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*The author of this computation has been verified*
R Software Module: /rwasp_decomposeloess.wasp (opens new window with default values)
Title produced by software: Decomposition by Loess
Date of computation: Fri, 10 Dec 2010 11:51:14 +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/10/t1291981776u1c19fdv826fmxu.htm/, Retrieved Fri, 10 Dec 2010 12:49:46 +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/10/t1291981776u1c19fdv826fmxu.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 «
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 time10 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal37210373
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
1235.1212.12541271306445.0468985211203213.027688765816-22.9745872869361
2280.7298.54252654650746.6655087267954216.19196472669817.8425265465068
3264.6285.88388151580923.9598777966112219.3562406875821.2838815158089
4240.7272.626869450512-14.2822170025075223.05534755199631.9268694505118
5201.4207.572096428406-31.5265508448178226.7544544164116.17209642840646
6240.8206.96608677140643.5856271490782231.048286079516-33.8339132285938
7241.1228.13865325517418.7192290022065235.34211774262-12.9613467448264
8223.8219.091771759493-11.3399106306268239.848138871133-4.70822824050651
9206.1197.032213898348-29.1863738979947244.354159999647-9.06778610165202
10174.7144.436345412184-46.32479373617251.288448323986-30.2636545878159
11203.3172.279836769342-23.9025734176668258.222736648325-31.0201632306583
12220.5191.483642378112-21.4147206884719270.93107831036-29.0163576218881
13299.5270.31368150648545.0468985211203283.639419972395-29.1863184935152
14347.4349.50698706628246.6655087267954298.6275042069232.10698706628199
15338.3339.02453376193823.9598777966112313.6155884414500.724533761938346
16327.7341.365426909548-14.2822170025075328.3167900929613.6654269095478
17351.6391.708559100349-31.5265508448178343.01799174446940.1085591003489
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20395.6424.830188179574-11.3399106306268377.70972245105329.2301881795738
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26479.1536.77853919333846.6655087267954374.75595207986657.6785391933385
27431.3473.18065760415923.9598777966112365.45946459922941.8806576041594
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33249243.043967385441-29.1863738979947284.142406512554-5.95603261455949
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36240.9257.737526362264-21.4147206884719245.47719432620816.8375263622639
37264.9250.25950373796345.0468985211203234.493597740917-14.6404962620370
38253.8234.09172856252646.6655087267954226.842762710679-19.7082714374743
39232.3221.44819452294723.9598777966112219.191927680441-10.8518054770526
40193.8187.205295464492-14.2822170025075214.676921538016-6.5947045355083
41177175.364635449228-31.5265508448178210.16191539559-1.63536455077244
42213.2175.48541489609943.5856271490782207.328957954823-37.7145851039015
43207.2191.18477048373718.7192290022065204.496000514056-16.0152295162629
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46175.4197.517877593167-46.32479373617199.60691614300422.1178775931665
47199223.352686084086-23.9025734176668198.54988733358024.3526860840863
48179.6182.800441368594-21.4147206884719197.8142793198773.20044136859437
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55208.5209.25678425125418.7192290022065189.0239867465400.756784251253805
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57172.8189.250472096410-29.1863738979947185.53590180158516.4504720964102
58148158.692088505912-46.32479373617183.63270523025810.6920885059125
59159.4160.973064758736-23.9025734176668181.7295086589311.57306475873617
60154.5151.089508174593-21.4147206884719179.325212513879-3.41049182540678
61213.2204.43218511005345.0468985211203176.920916368827-8.76781488994698
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67171135.32833056544218.7192290022065187.952440432352-35.6716694345583
68151.2116.873672754247-11.3399106306268196.86623787638-34.3263272457531
69161.9147.206338577587-29.1863738979947205.780035320408-14.6936614224133
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72236.4247.721639328671-21.4147206884719246.49308135980111.3216393286712
73356.1406.43469564857345.0468985211203260.71840583030650.3346956485735
74398.3475.09778840115746.6655087267954274.83670287204876.7977884011568
75403.7494.48512228959923.9598777966112288.9549999137990.7851222895991
76384.6482.29800718765-14.2822170025075301.18420981485797.6980071876503
77365.8449.713131128893-31.5265508448178313.41341971592583.913131128893
78368.1368.01871466481243.5856271490782324.59565818611-0.0812853351883405
79367.9381.30287434149818.7192290022065335.77789665629613.4028743414977
80347367.219064024287-11.3399106306268338.12084660633920.2190640242873
81343.3375.322577341612-29.1863738979947340.46379655638332.0225773416116
