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*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: Wed, 29 Dec 2010 15:33:41 +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/Dec/29/t1293636739mkuoya4v1ve1zvn.htm/, Retrieved Wed, 29 Dec 2010 16:32:20 +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/Dec/29/t1293636739mkuoya4v1ve1zvn.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 «

315.42 316.32 316.49 317.56 318.13 318.00 316.39 314.66 313.68 313.18 314.66 315.43 316.27 316.81 317.42 318.87 319.87 319.43 318.01 315.75 314.00 313.68 314.84 316.03 316.73 317.54 318.38 319.31 320.42 319.61 318.42 316.64 314.83 315.15 315.95 316.85 317.78 318.40 319.53 320.41 320.85 320.45 319.44 317.25 316.12 315.27 316.53 317.53 318.58 318.92 319.70 321.22 322.08 321.31 319.58 317.61 316.05 315.83 316.91 318.20 319.41 320.07 320.74 321.40 322.06 321.73 320.27 318.54 316.54 316.71 317.53 318.55 319.27 320.28 320.73 321.97 322.00 321.71 321.05 318.71 317.65 317.14 318.71 319.25 320.46 321.43 322.22 323.54 323.91 323.59 322.26 320.21 318.48 317.94 319.63 320.87 322.17 322.34 322.88 324.25 324.83 323.93 322.39 320.76 319.10 319.23 320.56 321.80 322.40 322.99 323.73 324.86 325.41 325.19 323.97 321.92 320.10 319.96 320.97 322.48 323.52 323.89 325.04 326.01 326.67 325.96 325.13 322.90 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	0.490123873180968
beta	0.0117016559417254
gamma	0.48466894728562

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	316.27	315.619353632479	0.65064636752129
14	316.81	316.4573905023	0.35260949770003
15	317.42	317.275541361277	0.144458638722881
16	318.87	318.857084356367	0.0129156436332778
17	319.87	319.930062397133	-0.0600623971330378
18	319.43	319.522761017715	-0.0927610177153042
19	318.01	317.392651255089	0.617348744910998
20	315.75	316.00704056251	-0.257040562510156
21	314	314.93806326788	-0.938063267880295
22	313.68	313.975753782891	-0.295753782890813
23	314.84	315.272809285349	-0.432809285348526
24	316.03	315.785208339915	0.244791660084729
25	316.73	316.866908201103	-0.136908201103438
26	317.54	317.240469640863	0.299530359136838
27	318.38	317.976037321785	0.403962678214555
28	319.31	319.648621361675	-0.33862136167528
29	320.42	320.525611124674	-0.105611124673715
30	319.61	320.081986289154	-0.471986289153733
31	318.42	317.933398918243	0.486601081756703
32	316.64	316.258782359435	0.381217640565296
33	314.83	315.329152881926	-0.499152881926022
34	315.15	314.738026695876	0.411973304124331
35	315.95	316.34948042651	-0.399480426509683
36	316.85	317.0472490057	-0.197249005700371
37	317.78	317.817017612636	-0.0370176126359638
38	318.4	318.34701342969	0.0529865703095993
39	319.53	318.985759980112	0.544240019888377
40	320.41	320.542602051311	-0.132602051310926
41	320.85	321.578343084311	-0.728343084311177
42	320.45	320.735586411055	-0.285586411055192
43	319.44	318.912937317738	0.527062682262113
44	317.25	317.230033595774	0.0199664042258405
45	316.12	315.901640353626	0.218359646373983
46	315.27	315.887310082261	-0.617310082260815
47	316.53	316.787824251422	-0.257824251421994
48	317.53	317.599874153057	-0.0698741530570715
49	318.58	318.46727589925	0.112724100750256
50	318.92	319.089371568564	-0.169371568563747
51	319.7	319.735724838927	-0.0357248389272513
52	321.22	320.832914709678	0.387085290321636
53	322.08	321.970991660223	0.109008339776608
54	321.31	321.647702806021	-0.337702806020957
55	319.58	319.999681449297	-0.419681449296888
56	317.61	317.721360266265	-0.111360266265308
57	316.05	316.370793298954	-0.320793298953731
58	315.83	315.875772920879	-0.0457729208794717
59	316.91	317.138598822251	-0.22859882225066
60	318.2	318.004938041601	0.195061958399208
61	319.41	319.042353461939	0.367646538061422
62	320.07	319.716181225981	0.35381877401926
63	320.74	320.651490458588	0.0885095414120656
64	321.4	321.914269351531	-0.51426935153097
65	322.06	322.536896152256	-0.476896152256018
66	321.73	321.807733410165	-0.0777334101646261
67	320.27	320.260045250604	0.00995474939628593
68	318.54	318.264130423408	0.27586957659156
