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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: Tue, 15 Dec 2009 06:50:07 -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/15/t1260885067zhosjv5udt2kbnd.htm/, Retrieved Tue, 15 Dec 2009 14:51:10 +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/15/t1260885067zhosjv5udt2kbnd.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 «

358.59 362.96 362.42 364.97 364.04 361.06 358.48 352.96 359.59 360.39 357.40 362.93 364.55 365.73 364.70 364.65 359.43 362.14 356.97 354.82 353.17 357.06 356.18 355.01 355.65 357.31 357.07 357.91 358.48 358.97 351.77 352.16 359.08 360.35 359.53 359.30 358.41 359.68 355.31 357.08 349.71 354.13 345.49 341.69 344.25 340.17 342.47 344.43 333.23 339.72 342.61 346.36 339.09 339.73 341.12 335.94 333.46 335.66 341.12 342.21 342.62 346.06 344.43 346.65 343.74 335.67 342.75 341.77 345.84 346.52 350.79 345.44 345.87 338.48 337.21 340.81 339.86 342.86 343.33 341.73 351.38 351.13 345.99 347.55 346.02 345.29 347.03 348.01 345.48 349.40 351.05 349.70 350.86 354.45 355.30 357.48 355.24 351.79 355.22 351.02 350.28 350.17 348.16 340.30 343.75 344.71 344.13 342.14 345.04 346.02 346.43 347.07 339.33 339.10 337.19 339.58 327.85 326.81 321.73 320.45 327.69 323.95 320.47 322.13 316.34 314.78 308.90 308.62 etc...

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	0.983802	19.5527	0
2	0.971251	19.3032	0
3	0.960806	19.0956	0
4	0.94794	18.8399	0
5	0.934823	18.5792	0
6	0.922704	18.3384	0
7	0.91057	18.0972	0
8	0.899334	17.8739	0
9	0.887726	17.6432	0
10	0.876127	17.4127	0
11	0.863496	17.1616	0
12	0.848382	16.8613	0
13	0.834158	16.5786	0
14	0.81815	16.2604	0
15	0.800889	15.9173	0
16	0.787566	15.6526	0
17	0.775497	15.4127	0
18	0.761773	15.1399	0
19	0.750329	14.9125	0
20	0.740647	14.7201	0
21	0.728924	14.4871	0
22	0.719312	14.296	0
23	0.709192	14.0949	0
24	0.699861	13.9095	0
25	0.689878	13.7111	0
26	0.680668	13.528	0
27	0.672537	13.3664	0
28	0.663843	13.1936	0
29	0.654866	13.0152	0
30	0.64464	12.812	0
31	0.633774	12.596	0
32	0.62496	12.4208	0
33	0.612651	12.1762	0
34	0.601091	11.9464	0
35	0.590503	11.736	0
36	0.580548	11.5382	0
37	0.571821	11.3647	0
38	0.562012	11.1698	0
39	0.551508	10.961	0
40	0.540999	10.7521	0
41	0.529803	10.5296	0
42	0.520898	10.3526	0
43	0.511931	10.1744	0
44	0.501831	9.9737	0
45	0.493254	9.8032	0
46	0.485928	9.6576	0
47	0.477602	9.4921	0
48	0.472192	9.3846	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.983802	19.5527	0
2	0.10532	2.0932	0.018485
3	0.072644	1.4438	0.074798
4	-0.065042	-1.2927	0.098438
5	-0.025413	-0.5051	0.306895
6	0.012453	0.2475	0.402326
7	0.001903	0.0378	0.484926
8	0.02834	0.5632	0.286796
9	-0.013194	-0.2622	0.396644
10	-0.00547	-0.1087	0.45674
11	-0.043901	-0.8725	0.191729
12	-0.093275	-1.8538	0.032256
13	-0.001837	-0.0365	0.485444
14	-0.066856	-1.3287	0.092351
15	-0.047765	-0.9493	0.171523
16	0.097836	1.9444	0.026276
17	0.058478	1.1622	0.122922
18	-0.028238	-0.5612	0.28748
19	0.042639	0.8474	0.198632
20	0.050312	0.9999	0.158978
21	-0.045336	-0.901	0.184058
22	0.058858	1.1698	0.121398
23	-0.008265	-0.1643	0.434806
24	0.035856	0.7126	0.238247
25	-0.015348	-0.305	0.380251
26	0.016901	0.3359	0.368564
27	0.013765	0.2736	0.392277
28	-0.01896	-0.3768	0.353256
29	-0.022452	-0.4462	0.327843
30	-0.086456	-1.7183	0.043265
31	-0.032065	-0.6373	0.262154
32	0.061055	1.2134	0.112843
33	-0.126965	-2.5234	0.006007
34	0.016943	0.3367	0.368249
35	0.017168	0.3412	0.366568
36	0.02066	0.4106	0.340789
37	0.046134	0.9169	0.17988
38	-0.023897	-0.4749	0.317544
39	-0.0274	-0.5446	0.293178
40	-0.023033	-0.4578	0.323686
41	-0.005731	-0.1139	0.454687
42	0.08375	1.6645	0.048404
43	0.022299	0.4432	0.328939
44	-0.01309	-0.2602	0.397438
45	0.012438	0.2472	0.402438
46	0.023768	0.4724	0.318456
47	-0.009349	-0.1858	0.426347
48	0.056211	1.1172	0.132299

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260885067zhosjv5udt2kbnd/1x5ev1260885004.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260885067zhosjv5udt2kbnd/1x5ev1260885004.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260885067zhosjv5udt2kbnd/2x1qf1260885004.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260885067zhosjv5udt2kbnd/2x1qf1260885004.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ;

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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