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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: Thu, 27 May 2010 09:43:37 +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/May/27/t12749535187p12pop36322es9.htm/, Retrieved Thu, 27 May 2010 11:45:19 +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/May/27/t12749535187p12pop36322es9.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 «

93.2 96 95.2 77.1 70.9 64.8 70.1 77.3 79.5 100.6 100.7 107.1 95.9 82.8 83.3 80 80.4 67.5 75.7 71.1 89.3 101.1 105.2 114.1 96.3 84.4 91.2 81.9 80.5 70.4 74.8 75.9 86.3 98.7 100.9 113.8 89.8 84.4 87.2 85.6 72 69.2 77.5 78.1 94.3 97.7 100.2 116.4 97.1 93 96 80.5 76.1 69.9 73.6 92.6 94.2 93.5 108.5 109.4 105.1 92.5 97.1 81.4 79.1 72.1 78.7 87.1 91.4 109.9 116.3 113 100 84.8 94.3 87.1 90.3 72.4 84.9 92.7 92.2 114.9 112.5 118.3 106 91.2 96.6 96.3 88.2 70.2 86.5 88.2 102.8 119.1 119.2 125.1 106.1 102.1 105.2 101 84.3 87.5 92.7 94.4 113 113.9 122.9 132.7 106.9 96.6 127.3 98.2 100.2 89.4 95.3 104.2 106.4 116.2 135.9 134 104.6 107.1 123.5 98.8 98.6 90.6 89.1 105.2 114 122.1 138 142.2 116.4 112.6 123.8 103.6 113.9 98.6 95 116 113.9 127.5 131.4 145.9 131.5 131 130.5 118.9 114.3 85.7 104.6 105.1 117.3 142.5 140 159.8 131.2 125.4 126.5 119.4 113.5 98.7 114.5 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	5 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0753244389726097
beta	0.0743497117620023
gamma	0.143887003920222

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	95.9	95.381704059829	0.518295940170901
14	82.8	82.4740695437544	0.325930456245615
15	83.3	82.9787705302623	0.32122946973773
16	80	79.4057497484978	0.594250251502189
17	80.4	79.7774554468708	0.622544553129217
18	67.5	66.5839455318979	0.916054468102146
19	75.7	70.1510076458758	5.54899235412422
20	71.1	78.3814528413874	-7.28145284138742
21	89.3	81.2130065973158	8.0869934026842
22	101.1	103.476636607267	-2.37663660726733
23	105.2	103.047122892837	2.15287710716323
24	114.1	109.279182457107	4.82081754289277
25	96.3	98.3706600558605	-2.07066005586051
26	84.4	85.3077252355168	-0.907725235516764
27	91.2	85.7772727842056	5.42272721579442
28	81.9	82.71181116461	-0.81181116460995
29	80.5	83.0604627821201	-2.56046278212007
30	70.4	69.727511993728	0.672488006272033
31	74.8	73.9525365786563	0.847463421343718
32	75.9	80.1553384195549	-4.25533841955489
33	86.3	85.310105078698	0.989894921301953
34	98.7	105.657749775832	-6.95774977583179
35	100.9	105.470929814007	-4.57092981400731
36	113.8	111.498950168258	2.30104983174151
37	89.8	99.4170748093222	-9.61707480932225
38	84.4	85.8315249720352	-1.43152497203523
39	87.2	86.9920305775212	0.207969422478783
40	85.6	82.5632218574948	3.03677814250524
41	72	82.8496131916392	-10.8496131916392
42	69.2	69.1565077417572	0.0434922582428072
43	77.5	73.1879919791273	4.31200802087265
44	78.1	78.8227978561815	-0.722797856181529
45	94.3	84.8112673966747	9.4887326033253
46	97.7	104.658998448065	-6.95899844806523
47	100.2	104.706981692591	-4.50698169259113
48	116.4	111.571819393128	4.82818060687229
49	97.1	98.0264512961416	-0.926451296141593
50	93	86.1651105756553	6.83488942434474
51	96	88.1932220050758	7.80677799492423
52	80.5	84.7825249040725	-4.28252490407246
53	76.1	82.69840156445	-6.59840156445006
54	69.9	70.8270144560965	-0.927014456096472
55	73.6	75.4000651704758	-1.80006517047585
