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Workshop 8 Time Series Analysis (Introduction)

*The author of this computation has been verified*
R Software Module: /rwasp_structuraltimeseries.wasp (opens new window with default values)
Title produced by software: Structural Time Series Models
Date of computation: Thu, 09 Dec 2010 10:56:42 +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/09/t1291892161hsnmxlv267qrulz.htm/, Retrieved Thu, 09 Dec 2010 11:56:08 +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/09/t1291892161hsnmxlv267qrulz.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:
Monthly Unemployment - Structural Time Series Model
 
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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time18 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
1235.1235.1000
2280.7276.8962457464363.229111104364533.803754253564151.42066536850972
3264.6265.9632656880241.50309838029571-1.36326568802440-0.734903317175399
4240.7241.861793222569-2.61698978913476-1.16179322256876-1.29364639323432
5201.4203.400415766129-9.37534169680783-2.00041576612935-1.77273380874495
6240.8231.511882607958-1.642019448515669.288117392041551.83018885734762
7241.1239.5350951176930.4562175836960761.564904882307260.467970804287585
8223.8224.505061647943-3.00534168567717-0.705061647942683-0.745971789300263
9206.1205.645977014897-6.60921346117450.454022985103203-0.761333449058833
10174.7175.353784412960-12.0454782999576-0.65378441296033-1.13525628391737
11203.3195.560687057504-4.600371867737447.739312942495971.54439538140152
12220.5216.3860104876521.288014278785824.113989512347491.21674486591375
13299.5288.87252393185017.209196231799810.62747606814973.83219210781693
14347.4340.17743829025724.91289891593037.22256170974261.44304877325921
15338.3345.19417374395820.4088069067425-6.89417374395811-0.92906051072369
16327.7331.37647503049712.5503273300090-3.67647503049708-1.61858159110898
17351.6356.28791668169915.3923602753652-4.687916681699050.58241132737304
18396.6388.49415021173119.25618031761328.105849788269150.792943773313948
19438.8433.77061443771525.23492682151365.02938556228451.22812182704405
20395.6408.51678164206413.6338028169110-12.9167816420640-2.38377846694245
21363.5368.9620761421741.41178666533705-5.46207614217434-2.51168776411731
22378.8379.1977135866543.43966199162084-0.3977135866536090.416786918307111
23357357.765284608398-2.27615910429012-0.765284608398099-1.17473599534849
24369371.8552428349101.47458226071715-2.85524283490960.771867331396886
25464.8442.46160297529817.23430816554322.33839702470243.41171560648142
26479.1468.28835545963919.188495518205710.81164454036150.388218586382179
27431.3443.0350378287039.14005702264729-11.7350378287034-2.05884882042737
28366.5386.564590181969-5.83242273931038-20.0645901819691-3.09038401698361
29326.3341.659844798958-14.7724877372127-15.3598447989579-1.83379091802764
30355.1347.791763889707-9.991314542009637.308236110292810.980729098423756
31331.6323.128939994948-13.34597293129548.47106000505236-0.688873297056043
32261.3273.48834682242-21.6446528615547-12.1883468224201-1.70504724215649
33249254.64933421962-21.0030953948592-5.649334219619920.131846043323911
34205.5206.688821874468-27.1678503835679-1.18882187446817-1.26703335947904
35235.6227.556153863895-16.18942654616108.043846136105362.25583371782921
36240.9250.468237384565-7.27612962854993-9.56823738456511.83820540238773
37264.9245.283880273413-6.7991444372305819.61611972658690.100357188161152
38253.8235.073024445799-7.575712872678518.7269755542005-0.157140897094586
39232.3230.443606941407-6.909010894819591.856393058592570.136371826127074
40193.8210.141200926888-9.95545651994976-16.341200926888-0.628836038130628
41177197.818978594456-10.4954130806697-20.8189785944561-0.110924628328793
42213.2200.357131974566-7.5220199631895212.84286802543370.61001382324628
43207.2192.275805825418-7.6495762653273414.9241941745816-0.0261898937478546
44180.6190.866810553892-6.22637470191672-10.26681055389220.292399399152816