82292.9295.619231500781-46.32479373617336.5055622353892.71923150078055
83311.5314.355245503271-23.9025734176668332.5473279143962.85524550327096
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85366.9368.23944001107945.0468985211203320.5136614678001.33944001107932
86356.9354.16977945355846.6655087267954312.964711819647-2.73022054644235
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103298.4303.39392923648818.7192290022065274.6868417613054.99392923648799
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113263.5280.017431767377-31.5265508448178278.50911907744016.5174317673774
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190339.4325.760746006643-46.32479373617399.364047729527-13.6392539933568
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193451.8463.94308390940245.0468985211203394.61001756947812.1430839094017
194446.1452.95133655619746.6655087267954392.5831547170076.85133655619734
195422.5430.48383033885223.9598777966112390.5562918645377.9838303388521
196383.1393.131049682923-14.2822170025075387.35116731958410.0310496829230
197352.8352.980508070186-31.5265508448178384.1460427746320.180508070185567
198445.3466.87236356146643.5856271490782380.14200928945621.5723635614658
199367.5340.14279519351418.7192290022065376.13797580428-27.3572048064864
200355.1349.263750047779-11.3399106306268372.276160582848-5.83624995222152
201326.2313.172028536578-29.1863738979947368.414345361417-13.0279714634220
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205394.1385.86946623643745.0468985211203357.283635242442-8.23053376356256
206417.2433.28557155158446.6655087267954354.44891972162016.0855715515842
207369.9364.2259180025923.9598777966112351.614204200799-5.67408199740993
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209321.4330.498165091903-31.5265508448178343.8283857529159.09816509190262
210405.7429.22637803987643.5856271490782338.58799481104623.5263780398763
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212316.5317.661673138165-11.3399106306268326.6782374924621.16167313816521
213284.2277.577502782248-29.1863738979947320.008871115747-6.62249721775243
214270.9274.181330794468-46.32479373617313.9434629417023.28133079446826
215288.8293.624518650010-23.9025734176668307.8780547676564.82451865001042
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223305302.21793700624618.7192290022065289.062833991547-2.78206299375393
224282.1287.180371634996-11.3399106306268288.3595389956315.0803716349962
225250.3242.130129898281-29.1863738979947287.656243999714-8.16987010171914
226246.5253.027364803299-46.32479373617286.2974289328716.52736480329884
227257.9254.763959551638-23.9025734176668284.938613866029-3.13604044836177
228266.5269.814135397828-21.4147206884719284.6005852906443.31413539782767
229315.9302.49054476362045.0468985211203284.26255671526-13.4094552363803
230318.4304.14894025848546.6655087267954285.985551014719-14.2510597415148
231295.4279.1315768892123.9598777966112287.708545314179-16.2684231107901
232266.4256.523100779594-14.2822170025075290.559116222914-9.87689922040619
233245.8229.716863713169-31.5265508448178293.409687131648-16.0831362868306
234362.8386.59985234753343.5856271490782295.41452050338923.7998523475327
235324.9333.66141712266418.7192290022065297.419353875138.76141712266354
236294.2301.992690714896-11.3399106306268297.7472199157317.7926907148958
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238295.2339.996116081785-46.32479373617296.72867765438544.7961160817854
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242328.7321.08746407934946.6655087267954289.647027193855-7.61253592065077
243292.9274.09291283163823.9598777966112287.747209371751-18.8070871683617
244249.1226.302724072290-14.2822170025075286.179492930217-22.7972759277096
245230.4207.714774356134-31.5265508448178284.611776488684-22.6852256438658
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255274.7250.55759701784323.9598777966112274.882525185546-24.1424029821571
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265340.6299.13939230363845.0468985211203337.013709175242-41.4606076963621
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268355.2351.890228691345-14.2822170025075372.791988311162-3.30977130865460
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270466.9488.03843857160443.5856271490782402.17593427931821.1384385716040
271451465.38003934633418.7192290022065417.9007316514614.3800393463337
272422423.513095317525-11.3399106306268431.8268153131021.51309531752452
273429.2441.83347492325-29.1863738979947445.75289897474512.6334749232499
274425.9442.044367302318-46.32479373617456.08042643385216.1443673023184
275460.7478.894619524708-23.9025734176668466.40795389295818.1946195247084
276463.6474.933189505937-21.4147206884719473.68153118253511.3331895059372
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278544.2555.57976059479746.6655087267954486.15473067840711.3797605947973