56	92.6	79.9171264194733	12.6828735805267
57	94.2	88.361597646559	5.83840235344103
58	93.5	105.813170849918	-12.3131708499181
59	108.5	105.821258742875	2.67874125712525
60	109.4	114.546798467673	-5.14679846767326
61	105.1	99.5059698136297	5.59403018637029
62	92.5	89.2264807140713	3.27351928592867
63	97.1	91.1537605923013	5.94623940769868
64	81.4	86.0221506542785	-4.62215065427846
65	79.1	83.6301169552013	-4.53011695520131
66	72.1	72.7064729310604	-0.606472931060438
67	78.7	77.2266845339013	1.4733154660987
68	87.1	83.9747556100307	3.12524438996927
69	91.4	90.7926357548406	0.607364245159374
70	109.9	105.409823970849	4.49017602915066
71	116.3	108.747060011172	7.55293998882813
72	113	116.894654216458	-3.89465421645802
73	100	103.480296227977	-3.48029622797719
74	84.8	92.2608272747916	-7.46082727479161
75	94.3	93.7273144879492	0.572685512050768
76	87.1	86.7469030318494	0.353096968150638
77	90.3	84.7318051597807	5.56819484021929
78	72.4	75.1373341218339	-2.73733412183394
79	84.9	79.8083067761149	5.09169322388514
80	92.7	87.1035350972503	5.59646490274974
81	92.2	93.8412151353293	-1.6412151353293
82	114.9	108.861698488487	6.0383015115128
83	112.5	112.787777999	-0.287777998999516
84	118.3	118.842509855483	-0.542509855482663
85	106	105.775377236359	0.224622763640582
86	91.2	94.3657203529248	-3.16572035292479
87	96.6	97.308983382073	-0.708983382073043
88	96.3	90.2800372416029	6.01996275839707
89	88.2	89.4946140803101	-1.29461408031014
90	70.2	78.3486897784115	-8.14868977841145
91	86.5	83.6939168760708	2.80608312392917
92	88.2	90.9115610551227	-2.71156105512271
93	102.8	96.0413701198732	6.75862988012685
94	119.1	112.744250641703	6.35574935829712
95	119.2	115.882275400714	3.31772459928608
96	125.1	122.224600958735	2.87539904126531
97	106.1	109.586030976262	-3.48603097626165
98	102.1	97.4940536459653	4.60594635403467
99	105.2	101.441366596375	3.75863340362481
100	101	95.7610271762296	5.23897282377041
101	84.3	94.056014736406	-9.75601473640597
102	87.5	81.4258608417262	6.07413915827377
103	92.7	89.444633904644	3.2553660953561
104	94.4	96.1092203073772	-1.70922030737715
105	113	102.727357239584	10.2726427604161
106	113.9	119.813835355396	-5.91383535539576
107	122.9	121.727250333659	1.17274966634101
108	132.7	127.940938705081	4.75906129491889
109	106.9	114.700205818255	-7.80020581825451
110	96.6	103.43806453785	-6.83806453784959
111	127.3	106.424710357986	20.8752896420142
112	98.2	102.340570652769	-4.1405706527692
113	100.2	97.9913954004071	2.20860459959286
114	89.4	88.4930698015795	0.906930198420554
115	95.3	95.8430703452157	-0.543070345215668
116	104.2	101.635215794541	2.56478420545876
117	106.4	110.267604481654	-3.86760448165367
118	116.2	124.154336949683	-7.95433694968334
119	135.9	126.864438340442	9.03556165955823
120	134	134.199102005128	-0.199102005127827
121	104.6	118.937694375548	-14.3376943755477
122	107.1	107.298311445254	-0.198311445254063
123	123.5	114.496685563189	9.00331443681051
124	98.8	106.147842883308	-7.34784288330833
125	98.6	102.341746917011	-3.741746917011
126	90.6	92.1286193075609	-1.52861930756092
127	89.1	98.995193784973	-9.89519378497306
128	105.2	104.336968082323	0.863031917676679
129	114	111.81639724639	2.1836027536101
130	122.1	125.480133134192	-3.38013313419226
131	138	130.685821024736	7.31417897526424