45188.6187.584002920041-5.555008115482221.015997079959250.137972873275236
46175.4185.610743806793-4.73813419169405-10.21074380679320.167873917119361
47199195.823781523251-1.331331761311563.176218476749220.700082153916336
48179.6191.066133336662-2.11072153932872-11.4661333366619-0.160867327763989
49225.8202.3106825434880.9317072538766223.4893174565120.632944796914796
50234213.7966163506033.3329135397086120.20338364939720.489358798826040
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53178.2201.034527500130-0.0322627465297564-22.83452750013030.119449884651829
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55208.5193.600244426597-1.2562913288837414.89975557340340.158640317293168
56191.8200.603141505870.624206066150487-8.803141505870040.386325319772337
57172.8178.115014484029-4.63845303385158-5.31501448402935-1.08145459380144
58148162.738497762663-7.08302320800164-14.7384977626631-0.502318076059569
59159.4155.131240906835-7.202257453470534.26875909316545-0.0245090284631111
60154.5164.759384085665-3.37772523608135-10.25938408566450.789313500587099
61213.2186.0398852113632.2339552416269927.16011478863741.16139267741862
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63182.8181.0094214822180.7094366500400361.790578517781630.263717777209698
64176.4190.7085301162272.74884963871863-14.30853011622710.420226611592031
65153.6178.752483911556-0.594882002718048-25.1524839115556-0.68805945279072
66173.2166.070709783992-3.344701127337627.12929021600784-0.564660424069981
67171158.400658416945-4.3285073062835712.5993415830546-0.201997954050124
68151.2154.440310784678-4.24477829670167-3.240310784678390.0171997209638105
69161.9161.654965742271-1.638647680655190.2450342577286510.535487880132261
70157.2169.7022467100610.563505660626315-12.50224671006080.452474823170065
71201.7195.7485758756046.35254562408615.951424124396011.19031490738173
72236.4242.92564954608415.6236193694043-6.525649546083791.91251566203823
73356.1314.58713800603828.365635652661541.51286199396232.63003757704954
74398.3374.37151947371335.504080788412223.92848052628691.46179374177377
75403.7406.42363404246034.7218466988930-2.72363404246044-0.160251694714049
76384.6404.92987775027626.5105104608203-20.3298777502760-1.69071578343394
77365.8396.01671045138218.4637279698899-30.2167104513815-1.65628644113175
78368.1369.1592284487258.16216465195293-1.05922844872476-2.11634606126391
79367.9357.5609546892393.6712958875241610.3390453107607-0.922181629831371
80347352.2866518552331.63858634942513-5.28665185523281-0.417529822839778
81343.3344.988779384932-0.391842891020289-1.68877938493156-0.417146795743169
82292.9315.881044410447-6.91405096756447-22.9810444104474-1.34009870556767
83311.5312.540534610527-6.10290411723046-1.040534610527330.166822716316396
84300.9317.600831218223-3.56900632605090-16.70083121822280.522441232848822
85366.9329.8231400949220.019067129889397237.07685990507820.739493093420309
86356.9332.8218570446450.69565984763554524.07814295535510.138679632715258
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90289.3286.494960820948-8.092442637336382.80503917905244-0.162071112278886
91266.2258.525748883542-12.6068132118737.6742511164576-0.927138232537102
92253.6253.761533229509-10.8259573243909-0.1615332295088090.365775326597855
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94228.4245.345949655374-7.24175206993727-16.94594965537361.26259640951459
95253.6254.264769176277-3.5757516846223-0.6647691762764990.75407129884528
96260.1275.2110517098581.98814378802694-15.11105170985751.14661550122318
97306.6272.3603008619970.88933108933076834.2396991380034-0.2262595661794
98309.2282.3332455359752.9509106700827426.86675446402470.422804537884767
99309.5303.5743754119987.09537499429935.925624588002260.849932548938598
100271283.8362056128241.01533570916185-12.8362056128238-1.25073240413275
101279.9302.3119416170964.97612343251904-22.41194161709580.815287982899893
102317.9310.4354670575415.690575859143637.464532942459050.146873773804008
