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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: Sun, 06 Jun 2010 16:48:19 +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/06/t12758429713lakcwzm7531rgn.htm/, Retrieved Sun, 06 Jun 2010 18:49:36 +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/06/t12758429713lakcwzm7531rgn.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	0.122923936061106
beta	0.0628781616526975
gamma	0.35503071893546

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2072	1985.84268162393	86.1573183760677
14	2434	2331.83381956774	102.166180432265
15	2956	2837.70749586882	118.292504131177
16	2828	2728.72779345768	99.2722065423186
17	2687	2639.26067236362	47.7393276363823
18	2629	2618.41124858815	10.5887514118508
19	3150	2809.57697266319	340.423027336813
20	4119	3751.37676577387	367.623234226128
21	3030	2757.36156032045	272.638439679548
22	3055	3592.02773556861	-537.027735568609
23	3821	4348.72407950558	-527.72407950558
24	4001	4209.7351640861	-208.735164086099
25	2529	2364.00602923632	164.993970763677
26	2472	2726.60730668541	-254.607306685407
27	3134	3192.82320107236	-58.8232010723636
28	2789	3053.95672088088	-264.956720880879
29	2758	2898.6628602674	-140.6628602674
30	2993	2836.62229787113	156.377702128866
31	3282	3143.07883611707	138.921163882932
32	3437	4061.68473144673	-624.684731446733
33	2804	2901.54979309679	-97.5497930967904
34	3076	3421.16448977267	-345.164489772670
35	3782	4188.40004272526	-406.400042725262
36	3889	4148.64968698426	-259.649686984263
37	2271	2397.63883920792	-126.638839207915
38	2452	2576.07994645867	-124.079946458666
39	3084	3102.66234208457	-18.6623420845667
40	2522	2888.21186409838	-366.211864098378
41	2769	2742.05940324039	26.9405967596081
42	3438	2777.29625715575	660.703742844251
43	2839	3128.38860904603	-289.388609046026
44	3746	3741.33388614964	4.6661138503614
45	2632	2812.33696108994	-180.336961089944
46	2851	3233.66251037908	-382.662510379085
47	3871	3965.92261036955	-94.9226103695464
48	3618	4001.26623179294	-383.26623179294
49	2389	2266.63210520868	122.367894791320
50	2344	2468.55758762906	-124.557587629064
51	2678	3019.9821309966	-341.982130996601
52	2492	2647.14080399939	-155.140803999393
53	2858	2640.56474709947	217.43525290053
54	2246	2889.24455719202	-643.244557192023
55	2800	2766.80344368023	33.196556319765
56	3869	3496.06213210009	372.937867899915
57	3007	2542.66774864412	464.332251355881
58	3023	2973.16047335934	49.8395266406642
59	3907	3844.45119617801	62.5488038219873
60	4209	3806.84868640701	402.151313592991
61	2353	2329.76460618054	23.2353938194615
62	2570	2445.40280050067	124.597199499333
63	2903	2964.46494134045	-61.4649413404509
64	2910	2691.16850706248	218.831492937523
65	3782	2856.35147252505	925.648527474953
66	2759	2939.32822162209	-180.328221622091
67	2931	3103.25163278733	-172.251632787325
68	3641	3930.28429496249	-289.284294962492
69	2794	2936.06447428926	-142.064474289257
70	3070	3170.3794106414	-100.379410641397
71	3576	4033.43241840469	-457.432418404686
72	4106	4039.91144206063	66.0885579393744
73	2452	2403.18067424855	48.8193257514458
74	2206	2553.37813390341	-347.378133903406
75	2488	2952.68895069317	-464.688950693167
76	2416	2710.19466911439	-294.194669114394
77	2534	3021.53097666638	-487.530976666377
78	2521	2564.60394020959	-43.6039402095853
79	3093	2727.10450740374	365.895492596256
80	3903	3567.26062737423	335.739372625771
81	2907	2683.95972539023	223.040274609765
82	3025	2967.20294616971	57.7970538302902
83	3812	3730.80775400432	81.1922459956754
84	4209	3962.96892683598	246.031073164016
85	2138	2340.82441112322	-202.824411123217
86	2419	2332.61676822983	86.3832317701654
87	2622	2747.97003496763	-125.970034967634
88	2912	2602.07257418404	309.927425815963
89	2708	2934.00668175509	-226.006681755093
90	2798	2656.02211769573	141.977882304272
91	3254	2978.844039266	275.155960734003
92	2895	3807.74977932082	-912.74977932082
93	3263	2735.53052504221	527.469474957786
94	3736	3006.73757444092	729.262425559083
95	4077	3867.35356930211	209.646430697892
96	4097	4174.81369316516	-77.8136931651561
97	2175	2378.76906557102	-203.769065571024
98	3138	2466.17086096644	671.829139033559
99	2823	2897.55952585991	-74.55952585991
100	2498	2904.30720429103	-406.307204291029
101	2822	2986.37093875851	-164.370938758506
102	2738	2836.08156851991	-98.08156851991
103	4137	3174.54150425071	962.458495749285
104	3515	3727.02166685362	-212.021666853620
105	3785	3203.81232021901	581.187679780989
106	3632	3559.27921233145	72.7207876685475
107	4504	4187.13378152134	316.866218478655
108	4451	4428.83653876027	22.1634612397338
109	2550	2617.20779232954	-67.2077923295383
110	2867	3006.45075866478	-139.450758664777
111	3458	3111.82887619607	346.171123803929