132	142.2	136.543072883903	5.65692711609688
133	116.4	119.755351746186	-3.35535174618593
134	112.6	110.799647532065	1.80035246793537
135	123.8	119.35924039449	4.44075960551035
136	103.6	108.452077391352	-4.85207739135211
137	113.9	105.288590804035	8.6114091959651
138	98.6	96.3444242308463	2.25557576915372
139	95	102.448083754534	-7.44808375453407
140	116	109.48446422977	6.51553577022977
141	113.9	117.675931447071	-3.77593144707137
142	127.5	130.227710935714	-2.72771093571427
143	131.4	136.986251838805	-5.58625183880486
144	145.9	141.65988801329	4.24011198670973
145	131.5	123.567035950785	7.932964049215
146	131	116.211459285026	14.7885407149744
147	130.5	126.23730279104	4.26269720896038
148	118.9	114.21594901124	4.68405098876039
149	114.3	113.751094733226	0.548905266773886
150	85.7	103.497863850553	-17.7978638505527
151	104.6	106.831518042338	-2.23151804233829
152	105.1	116.179459739376	-11.0794597393761
153	117.3	121.638571898801	-4.33857189880092
154	142.5	134.246529735205	8.25347026479454
155	140	141.472489434589	-1.47248943458877
156	159.8	147.807009750429	11.9929902495708
157	131.2	130.876518668219	0.323481331780613
158	125.4	123.904322692379	1.49567730762111
159	126.5	131.498427706537	-4.99842770653666
160	119.4	118.753669750189	0.646330249810788
161	113.5	117.33001186107	-3.83001186106954
162	98.7	104.176914087738	-5.47691408773758
163	114.5	110.449710240323	4.05028975967666
164	113.8	119.068787682872	-5.2687876828715
165	133.1	125.870164353433	7.22983564656671
166	143.4	141.097361069721	2.30263893027924
167	137.3	146.62022279027	-9.32022279026961
168	165.2	154.150405079901	11.0495949200988
169	126.9	135.586178042608	-8.68617804260757
170	124	128.03077542472	-4.03077542471965
171	135.7	134.253102194541	1.44689780545858
172	130	122.68949065839	7.31050934161026
173	109.4	121.154185771239	-11.7541857712387
174	117.8	107.122656914684	10.6773430853158
175	120.3	115.907887156526	4.39211284347357
176	121	123.342775254675	-2.34277525467476
177	132.3	132.073820708886	0.226179291114477
178	142.9	146.12503217166	-3.22503217166027
179	147.4	149.661279337455	-2.26127933745497
180	175.9	160.449046789983	15.450953210017
181	132.6	139.630872397595	-7.03087239759503
182	123.7	132.869164387094	-9.16916438709445
183	153.3	139.454079866162	13.8459201338383
184	134	129.694840201474	4.30515979852581
185	119.6	125.470069318725	-5.87006931872467
186	116.2	114.972644259717	1.22735574028304
187	118.6	122.263292068495	-3.66329206849461
188	130.7	128.203704346996	2.49629565300376
189	129.3	137.6765086935	-8.37650869349994
190	144.4	150.607832195131	-6.20783219513137
191	163.2	154.018207266885	9.18179273311478
192	179.4	168.059173621878	11.3408263781216
193	128.1	143.951872953372	-15.8518729533724
194	138.4	136.203476708882	2.19652329111824
195	152.7	146.732533214517	5.96746678548283
196	120	135.092242387971	-15.0922423879709
197	140.5	127.925714429328	12.5742855706717
198	116.2	119.738342107991	-3.53834210799118
199	121.4	125.969070213638	-4.56907021363833
200	127.8	132.605456933839	-4.80545693383912
201	143.6	139.98543090414	3.61456909586028
202	157.6	154.079453215698	3.52054678430238
203	166.2	160.295604180906	5.90439581909439
204	182.3	174.38402484431	7.91597515569026
205	153.1	146.388678469276	6.71132153072435
206	147.6	142.855406574161	4.74459342583881
