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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: Sun, 19 Dec 2010 19:49:49 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/19/t1292788077g9kohlpk61jho81.htm/, Retrieved Sun, 19 Dec 2010 20:47:57 +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/2010/Dec/19/t1292788077g9kohlpk61jho81.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

4.031636 3.702076 3.056176 3.280707 2.984728 3.693712 3.226317 2.190349 2.599515 3.080288 2.929672 2.922548 3.234943 2.983081 3.284389 3.806511 3.784579 2.645654 3.092081 3.204859 3.107225 3.466909 2.984404 3.218072 2.82731 3.182049 2.236319 2.033218 1.644804 1.627971 1.677559 2.330828 2.493615 2.257172 2.655517 2.298655 2.600402 3.04523 2.790583 3.227052 2.967479 2.938817 3.277961 3.423985 3.072646 2.754253 2.910431 3.174369 3.068387 3.089543 2.906654 2.931161 3.02566 2.939551 2.691019 3.19812 3.07639 2.863873 3.013802 3.053364 2.864753 3.057062 2.959365 3.252258 3.602988 3.497704 3.296867 3.602417 3.3001 3.40193 3.502591 3.402348 3.498551 3.199823 2.700064 2.801034 2.898628 2.800854 2.399942 2.402724 2.202331 2.102594 1.798293 1.202484 1.400201 1.200832 1.298083 1.099742 1.001377 0.8361743

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	-0.196193	-1.8509	0.033752
2	-0.115453	-1.0892	0.139507
3	0.043603	0.4113	0.340903
4	0.011413	0.1077	0.45725
5	0.04275	0.4033	0.343847
6	0.135358	1.277	0.102468
7	-0.027437	-0.2588	0.398179
8	-0.233167	-2.1997	0.01521
9	0.160143	1.5108	0.067193
10	0.054614	0.5152	0.303834
11	-0.020216	-0.1907	0.42459
12	-0.067217	-0.6341	0.263813
13	-0.023722	-0.2238	0.411715
14	-0.19556	-1.8449	0.034189
15	0.032667	0.3082	0.379334
16	0.146969	1.3865	0.084528
17	-0.10512	-0.9917	0.162017
18	0.054552	0.5146	0.304039
19	-0.066185	-0.6244	0.266986
20	-0.001948	-0.0184	0.49269
21	0.037399	0.3528	0.362528
22	0.089492	0.8443	0.200391
23	-0.055441	-0.523	0.301127
24	0.066239	0.6249	0.266818
25	-0.023809	-0.2246	0.411398
26	0.01185	0.1118	0.455621
27	0.033103	0.3123	0.377772
28	0.119384	1.1263	0.131541
29	-0.081034	-0.7645	0.223305
30	-0.088333	-0.8333	0.203444
31	0.036433	0.3437	0.365937
32	-0.063219	-0.5964	0.27621
33	0.081462	0.7685	0.222109
34	0.075204	0.7095	0.239944
35	-0.170403	-1.6076	0.055735
36	-0.062136	-0.5862	0.279616
37	-0.006348	-0.0599	0.476189
38	0.032411	0.3058	0.380247
39	-0.025553	-0.2411	0.405027
40	-0.014987	-0.1414	0.443943
41	-0.092193	-0.8697	0.193389
42	-0.020307	-0.1916	0.424255
43	0.037256	0.3515	0.363031
44	-0.017839	-0.1683	0.433369
45	-0.041894	-0.3952	0.34681
46	-0.022146	-0.2089	0.417494
47	0.014406	0.1359	0.446102
48	-0.030817	-0.2907	0.385969
49	0.002153	0.0203	0.491921
50	0.034455	0.325	0.372955
51	-0.048347	-0.4561	0.324713
52	0.038634	0.3645	0.358186
53	-0.043946	-0.4146	0.339722
54	0.011044	0.1042	0.458627
55	0.048661	0.4591	0.323654
56	0.032412	0.3058	0.380247
57	-0.010242	-0.0966	0.461622
58	-0.006603	-0.0623	0.475235
59	0.001089	0.0103	0.495915
60	-0.072664	-0.6855	0.247401

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.196193	-1.8509	0.033752
2	-0.160107	-1.5105	0.067235
3	-0.015036	-0.1419	0.443759
4	-0.000414	-0.0039	0.498446
5	0.054108	0.5105	0.305499
6	0.170603	1.6095	0.055528
7	0.060176	0.5677	0.285834
8	-0.208548	-1.9674	0.026123
9	0.057475	0.5422	0.294512
10	0.042169	0.3978	0.345857
11	0.022275	0.2101	0.417018
12	-0.077692	-0.7329	0.232759
13	-0.037312	-0.352	0.362837
14	-0.213982	-2.0187	0.023264
15	-0.119295	-1.1254	0.131718
16	0.045462	0.4289	0.33452
17	0.010784	0.1017	0.459598
18	0.129085	1.2178	0.113262
19	-0.016187	-0.1527	0.439489
20	0.007539	0.0711	0.47173
21	0.012506	0.118	0.453174
22	0.031707	0.2991	0.382773
23	0.030045	0.2834	0.388748
24	0.157162	1.4827	0.070848
25	-0.020445	-0.1929	0.423746
26	-0.014668	-0.1384	0.445126
27	-0.079736	-0.7522	0.22695
28	0.095092	0.8971	0.186044
29	-0.040123	-0.3785	0.352972
30	-0.044918	-0.4238	0.336384
31	-0.046829	-0.4418	0.329859
32	-0.076511	-0.7218	0.236154
33	-0.003888	-0.0367	0.485411
34	0.093763	0.8846	0.18939
35	-0.057281	-0.5404	0.295141
36	-0.008284	-0.0781	0.468943
37	-0.119244	-1.1249	0.131819
38	-0.005675	-0.0535	0.478712
39	-0.02726	-0.2572	0.398819
40	-0.010866	-0.1025	0.459292
41	-0.009124	-0.0861	0.465801
42	-0.01441	-0.1359	0.446085
43	-0.077805	-0.734	0.232435
44	-0.140482	-1.3253	0.094232
45	-0.055292	-0.5216	0.301613
46	-0.016561	-0.1562	0.438102
47	0.05786	0.5459	0.293267
48	-0.010426	-0.0984	0.460935
49	-0.110565	-1.0431	0.149871
50	-0.053847	-0.508	0.306357
51	-0.0532	-0.5019	0.308493
52	0.024208	0.2284	0.40994
53	0.033114	0.3124	0.377736
54	0.00129	0.0122	0.495159
55	0.038587	0.364	0.358348
56	-0.009822	-0.0927	0.463191
57	0.015725	0.1484	0.4412
58	0.016404	0.1548	0.438682
59	0.041473	0.3913	0.348271
60	-0.092056	-0.8685	0.193742

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292788077g9kohlpk61jho81/1odcu1292788186.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292788077g9kohlpk61jho81/1odcu1292788186.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292788077g9kohlpk61jho81/2z5ux1292788186.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292788077g9kohlpk61jho81/2z5ux1292788186.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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