Home » date » 2009 » Jun » 03 »

opdracht 10 - eigen reeks: droge witte wijn Australië - Evelien Anthonissen

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 03 Jun 2009 07:35:41 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/03/t1244036426djm4kouk0f09fwo.htm/, Retrieved Wed, 03 Jun 2009 15:40:26 +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/2009/Jun/03/t1244036426djm4kouk0f09fwo.htm/},
    year = {2009},
}
@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 = {2009},
    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:

Evelien Anthonissen

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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.122926496035536
beta	0.0628758944477284
gamma	0.3550319570393

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2072	1985.84268162393	86.1573183760681
14	2434	2331.8340299847	102.165970015300
15	2956	2837.70791816454	118.292081835465
16	2828	2728.72842567869	99.2715743213057
17	2687	2639.26142343894	47.738576561057
18	2629	2618.41196055895	10.5880394410538
19	3150	2809.57754848236	340.422451517636
20	4119	3751.37802201576	367.621977984239
21	3030	2757.36342998386	272.636570016143
22	3055	3592.02985353973	-537.029853539726
23	3821	4348.72438939199	-527.724389391993
24	4001	4209.73397170188	-208.733971701879
25	2529	2364.00438489807	164.995615101928
26	2472	2726.60613803078	-254.606138030775
27	3134	3192.82141403267	-58.8214140326686
28	2789	3053.95490779798	-264.954907797978
29	2758	2898.66056445638	-140.660564456383
30	2993	2836.61998289932	156.380017100676
31	3282	3143.07735942779	138.922640572210
32	3437	4061.68363251219	-624.683632512194
33	2804	2901.54715194120	-97.5471519411958
34	3076	3421.16186449278	-345.161864492782
35	3782	4188.39764373804	-406.397643738035
36	3889	4148.6473556987	-259.647355698698
37	2271	2397.63668945409	-126.636689454093
38	2452	2576.07782070433	-124.077820704326
39	3084	3102.66072416236	-18.6607241623569
40	2522	2888.21071493319	-366.210714933193
41	2769	2742.05805079658	26.9419492034181
42	3438	2777.29567812917	660.704321870835
43	2839	3128.39002998256	-289.390029982563
44	3746	3741.33435553267	4.66564446733264
45	2632	2812.33817008831	-180.338170088309
46	2851	3233.6632711899	-382.663271189899
47	3871	3965.92325211251	-94.9232521125068
48	3618	4001.26755773092	-383.267557730925
49	2389	2266.63298796773	122.367012032265
50	2344	2468.55887358033	-124.558873580335
51	2678	3019.98345992279	-341.983459922785
52	2492	2647.14131476486	-155.141314764858
53	2858	2640.56559660929	217.434403390708
54	2246	2889.24630185622	-643.246301856221
55	2800	2766.80294256553	33.197057434465
56	3869	3496.06223569706	372.937764302944
57	3007	2542.66942181805	464.330578181948
58	3023	2973.16342116909	49.836578830907
59	3907	3844.45490927291	62.5450907270874
60	4209	3806.85276087344	402.147239126561
61	2353	2329.76993975746	23.2300602425412
62	2570	2445.40734636475	124.592653635254
63	2903	2964.46944013528	-61.4694401352804
64	2910	2691.17247120066	218.827528799345
65	3782	2856.3558652183	925.6441347817
66	2759	2939.33394152907	-180.333941529074
67	2931	3103.25602286572	-172.256022865717
68	3641	3930.28742127508	-289.287421275078
69	2794	2936.06607224404	-142.066072244042
70	3070	3170.37978328149	-100.379783281490
71	3576	4033.43280332002	-457.43280332002
72	4106	4039.91085191032	66.0891480896753
73	2452	2403.18031074916	48.8196892508377
74	2206	2553.37776636195	-347.377766361951
75	2488	2952.68776171025	-464.687761710252
76	2416	2710.19276812224	-294.192768122236
77	2534	3021.52894889665	-487.528948896653
78	2521	2564.60006345212	-43.6000634521229
79	3093	2727.10156545076	365.898434549241
80	3903	3567.25938612931	335.740613870687
81	2907	2683.95986759605	223.040132403946
82	3025	2967.20360676387	57.7963932361326
83	3812	3730.80894968606	81.1910503139356
84	4209	3962.97097359688	246.029026403124
85	2138	2340.82685647277	-202.826856472768
86	2419	2332.61826815687	86.3817318431288
87	2622	2747.97188081392	-125.971880813917
88	2912	2602.07444211761	309.925557882394
89	2708	2934.00939929065	-226.009399290653
90	2798	2656.02354718919	141.976452810813
91	3254	2978.84576534434	275.154234655663
92	2895	3807.75159723942	-912.75159723942
93	3263	2735.52955902784	527.470440972156
94	3736	3006.73767993719	729.262320062809
95	4077	3867.35558805113	209.644411948873
96	4097	4174.81628681047	-77.8162868104691
97	2175	2378.77072385198	-203.770723851980
98	3138	2466.17178583668	671.828214163319
99	2823	2897.56192835713	-74.56192835713
100	2498	2904.30945959739	-406.309459597394
101	2822	2986.37158164533	-164.37158164533
102	2738	2836.08158976521	-98.0815897652083
103	4137	3174.54113837325	962.458861626747
104	3515	3727.02293230079	-212.022932300790
105	3785	3203.81346887837	581.186531121627
106	3632	3559.28067299368	72.7193270063226
107	4504	4187.13434804106	316.865651958936
