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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: Fri, 04 Dec 2009 07:59:38 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938827fqrzxqkge5kd931.htm/, Retrieved Fri, 04 Dec 2009 16:00:32 +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/2009/Dec/04/t1259938827fqrzxqkge5kd931.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:

WS9_expsmooth

Dataseries X:

» Textbox « » Textfile « » CSV «

235.1 280.7 264.6 240.7 201.4 240.8 241.1 223.8 206.1 174.7 203.3 220.5 299.5 347.4 338.3 327.7 351.6 396.6 438.8 395.6 363.5 378.8 357 369 464.8 479.1 431.3 366.5 326.3 355.1 331.6 261.3 249 205.5 235.6 240.9 264.9 253.8 232.3 193.8 177 213.2 207.2 180.6 188.6 175.4 199 179.6 225.8 234 200.2 183.6 178.2 203.2 208.5 191.8 172.8 148 159.4 154.5 213.2 196.4 182.8 176.4 153.6 173.2 171 151.2 161.9 157.2 201.7 236.4 356.1 398.3 403.7 384.6 365.8 368.1 367.9 347 343.3 292.9 311.5 300.9 366.9 356.9 329.7 316.2 269 289.3 266.2 253.6 233.8 228.4 253.6 260.1 306.6 309.2 309.5 271 279.9 317.9 298.4 246.7 227.3 209.1 259.9 266 320.6 308.5 282.2 262.7 263.5 313.1 284.3 252.6 250.3 246.5 312.7 333.2 446.4 511.6 515.5 506.4 483.2 522.3 509.8 460.7 405.8 375 378.5 406.8 467.8 469.8 429.8 355.8 332.7 378 360.5 334.7 319.5 323.1 363.6 352.1 411.9 388.6 416.4 360.7 338 417.2 388. 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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.934221760733587
beta	0.0075036315050239
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
5	201.4	217.379947764092	-15.9799477640918
6	240.8	239.352980762353	1.4470192376468
7	241.1	233.085430961968	8.01456903803162
8	223.8	219.620470056651	4.17952994334894
9	206.1	185.891673048118	20.2083269518816
10	174.7	243.861153356924	-69.1611533569236
11	203.3	171.600626496691	31.6993735033089
12	220.5	182.208870581636	38.2911294183635
13	299.5	182.223654279087	117.276345720913
14	347.4	340.632596952795	6.76740304720522
15	338.3	354.169519539684	-15.8695195396843
16	327.7	313.979933587329	13.7200664126711
17	351.6	281.229506072028	70.3704939279719
18	396.6	396.785120179258	-0.185120179257865
19	438.8	404.639217948954	34.1607820510465
20	395.6	409.074994727523	-13.4749947275229
21	363.5	346.617919319108	16.8820806808919
22	378.8	409.401584993034	-30.6015849930336
23	357	390.342706463704	-33.3427064637042
24	369	332.696131835951	36.3038681640492
25	464.8	321.789686318635	143.010313681365
26	479.1	512.58292867639	-33.4829286763903
27	431.3	495.575381423991	-64.2753814239908
28	366.5	410.582369346959	-44.0823693469586
29	326.3	328.941988867418	-2.64198886741821
30	355.1	355.996084234391	-0.896084234391196
31	331.6	361.691368845331	-30.0913688453306
32	261.3	313.325070826617	-52.0250708266165
33	249	235.506434814428	13.4935651855719
34	205.5	268.810747628503	-63.3107476285026
35	235.6	208.950577402542	26.6494225974583
36	240.9	215.888443848166	25.0115561518337
37	264.9	215.94964683916	48.9503531608402
38	253.8	277.486378346606	-23.6863783466061
39	232.3	263.845690184642	-31.5456901846423
40	193.8	216.382710275023	-22.5827102750232
41	177	175.978257940728	1.0217420592719
42	213.2	181.788432417131	31.411567582869
43	207.2	216.360357407464	-9.16035740746355
44	180.6	191.457803639127	-10.8578036391271
45	188.6	164.410064892517	24.1899351074830
46	175.4	194.570008868208	-19.1700088682075
47	199	177.5806362994	21.4193637006001
48	179.6	181.691916550140	-2.09191655014047
49	225.8	165.155550756757	60.6444492432428
50	234	228.697637782792	5.30236221720767
51	200.2	241.040847840189	-40.8408478401886
52	183.6	185.41432210187	-1.81432210187015
53	178.2	172.309531988000	5.89046801200018
54	203.2	178.97863601601	24.2213639839901
55	208.5	204.053576347174	4.4464236528257
56	191.8	193.163524884624	-1.36352488462373
