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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: Fri, 27 Nov 2009 08:04:36 -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/Nov/27/t1259334314udw0movhtq9652j.htm/, Retrieved Fri, 27 Nov 2009 16:05:19 +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/Nov/27/t1259334314udw0movhtq9652j.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:

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	0.834190584507086
beta	0.0314371802584989
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	299.5	237.627476186144	61.8725238138558
14	347.4	334.684203326373	12.7157966736274
15	338.3	337.124238319683	1.17576168031724
16	327.7	326.940117659162	0.759882340838374
17	351.6	351.053240979026	0.546759020973809
18	396.6	398.633000518542	-2.03300051854166
19	438.8	389.489846288352	49.3101537116478
20	395.6	405.364615816722	-9.76461581672157
21	363.5	370.107395833236	-6.60739583323613
22	378.8	311.426967384299	67.373032615701
23	357	425.406491421209	-68.4064914212094
24	369	393.290788189667	-24.2907881896666
25	464.8	513.533753724449	-48.7337537244489
26	479.1	521.378815401933	-42.2788154019327
27	431.3	463.753172723408	-32.4531727234081
28	366.5	415.288175047649	-48.7881750476486
29	326.3	395.158503716480	-68.8585037164795
30	355.1	376.753057716640	-21.6530577166395
31	331.6	353.723145062591	-22.1231450625905
32	261.3	304.340882187927	-43.0408821879271
33	249	246.960348181305	2.03965181869464
34	205.5	216.679853301282	-11.1798533012818
35	235.6	222.942117202152	12.6578827978481
36	240.9	251.58308497042	-10.6830849704202
37	264.9	328.25761734098	-63.35761734098
38	253.8	300.622155813587	-46.8221558135869
39	232.3	246.570735622218	-14.2707356222176
40	193.8	217.97402176317	-24.1740217631701
41	177	203.015550718155	-26.0155507181548
42	213.2	203.992818193705	9.20718180629467
43	207.2	205.596025477335	1.60397452266457
44	180.6	182.439793276172	-1.8397932761722
45	188.6	169.172749256155	19.4272507438454
46	175.4	158.310670109320	17.0893298906797
47	199	187.484815429955	11.5151845700454
48	179.6	207.498578232654	-27.8985782326538
49	225.8	239.439214992592	-13.6392149925919
50	234	249.392887806181	-15.3928878061805
51	200.2	226.171511133149	-25.9715111331492
52	183.6	186.658271387136	-3.05827138713602
53	178.2	187.212548205495	-9.01254820549545
54	203.2	207.693982599485	-4.49398259948549
55	208.5	195.846788769683	12.6532112303171
56	191.8	180.670410946861	11.1295890531393
57	172.8	180.531206710462	-7.73120671046246
58	148	147.725623704515	0.274376295484814
59	159.4	158.594147216810	0.805852783190488
60	154.5	160.696894105894	-6.19689410589396
61	213.2	204.071449171913	9.12855082808741
62	196.4	230.365107477265	-33.9651074772655
63	182.8	189.974333410757	-7.17433341075713
64	176.4	170.259943196256	6.14005680374376
65	153.6	176.720028868842	-23.120028868842
66	173.2	181.741312509294	-8.5413125092945
67	171	168.871827203458	2.12817279654195
68	151.2	148.165635554925	3.03436444507534
69	161.9	139.636010610007	22.2639893899932
70	157.2	134.80611764832	22.3938823516799
71	201.7	164.581538350014	37.1184616499865
72	236.4	196.544165103586	39.855834896414
73	356.1	307.954874815706	48.1451251842944
74	398.3	368.742319039759	29.5576809602414
75	403.7	382.882478201656	20.8175217983443
76	384.6	380.23681317963	4.36318682037029
77	365.8	380.127495156166	-14.3274951561659
78	368.1	438.947318995252	-70.8473189952516
79	367.9	376.476661613892	-8.57666161389199
80	347	325.426624966456	21.5733750335442
81	343.3	329.055570595194	14.2444294048058
82	292.9	293.809700047159	-0.909700047159447
