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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 11:51:41 +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/06/t1275825198pehuua0hci336q7.htm/, Retrieved Sun, 06 Jun 2010 13:53:19 +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/t1275825198pehuua0hci336q7.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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.124155812050704
beta	0.0536097781034414
gamma	0.356465314077196

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2072	2006.68440258247	65.3155974175252
14	2434	2346.51327867726	87.4867213227371
15	2956	2836.92741456618	119.072585433819
16	2828	2733.01775093605	94.9822490639458
17	2687	2642.01053242205	44.9894675779456
18	2629	2617.15256803355	11.8474319664538
19	3150	2786.13241341801	363.867586581986
20	4119	3816.43640110982	302.563598890181
21	3030	2690.17525022614	339.824749773859
22	3055	3640.99875004146	-585.998750041461
23	3821	4483.67975777213	-662.679757772129
24	4001	4321.76779125718	-320.76779125718
25	2529	2286.85990746329	242.140092536712
26	2472	2702.55848685276	-230.558486852761
27	3134	3220.58021592353	-86.580215923529
28	2789	3066.4813098099	-277.481309809904
29	2758	2897.77276404329	-139.772764043287
30	2993	2830.57717652293	162.422823477075
31	3282	3145.0765775793	136.923422420702
32	3437	4189.4568929726	-752.456892972604
33	2804	2888.78923666848	-84.7892366684832
34	3076	3487.56067145411	-411.560671454114
35	3782	4319.73779541977	-537.73779541977
36	3889	4262.51394493951	-373.513944939512
37	2271	2371.24121826183	-100.241218261831
38	2452	2580.17404194888	-128.174041948881
39	3084	3132.66698735364	-48.6669873536439
40	2522	2913.08527278898	-391.085272788984
41	2769	2762.20047918135	6.79952081864849
42	3438	2793.52873253637	644.471267463632
43	2839	3146.42547274745	-307.425472747449
44	3746	3814.28307101164	-68.2830710116427
45	2632	2812.27343210227	-180.273432102267
46	2851	3273.20390376262	-422.203903762625
47	3871	4025.83722224876	-154.837222248764
48	3618	4053.04567994648	-435.045679946483
49	2389	2275.37685166451	113.623148335492
50	2344	2492.20793929224	-148.207939292241
51	2678	3047.34185997103	-369.341859971025
52	2492	2681.60552468653	-189.60552468653
53	2858	2671.59250627004	186.407493729958
54	2246	2905.95801327411	-659.958013274107
55	2800	2785.52464524042	14.4753547595806
56	3869	3493.0534495958	375.946550404201
57	3007	2567.30721656218	439.692783437817
58	3023	3003.90058544109	19.099414558912
59	3907	3865.1081240935	41.8918759065036
60	4209	3823.99797686431	385.002023135691
61	2353	2316.2783716579	36.7216283420994
62	2570	2441.24990062065	128.750099379351
63	2903	2968.28129281068	-65.281292810675
64	2910	2692.85915208029	217.140847919707
65	3782	2863.13365363441	918.866346365593
66	2759	2924.79122102555	-165.791221025547
67	2931	3110.89015621442	-179.890156214422
68	3641	4011.18604398834	-370.186043988338
69	2794	2939.23060426681	-145.230604266809
70	3070	3192.69618549742	-122.696185497422
71	3576	4097.51371871536	-521.513718715363
72	4106	4097.2866256022	8.71337439780109
73	2452	2389.90307431267	62.0969256873268
74	2206	2551.00115020026	-345.001150200264
75	2488	2957.24765734082	-469.247657340819
76	2416	2716.1453476335	-300.1453476335
77	2534	3006.6231439636	-472.623143963604
78	2521	2577.90875343057	-56.9087534305713
79	3093	2735.82123433235	357.17876566765
80	3903	3552.85181776422	350.14818223578
81	2907	2693.33987981612	213.660120183878
82	3025	2974.78434636844	50.215653631556
83	3812	3724.92260379711	87.0773962028907
84	4209	3952.10928369196	256.890716308043
85	2138	2338.05063021236	-200.050630212359
86	2419	2332.48703844692	86.5129615530768
87	2622	2739.15511764967	-117.155117649666
88	2912	2595.00556722172	316.994432778283
89	2708	2915.50992618349	-207.509926183486
90	2798	2648.01182325873	149.988176741274
91	3254	2980.73482507422	273.26517492578
92	2895	3826.48267808477	-931.482678084767
93	3263	2764.04124349259	498.958756507412
94	3736	3035.59455896144	700.405441038556
95	4077	3918.67572839792	158.32427160208
96	4097	4229.81376411947	-132.813764119465
97	2175	2362.58427851089	-187.584278510886
98	3138	2456.68665562647	681.31334437353
99	2823	2907.03370140944	-84.0337014094366
100	2498	2911.35163174407	-413.351631744071
101	2822	2987.31679939038	-165.316799390376
102	2738	2834.91846173159	-96.9184617315932
103	4137	3192.55079473644	944.449205263558
104	3515	3774.56389739263	-259.563897392635
105	3785	3202.96659666942	582.033403330578
106	3632	3580.64368689807	51.3563131019318
107	4504	4268.98814790624	235.011852093761
108	4451	4524.27661165067	-73.2766116506718
109	2550	2498.78777913492	51.2122208650844
110	2867	2932.91430405926	-65.9143040592608
