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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: Tue, 08 Dec 2009 12:46:31 -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/08/t1260301677afknh731uif9pvm.htm/, Retrieved Tue, 08 Dec 2009 20:47:59 +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/08/t1260301677afknh731uif9pvm.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

8,55 8,56 8,57 8,59 8,61 8,62 8,62 8,63 8,71 8,72 8,74 8,75 8,79 8,82 8,82 8,84 8,86 8,86 8,85 8,86 8,86 8,87 8,88 8,9 8,91 8,96 8,98 8,99 9 9 9 9,01 9,01 8,99 8,99 8,99 9 9 9,02 9,05 9,05 9,05 9,06 9,06 9,08 9,07 9,06 9,08 9,07 9,11 9,15 9,15 9,17 9,2 9,23 9,26 9,27 9,28 9,29 9,29 9,11 9,06 9,11 9,13 9,13 9,19 9,2 9,23 9,24 9,28 9,32 9,32 9,32 9,36 9,37 9,38 9,41 9,44 9,44 9,44 9,47 9,48 9,56 9,58 9,56 9,58 9,7 9,74 9,76 9,78 9,84 9,88 9,96 9,97 9,96 9,96

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
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.950551	9.3135	0
2	0.897991	8.7985	0
3	0.84411	8.2706	0
4	0.78971	7.7375	0
5	0.739112	7.2418	0
6	0.690513	6.7656	0
7	0.644491	6.3147	0
8	0.599698	5.8758	0
9	0.559525	5.4822	0
10	0.521675	5.1113	1e-06
11	0.492334	4.8239	3e-06
12	0.463838	4.5447	8e-06
13	0.434138	4.2537	2.4e-05
14	0.405871	3.9767	6.8e-05
15	0.38187	3.7415	0.000156
16	0.357524	3.503	0.00035
17	0.33523	3.2846	0.000713
18	0.311387	3.051	0.001475
19	0.285445	2.7968	0.003118
20	0.260745	2.5548	0.006099
21	0.237036	2.3225	0.01116
22	0.213879	2.0956	0.019376
23	0.192507	1.8862	0.031147
24	0.173455	1.6995	0.046231
25	0.152971	1.4988	0.068603
26	0.13466	1.3194	0.095089
27	0.120855	1.1841	0.119642
28	0.109058	1.0685	0.143978
29	0.097304	0.9534	0.171396
30	0.087285	0.8552	0.19728
31	0.077743	0.7617	0.224046
32	0.072658	0.7119	0.239128
33	0.067992	0.6662	0.253445
34	0.062745	0.6148	0.270078
35	0.06016	0.5894	0.278473
36	0.053933	0.5284	0.29921
37	0.034409	0.3371	0.368374
38	0.013581	0.1331	0.44721
39	-0.006603	-0.0647	0.474276
40	-0.025708	-0.2519	0.400835
41	-0.045089	-0.4418	0.32982
42	-0.063348	-0.6207	0.268139
43	-0.080629	-0.79	0.215738
44	-0.097023	-0.9506	0.17209
45	-0.111561	-1.0931	0.138549
46	-0.127068	-1.245	0.10808
47	-0.141112	-1.3826	0.084996
48	-0.151761	-1.487	0.070152

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.950551	9.3135	0
2	-0.057614	-0.5645	0.286866
3	-0.040463	-0.3965	0.346324
4	-0.033865	-0.3318	0.370378
5	0.009719	0.0952	0.462166
6	-0.010481	-0.1027	0.459211
7	-0.004082	-0.04	0.484091
8	-0.017868	-0.1751	0.430697
9	0.019766	0.1937	0.423422
10	-0.004251	-0.0416	0.483433
11	0.062511	0.6125	0.270834
12	-0.017663	-0.1731	0.431482
13	-0.032675	-0.3201	0.374776
14	-0.004739	-0.0464	0.481532
15	0.031306	0.3067	0.379856
16	-0.021578	-0.2114	0.416504
17	0.005531	0.0542	0.478446
18	-0.03372	-0.3304	0.370914
19	-0.03054	-0.2992	0.382706
20	-0.001919	-0.0188	0.492521
21	-0.000433	-0.0042	0.498314
22	-0.014432	-0.1414	0.443922
23	-0.001322	-0.013	0.494846
24	0.006646	0.0651	0.47411
25	-0.025425	-0.2491	0.401901
26	0.003114	0.0305	0.487862
27	0.030214	0.296	0.38392
28	0.003518	0.0345	0.486288
29	-0.017196	-0.1685	0.433279
30	0.007853	0.0769	0.469416
31	-0.001236	-0.0121	0.495181
32	0.03649	0.3575	0.360741
33	-0.005975	-0.0585	0.47672
34	-0.010203	-0.1	0.460288
35	0.019815	0.1941	0.423235
36	-0.037359	-0.366	0.35757
37	-0.137384	-1.3461	0.090723
38	-0.016914	-0.1657	0.434363
39	-0.005825	-0.0571	0.477302
40	0.002407	0.0236	0.490615
41	-0.026984	-0.2644	0.396023
42	-0.004323	-0.0424	0.483151
43	-0.010224	-0.1002	0.460207
44	-0.012835	-0.1258	0.450094
45	-0.007302	-0.0715	0.471556
46	-0.032184	-0.3153	0.376596
47	-0.024255	-0.2377	0.406329
48	0.020523	0.2011	0.42053

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/08/t1260301677afknh731uif9pvm/1b3nl1260301589.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/08/t1260301677afknh731uif9pvm/1b3nl1260301589.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/08/t1260301677afknh731uif9pvm/2386i1260301589.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/08/t1260301677afknh731uif9pvm/2386i1260301589.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; 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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