57	172.8	180.95932493805	-8.1593249380499
58	148	175.443350677390	-27.4433506773903
59	159.4	148.875193054206	10.5248069457938
60	154.5	145.459172774719	9.04082722528128
61	213.2	143.587725909795	69.6122740902046
62	196.4	210.870964712572	-14.4709647125723
63	182.8	201.982010879535	-19.1820108795353
64	176.4	169.839394651471	6.56060534852892
65	153.6	168.223296042576	-14.6232960425761
66	173.2	150.439281680628	22.7607183193722
67	171	174.655587781533	-3.6555877815326
68	151.2	159.226084748562	-8.02608474856234
69	161.9	143.038416819806	18.8615831801938
70	157.2	159.191811049221	-1.99181104922056
71	201.7	157.967840891734	43.7321591082662
72	236.4	185.711723134034	50.6882768659657
73	356.1	225.818742892226	130.281257107775
74	398.3	349.008477874114	49.2915221258856
75	403.7	413.149767737602	-9.44976773760203
76	384.6	384.222220898058	0.377779101941542
77	365.8	380.559144599655	-14.7591445996553
78	368.1	362.712545359423	5.38745464057689
79	367.9	380.468649444428	-12.5686494444284
80	347	350.513764211258	-3.51376421125815
81	343.3	342.167131639463	1.13286836053726
82	292.9	340.375519318382	-47.4755193183819
83	311.5	304.120248836656	7.37975116334411
84	300.9	295.265659715086	5.63434028491429
85	366.9	295.691687041417	71.2083129585828
86	356.9	355.791395099203	1.10860490079745
87	329.7	372.590326026385	-42.8903260263853
88	316.2	316.102031301991	0.0979686980088559
89	269	315.158417609322	-46.1584176093223
90	289.3	262.406658932416	26.8933410675842
91	266.2	296.524858240556	-30.3248582405562
92	253.6	256.12699058419	-2.52699058419014
93	233.8	249.041046510085	-15.2410465100852
94	228.4	229.819394190820	-1.41939419081976
95	253.6	231.301022708827	22.2989772911729
96	260.1	242.242250446066	17.8577495539343
97	306.6	253.427596078652	53.1724039213478
98	309.2	299.661037960286	9.53896203971397
99	309.5	316.531836959027	-7.03183695902652
100	271	298.825677762622	-27.8256777626222
101	279.9	269.28796807547	10.6120319245299
102	317.9	273.031777901591	44.8682220984093
103	298.4	322.152399143839	-23.7523991438385
104	246.7	287.602797460292	-40.9027974602921
105	227.3	248.084564512618	-20.7845645126179
106	209.1	224.216074626107	-15.1160746261070
107	259.9	209.961178803572	49.9388211964284
108	266	244.000687431169	21.9993125688312
109	320.6	264.961903070009	55.6380969299911
110	308.5	313.448557916109	-4.94855791610865
111	282.2	316.890513195075	-34.6905131950754
112	262.7	269.15018160911	-6.45018160911019
113	263.5	265.161940896833	-1.66194089683307
114	313.1	256.592357572628	56.5076424273717
115	284.3	315.365271797906	-31.0652717979059
116	252.6	272.836218451920	-20.2362184519204
117	250.3	256.121761475997	-5.82176147599682
118	246.5	246.880033199873	-0.380033199872827
119	312.7	245.486738546584	67.213261453416
120	333.2	294.833046881028	38.3669531189722
121	446.4	336.511241701296	109.888758298704
122	511.6	437.200701956096	74.3992980439039
123	515.5	517.620199648103	-2.12019964810258
124	506.4	493.284131603443	13.1158683965568
125	483.2	521.755514880255	-38.555514880255
126	522.3	480.826750079151	41.473249920849
127	509.8	525.669179163278	-15.8691791632781
128	460.7	489.65751747629	-28.9575174762898
129	405.8	473.735058813069	-67.9350588130692
130	375	409.654034477823	-34.6540344778234
131	378.5	377.530821025100	0.969178974900444
132	406.8	360.748663989237	46.0513360107629
133	467.8	410.103188330889	57.6968116691108
134	469.8	466.383638947654	3.41636105234625
135	429.8	474.195226965321	-44.3952269653213
136	355.8	416.290424305038	-60.4904243050383
137	332.7	365.130767859327	-32.4307678593267
138	378	332.590410879715	45.4095891202845
139	360.5	375.000782902933	-14.5007829029329
140	334.7	345.507171739483	-10.8071717394826
141	319.5	341.796305835742	-22.2963058357415
142	323.1	323.308764829116	-0.208764829116376
143	363.6	319.045807387681	44.5541926123194
