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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 03 May 2010 17:25:04 +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/May/03/t1272907796eyf9gi5iz2hojew.htm/, Retrieved Mon, 03 May 2010 19:29:56 +0200

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/May/03/t1272907796eyf9gi5iz2hojew.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

132.8 132.5 131.4 131.4 130.7 131.5 131.2 130.1 130.5 129 128.2 128.4 127.3 127.7 127 123.9 125.4 124.6 124.5 124.8 124.1 124.2 122.8 122.3 121.1 121.7 122.2 122.2 122.7 121.7 121 119.8 120.2 116.6 116 118 117.1 116.2 113.3 114.3 113.6 113 112.9 112.7 112.5 113 111.9 110.9 109.8 108.3 109.2 109.2 108.7 109.8 110.8 110 109.6 109.5 110.8 111.6 113.1 114.3 114.1 113.8 112.6 112.7 111.5 110.7 110.4 109.7 110 111.3 109 108.2 107.2 108.7 110.3 110.3 109.5 109.5 109.4 109.6 111.3 110 109.5 110.693 109.195 108.095 108.199 106.87 105.278 108.711 111.192 109.641 109.42 109.935 111.126 110.733 110.34 111.766 111.294 111.54 112.008 111.007 114.963 112.045 110.703 108.894 107.51 111.35 112.964 115.203 115.182 115.191 112.346 110.774 113.07 111.138 109.092 107.971 107.051

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.953934	10.4933	0
2	0.909594	10.0055	0
3	0.87189	9.5908	0
4	0.836269	9.199	0
5	0.809444	8.9039	0
6	0.773832	8.5121	0
7	0.742297	8.1653	0
8	0.712901	7.8419	0
9	0.682573	7.5083	0
10	0.655587	7.2115	0
11	0.627132	6.8984	0
12	0.597001	6.567	0
13	0.562939	6.1923	0
14	0.529869	5.8286	0
15	0.501541	5.517	0
16	0.482334	5.3057	0
17	0.461363	5.075	1e-06
18	0.434861	4.7835	2e-06
19	0.406735	4.4741	9e-06
20	0.375379	4.1292	3.4e-05
21	0.345871	3.8046	0.000112
22	0.315353	3.4689	0.000362
23	0.287571	3.1633	0.000986
24	0.264255	2.9068	0.002172
25	0.242607	2.6687	0.00433
26	0.216628	2.3829	0.009367
27	0.189229	2.0815	0.019748
28	0.163942	1.8034	0.03691
29	0.138412	1.5225	0.065243
30	0.11169	1.2286	0.110804
31	0.084955	0.9345	0.175951
32	0.058697	0.6457	0.259859
33	0.033612	0.3697	0.356114
34	0.017185	0.189	0.425192
35	-0.002721	-0.0299	0.488084
36	-0.026915	-0.2961	0.383845
37	-0.050574	-0.5563	0.289512
38	-0.069229	-0.7615	0.223916
39	-0.07662	-0.8428	0.200496
40	-0.089168	-0.9809	0.164312
41	-0.102661	-1.1293	0.13051
42	-0.117954	-1.2975	0.098465
43	-0.133117	-1.4643	0.072855
44	-0.14474	-1.5921	0.056981
45	-0.152749	-1.6802	0.047746
46	-0.164495	-1.8094	0.036432
47	-0.175606	-1.9317	0.02787
48	-0.180567	-1.9862	0.024634

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.953934	10.4933	0
2	-0.004391	-0.0483	0.480777
3	0.050842	0.5593	0.288508
4	0.005567	0.0612	0.475638
5	0.084503	0.9295	0.177232
6	-0.106692	-1.1736	0.121427
7	0.038753	0.4263	0.335328
8	-0.002605	-0.0287	0.488592
9	-0.013691	-0.1506	0.440272
10	0.006248	0.0687	0.47266
11	-0.013867	-0.1525	0.439507
12	-0.037686	-0.4145	0.339606
13	-0.065312	-0.7184	0.236937
14	-0.005325	-0.0586	0.476693
15	0.018253	0.2008	0.420604
16	0.086318	0.9495	0.172131
17	-0.030618	-0.3368	0.368426
18	-0.05344	-0.5878	0.278868
19	-0.035388	-0.3893	0.348882
20	-0.054303	-0.5973	0.275701
21	-0.023014	-0.2532	0.400288
22	-0.035848	-0.3943	0.347017
23	0.019034	0.2094	0.417255
24	0.022189	0.2441	0.403793
25	0.017317	0.1905	0.424623
26	-0.074748	-0.8222	0.206281
27	-0.035107	-0.3862	0.350022
28	-0.011502	-0.1265	0.449765
29	-0.022512	-0.2476	0.402421
30	-0.027545	-0.303	0.381206
31	-0.003824	-0.0421	0.483258
32	-0.02028	-0.2231	0.411923
33	-0.029272	-0.322	0.374007
34	0.073186	0.8051	0.211185
35	-0.066738	-0.7341	0.232149
36	-0.060535	-0.6659	0.253375
37	-0.017453	-0.192	0.42404
38	0.062808	0.6909	0.245481
39	0.099995	1.0999	0.13677
40	-0.060216	-0.6624	0.254494
41	-0.020267	-0.2229	0.411981
42	-0.049796	-0.5478	0.292433
43	0.000355	0.0039	0.498447
44	-0.013874	-0.1526	0.439478
45	0.049265	0.5419	0.294435
46	-0.06186	-0.6805	0.248755
47	0.016034	0.1764	0.430147
48	0.069404	0.7634	0.223342

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/03/t1272907796eyf9gi5iz2hojew/1hcrf1272907500.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/03/t1272907796eyf9gi5iz2hojew/1hcrf1272907500.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/03/t1272907796eyf9gi5iz2hojew/2rlqi1272907500.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/03/t1272907796eyf9gi5iz2hojew/2rlqi1272907500.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; 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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