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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: Thu, 17 Dec 2009 08:36:19 -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/17/t1261064249refuypswby6kn2d.htm/, Retrieved Thu, 17 Dec 2009 16:37:31 +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/17/t1261064249refuypswby6kn2d.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 «

9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9 7.7 8 8 7.7 7.3 7.4 8.1 8.3 8.3

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.520702	3.6449	0.000323
2	-0.123205	-0.8624	0.196325
3	-0.496389	-3.4747	0.00054
4	-0.504493	-3.5315	0.000456
5	-0.143109	-1.0018	0.16069
6	0.237381	1.6617	0.051482
7	0.432393	3.0267	0.001967
8	0.327286	2.291	0.013151
9	-0.023264	-0.1628	0.435655
10	-0.204502	-1.4315	0.079316
11	-0.285504	-1.9985	0.025612
12	-0.249223	-1.7446	0.043666
13	-0.040102	-0.2807	0.390055
14	0.176661	1.2366	0.11106
15	0.204418	1.4309	0.0794
16	0.040228	0.2816	0.389718
17	-0.081927	-0.5735	0.284469
18	-0.09738	-0.6817	0.249332
19	-0.109012	-0.7631	0.224537
20	0.016335	0.1143	0.454716
21	0.122575	0.858	0.197528
22	0.009238	0.0647	0.474351
23	-0.117326	-0.8213	0.207732
24	-0.175107	-1.2257	0.113076
25	-0.067691	-0.4738	0.31886
26	0.057655	0.4036	0.344136
27	0.05249	0.3674	0.35744
28	0.002939	0.0206	0.491834
29	-0.076006	-0.532	0.298551
30	-0.150248	-1.0517	0.14904
31	-0.015789	-0.1105	0.456223
32	0.079869	0.5591	0.289326
33	0.089401	0.6258	0.267172
34	0.050726	0.3551	0.362025
35	-0.001764	-0.0123	0.4951
36	-0.019568	-0.137	0.445805
37	-0.026497	-0.1855	0.426809
38	0.015957	0.1117	0.455759
39	0.062526	0.4377	0.331769
40	0.054128	0.3789	0.353201
41	0.053372	0.3736	0.355155
42	-0.002352	-0.0165	0.493467
43	-0.041908	-0.2934	0.385244
44	-0.066767	-0.4674	0.321153
45	-0.042832	-0.2998	0.38279
46	0.02931	0.2052	0.419143
47	0.028555	0.1999	0.4212
48	-0.002184	-0.0153	0.493933
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
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	0.520702	3.6449	0.000323
2	-0.541024	-3.7872	0.000208
3	-0.224655	-1.5726	0.061125
4	-0.192	-1.344	0.092569
5	0.113623	0.7954	0.215119
6	0.013091	0.0916	0.46368
7	0.154294	1.0801	0.142702
8	0.024399	0.1708	0.432544
9	-0.072555	-0.5079	0.306906
10	0.202904	1.4203	0.080922
11	-0.193002	-1.351	0.091448
12	-0.106359	-0.7445	0.230061
13	-0.019316	-0.1352	0.4465
14	0.054385	0.3807	0.352539
15	-0.172342	-1.2064	0.116729
16	-0.106968	-0.7488	0.228787
17	0.121051	0.8474	0.200458
18	0.003306	0.0231	0.490815
19	-0.051315	-0.3592	0.360493
20	0.166411	1.1649	0.124854
21	-0.003649	-0.0255	0.489863
22	-0.251017	-1.7571	0.042572
23	0.021698	0.1519	0.439951
24	-0.141007	-0.987	0.164234
25	-0.032037	-0.2243	0.411745
26	-0.069335	-0.4853	0.314797
27	-0.124041	-0.8683	0.194735
28	-0.199358	-1.3955	0.084578
29	0.05528	0.387	0.35023
30	-0.034613	-0.2423	0.404784
31	0.093785	0.6565	0.257288
32	-0.078143	-0.547	0.293431
33	0.073417	0.5139	0.30481
34	-0.014163	-0.0991	0.460715
35	-0.032037	-0.2243	0.411743
36	0.028675	0.2007	0.420871
37	-0.009939	-0.0696	0.472407
38	0.018361	0.1285	0.449129
39	-0.119661	-0.8376	0.203154
40	0.099514	0.6966	0.244673
41	-0.052956	-0.3707	0.356233
42	-0.022391	-0.1567	0.438047
43	0.040204	0.2814	0.389783
44	-0.025693	-0.1799	0.429005
45	-0.013414	-0.0939	0.462785
46	-0.095004	-0.665	0.254575
47	-0.047951	-0.3357	0.369281
48	-0.089939	-0.6296	0.265948
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261064249refuypswby6kn2d/1uvg41261064177.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261064249refuypswby6kn2d/1uvg41261064177.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261064249refuypswby6kn2d/2ent21261064177.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261064249refuypswby6kn2d/2ent21261064177.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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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