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Double exponential smoothing eigen reeks

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 07 Jun 2010 07:15:01 +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/07/t1275894936v8dh70i9aavryte.htm/, Retrieved Mon, 07 Jun 2010 09:15:37 +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/07/t1275894936v8dh70i9aavryte.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 «

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 98.7 114.5 113. 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	4 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.692095688349756
beta	0.00660408012385285
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	95.2	98.8	-3.59999999999999
4	77.1	99.0920011625756	-21.9920011625756
5	70.9	86.5544597619951	-15.6544597619951
6	64.8	78.3315522987742	-13.5315522987742
7	70.1	71.5160518753103	-1.41605187531029
8	77.3	73.0791647720042	4.22083522799579
9	79.5	78.5628349118503	0.937165088149698
10	100.6	81.7781745645975	18.8218254354025
11	100.7	97.4574386089515	3.24256139104848
12	107.1	102.36918181121	4.73081818878975
13	95.9	108.332564065946	-12.4325640659457
14	82.8	102.360418498854	-19.5604184988543
15	83.3	91.3657116795303	-8.06571167953032
16	80	88.2895763002296	-8.28957630022958
17	80.4	85.0206163856606	-4.62061638566061
18	67.5	84.2698085635544	-16.7698085635544
19	75.7	75.0339482024756	0.666051797524403
20	71.1	77.868415913199	-6.76841591319905
21	89.3	75.5265844795528	13.7734155204472
22	101.1	87.4646195476795	13.6353804523205
23	105.2	99.369443765327	5.83055623467301
24	114.1	105.899232256831	8.20076774316915
25	96.3	114.106916797041	-17.806916797041
26	84.4	104.233405722965	-19.8334057229651
27	91.2	92.8667187382124	-1.66671873821244
28	81.9	94.0654994902402	-12.1654994902402
29	80.5	87.942515045174	-7.44251504517402
30	70.4	85.0542705992548	-14.6542705992548
31	74.8	77.1078216081807	-2.30782160818067
32	75.9	77.6957484730114	-1.79574847301137
33	86.3	78.6298711993946	7.67012880060541
34	98.7	86.1503442887578	12.5496557112422
35	100.9	97.1052770655435	3.79472293445649
36	113.8	102.018302986517	11.7816970134831
37	89.8	112.512929307377	-22.7129293073771
38	84.4	99.030160507817	-14.630160507817
39	87.2	91.0745717225363	-3.87457172253626
40	85.6	90.5451702291255	-4.94517022912547
41	72	89.2522094564416	-17.2522094564416
42	69.2	79.3627459942252	-10.1627459942252
43	77.5	74.3334192172755	3.16658078272445
44	78.1	78.543735380746	-0.443735380746062
45	94.3	80.2533391323942	14.0466608676058
46	97.7	92.055886096061	5.644113903939
47	100.2	98.0688638345937	2.13113616540629
48	116.4	101.660265515998	14.7397344840024
49	97.1	114.045393976544	-16.9453939765436
50	93	104.423930088605	-11.4239300886054
51	96	98.5716327033767	-2.57163270337665
52	80.5	98.8342181236054	-18.3342181236054
53	76.1	88.1037867445584	-12.0037867445584
54	69.9	81.6997544558886	-11.7997544558886
55	73.6	75.3829994233139	-1.7829994233139
56	92.6	75.9906478841345	16.6093521158655
57	94.2	89.4034791684281	4.79652083157185
58	93.5	94.6626240973995	-1.16262409739949
59	108.5	95.7921565606936	12.7078434393064
60	109.4	106.579462974512	2.82053702548848
61	105.1	110.536698952661	-5.43669895266105
62	92.5	108.754288235334	-16.2542882353335
63	97.1	99.4107778671714	-2.3107778671714
64	81.4	99.7069491359856	-18.3069491359856
65	79.1	88.8485644840035	-9.74856448400347
66	72.1	83.8688436201983	-11.7688436201983
67	78.7	77.4371049485696	1.26289505143036
68	87.1	80.0303486813362	7.0696513186638
69	91.4	86.6747363297819	4.7252636702181
70	109.9	91.7181809467305	18.1818190532695
71	116.3	106.157952353389	10.1420476466112
72	113	115.079788438814	-2.07978843881365
73	100	115.533438469583	-15.533438469583
74	84.8	106.604877327391	-21.8048773273913
75	94.3	93.2362178121113	1.06378218788868