83	311.5	318.635578971566	-7.13557897156625
84	300.9	314.220628238634	-13.3206282386343
85	366.9	403.388371531988	-36.4883715319876
86	356.9	389.091648366189	-32.1916483661891
87	329.7	348.65279769522	-18.9527976952199
88	316.2	311.307566239167	4.89243376083311
89	269	307.082879226767	-38.0828792267666
90	289.3	316.793051056817	-27.4930510568173
91	266.2	296.430059110568	-30.2300591105678
92	253.6	239.493123568234	14.1068764317660
93	233.8	237.186895038201	-3.38689503820149
94	228.4	198.028142145254	30.3718578547456
95	253.6	239.987535935056	13.6124640649436
96	260.1	249.948017694673	10.1519823053270
97	306.6	339.008756096236	-32.4087560962364
98	309.2	324.090947732778	-14.890947732778
99	309.5	300.026910500957	9.47308949904306
100	271	290.523410386492	-19.5234103864915
101	279.9	258.862884833046	21.0371151669538
102	317.9	320.26736367161	-2.36736367160978
103	298.4	320.511644503176	-22.1116445031757
104	246.7	274.904395761274	-28.2043957612742
105	227.3	234.090662576146	-6.79066257614608
106	209.1	197.37225093244	11.7277490675601
107	259.9	218.693594956765	41.2064050432348
108	266	250.742432249690	15.2575677503104
109	320.6	337.232706264193	-16.6327062641926
110	308.5	339.199022799016	-30.6990227990157
111	282.2	305.595219572508	-23.3952195725083
112	262.7	264.450583587072	-1.75058358707173
113	263.5	253.872312024747	9.627687975253
114	313.1	298.444961983378	14.6550380166224
115	284.3	308.950332594884	-24.6503325948843
116	252.6	260.242475622508	-7.64247562250821
117	250.3	239.712868323219	10.5871316767814
118	246.5	218.269383660311	28.2306163396887
119	312.7	260.619764852607	52.0802351473927
120	333.2	297.082219120493	36.117780879507
121	446.4	412.913301695448	33.4866983045515
122	511.6	461.750400301774	49.8495996982261
123	515.5	496.787333387604	18.7126666123960
124	506.4	485.619938972513	20.7800610274875
125	483.2	495.424325051488	-12.2243250514877
126	522.3	560.292748686061	-37.9927486860613
127	509.8	518.89282447781	-9.09282447780964
128	460.7	470.719734730927	-10.0197347309272
129	405.8	446.758347791267	-40.9583477912673
130	375	369.727123342129	5.27287665787145
131	378.5	408.946064638785	-30.4460646387847
132	406.8	371.003954022956	35.7960459770435
133	467.8	502.744824266615	-34.9448242666155
134	469.8	496.31155071398	-26.5115507139802
135	429.8	460.514091290277	-30.7140912902769
136	355.8	409.273950575544	-53.4739505755436
137	332.7	351.208595366422	-18.5085953664218
138	378	379.995421767594	-1.99542176759383
139	360.5	370.589625795166	-10.0896257951661
140	334.7	329.408747007206	5.29125299279366
141	319.5	315.046895443658	4.45310455634245
142	323.1	288.672697929491	34.4273020705092
143	363.6	339.595539717364	24.0044602826359
144	352.1	356.752272690985	-4.65227269098472
145	411.9	428.735450171522	-16.8354501715219
146	388.6	434.059236163854	-45.4592361638543
147	416.4	381.574523192319	34.8254768076811
148	360.7	380.716348230215	-20.0163482302155
149	338	355.979403173315	-17.9794031733147
150	417.2	389.070176523604	28.1298234763963
151	388.4	403.295842983107	-14.8958429831075
152	371.1	358.658924258201	12.4410757417992
153	331.5	348.865331958622	-17.3653319586215
154	353.7	307.660179942188	46.0398200578117
155	396.7	368.107853599126	28.5921464008740
156	447	384.129744589959	62.8702554100411
157	533.5	530.315291565205	3.1847084347952
158	565.4	553.883495924767	11.5165040752327
159	542.3	565.735654806396	-23.4356548063965
160	488.7	497.427065666698	-8.72706566669757
161	467.1	482.452878998958	-15.3528789989584
162	531.3	550.414094784214	-19.1140947842138
