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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 07:41:38 -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/t12621854544sz5j06vtdm5yft.htm/, Retrieved Wed, 30 Dec 2009 16:04:16 +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/t12621854544sz5j06vtdm5yft.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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.335149	-2.784	0.003462
2	-0.024948	-0.2072	0.418219
3	-0.009152	-0.076	0.469811
4	-0.058923	-0.4895	0.313038
5	0.111265	0.9242	0.179292
6	-0.352902	-2.9314	0.002287
7	0.122924	1.0211	0.155391
8	-0.043751	-0.3634	0.3587
9	-0.027294	-0.2267	0.410656
10	-0.010908	-0.0906	0.464033
11	-0.254189	-2.1115	0.019179
12	0.764058	6.3467	0
13	-0.270072	-2.2434	0.014043
14	0.001101	0.0091	0.496363
15	-0.001894	-0.0157	0.493746
16	-0.051944	-0.4315	0.333733
17	0.105419	0.8757	0.192123
18	-0.303498	-2.521	0.007008
19	0.10619	0.8821	0.190399
20	-0.041974	-0.3487	0.364202
21	-0.041851	-0.3476	0.364585
22	-0.013493	-0.1121	0.455542
23	-0.152205	-1.2643	0.105187
24	0.538699	4.4748	1.5e-05
25	-0.152615	-1.2677	0.104581
26	-0.017893	-0.1486	0.441141
27	0.016899	0.1404	0.444388
28	-0.060755	-0.5047	0.307699
29	0.087729	0.7287	0.234315
30	-0.229058	-1.9027	0.030627
31	0.098735	0.8202	0.207476
32	-0.044419	-0.369	0.356638
33	-0.049412	-0.4104	0.341375
34	0.023087	0.1918	0.42424
35	-0.109246	-0.9075	0.18366
36	0.330246	2.7432	0.003873
37	-0.07036	-0.5845	0.280411
38	-0.035698	-0.2965	0.383859
39	0.033036	0.2744	0.392291
40	-0.04973	-0.4131	0.340412
41	0.029544	0.2454	0.403432
42	-0.127119	-1.0559	0.147343
43	0.084258	0.6999	0.243172
44	-0.054368	-0.4516	0.326483
45	-0.027451	-0.228	0.410151
46	0.030742	0.2554	0.399601
47	-0.059519	-0.4944	0.311295
48	0.1615	1.3415	0.092075
49	-0.024151	-0.2006	0.420795
50	-0.020722	-0.1721	0.431918
51	0.023656	0.1965	0.422398
52	-0.031	-0.2575	0.398777
53	0.006155	0.0511	0.479686
54	-0.01856	-0.1542	0.438961
55	0.025616	0.2128	0.416062
56	-0.045726	-0.3798	0.352621
57	-0.014108	-0.1172	0.453525
58	0.019609	0.1629	0.435544
59	-0.007279	-0.0605	0.475981
60	0.044164	0.3669	0.357426

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.335149	-2.784	0.003462
2	-0.154643	-1.2846	0.101621
3	-0.081522	-0.6772	0.250281
4	-0.10985	-0.9125	0.182346
5	0.053341	0.4431	0.329544
6	-0.360009	-2.9905	0.00193
7	-0.16288	-1.353	0.090238
8	-0.185754	-1.543	0.063704
9	-0.199519	-1.6573	0.050997
10	-0.265966	-2.2093	0.015239
11	-0.636324	-5.2857	1e-06
12	0.381978	3.1729	0.001127
13	0.050474	0.4193	0.338161
14	0.029385	0.2441	0.403943
15	-0.042332	-0.3516	0.363093
16	-0.030064	-0.2497	0.40177
17	-0.027811	-0.231	0.408992
18	0.047867	0.3976	0.346072
19	-0.017339	-0.144	0.442949
20	-0.040484	-0.3363	0.368838
21	-0.070878	-0.5888	0.278973
22	-0.107766	-0.8952	0.186904
23	0.026704	0.2218	0.412556
24	-0.126732	-1.0527	0.148072
25	0.072112	0.599	0.275565
26	-0.065143	-0.5411	0.295083
27	0.002019	0.0168	0.493335
28	-0.083148	-0.6907	0.246042
29	-0.051665	-0.4292	0.334571
30	-0.01372	-0.114	0.454797
31	0.069858	0.5803	0.281806
32	0.017696	0.147	0.441783
33	0.01751	0.1455	0.442389
34	0.141883	1.1786	0.121309
35	0.0661	0.5491	0.292364
36	-0.020321	-0.1688	0.433225
37	-0.042087	-0.3496	0.363851
38	-0.027539	-0.2288	0.409867
39	-0.042088	-0.3496	0.363849
40	0.03356	0.2788	0.390629
41	-0.153093	-1.2717	0.103877
42	-0.039848	-0.331	0.370822
43	-0.038543	-0.3202	0.374906
44	-0.055621	-0.462	0.322758
45	0.020722	0.1721	0.431921
46	-0.031937	-0.2653	0.395788
47	0.034926	0.2901	0.386299
48	-0.082443	-0.6848	0.247875
49	-0.069683	-0.5788	0.282293
50	-0.044412	-0.3689	0.35666
51	-0.040246	-0.3343	0.36958
52	-0.046365	-0.3851	0.35066
53	0.043783	0.3637	0.358603
54	0.079733	0.6623	0.25499
55	-0.019595	-0.1628	0.435588
56	0.02161	0.1795	0.429033
57	-0.034898	-0.2899	0.386386
58	-0.016931	-0.1406	0.444281
59	0.016039	0.1332	0.447201
60	0.039142	0.3251	0.373032

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/30/t12621854544sz5j06vtdm5yft/1cput1262184093.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t12621854544sz5j06vtdm5yft/1cput1262184093.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t12621854544sz5j06vtdm5yft/2xdy01262184093.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t12621854544sz5j06vtdm5yft/2xdy01262184093.ps (open in new window)

Parameters (Session):

par1 = 0 ; par2 = 0 ;

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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