111	3458	3062.53179323574	395.468206764261
112	2961	3019.71213819939	-58.7121381993943
113	3163	3246.88031500576	-83.8803150057574
114	2880	3122.87638257488	-242.876382574884
115	3331	3860.99203964259	-529.992039642589
116	3062	3887.90037925996	-825.900379259963
117	3534	3491.87929395788	42.1207060421179
118	3622	3631.18281892709	-9.18281892708637
119	4464	4365.25842865509	98.741571344909
120	5411	4497.29671399659	913.70328600341
121	2564	2578.74666514878	-14.7466651487766
122	2820	2973.61356528424	-153.613565284244
123	3508	3235.34530925175	272.654690748249
124	3088	3028.52399453481	59.4760054651888
125	3299	3261.6193104287	37.380689571296
126	2939	3096.40155017272	-157.401550172723
127	3320	3763.0008003276	-443.000800327601
128	3418	3698.63033380649	-280.63033380649
129	3604	3641.11081164881	-37.1108116488108
130	3495	3758.97660881577	-263.976608815771
131	4163	4514.24377669472	-351.243776694721
132	4882	4837.96371859386	44.0362814061373
133	2211	2540.77422478325	-329.774224783253
134	3260	2834.20922019999	425.790779800008
135	2992	3291.53208341414	-299.532083414142
136	2425	2947.75341414884	-522.753414148842
137	2707	3076.47183036255	-369.471830362551
138	3244	2802.82297760127	441.177022398728
139	3965	3406.54928212812	558.450717871879
140	3315	3508.84602973994	-193.84602973994
141	3333	3530.68986793644	-197.689867936445
142	3583	3548.22052936961	34.7794706303889
143	4021	4286.81707791326	-265.817077913255
144	4904	4725.84302036935	178.156979630648
145	2252	2378.47203106419	-126.472031064187
146	2952	2920.46792025871	31.5320797412887
147	3573	3090.73098727129	482.269012728707
148	3048	2771.92875568447	276.071244315528
149	3059	3059.25805954162	-0.258059541619787
150	2731	3091.30730850174	-360.307308501737
151	3563	3641.73775166279	-78.7377516627898
152	3092	3429.39323341164	-337.393233411637
153	3478	3429.04665965143	48.9533403485739
154	3478	3548.78189383512	-70.7818938351211
155	4308	4173.95287106012	134.047128939877
156	5029	4805.03432873576	223.965671264239
157	2075	2353.67458243103	-278.674582431029
158	3264	2924.5783086329	339.421691367099
159	3308	3276.12800671071	31.871993289285
160	3688	2837.66307234422	850.336927655776
161	3136	3115.64191049181	20.3580895081859
162	2824	3037.35125485931	-213.351254859309
163	3644	3716.26649725859	-72.266497258589
164	4694	3418.99913678026	1275.00086321974
165	2914	3769.78903114743	-855.789031147428
166	3686	3754.3729589265	-68.3729589265013
167	4358	4500.77949409156	-142.779494091558
168	5587	5174.72277018426	412.277229815739
169	2265	2420.543607665	-155.543607665001
170	3685	3267.76220937619	417.237790623808
171	3754	3560.15730416595	193.842695834053
172	3708	3380.71195611707	327.288043882932
173	3210	3334.76665479184	-124.76665479184
174	3517	3159.97382358561	357.026176414389
175	3905	4030.43434869364	-125.434348693638
176	3670	4150.38515686925	-480.385156869245
177	4221	3594.50268454086	626.497315459143
178	4404	4044.38453469562	359.615465304384
179	5086	4905.08847376223	180.911526237766
180	5725	5904.43843243454	-179.438432434537
181	2367	2611.3595157129	-244.359515712898
182	3819	3733.69998593864	85.3000140613608
183	4067	3935.14530520931	131.854694790689
184	4022	3779.80711914581	242.192880854191
185	3937	3567.46347861794	369.536521382058
186	4365	3608.92975057157	756.070249428426
187	4290	4467.98885562927	-177.988855629271

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
188	4481.8087701323	4178.07553295887	4785.54200730573
189	4319.09458013844	4003.09434031588	4635.09481996101
190	4649.4897167909	4315.80131573456	4983.17811784725
191	5498.51133114115	5134.15069860457	5862.87196367773
192	6459.68754818531	6054.43573453662	6864.939361834
193	2813.61806306628	2484.09217619528	3143.14394993728
194	4232.15453554027	3843.99328295938	4620.31578812116
195	4470.40153230887	4055.90918673977	4884.89387787797
196	4322.75868422456	3898.38269665862	4747.1346717905
197	4100.38415613738	3670.68868123454	4530.07963104021
198	4223.86656629215	3769.78557606442	4677.94755651987
199	4728.11408053421	4323.90560368386	5132.32255738456

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275825198pehuua0hci336q7/1ugwh1275825097.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275825198pehuua0hci336q7/1ugwh1275825097.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275825198pehuua0hci336q7/2ugwh1275825097.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275825198pehuua0hci336q7/2ugwh1275825097.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275825198pehuua0hci336q7/3ugwh1275825097.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275825198pehuua0hci336q7/3ugwh1275825097.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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