69	316.54	317.049458304164	-0.509458304163843
70	316.71	316.526709589827	0.183290410173186
71	317.53	317.854716035073	-0.324716035072811
72	318.55	318.776181464897	-0.22618146489657
73	319.27	319.644908803802	-0.374908803801929
74	320.28	319.942240667534	0.337759332466419
75	320.73	320.794888495666	-0.0648884956655138
76	321.97	321.82341739966	0.146582600340366
77	322	322.772862833743	-0.772862833743204
78	321.71	321.989267463414	-0.279267463413646
79	321.05	320.355302561299	0.694697438701496
80	318.71	318.755467134038	-0.045467134038347
81	317.65	317.182143651322	0.46785634867831
82	317.14	317.308112716185	-0.168112716185476
83	318.71	318.33485328106	0.375146718940243
84	319.25	319.624206329527	-0.374206329526771
85	320.46	320.383298720883	0.076701279117458
86	321.43	321.080350161156	0.349649838843561
87	322.22	321.841650562462	0.378349437538304
88	323.54	323.144549556159	0.395450443841185
89	323.91	323.995053614859	-0.0850536148589072
90	323.59	323.68078951564	-0.0907895156402674
91	322.26	322.391212137663	-0.131212137663226
92	320.21	320.210254280073	-0.000254280072567781
93	318.48	318.792788953339	-0.312788953338782
94	317.94	318.381351703536	-0.441351703536156
95	319.63	319.409223079369	0.220776920630556
96	320.87	320.437650363106	0.43234963689406
97	322.17	321.708025220941	0.461974779059005
98	322.34	322.668110737088	-0.328110737087968
99	322.88	323.107180623739	-0.227180623738661
100	324.25	324.116911872274	0.133088127726126
101	324.83	324.717969450096	0.112030549903693
102	323.93	324.497900129437	-0.567900129436566
103	322.39	322.960770398411	-0.570770398411298
104	320.76	320.590496248208	0.169503751791808
105	319.1	319.173732323363	-0.0737323233631741
106	319.23	318.843795773626	0.386204226374446
107	320.56	320.441748197427	0.118251802573297
108	321.8	321.472471712104	0.327528287896257
109	322.4	322.698453096172	-0.298453096172068
110	322.99	323.085887655773	-0.0958876557728559
111	323.73	323.660349162699	0.0696508373010829
112	324.86	324.902928602873	-0.0429286028730189
113	325.41	325.409836891617	0.000163108383219424
114	325.19	324.963596328441	0.226403671558899
115	323.97	323.816302984335	0.153697015664534
116	321.92	321.989438435637	-0.069438435637096
117	320.1	320.399477517194	-0.299477517194305
118	319.96	320.075286238461	-0.115286238461124
119	320.97	321.361081671884	-0.391081671883853
120	322.48	322.190816334758	0.289183665241808
121	323.52	323.240021966002	0.279978033998304
122	323.89	323.961046171	-0.071046171000205
123	325.04	324.588762153664	0.4512378463358
124	326.01	325.99290525201	0.0170947479896313
125	326.67	326.542585053058	0.127414946942281
126	325.96	326.218056061906	-0.258056061906245
127	325.13	324.816005168611	0.313994831389095
128	322.9	323.014139354546	-0.114139354546069
129	321.61	321.346739992607	0.263260007392716
130	321.01	321.348422872469	-0.338422872469323
131	322.08	322.459964597141	-0.379964597140599
132	323.37	323.466585459418	-0.096585459418236
133	324.34	324.325558560418	0.0144414395819581
134	325.3	324.829285556214	0.470714443786107
135	326.29	325.854300014073	0.435699985926647
136	327.54	327.146153841339	0.39384615866129
137	327.54	327.912523858795	-0.372523858795262
138	327.21	327.249610518755	-0.0396105187552394
139	325.98	326.099149328545	-0.119149328545348
140	324.42	323.979862491167	0.440137508833118
141	322.91	322.681244001846	0.228755998153588
142	322.9	322.520982397408	0.379017602591659
143	323.85	323.981663001953	-0.131663001953143
144	324.96	325.189205462935	-0.22920546293517
145	326.01	326.019048903741	-0.00904890374084744
146	326.51	326.632316173966	-0.122316173965544
147	327.01	327.36291692505	-0.352916925050351
148	327.62	328.258282457538	-0.638282457537741
149	328.76	328.3238504967	0.436149503300385
150	328.4	328.138650267159	0.261349732840586
151	327.2	327.116860317305	0.083139682695446
152	325.28	325.236911083061	0.0430889169393822
153	323.2	323.691154922545	-0.491154922545263
154	323.4	323.21075388852	0.189246111479804
155	324.64	324.446707882353	0.193292117647047