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104246.7253.758852571771-8.72939905466156-7.05885257177118-2.03271815411588
105227.3232.351991249986-11.6058061083604-5.05199124998626-0.590843874409567
106209.1227.511162434422-10.0714484682707-18.41116243442180.315282177596033
107259.9256.357088079822-1.247328042373133.542911920178041.81520203010648
108266276.1129422728473.51640028363646-10.11294227284710.981311018740675
109320.6287.5232512718625.3079977617819733.07674872813780.368704526199885
110308.5286.9885360372113.9825533336213921.5114639627893-0.271940875743228
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112262.7279.1337460809981.21291655705064-16.43374608099850.169940192361629
113263.5285.794607362832.44813958466262-22.29460736283030.254235229920455
114313.1298.305516907084.7311680042224114.79448309292010.469427284328305
115284.3277.938403080755-0.9633191650402076.36159691924492-1.1698332708354
116252.6259.632824132898-4.89718704445881-7.03282413289794-0.807942088168546
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119312.7305.7989460031167.825154457728386.901053996883941.71697069786287
120333.2339.81640640900313.7637984686093-6.616406409002691.22292066220987
121446.4401.366434188624.60431466617445.03356581140012.23011564108407
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197352.8386.723152500398-3.3937339305948-33.9231525003985-1.18122236373882
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202319.8358.85161809364-4.29168926507082-39.05161809364040.541453636000035
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209321.4361.46482161225-0.16521955309542-40.0648216122503-0.375989811105973
210405.7357.581384697765-1.0067230320501448.1186153022351-0.173046760586368
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212316.5324.15476412986-7.50492574150523-7.65476412986016-0.7799642731101
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214270.9307.138434939738-7.83745170992196-36.2384349397380.0420114250306199
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217324.4283.155782284165-8.0996625025109141.2442177158347-0.0655062775219871
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237289.5319.1846056030894.95924879430311-29.68460560308850.417260070258003
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245230.4269.1765711979-3.56343168360672-38.77657119790020.211142036799101
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255274.7255.392061143224-2.6351864035246219.30793885677620.77128317257263
256254.2272.1773703272251.75626479572706-17.97737032722540.90259404796678
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265340.6299.5949129318801.6271498376066741.00508706811971.10828530427888
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267373.3355.07373469726711.954157093805518.22626530273290.773743124089708
268355.2372.67746725648813.2315668312864-17.47746725648790.262550677966618
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270466.9407.89465128893215.243416867686559.00534871106760.44273717908403
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275460.7475.68594731634313.7994305214966-14.98594731634280.497310004900852
276463.6486.93555715664813.2227962349415-23.3355571566479-0.118555822582261
277541.4505.66076732106614.467248841403335.73923267893440.255787531513889
278544.2502.8377418575210.557091472968941.3622581424804-0.803453589955128
279517.5502.5009753544128.0938656902436714.9990246455882-0.506130559087274
280469.4491.2082664680743.71072185958227-21.8082664680745-0.90088128570589
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282549491.7210420505042.4272880679128557.278957949496-0.0104793773995071
283533508.6558890389825.7082179638413224.34411096101820.674353754294185
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285484510.3235104577052.99775286502273-26.3235104577055-1.01726356337812
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291521.5501.3720001615790.72327405615439620.12799983842060.122310851518939