144	352.1	345.009466926614	7.09053307338615
145	411.9	357.768140764447	54.1318592355527
146	388.6	414.648918147557	-26.0489181475573
147	416.4	389.651560546716	26.7484394532844
148	360.7	394.688179696047	-33.9881796960473
149	338	372.201751372243	-34.2017513722433
150	417.2	340.221499203162	76.9785007968378
151	388.4	415.365958048884	-26.9659580488837
152	371.1	367.313718081863	3.78628191813749
153	331.5	380.339927766416	-48.8399277664162
154	353.7	341.063494811593	12.6365051884066
155	396.7	349.029694361414	47.6703056385863
156	447	372.56789952753	74.4321004724703
157	533.5	449.719403538552	83.7805964614475
158	565.4	547.43445129343	17.9655487065696
159	542.3	564.130297789759	-21.8302977897588
160	488.7	518.051753545877	-29.3517535458773
161	467.1	499.248021691552	-32.1480216915516
162	531.3	481.920918722575	49.3790812774253
163	496.1	525.183873973938	-29.0838739739382
164	444	473.526871376572	-29.5268713765719
165	403.4	453.137295318286	-49.7372953182856
166	386.3	421.565105920546	-35.265105920546
167	394.1	381.432363720162	12.6676362798384
168	404.1	372.843853288316	31.2561467116844
169	462.1	406.631560609873	55.4684393901267
170	448.1	476.934874495087	-28.8348744950873
171	432.3	446.091783349183	-13.7917833491827
172	386.3	412.423845479407	-26.1238454794072
173	395.2	393.414204773752	1.78579522624796
174	421.9	405.40875890475	16.4912410952500
175	382.9	417.812568974774	-34.9125689747744
176	384.2	365.419227055022	18.7807729449783
177	345.5	390.140854790550	-44.6408547905496
178	323.4	357.855611158753	-34.4556111587526
179	372.6	319.591995393697	53.0080046063031
180	376	353.292252018288	22.7077479817124
181	462.7	377.033892676003	85.6661073239968
182	487	471.648423525483	15.3515764745171
183	444.2	487.155674935576	-42.9556749355757
184	399.3	426.461026364487	-27.1610263644873
185	394.9	407.477675054509	-12.5776750545091
186	455.4	403.596004104367	51.803995895633
187	414	448.991697644219	-34.9916976442186
188	375.5	397.662312265537	-22.1623122655367
189	347	383.666298690123	-36.6662986901226
190	339.4	359.317361400204	-19.9173614002038
191	385.8	332.982291317379	52.8177086826213
192	378.8	365.538686264845	13.2613137351554
193	451.8	383.558051848994	68.2419481510058
194	446.1	462.750865775255	-16.6508657752548
195	422.5	444.179572201241	-21.6795722012406
196	383.1	403.041895221968	-19.9418952219679
197	352.8	393.244365753943	-40.4443657539425
198	445.3	362.278050466195	83.0219495338048
199	367.5	436.450117080613	-68.9501170806129
200	355.1	353.229970841988	1.87002915801168
201	326.2	361.378227251825	-35.1782272518253
202	319.8	341.266966966114	-21.4669669661135
203	331.8	309.839050073425	21.9609499265746
204	340.9	317.268558556815	23.6314414431848
205	394.1	342.778088942845	51.3219110571545
206	417.2	407.892306655864	9.30769334413634
207	369.9	406.715880386404	-36.8158803864037
208	349.2	358.188899594305	-8.98889959430466
209	321.4	354.905541320757	-33.5055413207575
210	405.7	334.688886534194	71.0111134658059
211	342.9	388.289050866499	-45.3890508664987
212	316.5	334.147616759449	-17.6476167594486
213	284.2	320.325785707875	-36.1257857078752
214	270.9	301.480030941029	-30.5800309410293
215	288.8	257.647178196095	31.1528218039053
216	278.8	277.808519281054	0.991480718946036
217	324.4	279.340810694885	45.0591893051151
218	310.9	339.084884231245	-28.1848842312451
219	299	300.267542972792	-1.26754297279228
220	273	287.960325462963	-14.9603254629631
221	279.3	277.029595472915	2.27040452708530
222	359.2	289.530757389357	69.6692426106427
223	305	343.016071506576	-38.0160715065764
224	282.1	295.243885368957	-13.1438853689565
225	250.3	287.489550943	-37.1895509430002
226	246.5	265.046665129393	-18.5466651293930
227	257.9	233.461359374328	24.4386406256715
228	266.5	246.781289560662	19.7187104393385
