3194 3013 2560 3074 2746 2846 3184 2354 3080 2963 2430 2296 2416 2647 2789 2685 2666 2882 2953 2127 2563 3061 2809 2861 2781 2555 3206 2570 2410 3195 2736 2743 2934 2668 2907 2866 2983 2878 3225 2515 3193 2663 2908 2896 2853 3028 3053 2455 3401 2969 3243 2849 3296 3121 3194 3023 2984 3525 3116 2383 3294 2882 2820 2583 2803 2767 2945 2716 2644 2956 2598 2171 2994 2645 2724 2550 2707 2679 2878 2307 2496 2637 2436 2426 2607 2533 2888 2520 2229 2804 2661 2547 2509 2465 2629 2706 2666 2432 2836 2888 2566 2802 2611 2683 2675 2434 2693 2619 2903 2550 2900 2456 2912 2883 2464 2655 2447 2592 2698 2274 2901 2397 3004 2614 2882 2671 2761 2806 2414 2673 2748 2112 2903 2633 2684 2861 2504 2708 2961 2535 2688 2699 2469 2585 2582 2480 2709 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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.137854413836711
beta	0.00578274385342074
gamma	0.233989636519689

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3458	3422.40518162393	35.5948183760665
14	3024	2998.60517426114	25.3948257388574
15	3100	3080.79429705722	19.2057029427774
16	2904	2882.68719896488	21.3128010351197
17	3056	3048.63756371472	7.36243628527927
18	2771	2782.37901160563	-11.3790116056325
19	2897	2951.98613043277	-54.9861304327719
20	2772	2842.95464845602	-70.954648456016
21	2857	2808.04027239026	48.9597276097415
22	3020	2893.61231857154	126.387681428457
23	2648	2969.37556993068	-321.375569930676
24	2364	2364.15648759912	-0.156487599118918
25	3194	3441.44106969978	-247.441069699777
26	3013	2976.20079574247	36.7992042575265
27	2560	3058.35775894735	-498.357758947352
28	3074	2788.55898274627	285.441017253727
29	2746	2987.54855207437	-241.548552074371
30	2846	2682.43953945554	163.560460544459
31	3184	2866.74908255775	317.250917442254
32	2354	2805.49072674787	-451.490726747872
33	3080	2741.68510612475	338.314893875249
34	2963	2882.37312077511	80.626879224892
35	2430	2861.07017885997	-431.070178859974
36	2296	2305.01311469469	-9.01311469469147
37	2416	3330.66759057353	-914.66759057353
38	2647	2829.73229124656	-182.732291246560
39	2789	2772.43638769641	16.5636123035883
40	2685	2730.91987024959	-45.9198702495883
41	2666	2776.83436164114	-110.834361641138
42	2882	2570.48872899831	311.511271001694
43	2953	2805.33628640245	147.663713597548
44	2127	2564.62161996628	-437.621619966281
45	2563	2661.07162863300	-98.0716286329962
46	3061	2688.28349738175	372.716502618251
47	2809	2602.91886874011	206.081131259893
48	2861	2219.24546054001	641.754539459988
49	2781	3151.83603455409	-370.836034554090
50	2555	2873.8848649455	-318.884864945500
51	3206	2838.27472611076	367.725273889239
52	2570	2833.09275401697	-263.092754016972
53	2410	2836.33082494429	-426.330824944294
54	3195	2671.79943704686	523.200562953137
55	2736	2903.0502878742	-167.050287874201
56	2743	2500.90305204697	242.096947953030
57	2934	2760.11919310883	173.880806891166
58	2668	2920.57670829879	-252.57670829879
59	2907	2715.68054441769	191.319455582312
60	2866	2418.13393696478	447.866063035221
61	2983	3119.84049864061	-136.840498640615
62	2878	2884.93089264961	-6.93089264961054
63	3225	3031.3896562673	193.610343732701
64	2515	2875.36213191657	-360.362131916567
65	3193	2832.59697759902	360.403022400985
66	2663	2969.03574533904	-306.035745339044
67	2908	2947.02867794113	-39.0286779411263
68	2896	2645.47282865107	250.527171348928
69	2853	2892.50086685623	-39.5008668562332
70	3028	2937.75327268027	90.2467273197299
71	3053	2870.17979355190	182.820206448097
72	2455	2623.72309981415	-168.723099814146
73	3401	3122.49152914244	278.50847085756
74	2969	2971.39388162149	-2.39388162148953
75	3243	3159.28471881766	83.7152811823435
76	2849	2876.61628131111	-27.6162813111146
77	3296	3025.65228971797	270.347710282028
78	3121	3015.69043134138	105.309568658622
79	3194	3105.03789434987	88.9621056501337
80	3023	2880.42577044919	142.574229550809
81	2984	3054.86431943051	-70.86431943051
82	3525	3122.74308615555	402.256913844450
83	3116	3117.8810162738	-1.88101627379910
84	2383	2775.92156185318	-392.921561853182
85	3294	3334.70299387297	-40.702993872972
86	2882	3083.37718221263	-201.377182212630
87	2820	3261.49359608024	-441.493596080236
88	2583	2883.8300793168	-300.830079316801
89	2803	3054.96031689203	-251.960316892034
90	2767	2938.93470629782	-171.93470629782
91	2945	2985.77636065501	-40.7763606550143
92	2716	2753.00249700534	-37.0024970053441
93	2644	2858.39275895808	-214.392758958081
94	2956	3000.58009200437	-44.5800920043748
95	2598	2850.88571684403	-252.885716844031
96	2171	2393.53238609267	-222.532386092675
97	2994	3045.08676700320	-51.0867670032048
98	2645	2758.13781534055	-113.137815340552
99	2724	2898.27093773928	-174.270937739278
100	2550	2584.32671806898	-34.3267180689845
101	2707	2800.77170315402	-93.7717031540164
102	2679	2721.54044517074	-42.5404451707391
