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*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: Wed, 17 Dec 2008 01:07:15 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/17/t1229501295oksisot1n1xslwj.htm/, Retrieved Wed, 17 Dec 2008 09:08:15 +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/2008/Dec/17/t1229501295oksisot1n1xslwj.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

31.58 27.88 27.32 28.89 28.05 28.73 32.00 34.53 33.47 34.09 35.47 34.59 34.32 32.78 28.38 29.18 28.62 28.20 29.33 29.72 26.29 26.82 27.64 27.10 27.05 26.02 25.76 25.94 24.97 21.74 18.16 16.95 16.46 16.44 18.20 16.44 15.70 13.94 12.23 14.75 14.62 15.04 15.50 16.10 15.44 15.14 15.42 15.69 17.57 18.42 17.96 18.39 17.63 17.95 17.79 17.73 18.99 19.83 20.23 20.24 21.12 21.25 21.80 21.84 22.21 22.64 23.54 23.78 23.65 23.93 24.77 26.26 27.69 29.54 29.31 29.26 28.69 26.16 27.12 29.40 30.99 32.96 32.20 31.67 32.49 33.66 32.44 34.38 32.36 30.73 30.31 27.26 25.05 22.33 18.26 18.30 16.00 14.36 14.98 16.88 16.56 13.31 9.61 9.34 7.89 1.71 0.81 0.71

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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.304776	3.1526	0.00105
2	0.081805	0.8462	0.199666
3	0.224777	2.3251	0.010977
4	0.026405	0.2731	0.392636
5	0.033455	0.3461	0.364987
6	0.084228	0.8713	0.19278
7	0.013871	0.1435	0.443091
8	0.116211	1.2021	0.11599
9	0.146905	1.5196	0.065781
10	0.003925	0.0406	0.483847
11	0.061315	0.6342	0.263636
12	0.158675	1.6413	0.051831
13	0.051706	0.5349	0.296932
14	0.053346	0.5518	0.291113
15	0.106129	1.0978	0.137376
16	0.111015	1.1483	0.126693
17	0.045811	0.4739	0.31828
18	-0.057631	-0.5961	0.276169
19	-0.003163	-0.0327	0.48698
20	-0.130788	-1.3529	0.089472
21	-0.107363	-1.1106	0.13462
22	-0.100901	-1.0437	0.149481
23	-0.112576	-1.1645	0.123406
24	-0.03072	-0.3178	0.375638
25	-0.077586	-0.8026	0.212005
26	-0.131897	-1.3644	0.087659
27	-0.039571	-0.4093	0.34156
28	-0.013809	-0.1428	0.44334
29	-0.056672	-0.5862	0.279482
30	-0.041933	-0.4338	0.332669
31	-0.075107	-0.7769	0.219463
32	-0.079656	-0.824	0.205896
33	-0.057048	-0.5901	0.278181
34	-0.096152	-0.9946	0.161086
35	-0.149621	-1.5477	0.062325
36	-0.03498	-0.3618	0.359094
37	-0.05208	-0.5387	0.295598
38	-0.069139	-0.7152	0.238028
39	0.023983	0.2481	0.402272
40	-0.068905	-0.7128	0.238774
41	-0.062537	-0.6469	0.259544
42	-0.057093	-0.5906	0.278026
43	-0.150562	-1.5574	0.061161
44	-0.095286	-0.9856	0.163266
45	-0.080228	-0.8299	0.204225
46	-0.064032	-0.6624	0.254585
47	-0.045351	-0.4691	0.319972
48	-0.06176	-0.6388	0.262143
49	-0.125005	-1.2931	0.099387
50	-0.07044	-0.7286	0.233907
51	-0.015678	-0.1622	0.435736
52	-0.087263	-0.9027	0.184369
53	-0.01988	-0.2056	0.41873
54	-0.04204	-0.4349	0.332269
55	-0.07994	-0.8269	0.205066
56	-0.008833	-0.0914	0.463686
57	-0.027463	-0.2841	0.388451
58	-0.03456	-0.3575	0.360714
59	-0.023731	-0.2455	0.403279
60	0.021696	0.2244	0.411428

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.304776	3.1526	0.00105
2	-0.012218	-0.1264	0.449832
3	0.224111	2.3182	0.011169
4	-0.122126	-1.2633	0.104618
5	0.071664	0.7413	0.230067
6	0.006229	0.0644	0.474373
7	0.007605	0.0787	0.468721
8	0.115088	1.1905	0.118245
9	0.064324	0.6654	0.253623
10	-0.058762	-0.6078	0.272291
11	0.042122	0.4357	0.33196
12	0.106245	1.099	0.137116
13	-0.006253	-0.0647	0.474273
14	0.017656	0.1826	0.427714
15	0.039248	0.406	0.342782
16	0.084813	0.8773	0.191142
17	-0.05583	-0.5775	0.282405
18	-0.105553	-1.0918	0.138676
19	0.030608	0.3166	0.376077
20	-0.205668	-2.1274	0.01784
21	0.000778	0.008	0.496797
22	-0.118701	-1.2278	0.111099
23	-0.006535	-0.0676	0.473115
24	-0.037684	-0.3898	0.348727
25	-0.075374	-0.7797	0.218652
26	-0.05697	-0.5893	0.278451
27	0.002416	0.025	0.490054
28	0.016538	0.1711	0.432246
29	0.012954	0.134	0.446829
30	-0.003108	-0.0321	0.487207
31	-0.057486	-0.5946	0.27667
32	0.024357	0.252	0.40078
33	-0.00782	-0.0809	0.467841
34	0.020705	0.2142	0.415411
35	-0.083536	-0.8641	0.194733
36	0.084742	0.8766	0.19134
37	0.007062	0.0731	0.470951
38	0.008637	0.0893	0.464487
39	0.083239	0.861	0.195572
40	-0.124936	-1.2923	0.099511
41	0.042198	0.4365	0.331675
42	-0.108006	-1.1172	0.1332
43	-0.079513	-0.8225	0.206314
44	-0.047737	-0.4938	0.311231
45	-0.093882	-0.9711	0.166838
46	0.028309	0.2928	0.385108
47	-0.059569	-0.6162	0.269541
48	-0.040671	-0.4207	0.337408
49	-0.12212	-1.2632	0.104628
50	0.027867	0.2883	0.386855
51	-0.007808	-0.0808	0.46789
52	-0.038649	-0.3998	0.345054
53	0.001221	0.0126	0.494975
54	-0.033276	-0.3442	0.365681
55	-0.043038	-0.4452	0.328541
56	0.037339	0.3862	0.350044
57	0.040978	0.4239	0.336254
58	-0.004608	-0.0477	0.481037
59	0.059035	0.6107	0.27136
60	0.040355	0.4174	0.338597

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t1229501295oksisot1n1xslwj/1pwln1229501230.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t1229501295oksisot1n1xslwj/1pwln1229501230.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t1229501295oksisot1n1xslwj/2hg1d1229501230.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t1229501295oksisot1n1xslwj/2hg1d1229501230.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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