156	325.85	325.785762398175	0.064237601824857
157	326.6	326.811866195474	-0.211866195474272
158	327.47	327.294605492033	0.17539450796653
159	327.58	328.11271084512	-0.532710845120164
160	329.56	328.846979875144	0.713020124856484
161	329.9	329.845663119934	0.0543368800664439
162	328.92	329.433235612136	-0.513235612135531
163	327.89	327.98642589514	-0.0964258951401007
164	326.17	326.006202509077	0.163797490923002
165	324.68	324.385910473558	0.294089526442292
166	325.04	324.461346451649	0.57865354835144
167	326.34	325.89422002552	0.445779974480445
168	327.39	327.331642699422	0.0583573005775406
169	328.37	328.293109543433	0.0768904565667867
170	329.4	329.021207968304	0.378792031695696
171	330.14	329.773314348127	0.366685651872558
172	331.33	331.27070262244	0.0592973775595169
173	332.31	331.796914037042	0.513085962958087
174	331.9	331.482410138702	0.417589861298154
175	330.7	330.613500106696	0.086499893304449
176	329.15	328.806966252033	0.343033747966501
177	327.34	327.327474605596	0.0125253944036672
178	327.02	327.354370724473	-0.334370724472535
179	327.99	328.320816668175	-0.330816668174975
180	328.48	329.291319705903	-0.811319705903088
181	329.18	329.835578442384	-0.655578442384069
182	330.55	330.279543151265	0.270456848734739
183	331.32	330.975199319535	0.344800680465198
184	332.48	332.385412784652	0.0945872153482696
185	332.92	333.040777407793	-0.120777407793241
186	332.08	332.388083533687	-0.308083533687181
187	331.02	331.073603093528	-0.0536030935278973
188	329.24	329.252911600492	-0.0129116004924867
189	327.28	327.506360850664	-0.22636085066415
190	327.21	327.318151489335	-0.108151489334773
191	328.29	328.385352320336	-0.0953523203359055
192	329.41	329.342871211338	0.0671287886624441
193	330.23	330.351555220713	-0.121555220712764
194	331.24	331.284552843404	-0.0445528434039488
195	331.87	331.840833010393	0.0291669896066651
196	333.14	333.029349431456	0.110650568544429
197	333.8	333.634293663075	0.165706336924927
198	333.42	333.072295793579	0.347704206420815
199	331.73	332.14245196993	-0.412451969929748
200	329.9	330.154209607847	-0.254209607846747
201	328.4	328.233535022639	0.166464977360761
202	328.17	328.266213864228	-0.0962138642275363
203	329.32	329.341639876897	-0.021639876896586
204	330.59	330.375073592389	0.214926407611415
205	331.58	331.410050677995	0.169949322004811
206	332.39	332.507104144556	-0.117104144555981
207	333.33	333.047780408478	0.282219591521539
208	334.41	334.383649080902	0.0263509190979221
209	334.71	334.96358682104	-0.253586821040471
210	334.17	334.241359463427	-0.0713594634270294
211	332.88	332.916169021443	-0.0361690214432997
212	330.77	331.151512167615	-0.381512167615483
213	329.14	329.271726243862	-0.131726243862147
214	328.77	329.090955861774	-0.320955861774451
215	330.14	330.070985213464	0.0690147865358313
216	331.52	331.204157348016	0.315842651983985
217	332.75	332.274905764935	0.475094235065228
218	333.25	333.449755806868	-0.199755806868154
219	334.53	334.047304564709	0.48269543529085
220	335.9	335.418051176717	0.481948823283176
221	336.57	336.154573266578	0.415426733421555
222	336.1	335.811578090286	0.288421909714145
223	334.76	334.679785267156	0.080214732844297
224	332.59	332.895860651059	-0.305860651059504
225	331.41	331.124345969761	0.2856540302393
226	330.98	331.113240022307	-0.133240022307234
227	332.24	332.294579007472	-0.0545790074718298
228	333.68	333.440398043896	0.239601956103968
229	334.8	334.524923036787	0.275076963213053
230	335.22	335.445612516158	-0.225612516158094
231	336.47	336.209630487087	0.260369512913485
232	337.59	337.480444340575	0.109555659425098
233	337.84	338.025091852195	-0.185091852194546
234	337.72	337.360021690324	0.359978309675967
235	336.37	336.215897454323	0.154102545676665
236	334.51	334.377252880813	0.132747119187286
237	332.6	332.973874887582	-0.37387488758236
238	332.37	332.539206707267	-0.169206707266994
239	333.75	333.725356286301	0.024643713698822
240	334.79	334.986156889784	-0.196156889783538
241	336.05	335.866827791615	0.183172208385201