163	496.1	515.561418835842	-19.4614188358421
164	444	465.666220719523	-21.6662207195231
165	403.4	418.149993873018	-14.7499938730181
166	386.3	386.058029451797	0.241970548203142
167	394.1	406.636200508395	-12.5362005083949
168	404.1	391.646507413507	12.4534925864932
169	462.1	474.973714289868	-12.8737142898677
170	448.1	480.776403728914	-32.6764037289139
171	432.3	447.02623672374	-14.7262367237404
172	386.3	394.483547810563	-8.18354781056314
173	395.2	377.601331590825	17.5986684091753
174	421.9	456.711511348712	-34.811511348712
175	382.9	409.284132305172	-26.3841323051724
176	384.2	357.588837148039	26.6111628519605
177	345.5	353.631653040669	-8.13165304066905
178	323.4	330.274534280740	-6.87453428073957
179	372.6	337.898426956668	34.7015730433322
180	376	365.578834618977	10.4211653810226
181	462.7	436.864725796116	25.8352742038841
182	487	471.108413806197	15.8915861938034
183	444.2	481.542046865483	-37.3420468654834
184	399.3	410.00614536983	-10.7061453698300
185	394.9	395.348280574100	-0.448280574100465
186	455.4	450.190661010296	5.20933898970418
187	414	436.88910858954	-22.8891085895402
188	375.5	395.730116735195	-20.2301167351949
189	347	347.072853683126	-0.0728536831256292
190	339.4	330.490866599814	8.90913340018642
191	385.8	359.008497551564	26.7915024484359
192	378.8	376.037977733818	2.76202226618238
193	451.8	443.623231885979	8.17676811402123
194	446.1	460.613734749189	-14.5137347491886
195	422.5	436.210923450448	-13.7109234504480
196	383.1	389.725762184658	-6.62576218465836
197	352.8	379.807791542914	-27.0077915429138
198	445.3	406.716204177373	38.5837958226275
199	367.5	416.756905232538	-49.2569052325378
200	355.1	354.771956438725	0.328043561274967
201	326.2	327.571762781223	-1.37176278122251
202	319.8	311.661779313680	8.13822068632032
203	331.8	340.127512628360	-8.32751262836035
204	340.9	323.682773119675	17.2172268803247
205	394.1	395.811999186641	-1.71199918664138
206	417.2	398.406613807325	18.7933861926746
207	369.9	402.044103018541	-32.1441030185406
208	349.2	344.027006482821	5.1729935171785
209	321.4	340.223476236548	-18.8234762365475
210	405.7	378.811876082819	26.8881239171810
211	342.9	366.447768672191	-23.547768672191
212	316.5	334.516743842692	-18.0167438426921
213	284.2	293.719817857925	-9.51981785792492
214	270.9	273.199229921646	-2.29922992164637
215	288.8	285.978936345554	2.82106365444639
216	278.8	282.599199646799	-3.79919964679857
217	324.4	322.367704763736	2.03229523626385
218	310.9	328.286624385005	-17.3866243850052
219	299	295.550365129289	3.44963487071067
220	273	276.590977095724	-3.59097709572376
221	279.3	262.187373292035	17.1126267079650
222	359.2	328.422826718438	30.7771732815623
223	305	315.485273708738	-10.4852737087383
224	282.1	295.993398946766	-13.8933989467657
225	250.3	262.117445690281	-11.8174456902813
226	246.5	241.702684633311	4.79731536668908
227	257.9	259.552901517866	-1.65290151786553
228	266.5	251.681559129235	14.8184408707646
229	315.9	305.866915288709	10.0330847112905
230	318.4	315.594337144102	2.80566285589759
231	295.4	303.953123143209	-8.55312314320912
232	266.4	274.663141610807	-8.26314161080745
233	245.8	260.326895347538	-14.5268953475375
234	362.8	295.474370342662	67.3256296573381
235	324.9	307.614504661452	17.2854953385485
236	294.2	311.327565494311	-17.1275654943113
237	289.5	275.026535702345	14.4734642976546
238	295.2	280.173125362550	15.0268746374505
239	290.3	310.393457438245	-20.0934574382453
240	272	291.134291337191	-19.1342913371907
241	307.4	318.39428897141	-10.9942889714102
242	328.7	309.619020626111	19.0809793738891
243	292.9	309.996014049050	-17.0960140490503