76	87.1	95.6997211274747	-8.59972112747467
77	90.3	91.4358491022902	-1.13584910229025
78	72.4	92.332499149321	-19.9324991493209
79	84.9	80.128964158924	4.77103584107599
80	92.7	85.0444459830097	7.65555401699032
81	92.2	91.991281298761	0.208718701239064
82	114.9	93.7851479818846	21.1148520181154
83	112.5	110.144568105642	2.35543189435806
84	118.3	113.531440313264	4.76855968673645
85	106	118.610223304411	-12.6102233044106
86	91.2	111.603588533639	-20.403588533639
87	96.6	99.1099415182966	-2.50994151829657
88	96.3	98.988938373423	-2.68893837342294
89	88.2	98.7317620662473	-10.5317620662473
90	70.2	92.9984642418397	-22.7984642418397
91	86.5	78.6712308082087	7.82876919179128
92	88.2	85.5767561860945	2.6232438139055
93	102.8	88.8915498377994	13.9084501622006
94	119.1	100.080356877847	19.0196431221527
95	119.2	114.893530761949	4.30646923805097
96	125.1	119.543463825712	5.55653617428784
97	106.1	125.083959838148	-18.9839598381483
98	102.1	113.55331523226	-11.4533152322596
99	105.2	107.182248131724	-1.98224813172445
100	101	107.357005562455	-6.35700556245465
101	84.3	104.474956556131	-20.1749565561306
102	87.5	91.937350471546	-4.43735047154603
103	92.7	90.271392103247	2.42860789675298
104	94.4	93.368434247784	1.03156575221597
105	113	95.5033044791985	17.4966955208015
106	113.9	109.113591397071	4.7864086029288
107	122.9	113.949020565624	8.95097943437591
108	132.7	121.70764309275	10.9923569072501
109	106.9	130.929336442375	-24.0293364423748
110	96.6	115.802837010147	-19.2028370101472
111	127.3	103.92896747451	23.3710325254902
112	98.2	121.627110416383	-23.427110416383
113	100.2	106.829383157166	-6.62938315716565
114	89.4	103.626989882339	-14.2269898823395
115	95.3	95.1012990834074	0.198700916592628
116	104.2	96.5604748812962	7.63952511870382
117	106.4	103.204330663813	3.19566933618673
118	116.2	106.787219322844	9.41278067715614
119	135.9	114.715966511585	21.1840334884147
120	134	130.888371934092	3.11162806590849
121	104.6	134.56716566513	-29.96716566513
122	107.1	115.215299292158	-8.1152992921581
123	123.5	110.949923181951	12.5500768180488
124	98.8	121.044326851863	-22.2443268518629
125	98.6	106.956002610945	-8.35600261094477
126	90.6	102.441535287287	-11.8415352872869
127	89.1	95.4606222497712	-6.3606222497712
128	105.2	92.2439532814389	12.9560467185611
129	114	102.455485243997	11.5445147560033
130	122.1	111.742868019771	10.3571319802294
131	138	120.255807177009	17.7441928229905
132	142.2	133.962401883477	8.23759811652278
133	116.4	141.127174604853	-24.7271746048533
134	112.6	125.364150864714	-12.7641508647144
135	123.8	117.82234373994	5.97765626005982
136	103.6	123.278982324845	-19.6789823248452
137	113.9	110.888826121169	3.01117387883144
138	98.6	114.216192232126	-15.6161922321261
139	95	104.580262339349	-9.58026233934862
140	116	99.077985422948	16.922014577052
141	113.9	111.995164788794	1.90483521120638
142	127.5	114.527725409667	12.9722745903328
143	131.4	124.779304902544	6.62069509745628
144	145.9	130.665244529851	15.2347554701489
145	131.5	142.582571017325	-11.0825710173245
146	131	136.235134701089	-5.23513470108867
147	130.5	133.910755850637	-3.41075585063689
148	118.9	132.833432346923	-13.9334323469233
149	114.3	124.409724892723	-10.1097248927229
150	85.7	118.586180812622	-32.8861808126219
151	104.6	96.8488383952368	7.75116160476317
152	105.1	103.271853339401	1.82814666059924
153	117.3	105.603931007046	11.6960689929541
154	142.5	114.819013874543	27.6809861254573
155	140	135.22370921621	4.77629078379002
156	159.8	139.797994448108	20.0020055518917
157	131.2	155.001353497324	-23.8013534973243
158	125.4	139.779808828946	-14.3798088289459
159	126.5	131.013149452571	-4.5131494525705
160	119.4	129.054534438178	-9.6545344381775
161	113.5	123.493461493336	-9.99346149333589
162	98.7	117.652141926422	-18.9521419264224
