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Verbetering (P)ACF

*The author of this computation has been verified*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Tue, 28 Dec 2010 19:28:48 +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/28/t1293564419ih07lbxedfvhlgj.htm/, Retrieved Tue, 28 Dec 2010 20:27:02 +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/28/t1293564419ih07lbxedfvhlgj.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 «

631923 654294 671833 586840 600969 625568 558110 630577 628654 603184 656255 600730 670326 678423 641502 625311 628177 589767 582471 636248 599885 621694 637406 595994 696308 674201 648861 649605 672392 598396 613177 638104 615632 634465 638686 604243 706669 677185 644328 644825 605707 600136 612166 599659 634210 618234 613576 627200 668973 651479 619661 644260 579936 601752 595376 588902 634341 594305 606200 610926 633685 639696 659451 593248 606677 599434 569578 629873 613438 604172 658328 612633 707372 739770 777535 685030 730234 714154 630872 719492 677023 679272 718317 645672

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.477272	4.3743	1.7e-05
2	0.436795	4.0033	6.7e-05
3	0.421454	3.8627	0.00011
4	0.070049	0.642	0.261307
5	0.139963	1.2828	0.101548
6	0.099852	0.9152	0.181363
7	-0.037394	-0.3427	0.366331
8	-0.009012	-0.0826	0.467183
9	0.035732	0.3275	0.372057
10	-0.049771	-0.4562	0.324727
11	0.084141	0.7712	0.221386
12	0.249267	2.2846	0.01243
13	-0.017917	-0.1642	0.434979
14	0.049527	0.4539	0.325528
15	-0.081994	-0.7515	0.22723
16	-0.235064	-2.1544	0.017036
17	-0.131372	-1.204	0.115978
18	-0.216326	-1.9827	0.025337
19	-0.253636	-2.3246	0.011253
20	-0.134948	-1.2368	0.109801
21	-0.189509	-1.7369	0.043037
22	-0.158628	-1.4538	0.074857
23	0.059943	0.5494	0.2921
24	0.026807	0.2457	0.403261
25	0.007615	0.0698	0.472264
26	0.054497	0.4995	0.309377
27	-0.157196	-1.4407	0.07669
28	-0.121455	-1.1132	0.134409
29	-0.103064	-0.9446	0.173787
30	-0.211744	-1.9407	0.027826
31	-0.119433	-1.0946	0.138405
32	-0.099686	-0.9136	0.181761
33	-0.153397	-1.4059	0.081721
34	0.02226	0.204	0.419418
35	0.054102	0.4959	0.310647
36	0.098837	0.9059	0.183803
37	0.136697	1.2528	0.106869
38	0.056117	0.5143	0.30419
39	-0.033377	-0.3059	0.380218
40	0.012011	0.1101	0.456304
41	-0.047322	-0.4337	0.332806
42	-0.075446	-0.6915	0.245587
43	0.039603	0.363	0.35877
44	-0.043192	-0.3959	0.346606
45	0.001138	0.0104	0.495853
46	0.157907	1.4472	0.075775
47	0.036488	0.3344	0.36945
48	0.178034	1.6317	0.053242
49	0.178037	1.6317	0.05324
50	0.045626	0.4182	0.338445
51	0.049953	0.4578	0.324129
52	0.033298	0.3052	0.380491
53	-0.053272	-0.4882	0.313324
54	-0.019597	-0.1796	0.428947
55	-0.007186	-0.0659	0.473824
56	-0.134467	-1.2324	0.110617
57	-0.031112	-0.2851	0.388117
58	-0.027834	-0.2551	0.399634
59	-0.074387	-0.6818	0.248631
60	0.088656	0.8125	0.209387

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.477272	4.3743	1.7e-05
2	0.270659	2.4806	0.007555
3	0.19595	1.7959	0.038052
4	-0.343312	-3.1465	0.001143
5	0.055982	0.5131	0.30462
6	0.06908	0.6331	0.264186
7	-0.029862	-0.2737	0.392496
8	-0.114273	-1.0473	0.148976
9	0.133444	1.223	0.112368
10	-0.023211	-0.2127	0.416026
11	0.127898	1.1722	0.122214
12	0.261411	2.3959	0.009401
13	-0.322665	-2.9573	0.002015
14	-0.190079	-1.7421	0.042575
15	-0.190542	-1.7463	0.042204
16	0.097739	0.8958	0.186462
17	-0.010747	-0.0985	0.460886
18	-0.024304	-0.2228	0.412134
19	-0.11565	-1.06	0.146103
20	0.109425	1.0029	0.159395
21	-0.01333	-0.1222	0.451529
22	0.031955	0.2929	0.385172
23	0.112379	1.03	0.15299
24	-0.101351	-0.9289	0.177801
25	-0.05935	-0.5439	0.293959
26	-0.075327	-0.6904	0.245927
27	-0.06031	-0.5527	0.290952
28	-0.002285	-0.0209	0.491669
29	0.013306	0.122	0.451615
30	-0.057452	-0.5266	0.299946
31	0.012274	0.1125	0.45535
32	-0.01056	-0.0968	0.461565
33	0.030451	0.2791	0.390431
34	0.142811	1.3089	0.097071
35	-0.139828	-1.2815	0.101765
36	0.068753	0.6301	0.26516
37	-0.132994	-1.2189	0.113146
38	0.023007	0.2109	0.416754
39	-0.044894	-0.4115	0.340891
40	0.101363	0.929	0.177773
41	-0.044385	-0.4068	0.342596
42	-0.002751	-0.0252	0.489974
43	0.074196	0.68	0.249181
44	-0.007415	-0.068	0.472989
45	0.078822	0.7224	0.236022
46	-0.020579	-0.1886	0.425427
47	-0.096372	-0.8833	0.189807
48	-0.081645	-0.7483	0.228187
49	0.103287	0.9466	0.173268
50	0.066597	0.6104	0.271631
51	-0.068673	-0.6294	0.265399
52	-0.000742	-0.0068	0.497295
53	0.007673	0.0703	0.472051
54	0.027459	0.2517	0.400958
55	-0.043357	-0.3974	0.34605
56	-0.081605	-0.7479	0.228298
57	-0.081859	-0.7502	0.227601
58	-0.026095	-0.2392	0.405781
59	0.067033	0.6144	0.270317
60	0.058416	0.5354	0.296896

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564419ih07lbxedfvhlgj/1g3hi1293564524.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564419ih07lbxedfvhlgj/1g3hi1293564524.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564419ih07lbxedfvhlgj/29cy31293564524.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564419ih07lbxedfvhlgj/29cy31293564524.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564419ih07lbxedfvhlgj/39cy31293564524.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293564419ih07lbxedfvhlgj/39cy31293564524.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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

if (par1 == 'Default') {

par1 = 10*log10(length(x))

} else {

par1 <- as.numeric(par1)

}

par2 <- as.numeric(par2)

par3 <- as.numeric(par3)

par4 <- as.numeric(par4)

par5 <- as.numeric(par5)

if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'

par7 <- as.numeric(par7)

if (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

dev.off()

(myacf <- c(racf$acf))

(mypacf <- c(rpacf$acf))

lengthx <- length(x)

sqrtn <- sqrt(lengthx)

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 2:(par1+1)) {

a<-table.row.start(a)

a<-table.element(a,i-1,header=TRUE)

a<-table.element(a,round(myacf[i],6))

mytstat <- myacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

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,'Partial Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:par1) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,round(mypacf[i],6))

mytstat <- mypacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

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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