244	249.1	273.990462735576	-24.8904627355763
245	230.4	244.940768552487	-14.5407685524866
246	361.5	288.566224119758	72.9337758802419
247	321.7	298.917593171253	22.7824068287475
248	277.2	301.90637000184	-24.70637000184
249	260.7	265.10978747999	-4.40978747998992
250	251	254.615925394851	-3.6159253948513
251	257.6	260.504177241373	-2.90417724137279
252	241.8	255.189722282258	-13.3897222822579
253	287.5	283.314531189407	4.18546881059319
254	292.3	291.457813777921	0.842186222079363
255	274.7	272.217121417553	2.48287858244726
256	254.2	252.261276718755	1.9387232812453
257	230	247.720219616292	-17.7202196162924
258	339	302.584682136063	36.4153178639372
259	318.2	278.256416029845	39.9435839701551
260	287	288.304590422258	-1.30459042225783
261	295.8	274.688373256309	21.1116267436907
262	284	286.288122087440	-2.28812208744034
263	271	296.208109798546	-25.2081097985464
264	262.7	271.071932395441	-8.37193239544115
265	340.6	311.519822589786	29.0801774102144
266	379.4	342.716415321822	36.6835846781776
267	373.3	351.260033996627	22.0399660033731
268	355.2	343.272390047954	11.9276099520458
269	338.4	343.450492533221	-5.05049253322102
270	466.9	460.097750349307	6.80224965069266
271	451	394.068581588599	56.9314184114012
272	422	403.082747400475	18.9172525995249
273	429.2	409.43878130931	19.7612186906898
274	425.9	415.008588082675	10.8914119173249
275	460.7	439.385387336559	21.3146126634412
276	463.6	460.228681221894	3.37131877810572
277	541.4	564.015329469431	-22.615329469431
278	544.2	562.696325620106	-18.4963256201063
279	517.5	514.811144778506	2.68885522149355
280	469.4	480.380068375344	-10.9800683753439
281	439.4	456.080747737613	-16.6807477376128
282	549	604.457449151712	-55.4574491517116
283	533	481.536498266277	51.4635017337229
284	506.1	472.240855626084	33.8591443739165
285	484	489.525707073122	-5.52570707312242
286	457	470.559693217319	-13.5596932173191
287	481.5	476.648188219886	4.85181178011368
288	469.5	479.682441849689	-10.1824418496889
289	544.7	567.718561709015	-23.0185617090148
290	541.2	565.287878180975	-24.0878781809745
291	521.5	514.60405384185	6.89594615814985
292	469.7	479.791550330909	-10.0915503309088
293	434.4	453.845780084513	-19.4457800845126
294	542.6	590.308879245888	-47.7088792458881
295	517.3	489.267013535977	28.0329864640233
296	485.7	457.601945873984	28.0980541260165
297	465.8	462.705841759742	3.09415824025808
298	447	448.684024928905	-1.68402492890539
299	426.6	466.008335457636	-39.4083354576363
300	411.6	427.865003909839	-16.2650039098388
301	467.5	494.845873504418	-27.345873504418
302	484.5	483.45987178046	1.04012821953984
303	451.2	459.313553104532	-8.1135531045324
304	417.4	412.586245341683	4.81375465831746
305	379.9	397.681557749069	-17.7815577490687
306	484.7	510.249071521564	-25.5490715215643
307	455	442.930130305126	12.0698696948738
308	420.8	402.607561684159	18.1924383158412
309	416.5	396.425220666065	20.074779333935
310	376.3	396.178937745945	-19.8789377459445
311	405.6	387.775019389321	17.8249806106787
312	405.8	400.414060858912	5.38593914108765
313	500.8	481.771557267497	19.0284427325030
314	514	515.647174743155	-1.64717474315535
315	475.5	486.806660292441	-11.3066602924408
316	430.1	437.949490856276	-7.84949085627557
317	414.4	408.104760330978	6.2952396690215
318	538	551.565953969052	-13.5659539690522
319	526	497.324324273183	28.6756757268171
320	488.5	466.213707712878	22.2862922871217
321	520.2	462.007834739661	58.1921652603393
322	504.4	483.750110769661	20.6498892303388
323	568.5	523.661646218294	44.8383537817058
324	610.6	559.200391015067	51.3996089849327
