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paper

*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 16:30:36 +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/t1293553741vq9aihhbjcmnqcw.htm/, Retrieved Tue, 28 Dec 2010 17:29:01 +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/t1293553741vq9aihhbjcmnqcw.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 «

36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509

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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.304956	-2.7783	0.003378
2	-0.051316	-0.4675	0.320679
3	0.011715	0.1067	0.457629
4	-0.052171	-0.4753	0.317911
5	0.084971	0.7741	0.22053
6	-0.249401	-2.2721	0.012832
7	0.063304	0.5767	0.282842
8	-0.039126	-0.3565	0.361201
9	0.006668	0.0608	0.475852
10	-0.082063	-0.7476	0.228398
11	-0.236775	-2.1571	0.016944
12	0.733406	6.6816	0
13	-0.221279	-2.0159	0.02352
14	-0.028944	-0.2637	0.396337
15	0.018351	0.1672	0.433814
16	-0.072127	-0.6571	0.256464
17	0.098028	0.8931	0.187198
18	-0.245771	-2.2391	0.013913
19	0.076277	0.6949	0.244525
20	-0.049502	-0.451	0.32659
21	-0.025091	-0.2286	0.409876
22	-0.069732	-0.6353	0.263492
23	-0.146446	-1.3342	0.092897
24	0.569891	5.192	1e-06
25	-0.152158	-1.3862	0.084695
26	-0.049441	-0.4504	0.326788
27	0.024894	0.2268	0.410571
28	-0.023283	-0.2121	0.416267
29	0.062384	0.5683	0.285668
30	-0.217473	-1.9813	0.025436
31	0.115184	1.0494	0.148525
32	-0.064281	-0.5856	0.279856
33	-0.023601	-0.215	0.415143
34	-0.031277	-0.2849	0.388198
35	-0.146868	-1.338	0.09227
36	0.424028	3.8631	0.000111
37	-0.098512	-0.8975	0.186027
38	-0.063731	-0.5806	0.281535
39	0.019856	0.1809	0.428446
40	0.03619	0.3297	0.371228
41	-0.027049	-0.2464	0.402979
42	-0.09495	-0.865	0.194757
43	0.055076	0.5018	0.308579
44	-0.061218	-0.5577	0.289266
45	-0.01902	-0.1733	0.431426
46	-0.031749	-0.2892	0.386556
47	-0.097629	-0.8894	0.188167
48	0.304515	2.7743	0.003416
49	-0.04486	-0.4087	0.341907
50	-0.073919	-0.6734	0.251271
51	0.040686	0.3707	0.355913
52	0.019209	0.175	0.430753
53	-0.048304	-0.4401	0.330516
54	-0.014412	-0.1313	0.447926
55	0.018527	0.1688	0.433186
56	-0.026629	-0.2426	0.404457
57	0.013664	0.1245	0.450617
58	-0.06646	-0.6055	0.273256
59	-0.066874	-0.6093	0.272011
60	0.175502	1.5989	0.056821

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.304956	-2.7783	0.003378
2	-0.159111	-1.4496	0.075473
3	-0.062153	-0.5662	0.28638
4	-0.086484	-0.7879	0.216497
5	0.042174	0.3842	0.350896
6	-0.250109	-2.2786	0.01263
7	-0.11027	-1.0046	0.159003
8	-0.139946	-1.275	0.10294
9	-0.081238	-0.7401	0.23066
10	-0.202199	-1.8421	0.034514
11	-0.452337	-4.121	4.4e-05
12	0.565388	5.1509	1e-06
13	0.154447	1.4071	0.081569
14	0.02828	0.2576	0.398659
15	0.003547	0.0323	0.48715
16	-0.07271	-0.6624	0.25477
17	-0.051128	-0.4658	0.321289
18	-0.083317	-0.7591	0.224985
19	0.003716	0.0339	0.486538
20	-0.065215	-0.5941	0.277017
21	-0.13282	-1.2101	0.114847
22	-0.067469	-0.6147	0.270225
23	0.048219	0.4393	0.330794
24	0.091877	0.837	0.202487
25	0.074517	0.6789	0.24955
26	-0.075051	-0.6837	0.24802
27	-0.083282	-0.7587	0.225079
28	0.057661	0.5253	0.30038
29	-0.030901	-0.2815	0.389505
30	-0.013766	-0.1254	0.45025
31	0.074837	0.6818	0.248632
32	-0.014786	-0.1347	0.446587
33	0.023221	0.2115	0.416489
34	0.127664	1.1631	0.124066
35	-0.02441	-0.2224	0.412278
36	-0.124161	-1.1312	0.130623
37	-0.076787	-0.6996	0.243077
38	-0.056425	-0.5141	0.30429
39	-0.0489	-0.4455	0.328559
40	0.087231	0.7947	0.214523
41	-0.105283	-0.9592	0.170128
42	0.121029	1.1026	0.136688
43	-0.062881	-0.5729	0.284141
44	-0.008345	-0.076	0.469789
45	-0.01254	-0.1142	0.454661
46	-0.086727	-0.7901	0.215855
47	-0.018704	-0.1704	0.432556
48	-0.071688	-0.6531	0.257747
49	0.051151	0.466	0.321215
50	0.044342	0.404	0.343635
51	0.044225	0.4029	0.344027
52	-0.083121	-0.7573	0.225516
53	-0.004435	-0.0404	0.483933
54	-0.008194	-0.0747	0.470336
55	-0.024612	-0.2242	0.411566
56	0.035269	0.3213	0.374388
57	0.05864	0.5342	0.297303
58	-0.00856	-0.078	0.469013
59	-0.059884	-0.5456	0.293413
60	-0.080564	-0.734	0.232516

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293553741vq9aihhbjcmnqcw/1r3961293553833.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293553741vq9aihhbjcmnqcw/1r3961293553833.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293553741vq9aihhbjcmnqcw/2r3961293553833.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293553741vq9aihhbjcmnqcw/2r3961293553833.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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 (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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