207	157.7	154.206631602585	3.49336839741531
208	137.2	139.69267301151	-2.49267301151002
209	151.5	137.341422046095	14.1585779539053
210	98.7	127.323715800007	-28.6237158000067
211	145.8	131.581374046164	14.2186259538363
212	151.7	139.760309125413	11.9396908745866
213	129.4	149.774481634233	-20.3744816342331
214	174.1	162.16729086279	11.9327091372096
215	197	169.499620798144	27.5003792018564
216	193.9	185.768699391705	8.13130060829465
217	164.1	157.916814857912	6.18318514208764
218	142.8	154.366653117081	-11.5666531170812
219	157.9	164.515982510186	-6.61598251018637
220	159.2	148.580705067377	10.6192949326226
221	162.2	149.642564175685	12.5574358243155
222	123.1	134.01318271328	-10.9131827132803
223	130	145.605246702785	-15.6052467027849
224	150.1	151.367729385919	-1.26772938591907
225	169.4	156.146956092896	13.2530439071045
226	179.7	175.618756045213	4.08124395478711
227	182.1	184.63455096641	-2.53455096640997
228	194.3	196.09963901259	-1.79963901259026
229	161.4	167.220307170115	-5.82030717011466
230	169.4	160.316960296293	9.08303970370676
231	168.8	172.708608296053	-3.90860829605307
232	158.1	159.313768770815	-1.21376877081482
233	158.5	159.719280564451	-1.21928056445054
234	135.3	139.82938794936	-4.52938794935955
235	149.3	151.213735539886	-1.91373553988581
236	143.4	159.927491603588	-16.5274916035877
237	142.2	165.416175238885	-23.216175238885
238	188.4	180.643332925942	7.75666707405759
239	166.2	188.799015287482	-22.5990152874823
240	199.2	198.481431742	0.718568258000431
241	182.7	168.901834010465	13.798165989535
242	145.2	165.213976921336	-20.0139769213365
243	182.1	173.277298797499	8.82270120250138
244	158.7	160.863196420228	-2.16319642022816
245	141.6	160.854355892029	-19.2543558920289
246	132.6	138.722468924335	-6.1224689243347
247	139.6	149.88279955737	-10.2827995573697
248	147	155.522919797583	-8.52291979758326
249	166.6	160.270552293466	6.32944770653421
250	157	181.555512957908	-24.5555129579079
251	180.4	182.768948090535	-2.36894809053496
252	210.2	196.721291484759	13.4787085152413
253	159.8	169.55826220591	-9.75826220591003
254	157.8	159.18063453672	-1.38063453671992
255	168.2	172.171810091403	-3.97181009140328
256	158.4	156.948276441041	1.45172355895852
257	152	154.573982923802	-2.57398292380242
258	142.2	135.175346758063	7.02465324193656
259	137.2	146.575707815325	-9.37570781532492
260	152.6	152.326641951858	0.273358048141517
261	166.8	159.570538830777	7.22946116922259
262	165.6	176.676726135823	-11.0767261358235
263	198.6	181.795465461335	16.8045345386649
264	201.5	199.3460569223	2.15394307770021
265	170.7	168.220427020237	2.47957297976296
266	164.4	159.929858819	4.47014118100006
267	179.7	173.100372500913	6.59962749908675
268	157	159.537309349504	-2.53730934950443
269	168	156.447177054426	11.5528229455736
270	139.3	139.589084951856	-0.289084951856069
271	138.6	148.414898343717	-9.81489834371675
272	153.4	155.57249153035	-2.17249153035036
273	138.9	163.699903926979	-24.7999039269786
274	172.1	175.920752047979	-3.8207520479788
275	198.4	185.299118667611	13.1008813323886
276	217.8	200.604256168537	17.1957438314633
277	173.7	170.721970685116	2.97802931488428
278	153.8	162.803587209743	-9.00358720974319
279	175.6	175.236863930835	0.363136069165392
280	147.1	159.947794057183	-12.8477940571833
281	160.3	157.857375041345	2.44262495865499
