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AutoCorrelation Function

*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, 09 Dec 2008 13:05:54 -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/09/t122885325949v6hm13g2xw505.htm/, Retrieved Tue, 09 Dec 2008 20:07:42 +0000

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/09/t122885325949v6hm13g2xw505.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},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply] 
test

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

5,7 5,7 5,6 5,8 5,6 5,6 5,6 5,5 5,4 5,4 5,5 5,4 5,4 5,2 5,4 5,2 5,1 5,1 5,0 5,0 4,9 5,1 5,0 5,0 4,8 4,7 4,7 4,7 4,7 4,7 4,6 4,7 4,7 4,5 4,4 4,5 4,4 4,6 4,5 4,4 4,5 4,5 4,6 4,7 4,7 4,7 4,8 4,7 5,0 4,9 4,8 5,1 5,0 5,5 5,5 5,7 6,1 6,1 6,5 6,7

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	0 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.250269	-1.9223	0.029697
2	0.240159	1.8447	0.035051
3	0.19913	1.5295	0.065737
4	-0.127893	-0.9824	0.164966
5	0.393059	3.0191	0.00187
6	0.01999	0.1535	0.439246
7	0.054181	0.4162	0.339397
8	0.124539	0.9566	0.171335
9	0.085094	0.6536	0.257949
10	-0.032404	-0.2489	0.402151
11	0.320954	2.4653	0.008309
12	-0.122925	-0.9442	0.174457
13	0.030107	0.2313	0.408959
14	0.148476	1.1405	0.12935
15	-0.158144	-1.2147	0.114655
16	0.258033	1.982	0.026072
17	-0.080613	-0.6192	0.269085
18	0.012307	0.0945	0.462503
19	-0.052991	-0.407	0.342728
20	-0.083254	-0.6395	0.262491
21	0.058622	0.4503	0.327079
22	-0.062864	-0.4829	0.315489
23	-0.015511	-0.1191	0.452784
24	-0.14165	-1.088	0.140503
25	0.020298	0.1559	0.438319
26	-0.069863	-0.5366	0.296771
27	-0.003477	-0.0267	0.489392
28	-0.062046	-0.4766	0.317709
29	-0.120246	-0.9236	0.179722
30	-0.013027	-0.1001	0.460316
31	-0.138263	-1.062	0.146278
32	0.093116	0.7152	0.238641
33	-0.227077	-1.7442	0.043165
34	0.09459	0.7266	0.235184
35	-0.136251	-1.0466	0.149785
36	-0.100083	-0.7687	0.222554
37	0.04421	0.3396	0.367689
38	-0.152655	-1.1726	0.122841
39	0.051107	0.3926	0.348028
40	-0.159437	-1.2247	0.112786
41	-0.023168	-0.178	0.429682
42	-0.042551	-0.3268	0.372472
43	-0.034485	-0.2649	0.396009
44	-0.070637	-0.5426	0.294735
45	0.002839	0.0218	0.491338
46	-0.047951	-0.3683	0.356977
47	-0.072574	-0.5575	0.289663
48	0.029495	0.2266	0.410776
49	-0.095507	-0.7336	0.233049
50	0.034343	0.2638	0.39643
51	-0.065143	-0.5004	0.309336
52	-0.023813	-0.1829	0.427746
53	0.015305	0.1176	0.453407
54	-0.041382	-0.3179	0.375855
55	0.009689	0.0744	0.470464
56	-0.004284	-0.0329	0.486931
57	-0.006612	-0.0508	0.479833
58	-0.000593	-0.0046	0.498191
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.250269	-1.9223	0.029697
2	0.189387	1.4547	0.075525
3	0.326695	2.5094	0.00743
4	-0.067898	-0.5215	0.301974
5	0.269468	2.0698	0.021428
6	0.206169	1.5836	0.059314
7	-0.009945	-0.0764	0.469683
8	-0.080111	-0.6153	0.270347
9	0.151948	1.1671	0.123925
10	-0.135442	-1.0403	0.151211
11	0.200802	1.5424	0.064163
12	-0.020928	-0.1607	0.436421
13	-0.156321	-1.2007	0.117329
14	-0.027053	-0.2078	0.418051
15	-0.000638	-0.0049	0.498053
16	0.01651	0.1268	0.449758
17	-0.011653	-0.0895	0.464491
18	0.033068	0.254	0.40019
19	-0.222856	-1.7118	0.046094
20	-0.156779	-1.2042	0.116652
21	0.068339	0.5249	0.300803
22	-0.065512	-0.5032	0.308346
23	-0.045082	-0.3463	0.365183
24	-0.02314	-0.1777	0.429767
25	-0.006481	-0.0498	0.480232
26	0.010088	0.0775	0.469249
27	0.036928	0.2836	0.388837
28	-0.023499	-0.1805	0.42869
29	-0.061199	-0.4701	0.320016
30	0.05341	0.4102	0.341554
31	-0.063261	-0.4859	0.314413
32	0.051147	0.3929	0.347917
33	-0.120863	-0.9284	0.1785
34	0.124118	0.9534	0.172146
35	0.015423	0.1185	0.453051
36	-0.053118	-0.408	0.342372
37	-0.074661	-0.5735	0.28425
38	0.047558	0.3653	0.358096
39	-0.025164	-0.1933	0.423698
40	-0.081144	-0.6233	0.267752
41	-0.011745	-0.0902	0.464211
42	0.009772	0.0751	0.470209
43	-0.091683	-0.7042	0.24203
44	0.006815	0.0523	0.479213
45	0.07758	0.5959	0.276759
46	-0.008537	-0.0656	0.47397
47	-0.000843	-0.0065	0.497429
48	-0.064735	-0.4972	0.310436
49	-0.00428	-0.0329	0.486942
50	-0.014139	-0.1086	0.456944
51	0.018194	0.1398	0.444667
52	-0.045416	-0.3488	0.364222
53	0.016002	0.1229	0.451297
54	0.062851	0.4828	0.315524
55	-0.050485	-0.3878	0.349785
56	0.003557	0.0273	0.489146
57	0.043584	0.3348	0.36949
58	0.029183	0.2242	0.411704
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t122885325949v6hm13g2xw505/1o5o01228853152.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t122885325949v6hm13g2xw505/1o5o01228853152.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t122885325949v6hm13g2xw505/2b5wo1228853152.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t122885325949v6hm13g2xw505/2b5wo1228853152.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = -2.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = -2.0 ; 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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