279517.5519.68576931868523.9598777966112491.3543528847042.18576931868495
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281439.4412.768708324609-31.5265508448178497.557842520209-26.6312916753909
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288469.5461.417597374229-21.4147206884719498.997123314243-8.0824026257709
289544.7546.69665541684845.0468985211203497.6564460620311.99665541684823
290541.2539.67845149372546.6655087267954496.05603977948-1.52154850627528
291521.5524.58448870646023.9598777966112494.4556334969283.08448870646038
292469.7461.318224911395-14.2822170025075492.363992091112-8.38177508860474
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294542.6555.38194771817443.5856271490782486.23242513274812.7819477181741
295517.3533.68827141759418.7192290022065482.19249958020016.3882714175938
296485.7505.837080499933-11.3399106306268476.90283013069420.1370804999331
297465.8489.173213216807-29.1863738979947471.61316068118823.3732132168070
298447474.31967931532-46.32479373617466.0051144208527.3196793153202
299426.6416.705505257155-23.9025734176668460.397068160512-9.89449474284527
300411.6389.927862588558-21.4147206884719454.686858099914-21.6721374114418
301467.5440.97645343956445.0468985211203448.976648039315-26.5235465604356
302484.5478.43427722175246.6655087267954443.900214051452-6.06572277824762
303451.2439.616342139823.9598777966112438.823780063589-11.5836578602004
304417.4413.17260962079-14.2822170025075435.909607381718-4.22739037921019
305379.9358.331116144972-31.5265508448178432.995434699846-21.5688838550283
306484.7492.93773760724443.5856271490782432.8766352436778.23773760724436
307455458.52293521028518.7192290022065432.7578357875093.52293521028457
308420.8418.459430075989-11.3399106306268434.480480554638-2.34056992401145
309416.5425.983248576227-29.1863738979947436.2031253217689.48324857622714
310376.3360.219547815757-46.32479373617438.705245920414-16.0804521842435
311405.6393.895206898607-23.9025734176668441.207366519059-11.7047931013926
312405.8387.596168076093-21.4147206884719445.418552612379-18.2038319239075
313500.8506.9233627731845.0468985211203449.6297387056996.12336277318036
314514524.6418857458646.6655087267954456.69260552734410.6418857458605
315475.5463.28464985440023.9598777966112463.755472348989-12.2153501456003
316430.1399.894662947463-14.2822170025075474.587554055044-30.2053370525368
317414.4374.906915083718-31.5265508448178485.419635761100-39.4930849162818
318538533.12648507848243.5856271490782499.28788777244-4.87351492151845
319526520.12463121401218.7192290022065513.156139783781-5.87536878598763
320488.5457.836931812756-11.3399106306268530.50297881787-30.6630681872436
321520.2521.736556046035-29.1863738979947547.849817851961.53655604603523
322504.4484.445951519744-46.32479373617570.678842216426-19.9540484802561
323568.5567.394706836774-23.9025734176668593.507866580893-1.10529316322607
324610.6624.970617465058-21.4147206884719617.64410322341414.3706174650581
325818949.17276161294545.0468985211203641.780339865935131.172761612945
326830.9955.05097190073346.6655087267954660.083519372472124.150971900733
327835.9969.4534233243823.9598777966112678.386698879009133.55342332438
328782882.55444870274-14.2822170025075695.727768299767100.55444870274
329762.3843.057713124291-31.5265508448178713.06883772052680.7577131242915
330856.9932.4689901635443.5856271490782737.74538268738275.56899016354
331820.9860.65884334355618.7192290022065762.42192765423739.7588433435562
332769.6780.5652883719-11.3399106306268769.97462225872810.9652883718993
333752.2756.059057034777-29.1863738979947777.5273168632183.85905703477704
334724.4724.905203548497-46.32479373617770.2195901876730.505203548496752
335723.1707.190709905538-23.9025734176668762.911863512129-15.909290094462
336719.5703.749398459973-21.4147206884719756.665322228499-15.7506015400269
337817.4839.33432053401145.0468985211203750.41878094486921.9343205340108
338803.3813.38625056245346.6655087267954746.54824071075110.0862505624535
339752.5738.36242172675623.9598777966112742.677700476633-14.1375782732443
340689652.365381078516-14.2822170025075739.916835923991-36.6346189214839
341630.4555.170579473468-31.5265508448178737.15597137135-75.229420526532
342765.5752.13717572852143.5856271490782735.2771971224-13.3628242714785
343757.7763.28234812434218.7192290022065733.3984228734515.58234812434239
344732.2743.308415083658-11.3399106306268732.4314955469711.1084150836575
345702.6702.921805677507-29.1863738979947731.4645682204880.3218056775072
346683.3682.955897837387-46.32479373617729.968895898783-0.344102162613353
347709.5714.429349840588-23.9025734176668728.4732235770794.92934984058752
348702.2701.595934563462-21.4147206884719724.21878612501-0.604065436538122
349784.8804.58875280593945.0468985211203719.96434867294119.7887528059388
350810.9860.25495753379946.6655087267954714.87953373940649.3549575337991
351755.6777.44540339751823.9598777966112709.7947188058721.8454033975185
