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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 02 Dec 2009 09:32:21 -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/02/t1259771594fcmgfn39ml5x8ga.htm/, Retrieved Wed, 02 Dec 2009 17:33:17 +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/02/t1259771594fcmgfn39ml5x8ga.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 «

17823,2 17872 17420,4 16704,4 15991,2 16583,6 19123,5 17838,7 17209,4 18586,5 16258,1 15141,6 19202,1 17746,5 19090,1 18040,3 17515,5 17751,8 21072,4 17170 19439,5 19795,4 17574,9 16165,4 19464,6 19932,1 19961,2 17343,4 18924,2 18574,1 21350,6 18594,6 19823,1 20844,4 19640,2 17735,4 19813,6 22160 20664,3 17877,4 20906,5 21164,1 21374,4 22952,3 21343,5 23899,3 22392,9 18274,1 22786,7 22321,5 17842,2 16373,5 15993,8 16446,1 17729 16643 16196,7 18252,1 17570,4 15836,8

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	0.515066	3.9897	9.1e-05
2	0.342204	2.6507	0.005128
3	0.456845	3.5387	0.000392
4	0.403231	3.1234	0.001376
5	0.257855	1.9973	0.025165
6	0.238844	1.8501	0.034614
7	0.078678	0.6094	0.272268
8	0.1544	1.196	0.118206
9	-0.032553	-0.2522	0.400891
10	-0.19552	-1.5145	0.067576
11	-0.057835	-0.448	0.327887
12	0.175644	1.3605	0.089376
13	-0.101849	-0.7889	0.216632
14	-0.21565	-1.6704	0.050023
15	-0.093055	-0.7208	0.236915
16	-0.010582	-0.082	0.467474
17	-0.099043	-0.7672	0.222991
18	-0.093349	-0.7231	0.236221
19	-0.058614	-0.454	0.325725
20	-0.050788	-0.3934	0.347707
21	-0.179468	-1.3902	0.084809
22	-0.191966	-1.487	0.07113
23	-0.104869	-0.8123	0.209913
24	0.007056	0.0547	0.478296
25	-0.097651	-0.7564	0.226184
26	-0.246307	-1.9079	0.030597
27	-0.132294	-1.0247	0.1548
28	-0.032121	-0.2488	0.402179
29	-0.164409	-1.2735	0.103874
30	-0.1309	-1.0139	0.157339
31	-0.071973	-0.5575	0.289629
32	-0.169164	-1.3103	0.097538
33	-0.202156	-1.5659	0.061317
34	-0.173657	-1.3451	0.091821
35	-0.189321	-1.4665	0.07387
36	-0.070763	-0.5481	0.292819
37	-0.136239	-1.0553	0.14776
38	-0.237546	-1.84	0.035356
39	-0.111097	-0.8606	0.196454
40	-0.081979	-0.635	0.263918
41	-0.136441	-1.0569	0.147405
42	-0.032026	-0.2481	0.402462
43	-0.023744	-0.1839	0.427349
44	-0.046139	-0.3574	0.361025
45	-0.013049	-0.1011	0.459913
46	0.023929	0.1853	0.42679
47	0.059195	0.4585	0.324116
48	0.123696	0.9581	0.170916
49	0.09934	0.7695	0.222313
50	0.083114	0.6438	0.26108
51	0.106771	0.827	0.205744
52	0.083144	0.644	0.261005
53	0.056493	0.4376	0.331625
54	0.067707	0.5245	0.300948
55	0.061676	0.4777	0.317287
56	0.041682	0.3229	0.373959
57	0.021766	0.1686	0.433339
58	0.014845	0.115	0.45442
59	0.010939	0.0847	0.466379
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.515066	3.9897	9.1e-05
2	0.104682	0.8109	0.210325
3	0.337326	2.6129	0.005665
4	0.0813	0.6297	0.265626
5	-0.04206	-0.3258	0.372855
6	-0.000534	-0.0041	0.498358
7	-0.250653	-1.9415	0.028446
8	0.162697	1.2602	0.10623
9	-0.336941	-2.6099	0.005709
10	-0.122065	-0.9455	0.174095
11	0.121379	0.9402	0.175443
12	0.422658	3.2739	0.000882
13	-0.164824	-1.2767	0.10331
14	-0.239673	-1.8565	0.034147
15	-0.005946	-0.0461	0.481709
16	0.064817	0.5021	0.308727
17	0.000271	0.0021	0.499165
18	-0.093595	-0.725	0.23564
19	0.093433	0.7237	0.236022
20	-0.221387	-1.7149	0.045766
21	-0.020119	-0.1558	0.43834
22	0.132589	1.027	0.154265
23	-0.038085	-0.295	0.384504
24	-0.110085	-0.8527	0.198604
25	0.057678	0.4468	0.328325
26	-0.017733	-0.1374	0.445604
27	-0.052537	-0.4069	0.342748
28	-0.014418	-0.1117	0.455724
29	-0.051316	-0.3975	0.346209
30	-0.038893	-0.3013	0.382129
31	-0.133832	-1.0367	0.152027
32	-0.052352	-0.4055	0.343269
33	0.025397	0.1967	0.422354
34	0.014159	0.1097	0.456516
35	-0.170505	-1.3207	0.095804
36	0.09003	0.6974	0.244132
37	-0.021547	-0.1669	0.434005
38	0.033681	0.2609	0.397534
39	-0.018315	-0.1419	0.443829
40	-0.124904	-0.9675	0.168589
41	0.01727	0.1338	0.447016
42	-0.03431	-0.2658	0.395667
43	0.058461	0.4528	0.326151
44	-0.010225	-0.0792	0.468568
45	0.01699	0.1316	0.447869
46	-0.00233	-0.018	0.492831
47	0.056802	0.44	0.330763
48	0.032488	0.2517	0.401085
49	-0.00297	-0.023	0.490861
50	-0.033962	-0.2631	0.396701
51	-0.055628	-0.4309	0.334044
52	-0.091361	-0.7077	0.240941
53	-0.08612	-0.6671	0.253638
54	-0.041206	-0.3192	0.37535
55	0.07373	0.5711	0.285029
56	0.075257	0.5829	0.28106
57	0.026179	0.2028	0.419995
58	-0.08287	-0.6419	0.26169
59	-0.049321	-0.382	0.351892
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259771594fcmgfn39ml5x8ga/19usy1259771539.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259771594fcmgfn39ml5x8ga/19usy1259771539.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259771594fcmgfn39ml5x8ga/25zey1259771539.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259771594fcmgfn39ml5x8ga/25zey1259771539.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 (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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