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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: Sun, 27 Dec 2009 05:43:22 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/27/t1261917849f16s3ovf85ktld9.htm/, Retrieved Sun, 27 Dec 2009 13:44:12 +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/27/t1261917849f16s3ovf85ktld9.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 «

40.22 44.23 45.85 53.38 53.26 51.8 55.3 57.81 63.96 63.77 59.15 56.12 57.42 63.52 61.71 63.01 68.18 72.03 69.75 74.41 74.33 64.24 60.03 59.44 62.5 55.04 58.34 61.92 67.65 67.68 70.3 75.26 71.44 76.36 81.71 92.6 90.6 92.23 94.09 102.79 109.65 124.05 132.69 135.81 116.07 101.42 75.73 55.48 43.8 45.29 44.01 47.48 51.07 57.84 69.04 65.61 72.87 68.41 73.25 77.43

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.542312	4.1656	5.1e-05
2	0.390578	3.0001	0.001975
3	0.060876	0.4676	0.320897
4	-0.04761	-0.3657	0.357948
5	-0.276217	-2.1217	0.019038
6	-0.303275	-2.3295	0.011638
7	-0.21147	-1.6243	0.054818
8	-0.198833	-1.5273	0.06602
9	-0.192741	-1.4805	0.072034
10	-0.129308	-0.9932	0.162327
11	0.009319	0.0716	0.471588
12	-0.094503	-0.7259	0.235387
13	-0.079398	-0.6099	0.272147
14	-0.053332	-0.4096	0.341774
15	0.008118	0.0624	0.475245
16	-0.061583	-0.473	0.318969
17	-0.07771	-0.5969	0.276428
18	-0.073165	-0.562	0.288125
19	-0.014351	-0.1102	0.4563
20	-0.078352	-0.6018	0.274796
21	0.04036	0.31	0.378823
22	0.056767	0.436	0.332201
23	0.162088	1.245	0.109024
24	0.091454	0.7025	0.242574
25	0.171068	1.314	0.096967
26	0.136857	1.0512	0.148722
27	0.044338	0.3406	0.36732
28	-0.012907	-0.0991	0.460681
29	-0.079247	-0.6087	0.272529
30	-0.040663	-0.3123	0.377943
31	-0.12071	-0.9272	0.178802
32	-0.011534	-0.0886	0.464851
33	-0.025267	-0.1941	0.423391
34	0.054088	0.4155	0.339657
35	0.050564	0.3884	0.349562
36	0.056054	0.4306	0.33418
37	0.035372	0.2717	0.393402
38	-0.021817	-0.1676	0.433745
39	-0.007021	-0.0539	0.478587
40	-0.012866	-0.0988	0.460805
41	-0.027687	-0.2127	0.416158
42	-0.043551	-0.3345	0.369587
43	-0.066623	-0.5117	0.305371
44	-0.084047	-0.6456	0.260528
45	-0.044078	-0.3386	0.368069
46	0.001967	0.0151	0.493997
47	-0.011894	-0.0914	0.463757
48	0.010362	0.0796	0.468416
49	-0.018123	-0.1392	0.44488
50	0.026034	0.2	0.421094
51	0.027827	0.2137	0.415741
52	0.008433	0.0648	0.474285
53	0.02525	0.194	0.42344
54	-0.016152	-0.1241	0.450841
55	0.013365	0.1027	0.459291
56	0.003498	0.0269	0.489327
57	0.005419	0.0416	0.483469
58	0.003665	0.0281	0.488819
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.542312	4.1656	5.1e-05
2	0.13667	1.0498	0.149049
3	-0.283102	-2.1745	0.016843
4	-0.04722	-0.3627	0.359062
5	-0.225002	-1.7283	0.044585
6	-0.08323	-0.6393	0.262551
7	0.158059	1.2141	0.114779
8	-0.149463	-1.148	0.127792
9	-0.17228	-1.3233	0.095419
10	0.02705	0.2078	0.418061
11	0.088123	0.6769	0.250562
12	-0.266931	-2.0503	0.022391
13	-0.06512	-0.5002	0.309398
14	0.057964	0.4452	0.328891
15	-0.058408	-0.4486	0.327667
16	-0.103223	-0.7929	0.215514
17	-0.122789	-0.9432	0.174723
18	-0.148424	-1.1401	0.129432
19	0.10253	0.7875	0.217057
20	-0.107844	-0.8284	0.205401
21	-0.018979	-0.1458	0.442295
22	-0.075253	-0.578	0.282722
23	0.118986	0.9139	0.182232
24	-0.074716	-0.5739	0.284107
25	0.003372	0.0259	0.489712
26	-0.006572	-0.0505	0.479954
27	-0.144326	-1.1086	0.136053
28	0.063717	0.4894	0.313179
29	-0.073012	-0.5608	0.288523
30	-0.04917	-0.3777	0.35351
31	-0.000312	-0.0024	0.499048
32	0.076164	0.585	0.28038
33	-0.064016	-0.4917	0.312373
34	-0.01844	-0.1416	0.443923
35	0.148543	1.141	0.129243
36	-0.152517	-1.1715	0.123052
37	-0.001981	-0.0152	0.493957
38	0.047952	0.3683	0.356975
39	-0.002075	-0.0159	0.49367
40	0.05857	0.4499	0.32722
41	-0.046187	-0.3548	0.362013
42	-0.055519	-0.4264	0.335667
43	-0.023012	-0.1768	0.430151
44	0.004199	0.0323	0.487188
45	0.074449	0.5719	0.284796
46	-0.035968	-0.2763	0.391651
47	-0.08545	-0.6564	0.257074
48	0.015552	0.1195	0.452658
49	-0.061858	-0.4751	0.318222
50	0.065243	0.5011	0.309068
51	-0.010784	-0.0828	0.467133
52	-0.030197	-0.2319	0.408692
53	-0.022415	-0.1722	0.431944
54	-0.01063	-0.0817	0.467599
55	0.023547	0.1809	0.428545
56	-0.037893	-0.2911	0.386014
57	-0.051729	-0.3973	0.346277
58	-0.022885	-0.1758	0.430532
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261917849f16s3ovf85ktld9/18yuw1261917800.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261917849f16s3ovf85ktld9/18yuw1261917800.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261917849f16s3ovf85ktld9/21j5c1261917800.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261917849f16s3ovf85ktld9/21j5c1261917800.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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