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WS 8 01

*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: Sat, 21 Nov 2009 01:59:55 -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/Nov/21/t1258794042h784t3r4xg5uyok.htm/, Retrieved Sat, 21 Nov 2009 10:00:44 +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/Nov/21/t1258794042h784t3r4xg5uyok.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 «

103,63 103,64 103,66 103,77 103,88 103,91 103,91 103,92 104,05 104,23 104,30 104,31 104,31 104,34 104,55 104,65 104,73 104,75 104,75 104,76 104,94 105,29 105,38 105,43 105,43 105,42 105,52 105,69 105,72 105,74 105,74 105,74 105,95 106,17 106,34 106,37 106,37 106,36 106,44 106,29 106,23 106,23 106,23 106,23 106,34 106,44 106,44 106,48 106,50 106,57 106,40 106,37 106,25 106,21 106,21 106,24 106,19 106,08 106,13 106,09

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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.961158	7.4451	0
2	0.916531	7.0994	0
3	0.870573	6.7434	0
4	0.825996	6.3981	0
5	0.782588	6.0619	0
6	0.737076	5.7094	0
7	0.68682	5.3201	1e-06
8	0.63291	4.9025	4e-06
9	0.581194	4.5019	1.6e-05
10	0.534132	4.1374	5.6e-05
11	0.485424	3.7601	0.000194
12	0.43243	3.3496	0.000702
13	0.3743	2.8993	0.002609
14	0.3132	2.426	0.009144
15	0.257282	1.9929	0.025413
16	0.20493	1.5874	0.058842
17	0.155567	1.205	0.116464
18	0.104168	0.8069	0.21146
19	0.050773	0.3933	0.34775
20	-0.002953	-0.0229	0.490913
21	-0.052191	-0.4043	0.343726
22	-0.092171	-0.714	0.239012
23	-0.129234	-1.001	0.160413
24	-0.166195	-1.2873	0.101459
25	-0.205013	-1.588	0.058769
26	-0.244167	-1.8913	0.031707
27	-0.27842	-2.1566	0.017526
28	-0.304759	-2.3607	0.010755
29	-0.328662	-2.5458	0.006745
30	-0.352096	-2.7273	0.00418
31	-0.375248	-2.9067	0.002556
32	-0.397639	-3.0801	0.00156
33	-0.412335	-3.1939	0.001119
34	-0.417892	-3.237	0.000984
35	-0.416901	-3.2293	0.001007
36	-0.414884	-3.2137	0.001055
37	-0.411408	-3.1868	0.001142
38	-0.407221	-3.1543	0.001257
39	-0.398844	-3.0894	0.001519
40	-0.391193	-3.0302	0.001802
41	-0.383627	-2.9716	0.002129
42	-0.375797	-2.9109	0.002526
43	-0.367269	-2.8449	0.003035
44	-0.357694	-2.7707	0.003718
45	-0.343394	-2.6599	0.005005
46	-0.324528	-2.5138	0.007323
47	-0.302965	-2.3468	0.011129
48	-0.27908	-2.1617	0.017319
49	-0.253756	-1.9656	0.02699
50	-0.225507	-1.7468	0.042897
51	-0.20185	-1.5635	0.061594
52	-0.176959	-1.3707	0.087785
53	-0.154345	-1.1955	0.118288
54	-0.132641	-1.0274	0.154171
55	-0.110783	-0.8581	0.197121
56	-0.087559	-0.6782	0.250116
57	-0.064591	-0.5003	0.309341
58	-0.043917	-0.3402	0.367455
59	-0.021363	-0.1655	0.434563
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.961158	7.4451	0
2	-0.09575	-0.7417	0.230587
3	-0.035467	-0.2747	0.392235
4	-0.004155	-0.0322	0.487217
5	-0.011459	-0.0888	0.464783
6	-0.054844	-0.4248	0.336244
7	-0.085333	-0.661	0.255576
8	-0.069048	-0.5348	0.297368
9	0.002975	0.023	0.490844
10	0.023599	0.1828	0.427786
11	-0.06465	-0.5008	0.309181
12	-0.086778	-0.6722	0.252024
13	-0.090694	-0.7025	0.242537
14	-0.069476	-0.5382	0.296229
15	0.022786	0.1765	0.430247
16	-0.015415	-0.1194	0.452677
17	-0.012905	-0.1	0.460354
18	-0.062905	-0.4873	0.313926
19	-0.055632	-0.4309	0.334035
20	-0.049678	-0.3848	0.350872
21	-0.003537	-0.0274	0.489117
22	0.052835	0.4093	0.341905
23	-0.020683	-0.1602	0.436626
24	-0.032785	-0.2539	0.400202
25	-0.056831	-0.4402	0.330683
26	-0.049758	-0.3854	0.350643
27	-0.003541	-0.0274	0.489105
28	0.027511	0.2131	0.415985
29	-0.031372	-0.243	0.404416
30	-0.028863	-0.2236	0.411925
31	-0.020465	-0.1585	0.437289
32	-0.041262	-0.3196	0.375186
33	0.033699	0.261	0.397481
34	0.041631	0.3225	0.374107
35	0.030985	0.24	0.405571
36	-0.004673	-0.0362	0.485622
37	0.008528	0.0661	0.473777
38	-0.021128	-0.1637	0.435275
39	0.002566	0.0199	0.492103
40	-0.07503	-0.5812	0.281648
41	-0.042488	-0.3291	0.371609
42	-0.000218	-0.0017	0.499329
43	0.005347	0.0414	0.48355
44	-0.01707	-0.1322	0.447624
45	0.011398	0.0883	0.464969
46	0.006654	0.0515	0.479531
47	0.008873	0.0687	0.472718
48	0.033409	0.2588	0.398344
49	0.027401	0.2123	0.416315
50	0.035006	0.2712	0.393603
51	-0.078662	-0.6093	0.272309
52	-0.000701	-0.0054	0.497842
53	-0.03647	-0.2825	0.389268
54	0.001143	0.0089	0.496483
55	0.017027	0.1319	0.447756
56	0.020381	0.1579	0.437546
57	-0.008171	-0.0633	0.474872
58	-0.0376	-0.2912	0.385933
59	0.028549	0.2211	0.412866
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794042h784t3r4xg5uyok/1b7qd1258793989.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794042h784t3r4xg5uyok/1b7qd1258793989.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794042h784t3r4xg5uyok/2kr5p1258793989.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258794042h784t3r4xg5uyok/2kr5p1258793989.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

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