229	315.9	267.480177150554	48.4198228494461
230	318.4	330.590302517190	-12.1903025171904
231	295.4	305.42541018664	-10.0254101866398
232	266.4	285.290415527991	-18.8904155279906
233	245.8	271.427570725925	-25.6275707259251
234	362.8	257.523685705886	105.276314294114
235	324.9	341.118489916949	-16.2184899169486
236	294.2	313.781640569003	-19.5816405690028
237	289.5	299.472172894172	-9.972172894172
238	295.2	310.688581317931	-15.4885813179305
239	290.3	276.951198569944	13.3488014300557
240	272	277.944297392058	-5.9442973920577
241	307.4	276.416327387815	30.9836726121854
242	328.7	326.853427976586	1.84657202341413
243	292.9	309.673520460121	-16.7735204601211
244	249.1	281.174837713217	-32.0748377132166
245	230.4	256.753668521682	-26.3536685216815
246	361.5	245.999090841682	115.500909158318
247	321.7	332.498426388912	-10.7984263889118
248	277.2	307.30504371797	-30.1050437179701
249	260.7	286.091278302775	-25.3912783027753
250	251	286.745155106907	-35.7451551069072
251	257.6	231.463568072559	26.1364319274412
252	241.8	242.033156373157	-0.2331563731573
253	287.5	247.577337696415	39.9226623035847
254	292.3	310.841763202449	-18.5417632024491
255	274.7	273.156240213553	1.54375978644725
256	254.2	258.257918715464	-4.05791871546404
257	230	263.179169154715	-33.1791691547148
258	339	249.303021905284	89.6969780947159
259	318.2	311.945989889734	6.25401011026582
260	287	299.024830424591	-12.0248304245913
261	295.8	295.654657135057	0.145342864942904
262	284	327.43452784741	-43.4345278474102
263	271	263.798144648314	7.20185535168577
264	262.7	253.064420787898	9.63557921210241
265	340.6	269.719962671700	70.8800373283005
266	379.4	368.715390129076	10.6846098709236
267	373.3	353.58323215875	19.7167678412500
268	355.2	349.480487048283	5.71951295171743
269	338.4	370.591778133650	-32.1917781336497
270	466.9	369.333243833597	97.5667561664033
271	451	431.409812497021	19.5901875029789
272	422	422.146569617097	-0.146569617097498
273	429.2	438.207336211451	-9.0073362114507
274	425.9	476.639001182337	-50.7390011823367
275	460.7	397.47098251503	63.2290174849698
276	463.6	427.368560806893	36.2314391931071
277	541.4	478.587887101442	62.812112898558
278	544.2	592.94921767412	-48.7492176741197
279	517.5	516.514380576684	0.985619423315939
280	469.4	482.871014300834	-13.4710143008336
281	439.4	489.260059191979	-49.8600591919794
282	549	481.304268776122	67.6957312238777
283	533	516.90357231415	16.0964276858506
284	506.1	495.494861012285	10.6051389877153
285	484	523.133738950091	-39.1337389500908
286	457	537.724775523308	-80.724775523308
287	481.5	435.58090908578	45.9190909142199
288	469.5	445.082917337034	24.4170826629662
289	544.7	480.824690840342	63.8753091596585
290	541.2	594.025836785133	-52.8258367851329
291	521.5	523.098024791139	-1.59802479113876
292	469.7	484.073741038731	-14.3737410387311
293	434.4	485.740650296926	-51.3406502969264
294	542.6	473.640655987115	68.9593440128846
295	517.3	519.935101632659	-2.6351016326588
296	485.7	479.339972284874	6.3600277151263
297	465.8	498.089436444208	-32.289436444208
298	447	514.773650195327	-67.7736501953268
299	426.6	431.849160588089	-5.24916058808947
300	411.6	395.376961017196	16.223038982804
301	467.5	418.574073562383	48.9259264376171
302	484.5	508.023154861304	-23.5231548613040
303	451.2	469.510356167094	-18.3103561670944
304	417.4	420.586409743221	-3.18640974322057
305	379.9	427.680955546179	-47.780955546179
306	484.7	414.259399270395	70.4406007296053
307	455	463.949943771018	-8.94994377101767
308	420.8	424.502934777636	-3.70293477763579
309	416.5	427.910154744238	-11.4101547442384
310	376.3	459.750212817967	-83.4502128179667
311	405.6	364.226093814154	41.3739061858458
312	405.8	375.288880988307	30.5111190116927
313	500.8	409.753859149245	91.0461408507555
314	514	539.039163818192	-25.0391638181920
315	475.5	503.79889622906	-28.2988962290601