112	2961	3076.37613699992	-115.376136999919
113	3163	3281.17149012045	-118.171490120448
114	2880	3169.19294939455	-289.192949394546
115	3331	3824.91406458938	-493.914064589375
116	3062	3831.90729050255	-769.907290502546
117	3534	3482.06129244458	51.9387075554214
118	3622	3604.99338399486	17.0066160051406
119	4464	4292.44644409626	171.553555903743
120	5411	4413.81936884119	997.180631158812
121	2564	2691.05023608226	-127.050236082257
122	2820	3046.81482232811	-226.814822328106
123	3508	3288.36918390758	219.630816092424
124	3088	3088.36093058357	-0.360930583570735
125	3299	3302.03297606169	-3.03297606168780
126	2939	3147.45246753272	-208.452467532723
127	3320	3746.47363493709	-426.473634937086
128	3418	3673.45993355708	-255.459933557082
129	3604	3644.38614000392	-40.3861400039191
130	3495	3745.99878241764	-250.998782417642
131	4163	4447.4672487195	-284.467248719498
132	4882	4765.1862314213	116.813768578697
133	2211	2572.63210130036	-361.632101300363
134	3260	2855.18846143743	404.81153856257
135	2992	3304.97813353914	-312.978133539136
136	2425	2958.45491158245	-533.454911582449
137	2707	3089.10291247523	-382.102912475235
138	3244	2804.36836860031	439.631631399694
139	3965	3400.58248683110	564.417513168898
140	3315	3495.70091234209	-180.700912342089
141	3333	3536.44233408617	-203.442334086170
142	3583	3544.82266004058	38.1773399594249
143	4021	4266.04483352958	-245.044833529581
144	4904	4708.4977029165	195.502297083496
145	2252	2372.17517874422	-120.175178744218
146	2952	2920.48238460767	31.5176153923312
147	3573	3095.39618782337	477.603812176634
148	3048	2778.03362813544	269.966371864562
149	3059	3061.41375285475	-2.41375285474896
150	2731	3089.00893130404	-358.008931304042
151	3563	3629.64351109778	-66.6435110977814
152	3092	3413.90280922877	-321.902809228772
153	3478	3427.84934703614	50.1506529638605
154	3478	3542.2437317922	-64.2437317922008
155	4308	4161.49572906673	146.504270933275
156	5029	4791.09931454002	237.900685459981
157	2075	2363.85625030521	-288.856250305212
158	3264	2939.52635862239	324.473641377605
159	3308	3292.48448941245	15.5155105875529
160	3688	2853.21933533991	834.780664660094
161	3136	3125.13319850902	10.8668014909777
162	2824	3047.65581804721	-223.655818047206
163	3644	3700.59537930672	-56.5953793067156
164	4694	3411.74437099281	1282.25562900719
165	2914	3756.2720860273	-842.272086027302
166	3686	3735.98583927871	-49.985839278705
167	4358	4433.36590475871	-75.3659047587116
168	5587	5073.19211581412	513.807884185875
169	2265	2527.00686188418	-262.006861884177
170	3685	3308.33757430996	376.662425690035
171	3754	3583.28421186176	170.715788138243
172	3708	3431.18598058334	276.814019416664
173	3210	3386.62104665384	-176.62104665384
174	3517	3220.28636201448	296.713637985523
175	3905	4000.45180595504	-95.451805955035
176	3670	4134.66673322833	-464.666733228330
177	4221	3600.33798063106	620.662019368937
178	4404	4015.3344371608	388.665562839199
179	5086	4770.86653169258	315.133468307419
180	5725	5657.30927147469	67.690728525311
181	2367	2826.40986638851	-459.409866388513
182	3819	3792.52826834768	26.4717316523179
183	4067	3967.77056413013	99.2294358698682
184	4022	3846.84221389780	175.157786102205
185	3937	3654.72035250663	282.279647493373
186	4365	3701.86740927603	663.132590723971
187	4290	4417.47133932666	-127.471339326661

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
188	4445.04617652993	3762.81519710919	5127.27715595067
189	4321.65230403539	3633.62303773862	5009.68157033217
190	4599.17301047653	3904.6967437247	5293.64927722836
191	5292.0872371324	4590.49350690679	5993.680967358
192	6068.36137167132	5358.96069890571	6777.76204443693
193	3070.10443495828	2352.19110218386	3788.0177677327
194	4252.64092707115	3525.49576242709	4979.78609171521
195	4455.72801470876	3718.62114498182	5192.8348844357
196	4353.92112982561	3606.11466703997	5101.72759261125
197	4179.94680165021	3420.69743073862	4939.1961725618
198	4315.12857909415	3543.69001812892	5086.56714005939
199	4702.04706140015	3917.67237049289	5486.4217523074

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t12758429713lakcwzm7531rgn/1sfx71275842896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t12758429713lakcwzm7531rgn/1sfx71275842896.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t12758429713lakcwzm7531rgn/23oes1275842896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t12758429713lakcwzm7531rgn/23oes1275842896.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t12758429713lakcwzm7531rgn/33oes1275842896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t12758429713lakcwzm7531rgn/33oes1275842896.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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