325	818	725.487160905127	92.5128390948735
326	830.9	833.897165879864	-2.99716587986450
327	835.9	791.704691011388	44.1953089886119
328	782	768.990281228768	13.0097187712316
329	762.3	750.190030562813	12.1099694371869
330	856.9	1018.79199894762	-161.891998947615
331	820.9	831.464573520263	-10.5645735202635
332	769.6	739.760527070064	29.8394729299358
333	752.2	741.568842369015	10.6311576309854
334	724.4	705.392509554544	19.0074904454564
335	723.1	761.351679831748	-38.2516798317477
336	719.5	728.32976810715	-8.82976810715081
337	817.4	872.180480638654	-54.7804806386544
338	803.3	838.572796558785	-35.2727965587854
339	752.5	774.049546250114	-21.5495462501136
340	689	693.188259910466	-4.18825991046617
341	630.4	659.132267092745	-28.7322670927454
342	765.5	816.947179271117	-51.4471792711173
343	757.7	744.981672382612	12.7183276173884
344	732.2	681.695467832295	50.5045321677052
345	702.6	696.063229409043	6.53677059095708
346	683.3	657.878919288956	25.4210807110439
347	709.5	704.740089448222	4.75991055177815
348	702.2	710.372544631912	-8.17254463191148
349	784.8	841.119473579327	-56.3194735793271
350	810.9	806.389810122558	4.51018987744192
351	755.6	775.406805500505	-19.806805500505
352	656.8	696.986623072271	-40.1866230722708
353	615.1	627.941855173591	-12.8418551735913
354	745.3	788.932087670052	-43.6320876700522
355	694.1	732.481713641621	-38.3817136416212
356	675.7	634.711142197008	40.9888578029925
357	643.7	634.131017095513	9.56898290448714
358	622.1	602.492838946037	19.6071610539633
359	634.6	636.370804951981	-1.77080495198106
360	588	631.757378193097	-43.7573781930971
361	689.7	700.600403664838	-10.9004036648379
362	673.9	707.896450127397	-33.9964501273973
363	647.9	643.094575297678	4.80542470232194
364	568.8	587.828381850703	-19.0283818507035
365	545.7	542.35613617488	3.34386382511968
366	632.6	689.663175681589	-57.063175681589
367	643.8	622.085854262794	21.7141457372056
368	593.1	589.735967559455	3.36403244054475
369	579.7	555.115000544701	24.5849994552991
370	546	539.777680419332	6.22231958066766
371	562.9	555.075261347661	7.82473865233908
372	572.5	550.403220489498	22.0967795105016

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
373	675.60500523734	622.799731966261	728.410278508418
374	687.55702355531	617.377763291092	757.736283819527
375	657.669963198287	575.506598032933	739.83332836364
376	593.946199397138	505.077273211728	682.815125582548
377	567.936068495899	469.834611644941	666.037525346857
378	708.351039657566	576.993485128054	839.708594187078
379	703.36061637895	562.251209095454	844.470023662447
380	646.901164119778	506.040242052541	787.762086187015
381	611.554367646235	467.594832512676	755.513902779794
382	571.504842362338	426.191861359819	716.817823364856
383	583.173504745255	424.881836927376	741.465172563134
384	574.497670206446	283.317387010523	865.677953402368

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259334314udw0movhtq9652j/1i23m1259334273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259334314udw0movhtq9652j/1i23m1259334273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259334314udw0movhtq9652j/290tc1259334273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259334314udw0movhtq9652j/290tc1259334273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259334314udw0movhtq9652j/3ehj71259334273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259334314udw0movhtq9652j/3ehj71259334273.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; 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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