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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: Mon, 22 Dec 2008 02:15:34 -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/22/t12299374143ynygrkvd44kdsm.htm/, Retrieved Mon, 22 Dec 2008 10:16:54 +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/22/t12299374143ynygrkvd44kdsm.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:

paper: tweede tijdsreeks D=1 d=1

Dataseries X:

» Textbox « » Textfile « » CSV «

99.4 102.7 109.3 93.9 95.3 101.8 85.6 81.1 109.5 104.0 94.5 79.0 92.8 95.6 101.7 90.8 89.5 91.8 83.8 77.4 112.7 98.8 85.7 72.8 96.9 95.0 94.2 87.3 80.6 87.9 79.6 71.9 94.6 91.4 86.6 68.5 90.1 91.6 95.4 85.4 81.6 88.9 84.1 74.7 97.1 95.3 85.1 67.3 80.6 87.9 89.2 81.3 79.7 83.7 82.1 69.3 91.2 85.7 85.2 70.0 85.8 91.4 97.5 87.1 85.1 94.1 85.8 74.7 99.9 90.7 86.8 74.8 91.8 97.6 100.8 85.4 84.0 90.6 80.5 73.9 93.6

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.298605	-2.4624	0.008171
2	-0.160809	-1.3261	0.094628
3	-0.068194	-0.5623	0.287865
4	0.178748	1.474	0.072549
5	0.02657	0.2191	0.413613
6	-0.047544	-0.3921	0.34812
7	0.095109	0.7843	0.217796
8	-0.330622	-2.7264	0.004069
9	0.278105	2.2933	0.012464
10	-0.073384	-0.6051	0.273549
11	0.138287	1.1403	0.129072
12	-0.305587	-2.5199	0.007046
13	0.030683	0.253	0.400507
14	0.050926	0.4199	0.337925
15	-0.041923	-0.3457	0.365315
16	0.090206	0.7439	0.229763
17	-0.221235	-1.8244	0.036246
18	0.191064	1.5756	0.059885
19	-0.102273	-0.8434	0.20099
20	0.100744	0.8308	0.20451
21	-0.026699	-0.2202	0.413202
22	0.041723	0.3441	0.365932
23	-0.048358	-0.3988	0.345656
24	-0.055906	-0.461	0.323131
25	0.208002	1.7152	0.045429
26	-0.166467	-1.3727	0.087175
27	0.142617	1.176	0.121838
28	-0.131379	-1.0834	0.141234
29	0.104204	0.8593	0.196601
30	-0.092984	-0.7668	0.222938
31	0.11161	0.9204	0.180319
32	-0.041713	-0.344	0.365964
33	-0.19932	-1.6436	0.052434
34	0.215592	1.7778	0.039952
35	0.00257	0.0212	0.491576
36	-0.047786	-0.3941	0.347387
37	-0.139003	-1.1462	0.127855
38	0.145784	1.2022	0.116734
39	-0.045522	-0.3754	0.354273
40	0.007393	0.061	0.475782
41	-0.010755	-0.0887	0.464794
42	-0.03039	-0.2506	0.401439
43	-0.005948	-0.0491	0.480511
44	0.046011	0.3794	0.352782
45	0.057387	0.4732	0.318784
46	-0.097948	-0.8077	0.211039
47	0.002508	0.0207	0.491781
48	0.029343	0.242	0.404767

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.298605	-2.4624	0.008171
2	-0.274444	-2.2631	0.013412
3	-0.25093	-2.0692	0.021164
4	0.017336	0.143	0.443372
5	0.060096	0.4956	0.3109
6	0.046583	0.3841	0.35104
7	0.193566	1.5962	0.057542
8	-0.300995	-2.4821	0.007769
9	0.103552	0.8539	0.198077
10	-0.105555	-0.8704	0.193564
11	0.13662	1.1266	0.131936
12	-0.193746	-1.5977	0.057376
13	-0.126578	-1.0438	0.15014
14	-0.145986	-1.2038	0.116415
15	-0.15276	-1.2597	0.106043
16	-0.041865	-0.3452	0.365496
17	-0.129561	-1.0684	0.144562
18	0.055693	0.4593	0.323756
19	0.03753	0.3095	0.378951
20	-0.077747	-0.6411	0.261801
21	0.142569	1.1757	0.121917
22	0.031302	0.2581	0.398546
23	0.053825	0.4439	0.32928
24	-0.074873	-0.6174	0.26951
25	0.028452	0.2346	0.407602
26	-0.083782	-0.6909	0.245994
27	0.041596	0.343	0.366326
28	-0.071318	-0.5881	0.279205
29	-0.003385	-0.0279	0.488908
30	-0.08198	-0.676	0.250659
31	0.093956	0.7748	0.220576
32	-0.080608	-0.6647	0.254242
33	-0.088879	-0.7329	0.233065
34	0.058557	0.4829	0.315368
35	0.184342	1.5201	0.066558
36	-0.115499	-0.9524	0.172126
37	0.074482	0.6142	0.27057
38	-0.099029	-0.8166	0.208499
39	0.093849	0.7739	0.220837
40	-0.109083	-0.8995	0.185774
41	-0.039187	-0.3231	0.37379
42	0.001568	0.0129	0.494861
43	-0.080973	-0.6677	0.253285
44	0.029834	0.246	0.403206
45	-0.060203	-0.4964	0.31059
46	0.002936	0.0242	0.490379
47	0.051894	0.4279	0.335027
48	-0.056279	-0.4641	0.322032

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299374143ynygrkvd44kdsm/1ceww1229937327.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299374143ynygrkvd44kdsm/1ceww1229937327.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299374143ynygrkvd44kdsm/2y8iw1229937327.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299374143ynygrkvd44kdsm/2y8iw1229937327.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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