316	430.1	444.468451458244	-14.3684514582438
317	414.4	440.720042514029	-26.3200425140292
318	538	445.858779666773	92.1412203332268
319	526	519.472733614244	6.52726638575643
320	488.5	490.540956685554	-2.04095668555385
321	520.2	499.071276341301	21.1287236586986
322	504.4	565.471033669614	-61.0710336696136
323	568.5	491.10241749841	77.3975825015905
324	610.6	525.507660611727	85.092339388273
325	818	620.543632685692	197.456367314308
326	830.9	870.127160676904	-39.2271606769042
327	835.9	821.138446830896	14.7615531691036
328	782	780.44087172965	1.55912827034979
329	762.3	808.350695091502	-46.0506950915016
330	856.9	811.263856204082	45.6361437959182
331	820.9	844.87212984527	-23.9721298452699
332	769.6	767.883318676583	1.71668132341688
333	752.2	792.140068603051	-39.9400686030514
334	724.4	806.023160668627	-81.6231606686272
335	723.1	717.525921432478	5.57407856752218
336	719.5	675.681204863828	43.8187951361724
337	817.4	734.737449820568	82.662550179432
338	803.3	863.905805244538	-60.6058052445377
339	752.5	800.403630971258	-47.9036309712579
340	689	709.037907533863	-20.0379075338631
341	630.4	709.449024093298	-79.0490240932977
342	765.5	667.53091164246	97.9690883575403
343	757.7	752.904751381105	4.79524861889536
344	732.2	712.256198896188	19.9438011038125
345	702.6	746.601042269926	-44.0010422699255
346	683.3	753.807139675773	-70.5071396757727
347	709.5	676.455517870851	33.0444821291489
348	702.2	665.809041552434	36.3909584475665
349	784.8	710.435272724031	74.3647272759686
350	810.9	831.49896314469	-20.5989631446902
351	755.6	807.282510236975	-51.6825102369748
352	656.8	714.90304313004	-58.1030431300403
353	615.1	672.283815559863	-57.1838155598628
354	745.3	653.695099423757	91.604900576243
355	694.1	732.286467421055	-38.1864674210552
356	675.7	654.950642684134	20.7493573158657
357	643.7	686.104047038175	-42.4040470381749
358	622.1	692.824095747583	-70.7240957475829
359	634.6	612.915721186644	21.6842788133564
360	588	598.309082325298	-10.3090823252978
361	689.7	594.645382957527	95.0546170424727
362	673.9	730.373942491544	-56.4739424915437
363	647.9	669.450019551616	-21.5500195516164
364	568.8	611.541869383852	-42.7418693838524
365	545.7	583.225012704288	-37.5250127042875
366	632.6	576.44873962445	56.1512603755505
367	643.8	623.100883132432	20.6991168675679
368	593.1	603.357344154358	-10.2573441543578
369	579.7	606.247501755565	-26.5475017555653
370	546	618.069996908006	-72.0699969080056
371	562.9	543.074145986271	19.8258540137292
372	572.5	525.21874086158	47.281259138420

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
373	580.099455369910	497.41247545428	662.786435285539
374	613.166933372231	496.573630616928	729.760236127534
375	611.794416567326	471.528765899302	752.06006723535
376	574.281613766588	351.007546890132	797.555680643044

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938827fqrzxqkge5kd931/1l5451259938773.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938827fqrzxqkge5kd931/1l5451259938773.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938827fqrzxqkge5kd931/20xsg1259938773.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938827fqrzxqkge5kd931/20xsg1259938773.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938827fqrzxqkge5kd931/3zpms1259938773.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938827fqrzxqkge5kd931/3zpms1259938773.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 4 ; par2 = Triple ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)

if (par2 == 'Single') K <- 1

if (par2 == 'Double') K <- 2

if (par2 == 'Triple') K <- par1

nx <- length(x)

nxmK <- nx - K

x <- ts(x, frequency = par1)

if (par2 == 'Single') fit <- HoltWinters(x, gamma=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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