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D=d=1

*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: Sun, 13 Dec 2009 08:09:11 -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/Dec/13/t12607169834h22mtsq1rg8znv.htm/, Retrieved Sun, 13 Dec 2009 16:09:45 +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/Dec/13/t12607169834h22mtsq1rg8znv.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 «

627 696 825 677 656 785 412 352 839 729 696 641 695 638 762 635 721 854 418 367 824 687 601 676 740 691 683 594 729 731 386 331 707 715 657 653 642 643 718 654 632 731 392 344 792 852 649 629 685 617 715 715 629 916 531 357 917 828 708 858 775 785 1006 789 734 906 532 387 991 841

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.350712	-2.6478	0.00523
2	-0.221817	-1.6747	0.049737
3	0.281317	2.1239	0.019015
4	-0.323783	-2.4445	0.00881
5	0.045943	0.3469	0.364987
6	0.199778	1.5083	0.068501
7	-0.274462	-2.0721	0.021393
8	0.223587	1.688	0.048433
9	0.052425	0.3958	0.346866
10	-0.158966	-1.2002	0.117519
11	0.221946	1.6757	0.049641
12	-0.166046	-1.2536	0.107549
13	-0.227083	-1.7144	0.045941
14	0.267953	2.023	0.023886
15	0.018278	0.138	0.445364
16	-0.167855	-1.2673	0.105104
17	0.149104	1.1257	0.132503
18	0.02377	0.1795	0.429107
19	-0.149324	-1.1274	0.132155
20	0.150989	1.1399	0.12954
21	-0.040564	-0.3062	0.380265
22	-0.095519	-0.7212	0.236882
23	0.16726	1.2628	0.105903
24	-0.196251	-1.4817	0.071969
25	0.08366	0.6316	0.265079
26	0.039414	0.2976	0.383558
27	-0.158683	-1.198	0.117932
28	0.150349	1.1351	0.13054
29	0.091482	0.6907	0.246286
30	-0.165854	-1.2522	0.10781
31	0.092996	0.7021	0.242736
32	-0.117392	-0.8863	0.189592
33	-0.05055	-0.3816	0.352071
34	0.126556	0.9555	0.171685
35	-0.046795	-0.3533	0.362586
36	0.008017	0.0605	0.475972
37	0.067383	0.5087	0.306451
38	-0.032853	-0.248	0.4025
39	0.03756	0.2836	0.388882
40	-0.090643	-0.6843	0.248267
41	-0.03307	-0.2497	0.401869
42	0.018941	0.143	0.443396
43	0.051666	0.3901	0.348968
44	0.006186	0.0467	0.481456
45	0.033009	0.2492	0.402046
46	-0.045753	-0.3454	0.365523
47	0.010293	0.0777	0.469165
48	-0.026775	-0.2021	0.42026
49	-0.055719	-0.4207	0.337788
50	0.048357	0.3651	0.358198
51	0.008427	0.0636	0.474747
52	0.041876	0.3162	0.376519
53	-0.01533	-0.1157	0.454133
54	-0.011311	-0.0854	0.466123
55	-0.011598	-0.0876	0.465265
56	0.016183	0.1222	0.451595
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.350712	-2.6478	0.00523
2	-0.393176	-2.9684	0.002186
3	0.047266	0.3569	0.361261
4	-0.347502	-2.6236	0.005572
5	-0.166432	-1.2565	0.107024
6	-0.064266	-0.4852	0.314699
7	-0.241482	-1.8231	0.036763
8	0.018949	0.1431	0.443372
9	-0.006307	-0.0476	0.481095
10	0.06381	0.4818	0.315911
11	0.19306	1.4576	0.075223
12	0.042498	0.3208	0.374749
13	-0.175121	-1.3221	0.095702
14	-0.058391	-0.4408	0.330496
15	0.130761	0.9872	0.163853
16	-0.11578	-0.8741	0.19286
17	-0.114922	-0.8676	0.194615
18	0.082935	0.6261	0.26686
19	-0.094119	-0.7106	0.240119
20	0.01784	0.1347	0.446667
21	0.087517	0.6607	0.255721
22	0.058747	0.4435	0.329529
23	0.142651	1.077	0.14301
24	-0.086169	-0.6506	0.258971
25	0.036196	0.2733	0.392815
26	-0.213871	-1.6147	0.055951
27	-0.066033	-0.4985	0.310013
28	-0.074031	-0.5589	0.289201
29	-0.02281	-0.1722	0.43194
30	0.05042	0.3807	0.352436
31	0.018765	0.1417	0.44392
32	-0.146253	-1.1042	0.137077
33	-0.086941	-0.6564	0.257106
34	-0.017332	-0.1309	0.448177
35	-0.012511	-0.0945	0.462538
36	-0.097009	-0.7324	0.233463
37	-0.04608	-0.3479	0.364599
38	-0.010638	-0.0803	0.468134
39	0.016636	0.1256	0.450246
40	-0.088542	-0.6685	0.253263
41	0.00803	0.0606	0.475935
42	0.002516	0.019	0.492454
43	0.030778	0.2324	0.408542
44	-0.031037	-0.2343	0.407787
45	0.008734	0.0659	0.473828
46	-0.068481	-0.517	0.303572
47	0.073061	0.5516	0.291691
48	-0.09333	-0.7046	0.241957
49	-0.144935	-1.0942	0.139227
50	-0.038272	-0.2889	0.386834
51	-0.015374	-0.1161	0.454003
52	0.026935	0.2034	0.419791
53	-0.053354	-0.4028	0.344297
54	0.044355	0.3349	0.369475
55	0.029882	0.2256	0.411159
56	-0.018671	-0.141	0.444197
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/13/t12607169834h22mtsq1rg8znv/1g2sq1260716947.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t12607169834h22mtsq1rg8znv/1g2sq1260716947.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t12607169834h22mtsq1rg8znv/26ghe1260716947.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t12607169834h22mtsq1rg8znv/26ghe1260716947.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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 (par2 == 0) {

x <- log(x)

} else {

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

}

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

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

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

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

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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