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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: Tue, 21 Dec 2010 19:29:51 +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/21/t1292959678vq122ne8s249u6g.htm/, Retrieved Tue, 21 Dec 2010 20:27:58 +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/21/t1292959678vq122ne8s249u6g.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 «

320 324 343 295 301 367 196 182 342 361 333 330 345 323 365 323 316 358 235 169 430 409 407 341 326 374 364 349 300 385 304 196 443 414 325 388 356 386 444 387 327 448 225 182 460 411 342 361 377 331 428 340 352 461 221 198 422 329 320 375 364 351 380 319 322 386 221 187 343 342 365 313 356 337 389 326 343 357 220 218 391 425 332 298 360 336 325 393 301 426 265 210 429 440 357 431 442 422 544 420 396 482 261 211 448 468 464 425

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	1081	0	109
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	320	321.861771680105	18.6876172605011	299.450611059394	1.86177168010505
2	324	336.265809930374	10.7968818919555	300.93730817767	12.2658099303742
3	343	329.558743537845	54.0172511662081	302.424005295947	-13.4412564621548
4	295	280.766745543193	5.34092248773241	303.892331969075	-14.2332544568073
5	301	313.752525591307	-17.1131842335102	305.360658642203	12.7525255913071
6	367	366.113594646592	61.0779286477992	306.808476705609	-0.886405353407781
7	196	192.696893113013	-108.953187882027	308.256294769014	-3.30310688698711
8	182	208.093843496550	-153.844477018832	309.750633522281	26.0938434965504
9	342	310.379676540842	62.3753511836095	311.244972275549	-31.6203234591583
10	361	360.149117499258	49.1645555534664	312.686326947275	-0.850882500741704
11	333	343.140757779818	8.73156060118037	314.127681619002	10.1407577798177
12	330	335.008734531981	9.71877099769739	315.272494470322	5.00873453198102
13	345	354.895075417858	18.6876172605011	316.417307321641	9.89507541785758
14	323	316.505786918562	10.7968818919555	318.697331189482	-6.49421308143758
15	365	355.005393776469	54.0172511662081	320.977355057323	-9.99460622353098
16	323	315.877964164635	5.34092248773241	324.781113347633	-7.12203583536495
17	316	320.528312595568	-17.1131842335102	328.584871637942	4.52831259556791
18	358	323.203959400693	61.0779286477992	331.718111951508	-34.7960405993074
19	235	244.101835616953	-108.953187882027	334.851352265074	9.10183561695271
20	169	154.919635306076	-153.844477018832	336.924841712756	-14.0803646939240
21	430	458.626317655953	62.3753511836095	338.998331160437	28.626317655953
22	409	428.725732472555	49.1645555534664	340.109711973979	19.7257324725547
23	407	464.047346611299	8.73156060118037	341.221092787520	57.0473466112992
24	341	329.870426661826	9.71877099769739	342.410802340477	-11.1295733381741
25	326	289.711870846066	18.6876172605011	343.600511893433	-36.2881291539341
26	374	392.43996137956	10.7968818919555	344.763156728485	18.4399613795598
27	364	328.056947270256	54.0172511662081	345.925801563536	-35.9430527297444
28	349	346.224932439508	5.34092248773241	346.43414507276	-2.77506756049212
29	300	270.170695651527	-17.1131842335102	346.942488581983	-29.8293043484729
30	385	360.746957361847	61.0779286477992	348.175113990354	-24.2530426381534
31	304	367.545448483302	-108.953187882027	349.407739398725	63.5454484833018
32	196	193.404976952147	-153.844477018832	352.439500066685	-2.59502304785349
33	443	468.153388081745	62.3753511836095	355.471260734646	25.1533880817449
34	414	420.349033353893	49.1645555534664	358.486411092641	6.34903335389288
35	325	279.766877948184	8.73156060118037	361.501561450636	-45.2331220518164
36	388	403.876816228581	9.71877099769739	362.404412773721	15.8768162285812
37	356	330.005118642692	18.6876172605011	363.307264096807	-25.9948813573081
38	386	398.323390563869	10.7968818919555	362.879727544176	12.3233905638687
39	444	471.530557842247	54.0172511662081	362.452190991545	27.5305578422473
40	387	406.162837251437	5.34092248773241	362.49624026083	19.1628372514373
41	327	308.572894703394	-17.1131842335102	362.540289530116	-18.4271052966059
42	448	473.056570574445	61.0779286477992	361.865500777756	25.0565705744451
43	225	197.762475856632	-108.953187882027	361.190712025395	-27.2375241433683
44	182	158.670522908269	-153.844477018832	359.173954110563	-23.3294770917307
45	460	500.467452620661	62.3753511836095	357.15719619573	40.4674526206606
46	411	417.012768944695	49.1645555534664	355.822675501838	6.01276894469538
47	342	320.780284590873	8.73156060118037	354.488154807947	-21.2197154091269
48	361	357.729101667167	9.71877099769739	354.552127335136	-3.27089833283316
49	377	380.696282877174	18.6876172605011	354.616099862325	3.69628287717393
50	331	297.11222000792	10.7968818919555	354.090898100124	-33.88777999208
51	428	448.417052495868	54.0172511662081	353.565696337924	20.4170524958679
52	340	323.228237737692	5.34092248773241	351.430839774575	-16.7717622623078
53	352	371.817201022283	-17.1131842335102	349.295983211227	19.8172010222833
54	461	513.077778829681	61.0779286477992	347.84429252252	52.0777788296809