163	114.5	105.523934549022	8.97606545097764
164	113.8	112.765745582697	1.0342544173034
165	133.1	114.515790662792	18.5842093372077
166	143.4	128.497025890062	14.9029741099377
167	137.3	139.99861044752	-2.69861044751971
168	165.2	139.305879806279	25.8941201937212
169	126.9	158.520407859741	-31.6204078597406
170	124	137.784853042653	-13.7848530426527
171	135.7	129.330203001086	6.36979699891427
172	130	134.853613500403	-4.85361350040318
173	109.4	132.587165789909	-23.1871657899093
174	117.8	117.526165043667	0.273834956333403
175	120.3	118.703673363485	1.59632663651495
176	121	120.803768731964	0.196231268036215
177	132.3	121.935761038141	10.3642389618593
178	142.9	130.152358992882	12.7476410071175
179	147.4	140.076764300693	7.32323569930679
180	175.9	146.280434069749	29.619565930251
181	132.6	168.050678686013	-35.4506786860133
182	123.7	144.624054728263	-20.9240547282634
183	153.3	131.155607934651	22.1443920653487
184	134	147.595861855532	-13.5958618555325
185	119.6	139.238298138121	-19.6382981381209
186	116.2	126.609030429378	-10.4090304293778
187	118.6	120.319723017557	-1.71972301755677
188	130.7	120.036387538942	10.6636124610583
189	129.3	128.372244850122	0.92775514987818
190	144.4	129.974197742912	14.4258022570878
191	163.2	140.98402621043	22.2159737895696
192	179.4	157.48694036719	21.9130596328096
193	128.1	173.880365986003	-45.780365986003
194	138.4	143.214217328353	-4.81421732835315
195	152.7	140.878559396629	11.8214406033707
196	120	150.110400323397	-30.110400323397
197	140.5	130.183770676972	10.3162293230281
198	116.2	138.283389032399	-22.0833890323988
199	121.4	123.858435658984	-2.45843565898443
200	127.8	123.004591237206	4.79540876279408
201	143.6	127.193019424558	16.4069805754425
202	157.6	139.492757052431	18.1072429475692
203	166.2	153.052000904498	13.1479990955023
204	182.3	163.239068441866	19.0609315581339
205	153.1	177.605571991485	-24.5055719914846
206	147.6	161.707879753494	-14.1078797534936
207	157.7	152.941903225719	4.75809677428092
208	137.2	157.254735329941	-20.0547353299413
209	151.5	144.30305003517	7.19694996483005
210	98.7	150.245033411245	-51.5450334112451
211	145.8	115.296348783392	30.5036512166083
212	151.7	137.272626698764	14.4273733012359
213	129.4	148.188524535582	-18.7885245355823
214	174.1	136.029966824136	38.0700331758638
215	197	163.396976752491	33.6030232475094
216	193.9	187.82597620858	6.07402379141982
217	164.1	193.230036106043	-29.1300361060432
218	142.8	174.13637457984	-31.3363745798401
219	157.9	153.372487939843	4.52751206015702
220	159.2	157.450536308205	1.7494636917954
221	162.2	159.61390557443	2.58609442557028
222	123.1	162.368123510639	-39.2681235106388
223	130	135.97573661399	-5.97573661399016
224	150.1	132.597554110684	17.5024458893157
225	169.4	145.548518136659	23.8514818633411
226	179.7	163.002639489315	16.6973605106846
227	182.1	175.581742180505	6.5182578194954
228	194.3	181.145724498018	13.1542755019818
229	161.4	191.362589701477	-29.9625897014765
230	169.4	171.601509730669	-2.20150973066885
231	168.8	171.043691169297	-2.24369116929702
232	158.1	170.44642387701	-12.34642387701
233	158.5	162.800667588457	-4.30066758845695
234	135.3	160.703687667277	-25.4036876672769
235	149.3	143.885287036698	5.41471296330158
236	143.4	148.420917391311	-5.02091739131143
237	142.2	145.711144089202	-3.51114408920165
238	188.4	144.030230150249	44.369769849751
239	166.2	175.69028922993	-9.49028922993045
240	199.2	170.030656804782	29.169343195218
241	182.7	191.260512309649	-8.56051230964914
242	145.2	186.338570345901	-41.1385703459013
243	182.1	158.68146465261	23.4185353473903
244	158.7	175.811091516544	-17.1110915165441
245	141.6	164.81212947504	-23.2121294750403
246	132.6	149.484570723555	-16.8845707235545
247	139.6	138.459114547748	1.14088545225184
248	147	139.914213465984	7.08578653401574