282	135.2	138.588160114225	-3.38816011422546
283	148.8	145.746432814856	3.05356718514437
284	151	154.795510298768	-3.79551029876791
285	148.2	159.686391591131	-11.4863915911307
286	182.2	175.672155644462	6.52784435553843
287	189.2	188.110215381173	1.0897846188272
288	183.1	203.016961886855	-19.9169618868553
289	170	168.201210314067	1.798789685933
290	158.4	158.346934913543	0.053065086456968
291	176.1	172.50642386082	3.59357613917956
292	156.2	155.518872038426	0.681127961574077
293	153.2	156.373535341611	-3.17353534161109
294	117.9	135.765706907933	-17.8657069079327
295	149.8	142.469650797894	7.3303492021061
296	156.6	150.732684669396	5.86731533060401
297	166.7	155.185337288156	11.5146627118439
298	156.8	175.286416123188	-18.486416123188
299	158.6	184.962675665886	-26.3626756658861
300	210.8	194.698827519082	16.1011724809179
301	203.6	165.379259332456	38.2207406675438
302	175.2	158.134039104192	17.0659608958078
303	168.7	174.239212497778	-5.53921249777815
304	155.9	156.318230836684	-0.418230836683591
305	147.3	156.713060514289	-9.4130605142886
306	137	133.781357352957	3.21864264704291
307	141.1	145.644742463477	-4.54474246347695
308	167.4	152.97110163678	14.4288983632204
309	160.2	159.020436143086	1.1795638569144
310	191.9	174.493954539771	17.4060454602288
311	174.4	186.169409628363	-11.7694096283628
312	208.2	203.079825196952	5.1201748030476
313	159.4	176.239874269589	-16.8398742695886
314	161.1	162.088040230811	-0.988040230810782
315	172.1	173.780020381115	-1.68002038111496
316	158.4	156.806988841516	1.59301115848351
317	114.6	156.143744790002	-41.5437447900019
318	159.6	132.279687527072	27.3203124729278
319	159.7	144.867824914876	14.8321750851243
320	159.4	156.228893688965	3.171106311035
321	160.7	159.655119828904	1.04488017109648
322	165.5	177.264339327424	-11.7643393274238
323	205	182.684360231908	22.3156397680923
324	205.2	204.423807975044	0.776192024956288
325	141.6	174.325019142401	-32.7250191424015
326	148.1	160.98687878748	-12.8868787874801
327	184.9	171.525046683747	13.3749533162529
328	132.5	156.04033683494	-23.5403368349404
329	137.3	147.522729784611	-10.222729784611
330	135.5	135.133684757054	0.366315242946087
331	121.7	143.832538394001	-22.1325383940011
332	166.1	150.453296970186	15.6467030298135
333	146.8	154.201743585898	-7.40174358589752
334	162.8	169.088565583847	-6.2885655838474
335	186.8	179.10410344175	7.69589655824987
336	185.5	196.443411135034	-10.9434111350338
337	151.5	160.505801568835	-9.00580156883541
338	158.1	151.227822201273	6.87217779872691
339	143	166.493176272817	-23.493176272817
340	151.2	142.858127072996	8.3418729270036
341	147.6	138.230739452282	9.3692605477176
342	130.7	128.55285008826	2.14714991174031
343	137.5	134.228912297003	3.27108770299665
344	146.1	147.768450139479	-1.66845013947932
345	133.6	147.027886354299	-13.4278863542992
346	167.9	161.456962882339	6.44303711766145
347	181.9	174.211482218352	7.68851778164824
348	202	188.989620133082	13.0103798669176
349	166.5	155.167586148579	11.3324138514212
350	151.3	149.701491710726	1.59850828927424
351	146.2	160.667375611316	-14.4673756113159
352	148.3	142.136192225056	6.16380777494425
353	144.7	137.657625300316	7.04237469968373
354	123.6	127.006729609647	-3.40672960964676
355	151.6	132.546042027963	19.0539579720366
356	133.9	146.83766025704	-12.9376602570404
