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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: Tue, 15 Dec 2009 10:10:26 -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/15/t1260897072p0znl4qljwbxkki.htm/, Retrieved Tue, 15 Dec 2009 18:11:14 +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/15/t1260897072p0znl4qljwbxkki.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 «

87,00 96,30 107,1 115,2 106,1 89,50 91,30 97,60 100,7 104,6 94,70 101,8 102,5 105,3 110,3 109,8 117,3 118,8 131,3 125,9 133,1 147,0 145,8 164,4 149,8 137,7 151,7 156,8 180,0 180,4 170,4 191,6 199,5 218,2 217,5 205,0 194,0 199,3 219,3 211,1 215,2 240,2 242,2 240,7 255,4 253,0 218,2 203,7 205,6 215,6

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.943294	6.6701	0
2	0.889374	6.2888	0
3	0.851396	6.0203	0
4	0.813445	5.7519	0
5	0.760624	5.3784	1e-06
6	0.688606	4.8692	6e-06
7	0.624422	4.4153	2.7e-05
8	0.559729	3.9579	0.00012
9	0.501835	3.5485	0.000427
10	0.460211	3.2542	0.001021
11	0.397815	2.813	0.003499
12	0.325989	2.3051	0.012675
13	0.255936	1.8097	0.038174
14	0.192837	1.3636	0.089407
15	0.131643	0.9309	0.1782
16	0.060856	0.4303	0.334408
17	-0.0054	-0.0382	0.484846
18	-0.066513	-0.4703	0.320085
19	-0.114132	-0.807	0.211734
20	-0.152613	-1.0791	0.142852
21	-0.198093	-1.4007	0.083735
22	-0.241799	-1.7098	0.046753
23	-0.2803	-1.982	0.026493
24	-0.302017	-2.1356	0.018817
25	-0.325027	-2.2983	0.012882
26	-0.361287	-2.5547	0.00686
27	-0.397634	-2.8117	0.003511
28	-0.423999	-2.9981	0.002112
29	-0.433439	-3.0649	0.001753
30	-0.43671	-3.088	0.001642
31	-0.446687	-3.1586	0.001345
32	-0.451417	-3.192	0.001222
33	-0.4468	-3.1594	0.001341
34	-0.427916	-3.0258	0.001955
35	-0.40412	-2.8576	0.003103
36	-0.387631	-2.741	0.004237
37	-0.375311	-2.6538	0.005321
38	-0.358854	-2.5375	0.007165
39	-0.331967	-2.3474	0.011453
40	-0.304565	-2.1536	0.018059
41	-0.279354	-1.9753	0.026882
42	-0.244596	-1.7296	0.04494
43	-0.213013	-1.5062	0.06915
44	-0.179236	-1.2674	0.105443
45	-0.131689	-0.9312	0.178117
46	-0.088196	-0.6236	0.26785
47	-0.066847	-0.4727	0.319249
48	-0.050833	-0.3594	0.360389
49	-0.030017	-0.2123	0.416386
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	0.943294	6.6701	0
2	-0.003895	-0.0275	0.489068
3	0.116715	0.8253	0.206562
4	-0.013992	-0.0989	0.46079
5	-0.137983	-0.9757	0.166958
6	-0.214838	-1.5191	0.067514
7	-0.0169	-0.1195	0.45268
8	-0.091997	-0.6505	0.259168
9	0.049877	0.3527	0.362903
10	0.166289	1.1758	0.122614
11	-0.176727	-1.2496	0.108623
12	-0.123576	-0.8738	0.193199
13	-0.106988	-0.7565	0.226444
14	-0.093081	-0.6582	0.25672
15	-0.043669	-0.3088	0.379383
16	-0.03567	-0.2522	0.400951
17	0.003525	0.0249	0.490107
18	0.006235	0.0441	0.482505
19	0.089757	0.6347	0.264266
20	-0.001176	-0.0083	0.496698
21	-0.093509	-0.6612	0.255758
22	-0.049992	-0.3535	0.362602
23	-0.052514	-0.3713	0.35598
24	0.069562	0.4919	0.31248
25	-0.032167	-0.2275	0.410499
26	-0.099094	-0.7007	0.243369
27	-0.080587	-0.5698	0.285669
28	-0.004767	-0.0337	0.486623
29	0.055362	0.3915	0.348556
30	0.048013	0.3395	0.367827
31	-0.027462	-0.1942	0.423407
32	0.010823	0.0765	0.46965
33	0.021658	0.1531	0.43945
34	0.011774	0.0833	0.46699
35	0.002196	0.0155	0.493836
36	-0.03227	-0.2282	0.410217
37	-0.038739	-0.2739	0.392634
38	0.019195	0.1357	0.446291
39	0.020042	0.1417	0.443936
40	-0.031046	-0.2195	0.413567
41	0.02914	0.2061	0.418793
42	0.12722	0.8996	0.186327
43	-0.045278	-0.3202	0.375088
44	-0.0452	-0.3196	0.375298
45	0.087316	0.6174	0.269881
46	-0.041826	-0.2958	0.384321
47	-0.176132	-1.2454	0.109388
48	-0.044512	-0.3147	0.377131
49	-0.097013	-0.686	0.247945
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/15/t1260897072p0znl4qljwbxkki/1rb7u1260897024.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260897072p0znl4qljwbxkki/1rb7u1260897024.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260897072p0znl4qljwbxkki/2z69y1260897024.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260897072p0znl4qljwbxkki/2z69y1260897024.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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