103	2878	2811.62534044241	66.3746595575903
104	2307	2593.41613650956	-286.416136509562
105	2496	2627.47141273665	-131.471412736649
106	2637	2814.24604208603	-177.246042086033
107	2436	2603.03455725743	-167.034557257429
108	2426	2162.50152212482	263.498477875175
109	2607	2914.89317901695	-307.893179016946
110	2533	2579.06937186539	-46.0693718653852
111	2888	2715.21385861468	172.786141385321
112	2520	2476.71930043956	43.2806995604383
113	2229	2691.30757987716	-462.307579877164
114	2804	2570.75007086764	233.249929132360
115	2661	2720.18852953502	-59.1885295350189
116	2547	2412.76305513361	134.236944866393
117	2509	2535.66279636221	-26.6627963622095
118	2465	2727.33314429513	-262.333144295130
119	2629	2506.06583979411	122.934160205891
120	2706	2192.20402442006	513.795975579937
121	2666	2863.87617318974	-197.876173189741
122	2432	2596.16944140611	-164.169441406112
123	2836	2760.22178266141	75.7782173385922
124	2888	2482.18944523287	405.810554767129
125	2566	2645.00988814034	-79.0098881403383
126	2802	2718.16393883837	83.8360611616349
127	2611	2788.44668684973	-177.446686849731
128	2683	2504.08103447305	178.918965526947
129	2675	2601.05910430652	73.9408956934803
130	2434	2759.51332030403	-325.513320304027
131	2693	2607.66488658061	85.3351134193904
132	2619	2367.84703867423	251.152961325766
133	2903	2859.9128476899	43.0871523101023
134	2550	2632.58383963681	-82.5838396368113
135	2900	2856.71364829638	43.2863517036203
136	2456	2641.17985851695	-185.179858516947
137	2912	2624.65343156555	287.346568434448
138	2883	2781.38292484963	101.617075150371
139	2464	2801.64181612116	-337.641816121165
140	2655	2567.18995275480	87.8100472452034
141	2447	2630.46470664228	-183.464706642280
142	2592	2672.68008166223	-80.6800816622299
143	2698	2637.48871502547	60.5112849745274
144	2274	2427.703940712	-153.703940712002
145	2901	2821.66612296754	79.3338770324572
146	2397	2573.69222964465	-176.692229644645
147	3004	2809.87629489622	194.123705103777
148	2614	2568.80246543478	45.1975345652249
149	2882	2679.29803629241	202.701963707590
150	2671	2786.76284915367	-115.762849153666
151	2761	2688.14034050735	72.8596594926476
152	2806	2596.13135090133	209.86864909867
153	2414	2621.63031466415	-207.630314664154
154	2673	2681.35315273477	-8.35315273476772
155	2748	2684.77674091374	63.2232590862577
156	2112	2432.31506942704	-320.315069427041
157	2903	2850.35135629665	52.6486437033468
158	2633	2547.05929964404	85.9407003559568
159	2684	2894.47316074841	-210.473160748406
160	2861	2567.47681661262	293.523183387385
161	2504	2744.07328749078	-240.073287490779
162	2708	2725.99595467241	-17.9959546724108
163	2961	2678.72167222405	282.278327775951
164	2535	2643.2073854769	-108.207385476902
165	2688	2540.3673898731	147.632610126898
166	2699	2689.28140326720	9.71859673279778
167	2469	2709.66580900261	-240.665809002614
168	2585	2337.72725984697	247.272740153027
169	2582	2909.48759748182	-327.487597481824
170	2480	2560.44558509239	-80.4455850923878
171	2709	2824.93061849702	-115.930618497020
172	2441	2612.52026222978	-171.520262229780
173	2182	2616.87375213901	-434.873752139014
174	2585	2616.09677912458	-31.0967791245835
175	2881	2626.93542578866	254.064574211342
176	2422	2508.07901519761	-86.0790151976094
177	2690	2459.23972970158	230.760270298420
178	2659	2591.19651239118	67.8034876088223
179	2535	2568.52873052359	-33.5287305235893
180	2613	2323.19482294785	289.805177052150

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
181	2784.52065649376	2326.3872135876	3242.65409939993
182	2530.37229437991	2067.85617560233	2992.8884131575
183	2798.76420968343	2331.85672472334	3265.67169464353
184	2591.18915497455	2119.88157343289	3062.49673651621
185	2566.26510468715	2090.54865803925	3041.98155133505
186	2707.44402167060	2227.30990514554	3187.57813819565
187	2780.67220952523	2296.11158390634	3265.23283514413
188	2558.54732977307	2069.55132312321	3047.54333642293
189	2585.93370368901	2092.49341300445	3079.37399437356
190	2653.46373136613	2155.57022416224	3151.35723857002
191	2601.21117131641	2098.85548714845	3103.56685548436
192	2425.95753515185	1919.13068707391	2932.78438322979

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911335699w7tfx8mp473irm/1lzip1291133504.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911335699w7tfx8mp473irm/1lzip1291133504.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911335699w7tfx8mp473irm/2lzip1291133504.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911335699w7tfx8mp473irm/2lzip1291133504.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911335699w7tfx8mp473irm/3d8ir1291133504.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911335699w7tfx8mp473irm/3d8ir1291133504.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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