242	336.59	336.619169609673	-0.0291696096730902
243	337.79	337.601120016996	0.188879983004199
244	338.71	338.800770496998	-0.0907704969984025
245	339.3	339.174415470458	0.125584529542266
246	339.12	338.798091100436	0.321908899564164
247	337.56	337.585991077537	-0.0259910775374124
248	335.92	335.654327249304	0.26567275069624
249	333.74	334.192190950487	-0.452190950486681
250	333.7	333.770555535768	-0.0705555357685057
251	335.13	335.054366240094	0.0756337599058838
252	336.56	336.287291526854	0.27270847314594
253	337.84	337.495891573297	0.344108426702803
254	338.19	338.279947739329	-0.0899477393289771
255	339.9	339.290955231107	0.609044768892716
256	340.6	340.634801952605	-0.0348019526052212
257	341.29	341.097036328383	0.192963671617122
258	341	340.810330405585	0.189669594414511
259	339.39	339.454763303222	-0.0647633032217527
260	337.43	337.583270201182	-0.153270201181556
261	335.72	335.743095553196	-0.023095553195617
262	335.84	335.63323606283	0.206763937169967
263	336.93	337.097840477184	-0.167840477184313
264	338.04	338.267484517072	-0.227484517072241
265	339.06	339.25305370165	-0.193053701650058
266	340.3	339.667969898447	0.632030101553482
267	341.21	341.21111297467	-0.00111297466992255
268	342.33	342.098840472503	0.231159527497312
269	342.74	342.751281754361	-0.0112817543613346
270	342.07	342.366051973324	-0.296051973323586
271	340.32	340.709155387985	-0.38915538798517
272	338.27	338.654547580585	-0.384547580585149
273	336.52	336.729610360951	-0.209610360950649
274	336.68	336.580492023293	0.0995079767067182
275	338.19	337.894693302117	0.295306697883461
276	339.44	339.273992032701	0.166007967298754
277	340.57	340.460581147397	0.109418852602914
278	341.44	341.229028048973	0.210971951026522
279	342.53	342.408308612354	0.121691387646422
280	343.39	343.413300385548	-0.0233003855481684
281	343.96	343.879328516256	0.08067148374397
282	343.18	343.467537940661	-0.28753794066057
283	341.88	341.790598760842	0.0894012391580077
284	339.65	339.973218610239	-0.323218610238769
285	337.8	338.123459545981	-0.323459545980825
286	337.69	337.996166401831	-0.306166401831433
287	339.09	339.158832060433	-0.0688320604332375
288	340.32	340.32452589084	-0.00452589084045485
289	341.2	341.409390514849	-0.209390514849019
290	342.35	342.040691385622	0.309308614378381
291	342.93	343.240684103608	-0.310684103607912
292	344.77	343.990026131506	0.779973868493983
293	345.58	344.872157118997	0.707842881002819
294	345.14	344.677068204753	0.4629317952473
295	343.81	343.465708247176	0.344291752823665
296	342.22	341.677357258495	0.542642741505006
297	339.69	340.262952231831	-0.572952231831437
298	339.82	340.027253620308	-0.207253620307995
299	340.98	341.307219767604	-0.327219767603538
300	342.82	342.370851749792	0.449148250208339
301	343.52	343.63873718665	-0.118737186650094
302	344.33	344.454461513091	-0.124461513090807
303	345.11	345.297962635569	-0.187962635569363
304	346.88	346.387004647881	0.492995352119237
305	347.25	347.119036263342	0.13096373665752
306	346.61	346.585754593661	0.0242454063393893
307	345.22	345.132621710642	0.08737828935773
308	343.11	343.268450761448	-0.158450761447625
309	340.9	341.231797773597	-0.331797773597373
310	341.17	341.203111442945	-0.0331114429451986
311	342.8	342.538226281409	0.261773718591485
312	344.04	344.085216624198	-0.0452166241976215
313	344.79	344.970451887514	-0.180451887513584
314	345.82	345.754146155681	0.0658538443193493
315	347.25	346.675956809567	0.574043190433258
316	348.17	348.311849375548	-0.141849375548247
317	348.75	348.644715976143	0.105284023856996
318	348.07	348.073781634647	-0.00378163464688441
319	346.38	346.623658678869	-0.243658678868599
320	344.52	344.535735653508	-0.0157356535078179
321	342.92	342.526258143353	0.393741856646841
322	342.63	342.931214072759	-0.301214072758683
323	344.06	344.210486390495	-0.150486390494621
324	345.38	345.479878619051	-0.0998786190505143
325	346.12	346.304913948692	-0.184913948692099
326	346.79	347.147273718221	-0.357273718221279
327	347.69	347.984842142941	-0.294842142941263
328	349.38	349.010536170525	0.369463829474569