55	221	204.560586048214	-108.953187882027	346.392601833813	-16.4394139517860
56	198	205.023222036216	-153.844477018832	344.821254982616	7.02322203621554
57	422	438.374740684971	62.3753511836095	343.24990813142	16.3747406849708
58	329	268.185977336635	49.1645555534664	340.649467109898	-60.8140226633648
59	320	293.219413310443	8.73156060118037	338.049026088377	-26.7805866895575
60	375	404.824007520458	9.71877099769739	335.457221481845	29.8240075204579
61	364	376.446965864187	18.6876172605011	332.865416875312	12.4469658641866
62	351	359.991848621495	10.7968818919555	331.21126948655	8.99184862149457
63	380	376.425626736004	54.0172511662081	329.557122097787	-3.5743732639956
64	319	304.421345184527	5.34092248773241	328.237732327741	-14.5786548154734
65	322	334.194841675816	-17.1131842335102	326.918342557694	12.1948416758157
66	386	385.407783748752	61.0779286477992	325.514287603449	-0.592216251248374
67	221	226.842955232823	-108.953187882027	324.110232649204	5.8429552328231
68	187	204.434899742192	-153.844477018832	323.40957727664	17.4348997421921
69	343	300.915726912315	62.3753511836095	322.708921904076	-42.0842730876852
70	342	311.849045745790	49.1645555534664	322.986398700744	-30.1509542542103
71	365	398.004563901407	8.73156060118037	323.263875497412	33.0045639014074
72	313	292.382229705278	9.71877099769739	323.898999297025	-20.6177702947223
73	356	368.778259642861	18.6876172605011	324.534123096638	12.7782596428613
74	337	336.599819857894	10.7968818919555	326.603298250151	-0.400180142106137
75	389	395.310275430128	54.0172511662081	328.672473403664	6.31027543012823
76	326	315.684376390375	5.34092248773241	330.974701121892	-10.3156236096249
77	343	369.836255393389	-17.1131842335102	333.276928840121	26.8362553933889
78	357	319.324337243584	61.0779286477992	333.597734108616	-37.6756627564156
79	220	215.034648504915	-108.953187882027	333.918539377112	-4.96535149508463
80	218	256.772093017706	-153.844477018832	333.072384001126	38.7720930177061
81	391	387.398420191250	62.3753511836095	332.22622862514	-3.60157980874959
82	425	468.794702907111	49.1645555534664	332.040741539423	43.7947029071111
83	332	323.413184945114	8.73156060118037	331.855254453705	-8.5868150548855
84	298	253.237973887785	9.71877099769739	333.043255114518	-44.7620261122151
85	360	367.081126964169	18.6876172605011	334.231255775330	7.0811269641685
86	336	324.83605770557	10.7968818919555	336.367060402474	-11.1639422944298
87	325	257.479883804174	54.0172511662081	338.502865029618	-67.5201161958263
88	393	438.45076598632	5.34092248773241	342.208311525947	45.4507659863204
89	301	273.199426211234	-17.1131842335102	345.913758022276	-27.800573788766
90	426	438.236206936702	61.0779286477992	352.685864415499	12.2362069367022
91	265	279.495217073306	-108.953187882027	359.457970808721	14.4952170733058
92	210	205.393458657205	-153.844477018832	368.451018361626	-4.60654134279457
93	429	418.180582901859	62.3753511836095	377.444065914532	-10.8194170981412
94	440	445.073139830868	49.1645555534664	385.762304615665	5.0731398308684
95	357	311.187896082021	8.73156060118037	394.080543316799	-45.8121039179791
96	431	453.271723581763	9.71877099769739	399.00950542054	22.2717235817626
97	442	461.373915215217	18.6876172605011	403.938467524281	19.3739152152175
98	422	427.252039443159	10.7968818919555	405.951078664885	5.25203944315945
99	544	626.019059028303	54.0172511662081	407.963689805489	82.0190590283032
100	420	425.971592548039	5.34092248773241	408.687484964229	5.97159254803887
101	396	399.701904110541	-17.1131842335102	409.411280122969	3.70190411054148
102	482	492.540956596872	61.0779286477992	410.381114755329	10.5409565968722
103	261	219.602238494338	-108.953187882027	411.350949387689	-41.3977615056616
104	211	164.162446576726	-153.844477018832	411.682030442106	-46.8375534232744
105	448	421.611537319867	62.3753511836095	412.013111496524	-26.3884626801334
106	468	474.784949651933	49.1645555534664	412.050494794601	6.784949651933
107	464	507.180561306142	8.73156060118037	412.087878092677	43.1805613061423
108	425	428.086487437644	9.71877099769739	412.194741564659	3.08648743764377

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959678vq122ne8s249u6g/13g9i1292959786.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959678vq122ne8s249u6g/13g9i1292959786.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959678vq122ne8s249u6g/23g9i1292959786.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959678vq122ne8s249u6g/23g9i1292959786.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959678vq122ne8s249u6g/3vpqk1292959786.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959678vq122ne8s249u6g/3vpqk1292959786.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959678vq122ne8s249u6g/4vpqk1292959786.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959678vq122ne8s249u6g/4vpqk1292959786.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

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')

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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