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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: Wed, 30 Dec 2009 08:05:16 -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/30/t12621855450loam0ni4ic3knj.htm/, Retrieved Wed, 30 Dec 2009 16:05:48 +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/30/t12621855450loam0ni4ic3knj.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 «

28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509 25447 24090 27786 26195 20516 22759 19028 16971 20036 22485

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.514935	3.9216	0.000118
2	0.441961	3.3659	0.000679
3	0.205566	1.5655	0.061448
4	0.119697	0.9116	0.18288
5	0.088037	0.6705	0.252609
6	0.114585	0.8727	0.193225
7	0.052717	0.4015	0.34477
8	0.083616	0.6368	0.263381
9	-0.079382	-0.6046	0.273917
10	-0.222497	-1.6945	0.047768
11	-0.320485	-2.4407	0.008866
12	-0.41993	-3.1981	0.001121
13	-0.356066	-2.7117	0.004396
14	-0.258037	-1.9652	0.027096
15	-0.153227	-1.1669	0.124005
16	-0.088466	-0.6737	0.251577
17	-0.059927	-0.4564	0.324906
18	-0.074033	-0.5638	0.287526
19	-0.064275	-0.4895	0.313167
20	-0.037552	-0.286	0.387953
21	0.07409	0.5643	0.287379
22	0.01825	0.139	0.444971
23	0.21384	1.6286	0.054414
24	0.14662	1.1166	0.134379
25	0.210011	1.5994	0.057583
26	0.136384	1.0387	0.151634
27	0.07402	0.5637	0.287558
28	-0.022329	-0.17	0.432782
29	0.005027	0.0383	0.484797
30	-0.108796	-0.8286	0.205372
31	-0.10475	-0.7978	0.214134
32	-0.127494	-0.971	0.167799
33	-0.154438	-1.1762	0.122167
34	-0.098744	-0.752	0.227543
35	-0.159005	-1.2109	0.115413
36	-0.196891	-1.4995	0.069587
37	-0.177866	-1.3546	0.090401
38	-0.172147	-1.311	0.097506
39	-0.091108	-0.6939	0.24527
40	-0.034894	-0.2657	0.395688
41	-0.028849	-0.2197	0.413435
42	0.021368	0.1627	0.435646
43	0.038791	0.2954	0.384362
44	0.035937	0.2737	0.392648
45	0.049995	0.3808	0.352389
46	0.062652	0.4771	0.317526
47	0.081358	0.6196	0.268973
48	0.05339	0.4066	0.342897
49	0.095139	0.7246	0.235819
50	0.122159	0.9303	0.178027
51	0.060489	0.4607	0.323378
52	0.015351	0.1169	0.453667
53	-0.008541	-0.065	0.47418
54	-0.007088	-0.054	0.478567
55	-0.008495	-0.0647	0.47432
56	-0.002975	-0.0227	0.491002
57	0.002302	0.0175	0.493037
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.514935	3.9216	0.000118
2	0.240601	1.8324	0.036017
3	-0.131666	-1.0027	0.160076
4	-0.041881	-0.319	0.375452
5	0.069906	0.5324	0.298244
6	0.093846	0.7147	0.238827
7	-0.073524	-0.5599	0.288836
8	0.03157	0.2404	0.405422
9	-0.173318	-1.32	0.096019
10	-0.250736	-1.9096	0.030571
11	-0.129332	-0.985	0.164366
12	-0.170891	-1.3015	0.099122
13	-0.024093	-0.1835	0.427528
14	0.057524	0.4381	0.331474
15	0.077219	0.5881	0.27938
16	0.02518	0.1918	0.424299
17	0.039835	0.3034	0.381346
18	0.03641	0.2773	0.391271
19	-0.003743	-0.0285	0.48868
20	0.015889	0.121	0.452053
21	0.076839	0.5852	0.280345
22	-0.23678	-1.8033	0.038271
23	0.122352	0.9318	0.17765
24	-0.06392	-0.4868	0.314118
25	0.009522	0.0725	0.471221
26	-0.001228	-0.0094	0.496285
27	-0.044634	-0.3399	0.367572
28	-0.087447	-0.666	0.254033
29	0.003019	0.023	0.490868
30	-0.091076	-0.6936	0.245347
31	-0.145968	-1.1117	0.135436
32	-0.009906	-0.0754	0.470061
33	-0.005292	-0.0403	0.483996
34	0.044121	0.336	0.369037
35	-0.012592	-0.0959	0.461967
36	-0.05353	-0.4077	0.342509
37	0.009381	0.0714	0.471644
38	0.00679	0.0517	0.479469
39	0.055727	0.4244	0.336421
40	-0.049117	-0.3741	0.354861
41	-0.106476	-0.8109	0.21037
42	-0.049019	-0.3733	0.355135
43	-0.010854	-0.0827	0.467201
44	-0.100564	-0.7659	0.223429
45	0.028058	0.2137	0.415773
46	-0.041304	-0.3146	0.377112
47	0.024365	0.1856	0.426721
48	-0.127827	-0.9735	0.167173
49	0.064374	0.4903	0.312901
50	0.062599	0.4767	0.31767
51	-0.038492	-0.2931	0.385229
52	-0.097216	-0.7404	0.231031
53	0.019257	0.1467	0.441955
54	0.033154	0.2525	0.400775
55	-0.062951	-0.4794	0.31672
56	0.075542	0.5753	0.283653
57	0.003331	0.0254	0.489924
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/30/t12621855450loam0ni4ic3knj/1r0og1262185510.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t12621855450loam0ni4ic3knj/1r0og1262185510.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t12621855450loam0ni4ic3knj/2poad1262185510.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t12621855450loam0ni4ic3knj/2poad1262185510.ps (open in new window)

Parameters (Session):

par1 = 0 ; par2 = 0 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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