352656.8623.972497864250-14.2822170025075703.909719138257-32.8275021357495
353615.1563.701831374175-31.5265508448178698.024719470643-51.3981686258254
354745.3756.52245934914243.5856271490782690.4919135017811.2224593491419
355694.1686.52166346487718.7192290022065682.959107532917-7.57833653512319
356675.7688.031665594282-11.3399106306268674.70824503634412.3316655942824
357643.7650.128991358223-29.1863738979947666.4573825397726.42899135822256
358622.1632.172395258136-46.32479373617658.35239847803410.0723952581358
359634.6642.85515900137-23.9025734176668650.2474144162968.25515900137032
360588554.98177572052-21.4147206884719642.432944967952-33.0182242794797
361689.7699.73462595927345.0468985211203634.61847551960710.0346259592731
362673.9673.0034464429646.6655087267954628.131044830244-0.896553557039283
363647.9650.19650806250823.9598777966112621.6436141408812.29650806250766
364568.8534.380882006432-14.2822170025075617.501334996075-34.4191179935679
365545.7509.567494993549-31.5265508448178613.35905585127-36.1325050064515
366632.6612.4754075703443.5856271490782609.138965280582-20.1245924296599
367643.8663.961896287918.7192290022065604.91887470989420.1618962878995
368593.1596.532475674307-11.3399106306268601.007434956323.4324756743074
369579.7591.49037869525-29.1863738979947597.09599520274511.7903786952500
370546544.805824045201-46.32479373617593.518969690969-1.19417595479854
371562.9559.760629238475-23.9025734176668589.941944179192-3.13937076152547
372572.5579.853423528091-21.4147206884719586.5612971603817.35342352809118
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981776u1c19fdv826fmxu/1cprz1291981863.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981776u1c19fdv826fmxu/1cprz1291981863.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981776u1c19fdv826fmxu/2cprz1291981863.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981776u1c19fdv826fmxu/2cprz1291981863.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981776u1c19fdv826fmxu/35y821291981863.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981776u1c19fdv826fmxu/35y821291981863.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981776u1c19fdv826fmxu/4gq7n1291981863.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981776u1c19fdv826fmxu/4gq7n1291981863.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = TRUE ;
 
Parameters (R input):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = TRUE ;
 
R code (references can be found in the software module):
par1 <- as.numeric(par1) #seasonal period
if (par2 != 'periodic') par2 <- as.numeric(par2) #s.window
par3 <- as.numeric(par3) #s.degree
if (par4 == '') par4 <- NULL else par4 <- as.numeric(par4)#t.window
par5 <- as.numeric(par5)#t.degree
if (par6 != '') par6 <- as.numeric(par6)#l.window
par7 <- as.numeric(par7)#l.degree
if (par8 == 'FALSE') par8 <- FALSE else par9 <- TRUE #robust
nx <- length(x)
x <- ts(x,frequency=par1)
if (par6 != '') {
m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.window=par6, l.degree=par7, robust=par8)
} else {
m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.degree=par7, robust=par8)
}
m$time.series
m$win
m$deg
m$jump
m$inner
m$outer
bitmap(file='test1.png')
plot(m,main=main)
dev.off()
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(as.numeric(m$time.series[,'trend']),na.action=na.pass,lag.max = mylagmax,main='Trend')
acf(as.numeric(m$time.series[,'seasonal']),na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(as.numeric(m$time.series[,'remainder']),na.action=na.pass,lag.max = mylagmax,main='Remainder')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Seasonal Decomposition by Loess - Parameters',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Component',header=TRUE)
a<-table.element(a,'Window',header=TRUE)
a<-table.element(a,'Degree',header=TRUE)
a<-table.element(a,'Jump',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,m$win['s'])
a<-table.element(a,m$deg['s'])
a<-table.element(a,m$jump['s'])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Trend',header=TRUE)
a<-table.element(a,m$win['t'])
a<-table.element(a,m$deg['t'])
a<-table.element(a,m$jump['t'])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Low-pass',header=TRUE)
a<-table.element(a,m$win['l'])
a<-table.element(a,m$deg['l'])
a<-table.element(a,m$jump['l'])
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,'Seasonal Decomposition by Loess - Time Series Components',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,'Fitted',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,'Trend',header=TRUE)
a<-table.element(a,'Remainder',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,x[i]+m$time.series[i,'remainder'])
a<-table.element(a,m$time.series[i,'seasonal'])
a<-table.element(a,m$time.series[i,'trend'])
a<-table.element(a,m$time.series[i,'remainder'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
 





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