357	137.4	143.84100328795	-6.44100328794966
358	181.6	161.636626877577	19.9633731224228
359	182	175.847447828519	6.15255217148146
360	190	191.481535580967	-1.48153558096652
361	161.2	156.527073276355	4.67292672364474
362	155.5	149.40939526856	6.09060473143956
363	141.9	158.746377594347	-16.8463775943467
364	164.6	142.937908376727	21.6620916232729
365	136.2	139.987386125708	-3.78738612570817
366	126.8	127.313606439873	-0.513606439873229
367	152.5	136.258514094495	16.2414859055047
368	126.6	146.265392239242	-19.6653922392418
369	150.1	143.772221451339	6.3277785486612
370	186.3	166.260102943253	20.0398970567466
371	147.5	178.856989558717	-31.3569895587165
372	200.4	190.657734007785	9.74226599221484
373	177.2	157.438147348888	19.7618526511122
374	127.4	151.800763133638	-24.4007631336375
375	177.1	155.773608615681	21.3263913843187
376	154.4	148.162114370919	6.23788562908089
377	135.2	140.775496221925	-5.57549622192477
378	126.4	128.504332689485	-2.10433268948498
379	147.3	139.651488119595	7.64851188040515
380	140.6	144.278438217088	-3.67843821708757
381	152.3	146.582068202691	5.71793179730858
382	151.2	170.979211185298	-19.779211185298
383	172.2	173.646267966007	-1.44626796600662
384	215.3	193.243553768482	22.0564462315179
385	154.1	162.42891005253	-8.32891005252992
386	159.3	148.786794205464	10.5132057945358
387	160.4	161.655960293943	-1.25596029394313
388	151.9	150.391989100535	1.50801089946489
389	148.4	141.106884150291	7.29311584970915
390	139.6	130.368489059299	9.23151094070087
391	148.2	143.832212802859	4.36778719714061
392	153.5	146.851731896344	6.64826810365594
393	145.1	151.387948948841	-6.28794894884072
394	183.7	171.625712373505	12.0742876264947
395	210.5	179.447003708627	31.0529962913733
396	203.3	205.117005055233	-1.81700505523315
397	153.3	168.825391120635	-15.5253911206353
398	144.3	157.471841566143	-13.1718415661434
399	169.6	167.182143171211	2.4178568287889
400	143.7	156.774289693994	-13.0742896939945
401	160.1	147.290462852393	12.8095371476074
402	135.6	137.38636459677	-1.78636459677031
403	141.8	149.472230858216	-7.67223085821561
404	159.9	151.919999666434	7.98000033356635
405	145.7	154.874580845336	-9.17458084533581
406	183.5	177.361017909495	6.13898209050507
407	198.2	187.250124331638	10.9498756683622
408	186.8	206.909765079185	-20.1097650791855
409	172	167.19113892143	4.80886107857046
410	150.6	157.571035301468	-6.9710353014677
411	163.3	169.745969310568	-6.44596931056776
412	153.7	156.482970675534	-2.78297067553416
413	152.9	151.14950767293	1.75049232706954
414	135.5	138.339855399218	-2.83985539921773
415	148.5	149.426790202806	-0.926790202806416
416	148.4	154.366472456479	-5.96647245647861
417	133.6	153.811348286886	-20.2113482868856
418	194.1	177.265289646598	16.834710353402
419	208.6	188.421420722325	20.1785792776753
420	197.3	204.516735881192	-7.21673588119171
421	164.4	169.029843902297	-4.62984390229744
422	148.1	157.023794817004	-8.9237948170044
423	152	169.002882294934	-17.0028822949341
424	144.1	155.254309845245	-11.1543098452449
425	155	149.668831953488	5.33116804651152
426	124.5	136.313584612084	-11.8135846120839
427	153	146.724286072235	6.275713927765
428	146	151.321482552468	-5.32148255246798
429	138	148.708803775667	-10.7088037756675
430	190	177.649795518744	12.350204481256
431	192	188.730259684113	3.26974031588719
