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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: Fri, 19 Dec 2008 03:50:22 -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/19/t1229683893jq5lj4z7hvi24dc.htm/, Retrieved Fri, 19 Dec 2008 11:51:39 +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/19/t1229683893jq5lj4z7hvi24dc.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 «

101.7 101.9 102 102.2 102.4 102.6 102.6 102.5 102.5 102.6 102.7 102.9 103.1 103.2 103.2 103 102.8 102.6 102.4 102.2 101.9 101.6 101.3 101.2 111.7 111.4 111.1 111.1 111.3 111.9 112.4 112.9 113 113 112.7 112.4 112.3 112.5 112.8 113.2 114 114.9 115.6 115.5 115 114.9 115.2 115.4 115 114.6 114.5 114.4 113.9 113.2 112.7 112.6 112.5 112.3 112 111.7 119.2

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	0.911741	7.1209	0
2	0.866028	6.7639	0
3	0.822626	6.4249	0
4	0.780612	6.0968	0
5	0.738946	5.7714	0
6	0.69543	5.4315	1e-06
7	0.651944	5.0918	2e-06
8	0.606937	4.7403	7e-06
9	0.560743	4.3795	2.4e-05
10	0.513265	4.0087	8.4e-05
11	0.467327	3.6499	0.000273
12	0.424582	3.3161	0.000771
13	0.382226	2.9853	0.002037
14	0.335859	2.6231	0.005495
15	0.28795	2.249	0.014069
16	0.239311	1.8691	0.033207
17	0.187614	1.4653	0.073986
18	0.12886	1.0064	0.159093
19	0.062358	0.487	0.313991
20	-0.004841	-0.0378	0.484982
21	-0.069137	-0.54	0.295589
22	-0.131594	-1.0278	0.154056
23	-0.19577	-1.529	0.065716
24	-0.261134	-2.0395	0.022868
25	-0.280914	-2.194	0.016027
26	-0.298606	-2.3322	0.011504
27	-0.317401	-2.479	0.007978
28	-0.337644	-2.6371	0.005297
29	-0.355195	-2.7742	0.003667
30	-0.368312	-2.8766	0.002766
31	-0.376254	-2.9386	0.002324
32	-0.381702	-2.9812	0.00206
33	-0.384139	-3.0002	0.001952
34	-0.384772	-3.0052	0.001924
35	-0.384069	-2.9997	0.001955
36	-0.383692	-2.9967	0.001971
37	-0.428039	-3.3431	0.00071
38	-0.414747	-3.2393	0.000971
39	-0.400065	-3.1246	0.001362
40	-0.38445	-3.0027	0.001938
41	-0.366142	-2.8597	0.002899
42	-0.34511	-2.6954	0.004536
43	-0.321557	-2.5114	0.007344
44	-0.298568	-2.3319	0.011512
45	-0.277712	-2.169	0.016995
46	-0.257425	-2.0106	0.024399
47	-0.236939	-1.8506	0.034539
48	-0.215875	-1.686	0.048449
49	-0.196403	-1.534	0.065106
50	-0.177995	-1.3902	0.084763
51	-0.159113	-1.2427	0.109366
52	-0.140332	-1.096	0.138688
53	-0.122845	-0.9595	0.170559
54	-0.107587	-0.8403	0.202015
55	-0.094737	-0.7399	0.231093
56	-0.082997	-0.6482	0.259634
57	-0.071297	-0.5569	0.289833
58	-0.060052	-0.469	0.320363
59	-0.049269	-0.3848	0.350862
60	-0.039925	-0.3118	0.37812

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.911741	7.1209	0
2	0.205988	1.6088	0.05641
3	0.048722	0.3805	0.352437
4	0.00667	0.0521	0.479313
5	-0.010723	-0.0837	0.466766
6	-0.030661	-0.2395	0.405771
7	-0.029243	-0.2284	0.410053
8	-0.037628	-0.2939	0.384922
9	-0.040982	-0.3201	0.375002
10	-0.043851	-0.3425	0.36658
11	-0.028525	-0.2228	0.412223
12	-0.010052	-0.0785	0.46884
13	-0.017507	-0.1367	0.445845
14	-0.049805	-0.389	0.349319
15	-0.053096	-0.4147	0.33991
16	-0.050446	-0.394	0.34748
17	-0.065325	-0.5102	0.305875
18	-0.10113	-0.7899	0.216337
19	-0.129881	-1.0144	0.157199
20	-0.107786	-0.8418	0.201585
21	-0.074968	-0.5855	0.280179
22	-0.064381	-0.5028	0.308446
23	-0.083576	-0.6527	0.258186
24	-0.096786	-0.7559	0.226303
25	0.205299	1.6034	0.057002
26	0.129676	1.0128	0.157577
27	0.051354	0.4011	0.34488
28	0.003454	0.027	0.489283
29	0.000288	0.0022	0.499106
30	0.005186	0.0405	0.483911
31	0.017934	0.1401	0.444534
32	0.006441	0.0503	0.480023
33	0.005307	0.0414	0.483536
34	0.002574	0.0201	0.492013
35	0.011914	0.0931	0.463083
36	0.012801	0.1	0.460344
37	-0.321616	-2.5119	0.007335
38	0.158224	1.2358	0.110641
39	0.106397	0.831	0.204611
40	0.033827	0.2642	0.39626
41	8.6e-05	7e-04	0.499734
42	-0.024231	-0.1893	0.425263
43	-0.051395	-0.4014	0.344761
44	-0.062003	-0.4843	0.314968
45	-0.073837	-0.5767	0.283136
46	-0.070958	-0.5542	0.290733
47	-0.076365	-0.5964	0.276548
48	-0.045125	-0.3524	0.362864
49	0.064552	0.5042	0.30798
50	0.027541	0.2151	0.415201
51	0.022932	0.1791	0.429226
52	0.018227	0.1424	0.443634
53	0.021607	0.1688	0.433273
54	0.023196	0.1812	0.428419
55	0.000156	0.0012	0.499517
56	-0.047226	-0.3688	0.356759
57	-0.054541	-0.426	0.335812
58	-0.037322	-0.2915	0.385831
59	-0.01584	-0.1237	0.450974
60	-0.063276	-0.4942	0.31147

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t1229683893jq5lj4z7hvi24dc/1xebg1229683820.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t1229683893jq5lj4z7hvi24dc/1xebg1229683820.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t1229683893jq5lj4z7hvi24dc/251as1229683820.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t1229683893jq5lj4z7hvi24dc/251as1229683820.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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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