329	350.04	349.650589061349	0.389410938651395
330	349.38	349.189096815436	0.190903184564434
331	347.78	347.773368560282	0.00663143971837599
332	345.75	345.864132479149	-0.114132479149191
333	344.7	343.906743734766	0.793256265234106
334	344.01	344.337189097174	-0.32718909717363
335	345.5	345.642245631512	-0.142245631512253
336	346.75	346.929497566797	-0.179497566796556
337	347.86	347.695353552143	0.164646447856626
338	348.32	348.669310126099	-0.349310126098658
339	349.26	349.52911818109	-0.269118181089596
340	350.84	350.734640032288	0.105359967712104
341	351.7	351.251719819105	0.448280180894926
342	351.11	350.77190411661	0.338095883389542
343	349.37	349.385504046671	-0.0155040466707419
344	347.97	347.438171537429	0.531828462571468
345	346.31	346.027919371956	0.282080628044355
346	346.22	345.934308678693	0.285691321306956
347	347.68	347.592340050739	0.0876599492611945
348	348.82	348.991271103846	-0.171271103846152
349	350.29	349.854454156557	0.435545843443379
350	351.58	350.843978968357	0.736021031642565
351	352.08	352.271579019089	-0.191579019089431
352	353.45	353.624118994981	-0.174118994981029
353	354.08	354.103832283072	-0.0238322830720676
354	353.66	353.377556419222	0.282443580777908
355	352.25	351.888340929646	0.361659070354165
356	350.3	350.27512873802	0.0248712619795128
357	348.58	348.565785492138	0.0142145078619933
358	348.74	348.351341927321	0.388658072679448
359	349.93	350.021054998154	-0.0910549981536519
360	351.21	351.277534250244	-0.0675342502438525
361	352.62	352.351241450934	0.268758549066263
362	352.93	353.342039978529	-0.412039978529378
363	353.54	353.979900305955	-0.439900305955348
364	355.27	355.215804598691	0.0541954013089594
365	355.52	355.846626453991	-0.326626453991366
366	354.97	355.047961780545	-0.0779617805453086
367	353.74	353.399942427528	0.340057572472062
368	351.51	351.691055140777	-0.181055140777119
369	349.63	349.875107595047	-0.245107595046875
370	349.82	349.621568367382	0.198431632617655
371	351.12	351.073880061725	0.0461199382747282
372	352.35	352.398571609853	-0.0485716098528997
373	353.47	353.559953775287	-0.0899537752874267
374	354.51	354.199917688749	0.310082311251222
375	355.18	355.182182632139	-0.00218263213895398
376	355.98	356.754594836809	-0.774594836808888
377	356.94	356.880214899662	0.0597851003379333
378	355.99	356.329723433625	-0.33972343362467
379	354.58	354.652541972773	-0.0725419727727967
380	352.68	352.606117586872	0.0738824131283877
381	350.72	350.894220189592	-0.17422018959229
382	350.92	350.780366924328	0.139633075671782
383	352.55	352.161217819261	0.388782180738758
384	353.91	353.62741850268	0.282581497319882

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
385	354.939742025576	354.338480744576	355.541003306576
386	355.722029429422	355.050908633146	356.393150225697
387	356.47274759178	355.73697641666	357.208518766899
388	357.852961927731	357.056465093054	358.649458762408
389	358.566476569559	357.712327365656	359.420625773462
390	357.889667364963	356.980341257584	358.798993472342
391	356.44867842009	355.486212674445	357.411144165734
392	354.478068960585	353.464168733118	355.491969188052
393	352.672300714118	351.60841264129	353.736188786946
394	352.726047973156	351.613413003782	353.838682942531
395	354.103881817386	352.943574235423	355.264189399348
396	355.35490731875	354.147864260963	356.561950376536

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293636739mkuoya4v1ve1zvn/1z1v31293636814.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293636739mkuoya4v1ve1zvn/1z1v31293636814.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293636739mkuoya4v1ve1zvn/2rtvo1293636814.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293636739mkuoya4v1ve1zvn/2rtvo1293636814.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293636739mkuoya4v1ve1zvn/3rtvo1293636814.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293636739mkuoya4v1ve1zvn/3rtvo1293636814.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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