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295517.3493.249150387681-0.0017152535262867624.05084961231870.32751867695296
296485.7497.7211371945581.00987043461508-12.02113719455820.207869673842038
297465.8489.646686673921-1.04400292306498-23.8466866739207-0.422043357401605
298447483.626205184494-2.16905243036545-36.626205184494-0.231233215745532
299426.6447.742615951707-9.7913492526698-21.1426159517071-1.56699492469741
300411.6437.480010248131-9.89790445223553-25.8800102481308-0.0219061398677360
301467.5425.219563293899-10.432128847190342.280436706101-0.109804406449636
302484.5437.164498254789-5.3724631093803947.3355017452111.03971382272012
303451.2429.921202363620-5.7954233521006421.2787976363804-0.0869130098327377
304417.4436.42558115812-3.01486069394283-19.02558115811980.571496002388501
305379.9433.083710440794-3.08879002853351-53.1837104407943-0.0151982901508905
306484.7431.393433151425-2.7725846785187353.30656684857530.0650054413476646
307455431.319707606675-2.1623362140597423.68029239332490.125428757032217
308420.8430.550673838842-1.84730879676943-9.750673838842020.0647362245934188
309416.5436.599694138174-0.062138104314942-20.09969413817410.366837616689234
310376.3411.316769794323-5.76358333600165-35.0167697943229-1.17182754949850
311405.6421.969839854673-2.05226590504543-16.36983985467300.762953912275703
312405.8429.7658149344680.174350098770916-23.96581493446780.457745007463725
313500.8457.2404231496616.3470768862842343.5595768503391.26873592163761
314514466.4735196385486.999587053069847.52648036145170.134087975200663
315475.5459.9322912770553.9384333749433515.5677087229448-0.629044761149715
316430.1451.4793784267341.13731066587169-21.3793784267341-0.575721248012182
317414.4464.7966923220333.89077475614269-50.3966923220330.566038384919772
318538482.4301711067856.9978069037433755.56982889321460.638726966327017
319526500.4672368466259.4937498437503825.53276315337460.51300857136197
320488.5501.3436907027847.54549836098504-12.8436907027843-0.400362586458208
321520.2529.8578102986312.2857439374073-9.657810298630490.9741024025355
322504.4543.33663613326712.5554409909930-38.93663613326750.0554313015773138
323568.5581.68421541288418.3859779910227-13.18421541288431.19858392866318
324610.6633.51149611534925.9463411796169-22.91149611534911.55420941635810
325818753.7164054811147.25721287057564.28359451889054.38019872048443
326830.9785.53756228308643.76744023974745.3624377169144-0.717148372343394
327835.9819.13526943216641.468496532007316.7647305678335-0.472426924141822
328782815.85497305983531.3532510171421-33.8549730598353-2.07900862042706
329762.3820.4617405613225.3071171687972-58.1617405613209-1.24289394366871
330856.9810.48885691928717.331279500751646.4111430807126-1.63959244282641
331820.9799.15544961650510.850700281973921.7445503834948-1.33199702412146
332769.6790.3669700454456.41081527911091-20.7669700454450-0.912407056502885
333752.2768.396407552786-0.00487921117583223-16.1964075527864-1.31842711895323
334724.4769.001862833520.133081653900837-44.60186283352060.0283553420553480
335723.1750.735003739746-4.02619649841715-27.6350037397463-0.855005024104147
336719.5760.062165630755-1.00745509393259-40.56216563075510.620558464189512
337817.4752.366831652536-2.5194220204153965.0331683474643-0.310766030662437
338803.3754.309755928474-1.5106339060152748.99024407152610.207309923038306
339752.5731.135554365179-6.407629077510921.3644456348209-1.00633997825789
340689717.801134737823-7.97333699634157-28.8011347378232-0.321803261535785
341630.4685.967223298505-13.3668716359386-55.5672232985046-1.10871725980074
342765.5704.742076924504-6.1008934473728960.75792307549651.49363610221800
343757.7725.833952711360.046559075420122831.86604728864021.26352556584967
344732.2743.4857538282324.02641819407114-11.28575382823160.817884789825429
345702.6724.251769453248-1.23144295479674-21.6517694532477-1.08051137108376
346683.3723.511488324502-1.12042408609813-40.21148832450230.0228179106674392