249	166.6	145.516139478913	21.0838605210872
250	157	160.902439204	-3.9024392040001
251	180.4	158.9779919168	21.4220080832001
252	210.2	174.678398023391	35.5216019766089
253	159.8	200.299429272246	-40.4994292722465
254	157.8	173.121523635608	-15.3215236356079
255	168.2	163.299108527341	4.90089147265925
256	158.4	167.494940009497	-9.09494000949675
257	152	161.962747031505	-9.96274703150465
258	142.2	155.78441227195	-13.5844122719497
259	137.2	147.037448947812	-9.83744894781205
260	152.6	140.838779195763	11.7612208042366
261	166.8	149.642212140333	17.1577878596668
262	165.6	162.259008211233	3.34099178876684
263	198.6	165.328529816747	33.2714701832533
264	201.5	189.264878893498	12.235121106502
265	170.7	198.69798399771	-27.9979839977104
266	164.4	180.157961394208	-15.7579613942079
267	179.7	170.017181448881	9.68281855111911
268	157	177.528112438666	-20.5281124386664
269	168	164.036361421846	3.96363857815396
270	139.3	167.513362109891	-28.2133621098914
271	138.6	148.59184580242	-9.99184580241956
272	153.4	142.235693082778	11.1643069172216
273	138.9	150.572650641937	-11.6726506419365
274	172.1	143.050896675928	29.0491033240716
275	198.4	163.845266492204	34.5547335077958
276	217.8	188.607996998869	29.1920030011308
277	173.7	209.792631429637	-36.0926314296375
278	153.8	185.629084875386	-31.8290848753863
279	175.6	164.270840730409	11.3291592695909
280	147.1	172.834012957674	-25.7340129576745
281	160.3	155.628302185131	4.67169781486925
282	135.2	159.487605460222	-24.287605460222
283	148.8	143.193289526464	5.60671047353594
284	151	147.614327098011	3.38567290198887
285	148.2	150.513668886689	-2.31366888668947
286	182.2	149.457945813849	32.7420541861508
287	189.2	172.813790177798	16.3862098222021
288	183.1	184.924720896207	-1.82472089620714
289	170	184.423604813189	-14.4236048131894
290	158.4	175.136930166282	-16.7369301662818
291	176.1	164.172714276852	11.9272857231477
292	156.2	173.101394127074	-16.9013941270738
293	153.2	162.000618504158	-8.80061850415797
294	117.9	156.466130167844	-38.5661301678444
295	149.8	130.154787057261	19.6452129427389
296	156.6	144.221055024774	12.3789449752262
297	166.7	153.314950153017	13.3850498469828
298	156.8	163.166344575116	-6.3663445751155
299	158.6	159.318785711706	-0.718785711705863
300	210.8	159.376592665584	51.4234073344163
301	203.6	195.756825281135	7.84317471886499
302	175.2	202.011215254903	-26.8112152549029
303	168.7	184.158906520206	-15.4589065202063
304	155.9	174.092824379365	-18.1928243793649
305	147.3	162.051456345284	-14.7514563452844
306	137	152.32442046632	-15.3244204663195
307	141.1	142.130795944769	-1.03079594476912
308	167.4	141.825015912444	25.5749840875558
309	160.2	160.049875964267	0.150124035732915
310	191.9	160.678986162559	31.2210138374411
311	174.4	182.954825720645	-8.55482572064454
312	208.2	177.662877059889	30.537122940111
313	159.4	199.565872181665	-40.165872181665
314	161.1	172.352044866497	-11.2520448664972
315	172.1	165.09792355045	7.00207644955003
316	158.4	170.509404970242	-12.1094049702423
317	114.6	162.638564584453	-48.0385645844534
318	159.6	129.68174002001	29.9182599799899
319	159.7	150.815243669971	8.88475633002872
320	159.4	157.432159292218	1.96784070778153
321	160.7	159.270901757346	1.42909824265416
322	165.5	160.743314800798	4.75668519920214
323	205	164.540477598279	40.4595224017213
324	205.2	193.232346619183	11.967653380817
325	141.6	202.259815956995	-60.6598159569953
326	148.1	160.744871796246	-12.6448717962464
327	184.9	152.403068114211	32.4969318857892
328	132.5	175.452244401376	-42.9522444013756
329	137.3	146.08705118373	-8.78705118372963
330	135.5	140.327278300892	-4.82727830089229
331	121.7	137.285983331578	-15.5859833315779
332	166.1	126.727396839744	39.372603160256
333	146.8	154.385369697134	-7.58536969713441
334	162.8	149.50926189547	13.2907381045297
