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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: Tue, 16 Nov 2010 14:41:05 +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/Nov/16/t1289918433qotuct5584mn9l7.htm/, Retrieved Tue, 16 Nov 2010 15:40:35 +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/Nov/16/t1289918433qotuct5584mn9l7.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:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

98,6 100,1 98,8 98,3 102,8 103,6 105,2 100,1 98,2 98,4 97,4 98,4 100,3 101,1 104,1 107,3 110,1 112,6 114,3 115,3 109,9 108,2 103,2 101,8 105,6 108,2 109,8 114,6 117,2 116,5 116,1 112,1 106,8 106,9 104,5 103 105,9 107,7 107,1 112,5 114,5 114,6 113,1 112,8 111,9 112 112,4 110 112,3 109,6 111,9 110,8 110,4 110,8 114 108,4 110,5 105,1 102,3 104,3 103,4 102,4 104,5 107,3 110,1 111,8 111,8 105,7 106 106,4 107,1 111,5 109,6 109,9 109,3 111,4 112,9 115,5 118,4 116,2 113,3 113,8 114,1 117,1 115,5 115,2 114,2 115,3 118,8 118 118,1 111,8 112 114,3 115 118,5 117,6 119,1 120,6 123,6 122,7 123,8 123,1 124,5 120,7 118,7 119 122,3 118,6 118,1 118,2 120,8 119,7 119,7 117,1 114,5 116,5 116,4 114,9 115,5

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.912912	10.0005	0
2	0.815688	8.9354	0
3	0.701835	7.6882	0
4	0.599423	6.5663	0
5	0.538757	5.9018	0
6	0.502934	5.5094	0
7	0.479031	5.2475	0
8	0.475568	5.2096	0
9	0.491464	5.3837	0
10	0.505773	5.5405	0
11	0.498742	5.4634	0
12	0.475189	5.2054	0
13	0.405344	4.4403	1e-05
14	0.321528	3.5222	0.000303
15	0.241605	2.6466	0.00461
16	0.163741	1.7937	0.037691
17	0.12765	1.3983	0.082296
18	0.110412	1.2095	0.114423
19	0.114731	1.2568	0.105632
20	0.139909	1.5326	0.064
21	0.167419	1.834	0.034567
22	0.200807	2.1997	0.014871
23	0.21795	2.3875	0.009262
24	0.202841	2.222	0.014079
25	0.155081	1.6988	0.045972
26	0.100379	1.0996	0.136854
27	0.048016	0.526	0.299933
28	0.015074	0.1651	0.434561
29	0.009753	0.1068	0.457548
30	-0.007194	-0.0788	0.46866
31	-0.006885	-0.0754	0.470002
32	0.004115	0.0451	0.482058
33	0.014194	0.1555	0.438348
34	0.0291	0.3188	0.375228
35	0.032632	0.3575	0.360686
36	0.002477	0.0271	0.489198
37	-0.040186	-0.4402	0.330287
38	-0.078576	-0.8608	0.195543
39	-0.12693	-1.3904	0.083483
40	-0.15738	-1.724	0.043641
41	-0.167016	-1.8296	0.034899
42	-0.163419	-1.7902	0.037974
43	-0.15314	-1.6776	0.048018
44	-0.117187	-1.2837	0.100857
45	-0.076221	-0.835	0.202701
46	-0.039063	-0.4279	0.334741
47	0.006649	0.0728	0.471029
48	0.020868	0.2286	0.409784

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.912912	10.0005	0
2	-0.106372	-1.1653	0.123114
3	-0.151284	-1.6572	0.050042
4	0.012971	0.1421	0.443624
5	0.197073	2.1588	0.016427
6	0.078024	0.8547	0.197207
7	-0.017931	-0.1964	0.422307
8	0.09946	1.0895	0.139051
9	0.170112	1.8635	0.032419
10	0.021967	0.2406	0.405125
11	-0.129614	-1.4198	0.079122
12	-0.028957	-0.3172	0.37582
13	-0.183401	-2.0091	0.023388
14	-0.085823	-0.9401	0.174515
15	-0.015622	-0.1711	0.432204
16	-0.07276	-0.797	0.213501
17	0.114695	1.2564	0.105702
18	-0.001922	-0.0211	0.491617
19	0.030269	0.3316	0.370394
20	0.078866	0.8639	0.194673
21	0.032566	0.3567	0.360957
22	0.098277	1.0766	0.141916
23	0.008292	0.0908	0.463888
24	-0.105748	-1.1584	0.124498
25	-0.084978	-0.9309	0.176891
26	0.047277	0.5179	0.302745
27	-0.014276	-0.1564	0.437998
28	0.018249	0.1999	0.420944
29	0.006095	0.0668	0.473441
30	-0.195291	-2.1393	0.017218
31	0.025394	0.2782	0.390677
32	0.010771	0.118	0.453137
33	-0.011479	-0.1257	0.450072
34	0.001799	0.0197	0.492155
35	0.002162	0.0237	0.490573
36	-0.073435	-0.8044	0.211368
37	-0.005805	-0.0636	0.474701
38	0.069314	0.7593	0.224583
39	-0.105802	-1.159	0.124379
40	-0.003758	-0.0412	0.483614
41	0.017554	0.1923	0.423919
42	0.088844	0.9732	0.166197
43	-0.068238	-0.7475	0.228109
44	0.100567	1.1017	0.136408
45	0.142955	1.566	0.059992
46	-0.042662	-0.4673	0.320552
47	0.154587	1.6934	0.046486
48	-0.030107	-0.3298	0.371062

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918433qotuct5584mn9l7/1afkn1289918463.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918433qotuct5584mn9l7/1afkn1289918463.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918433qotuct5584mn9l7/2afkn1289918463.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918433qotuct5584mn9l7/2afkn1289918463.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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