347709.5736.7506368324372.12540535273070-27.25063683243680.667218711915087
348702.2741.2667094473852.66582765057565-39.06670944738520.111091579015141
349784.8724.598249785128-1.7049492676193960.2017502148716-0.898356525411895
350810.9750.0379462082494.4312513147888160.86205379175081.26103449508698
351755.6736.6109161563580.39458864904133718.9890838436419-0.829555114354953
352656.8690.936628274836-10.0183138251303-34.1366282748364-2.14018539275203
353615.1677.887200765204-10.7034525153017-62.7872007652036-0.140837366275811
354745.3686.598199094553-6.3148132984562258.70180090544660.90213729574752
355694.1668.763959778752-8.918870931297525.3360402212484-0.535228028477995
356675.7677.598717531271-4.90565262737369-1.898717531270780.824752989520805
357643.7667.598197826943-6.05727102667674-23.8981978269424-0.236665946532376
358622.1664.791045458083-5.3226599066622-42.69104545808280.150985995657187
359634.6661.700982284916-4.81802283245066-27.10098228491580.103732396737968
360588629.977328609767-10.8999120060805-41.9773286097675-1.25019715573291
361689.7631.650626368857-8.0577034609948758.04937363114340.58417775578989
362673.9611.230051665396-10.852279139146462.6699483346035-0.574314425652469
363647.9615.010178770356-7.5449029272803132.88982122964420.679693673594418
364568.8603.910771282709-8.34830034681481-35.1107712827095-0.165123916304263
365545.7609.211241944966-5.2632984494298-63.51124194496560.634143917595974
366632.6578.102022509692-11.105533396986954.4979774903076-1.20092165581762
367643.8611.44087524126-1.0589768647568132.35912475874032.06492794104384
368593.1598.040111655164-3.84873130642758-4.94011165516412-0.57332782234761
369579.7602.167785929496-2.04584338606191-22.46778592949640.370511849882817
370546590.819908195391-4.14828515309988-44.8199081953906-0.432118871984039
371562.9584.542712347467-4.62947096377678-21.6427123474668-0.0989103253980718
372572.5609.9049697741912.14975666993044-37.40496977419131.39352018215765
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291892161hsnmxlv267qrulz/17pff1291892183.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291892161hsnmxlv267qrulz/17pff1291892183.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291892161hsnmxlv267qrulz/2iywi1291892183.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291892161hsnmxlv267qrulz/2iywi1291892183.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291892161hsnmxlv267qrulz/3a7w31291892183.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291892161hsnmxlv267qrulz/3a7w31291892183.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291892161hsnmxlv267qrulz/4a7w31291892183.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291892161hsnmxlv267qrulz/4a7w31291892183.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291892161hsnmxlv267qrulz/5a7w31291892183.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291892161hsnmxlv267qrulz/5a7w31291892183.ps (open in new window)


 
Parameters (Session):
par1 = 12 ;
 
Parameters (R input):
par1 = 12 ;
 
R code (references can be found in the software module):
par1 <- as.numeric(par1)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
m$coef
m$fitted
m$resid
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time',type='b')
grid()
dev.off()
bitmap(file='test5.png')
op <- par(mfrow = c(2,2))
hist(m$resid,main='Residual Histogram')
plot(density(m$resid),main='Residual Kernel Density')
qqnorm(m$resid,main='Residual Normal QQ Plot')
qqline(m$resid)
plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit')
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model',6,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,'Level',header=TRUE)
a<-table.element(a,'Slope',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,'Stand. Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,mylevel[i])
a<-table.element(a,myslope[i])
a<-table.element(a,myseas[i])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
 





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