432	192	199.629545156666	-7.62954515666601
433	147	164.175962359629	-17.1759623596293
434	133	150.303537227622	-17.3035372276222
435	163	160.179541241248	2.82045875875193
436	150	148.416342806543	1.58365719345682
437	129	145.769101648067	-16.7691016480674
438	131	128.129689464188	2.8703105358116
439	145	141.797055711462	3.20294428853779
440	137	144.346445157159	-7.34644515715863
441	138	140.579760749587	-2.5797607495868
442	168	172.961867018186	-4.96186701818618
443	176	181.19403625308	-5.19403625307993
444	188	189.622127547596	-1.62212754759554
445	139	153.001026292929	-14.0010262929288
446	143	139.018674007532	3.98132599246753
447	150	152.962520781902	-2.96252078190236
448	154	140.353879928992	13.6461200710079
449	137	135.995690799327	1.00430920067254
450	129	122.229854538622	6.77014546137795
451	128	136.178874201569	-8.17887420156859
452	140	136.347252836529	3.65274716347074
453	143	133.984779218247	9.01522078175321
454	151	166.929771729927	-15.929771729927
455	177	174.249912885279	2.7500871147214
456	184	183.741131869213	0.258868130786823
457	151	145.614755119355	5.38524488064542
458	134	135.593800201548	-1.59380020154805
459	164	148.271217655407	15.7287823445926
460	126	139.462310625354	-13.4623106253537
461	131	131.410461968137	-0.410461968137071
462	125	118.327518744118	6.67248125588215
463	127	130.302008191566	-3.30200819156576
464	143	132.461004513689	10.5389954863109
465	143	131.418357261673	11.5816427383273
466	160	161.339788623503	-1.33978862350315
467	190	172.427979595608	17.572020404392
468	182	182.970941515961	-0.970941515960732
469	138	145.693843747809	-7.69384374780898
470	136	133.945768241187	2.05423175881336
471	152	149.409758635789	2.59024136421053
472	127	135.860816396765	-8.86081639676465
473	151	130.05133323589	20.9486667641101
474	130	119.798477847503	10.2015221524967
475	119	131.010306751809	-12.0103067518089
476	153	134.604724967246	18.3952750327535

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
477	134.586409164776	114.814870639324	154.357947690229
478	162.14525628071	142.309083263991	181.98142929743
479	176.087040169628	156.177234177619	195.996846161637
480	182.977351949697	162.984400669025	202.970303230368
481	145.022424568521	124.936323405228	165.108525731814
482	135.337450266373	115.147725827717	155.527174705029
483	150.893114851834	130.588850250796	171.197379452872
484	135.786101040228	115.355962877219	156.216239203236
485	134.820379779293	114.252646622768	155.388112935817
486	121.652573324972	100.935165483224	142.369981166721
487	129.176479261339	108.296989612719	150.05596890996
488	137.824013129657	116.7697387586	158.878287500714

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/27/t12749535187p12pop36322es9/1ju9h1274953410.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/27/t12749535187p12pop36322es9/1ju9h1274953410.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/27/t12749535187p12pop36322es9/2ju9h1274953410.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/27/t12749535187p12pop36322es9/2ju9h1274953410.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/27/t12749535187p12pop36322es9/3611d1274953410.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/27/t12749535187p12pop36322es9/3611d1274953410.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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