335	186.8	159.142165676474	27.6578343235258
336	185.5	178.84488923398	6.65511076601987
337	151.5	184.042136591556	-32.5421365915565
338	158.1	161.962399166111	-3.86239916611137
339	143	159.714130660295	-16.7141306602946
340	151.2	148.494839668313	2.70516033168684
341	147.6	150.727920598313	-3.12792059831304
342	130.7	148.909654719756	-18.2096547197563
343	137.5	136.570155626612	0.929844373387567
344	146.1	137.481271331195	8.6187286688054
345	133.6	143.753223943408	-10.1532239434078
346	167.9	136.986782203169	30.9132177968312
347	181.9	158.783541392428	23.1164586075718
348	202	175.289854529583	26.7101454704166
349	166.5	194.405425719867	-27.9054257198672
350	151.3	175.59424948842	-24.29424948842
351	146.2	159.17131211452	-12.9713121145199
352	148.3	150.525643479058	-2.22564347905833
353	144.7	149.306833125295	-4.60683312529517
354	123.6	146.418955437623	-22.818955437623
355	151.6	130.822248840471	20.7777511595291
356	133.9	145.493602845563	-11.5936028455628
357	137.4	137.707891954476	-0.30789195447619
358	181.6	137.731565643055	43.8684343569454
359	182	168.529991794372	13.4700082056281
360	190	178.351365039207	11.6486349607925
361	161.2	186.965415610461	-25.765415610461
362	155.5	169.567598262192	-14.0675982621921
363	141.9	160.201491720093	-18.301491720093
364	164.6	147.82147595927	16.7785240407299
365	136.2	159.796876704917	-23.5968767049165
366	126.8	143.720783487663	-16.9207834876631
367	152.5	132.187846531023	20.312153468977
368	126.6	146.516504560189	-19.9165045601887
369	150.1	132.912050340568	17.1879496594316
370	186.3	145.065989099487	41.2340109005129
371	147.5	174.050569618882	-26.5505696188823
372	200.4	156.000380720357	44.3996192796432
373	177.2	187.257447004798	-10.0574470047981
374	127.4	180.779043389347	-53.3790433893468
375	177.1	144.073972491915	33.026027508085
376	154.4	167.320429204435	-12.9204292044354
377	135.2	158.708486502026	-23.5084865020264
378	126.4	142.661145805666	-16.2611458056664
379	147.3	131.55533426371	15.7446657362904
380	140.6	142.672570333218	-2.07257033321787
381	152.3	141.449101135967	10.8508988640327
382	151.2	149.219504967917	1.98049503208281
383	172.2	150.859792714125	21.3402072858747
384	215.3	165.9963925721	49.3036074279001
385	154.1	200.711690898475	-46.6116908984753
386	159.3	168.831378830645	-9.53137883064531
387	160.4	162.5706262197	-2.17062621970007
388	151.9	161.394297569392	-9.49429756939188
389	148.4	155.105892392814	-6.70589239281375
390	139.6	150.71668009318	-11.1166800931797
391	148.2	143.223970130229	4.97602986977088
392	153.5	146.891699064191	6.60830093580873
393	145.1	151.719320031396	-6.61932003139617
394	183.7	147.361906929365	36.3380930706347
395	210.5	172.901223118474	37.5987768815262
396	203.3	199.484904189279	3.81509581072117
397	153.3	202.704482742586	-49.404482742586
398	144.3	168.865209578552	-24.5652095785524
399	169.6	152.104811165786	17.495188834214
400	143.7	164.534197623724	-20.834197623724
401	160.1	150.340755039591	9.75924496040935
402	135.6	157.365508305187	-21.7655083051874
403	141.8	142.472633121758	-0.672633121757826
404	159.9	142.174971533483	17.7250284665168
405	145.7	154.691267202879	-8.99126720287902
406	183.5	148.676233847002	34.8237661529983
407	198.2	173.14456359572	25.0554364042797
408	186.8	190.966794208152	-4.16679420815231
409	172	188.545400029396	-16.5454000293963
410	150.6	177.48120281233	-26.8812028123301
411	163.3	159.140776339328	4.15922366067244
412	153.7	162.302305570826	-8.60230557082582
413	152.9	156.592317270224	-3.69231727022361
414	135.5	154.263634392523	-18.763634392523
415	148.5	141.418395810257	7.0816041897431
416	148.4	146.492902987431	1.90709701256858
417	133.6	147.994872741168	-14.3948727411678
418	194.1	138.148525514207	55.9514744857927
419	208.6	177.244316802016	31.3556831979844
420	197.3	199.46078301006	-2.16078301005965