108	4451	4428.83762954531	22.1623704546910
109	2550	2617.20838351865	-67.2083835186463
110	2867	3006.45119889580	-139.451198895796
111	3458	3111.82800207176	346.171997928244
112	2961	3076.37637597602	-115.376375976025
113	3163	3281.17142891415	-118.171428914148
114	2880	3169.19245135751	-289.192451357508
115	3331	3824.91286352036	-493.912863520358
116	3062	3831.90335835759	-769.903358357587
117	3534	3482.05671602383	51.9432839761744
118	3622	3604.98847283266	17.0115271673412
119	4464	4292.4418484161	171.558151583899
120	5411	4413.81564891984	997.184351080162
121	2564	2691.04947042788	-127.049470427883
122	2820	3046.81419779610	-226.814197796104
123	3508	3288.36791028975	219.632089710246
124	3088	3088.36034768323	-0.360347683228156
125	3299	3302.03285500293	-3.03285500292941
126	2939	3147.45257798524	-208.452577985241
127	3320	3746.47360320174	-426.473603201739
128	3418	3673.45823051455	-255.458230514551
129	3604	3644.38533326350	-40.3853332634958
130	3495	3745.99717247956	-250.997172479556
131	4163	4447.46493076533	-284.464930765332
132	4882	4765.18339065509	116.816609344907
133	2211	2572.62900626506	-361.629006265062
134	3260	2855.18544957032	404.814550429679
135	2992	3304.97692607819	-312.97692607819
136	2425	2958.45309332827	-533.453093328269
137	2707	3089.10059535481	-382.100595354811
138	3244	2804.36593210832	439.634067891679
139	3965	3400.58228740883	564.417712591167
140	3315	3495.70243563438	-180.702435634384
141	3333	3536.44455974871	-203.444559748712
142	3583	3544.82375321426	38.1762467857429
143	4021	4266.04603436235	-245.046034362346
144	4904	4708.49844443965	195.501555560354
145	2252	2372.17554589575	-120.175545895752
146	2952	2920.48320640357	31.5167935964296
147	3573	3095.39678166789	477.603218332115
148	3048	2778.03554126245	269.964458737551
149	3059	3061.41680034781	-2.41680034781075
150	2731	3089.01212149424	-358.012121494243
151	3563	3629.64534753971	-66.6453475397057
152	3092	3413.90371013267	-321.903710132667
153	3478	3427.85033990152	50.1496600984797
154	3478	3542.24466528959	-64.2446652895878
155	4308	4161.49633424889	146.503665751109
156	5029	4791.10060577057	237.899394229431
157	2075	2363.85710834031	-288.857108340314
158	3264	2939.52692001224	324.473079987761
159	3308	3292.48557788780	15.514422112195
160	3688	2853.2199254804	834.780074519599
161	3136	3125.13594752314	10.8640524768607
162	2824	3047.6584912207	-223.6584912207
163	3644	3700.59738569295	-56.5973856929468
164	4694	3411.74549664248	1282.25450335752
165	2914	3756.27703309174	-842.277033091744
166	3686	3735.98764230341	-49.9876423034134
167	4358	4433.36712797424	-75.3671279742439
168	5587	5073.19288437053	513.807115629471
169	2265	2527.00768169796	-262.007681697959
170	3685	3308.33804125099	376.661958749015
171	3754	3583.28479624520	170.715203754796
172	3708	3431.18647571931	276.813524280691
173	3210	3386.62118186770	-176.621181867704
174	3517	3220.2860031215	296.713996878497
175	3905	4000.45244280169	-95.4524428016935
176	3670	4134.66680512631	-464.66680512631
177	4221	3600.3359147728	620.664085227198
178	4404	4015.33478510540	388.665214894605
179	5086	4770.86756869772	315.132431302284
180	5725	5657.31086873862	67.6891312613761
181	2367	2826.40991027566	-459.409910275665
182	3819	3792.5275941798	26.4724058202037
183	4067	3967.76905004861	99.230949951395
184	4022	3846.84062861367	175.15937138633
185	3937	3654.71835916725	282.281640832750
186	4365	3701.86648290655	663.133517093449
187	4290	4417.47188522259	-127.471885222589

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
188	4445.04604995019	3762.81506415528	5127.2770357451
189	4321.65189444895	3633.62240586567	5009.68138303223
190	4599.17223482365	3904.69553214278	5293.64893750451
191	5292.08587486447	4590.49149909386	5993.68025063509
192	6068.35962136604	5358.95809915529	6777.7611435768
193	3070.10151426559	2352.18713546563	3788.01589306555
194	4252.6386952039	3525.49229677598	4979.78509363182
195	4455.72498040837	3718.61669934842	5192.83326146832
196	4353.91753347077	3606.109493273	5101.72557366854
197	4179.94222204467	3420.69112023852	4939.19332385083
198	4315.12377385411	3543.68334209623	5086.56420561198
199	4702.0413293212	3917.66464215456	5486.41801648784

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244036426djm4kouk0f09fwo/1k5fi1244036135.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244036426djm4kouk0f09fwo/1k5fi1244036135.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244036426djm4kouk0f09fwo/2az3x1244036135.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244036426djm4kouk0f09fwo/2az3x1244036135.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244036426djm4kouk0f09fwo/3k61u1244036135.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244036426djm4kouk0f09fwo/3k61u1244036135.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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