421	164.4	198.470771272308	-34.0707712723079
422	148.1	175.240268488972	-27.1402684889723
423	152	156.682287985916	-4.68228798591628
424	144.1	153.645977833298	-9.54597783329828
425	155	147.199897532903	7.80010246709713
426	124.5	152.79461619848	-28.2946161984796
427	153	133.279010763682	19.7209892363178
428	146	147.084936669348	-1.08493666934805
429	138	146.486212091954	-8.4862120919542
430	190	140.726309155338	49.2736908446618
431	192	175.166999060768	16.8330009392316
432	192	187.23256520185	4.76743479814951
433	147	190.969395340696	-43.9693953406962
434	133	160.774706523277	-27.7747065232767
435	163	141.661343398782	21.3386566012181
436	150	156.636658778686	-6.6366587786859
437	129	152.220045123787	-23.2200451237868
438	131	136.220010457054	-5.220010457054
439	145	132.653863304438	12.3461366955621
440	137	141.301600793165	-4.30160079316514
441	138	138.407849810361	-0.407849810361029
442	168	138.207082953334	29.7929170466664
443	176	159.044309779474	16.9556902205265
444	188	171.074445885589	16.9255541144107
445	139	183.161085797558	-44.1610857975582
446	143	152.768080506326	-9.7680805063259
447	150	146.133679356835	3.86632064316524
448	154	148.953260075383	5.04673992461707
449	137	152.612870798053	-15.6128707980529
450	129	141.90269296468	-12.9026929646801
451	128	133.00924376144	-5.00924376144016
452	140	129.555921191026	10.4440788089738
453	143	136.845512827263	6.15448717273685
454	151	141.194426627182	9.80557337281817
455	177	148.115059340653	28.884940659347
456	184	168.372462998976	15.6275370010243
457	151	179.525902832719	-28.5259028327189
458	134	159.990555260488	-25.9905552604882
459	164	142.091116940256	21.9088830597443
460	126	157.442811310041	-31.4428113100413
461	131	135.726313785692	-4.72631378569176
462	125	132.478586654223	-7.47858665422297
463	127	127.291841294962	-0.291841294961515
464	143	127.077677506128	15.9223224938722
465	143	138.158042014699	4.84195798530078
466	160	141.591864942856	18.4081350571438
467	190	154.498917771346	35.5010822286543
468	182	179.398188850885	2.60181114911515
469	138	181.53990824855	-43.5399082485496
470	136	151.548136682199	-15.5481366821986
471	152	140.858284351627	11.1417156483732
472	127	148.691288684298	-21.6912886842977
473	151	133.701568877451	17.2984311225493
474	130	145.77553120615	-15.7755312061502
475	119	134.887042293947	-15.8870422939469
476	153	123.848762843355	29.1512371566447

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
477	144.114522670131	106.814625507445	181.414419832817
478	144.204836950732	98.7457030935747	189.663970807889
479	144.295151231332	91.8482948734323	196.742007589232
480	144.385465511933	85.7019062218673	203.069024801999
481	144.475779792534	80.0874800116721	208.864079573395
482	144.566094073134	74.873842529377	214.258345616891
483	144.656408353735	69.9751617726205	219.337654934849
484	144.746722634336	65.3316908334446	224.161754435226
485	144.837036914936	60.8998931073578	228.774180722515
486	144.927351195537	56.6469047474374	233.207797643636
487	145.017665476137	52.5472120886077	237.488118863667
488	145.107979756738	48.580549382328	241.635410131148

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275894936v8dh70i9aavryte/1wz1x1275894895.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275894936v8dh70i9aavryte/1wz1x1275894895.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275894936v8dh70i9aavryte/2jnbu1275894895.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275894936v8dh70i9aavryte/2jnbu1275894895.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275894936v8dh70i9aavryte/3jnbu1275894895.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275894936v8dh70i9aavryte/3jnbu1275894895.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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