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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: Mon, 13 Dec 2010 09:19:49 +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/Dec/13/t1292231904ztks9401q4e3gg8.htm/, Retrieved Mon, 13 Dec 2010 10:20:53 +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/Dec/13/t1292231904ztks9401q4e3gg8.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

113 95,4 86,2 111,7 97,5 99,7 111,5 91,8 86,3 88,7 95,1 105,1 104,5 89,1 82,6 102,7 91,8 94,1 103,1 93,2 91 94,3 99,4 115,7 116,8 99,8 96 115,9 109,1 117,3 109,8 112,8 110,7 100 113,3 122,4 112,5 104,2 92,5 117,2 109,3 106,1 118,8 105,3 106 102 112,9 116,5 114,8 100,5 85,4 114,6 109,9 100,7 115,5 100,7 99 102,3

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	13 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.311548	2.3727	0.010498
2	0.04191	0.3192	0.375368
3	0.224819	1.7122	0.046104
4	0.159133	1.2119	0.115229
5	0.379438	2.8897	0.002708
6	0.409546	3.119	0.001412
7	0.294922	2.2461	0.014262
8	0.124851	0.9508	0.172816
9	-0.001647	-0.0125	0.495016
10	-0.086591	-0.6595	0.256106
11	0.102686	0.782	0.218688
12	0.472031	3.5949	0.000335
13	0.033594	0.2558	0.399488
14	-0.228572	-1.7408	0.043515
15	-0.134922	-1.0275	0.154218
16	-0.111397	-0.8484	0.199859
17	0.046538	0.3544	0.362155
18	0.01918	0.1461	0.442185
19	-0.033869	-0.2579	0.398684
20	-0.143693	-1.0943	0.139167
21	-0.25876	-1.9707	0.026771
22	-0.263023	-2.0031	0.024922
23	-0.094248	-0.7178	0.23789
24	0.13297	1.0127	0.157713
25	-0.123203	-0.9383	0.175995
26	-0.325034	-2.4754	0.008126
27	-0.238877	-1.8192	0.03702
28	-0.139093	-1.0593	0.146927
29	-0.049458	-0.3767	0.353899
30	-0.053184	-0.405	0.34347
31	-0.049964	-0.3805	0.352475
32	-0.185478	-1.4126	0.081565
33	-0.170198	-1.2962	0.100022
34	-0.153414	-1.1684	0.12372
35	-0.102391	-0.7798	0.219344
36	0.146491	1.1156	0.134589
37	-0.063956	-0.4871	0.314019
38	-0.209496	-1.5955	0.058021
39	-0.055694	-0.4242	0.336511
40	-0.07096	-0.5404	0.295491
41	-0.002877	-0.0219	0.491296
42	0.059183	0.4507	0.326934
43	0.004004	0.0305	0.487888
44	-0.087582	-0.667	0.253707
45	-0.039995	-0.3046	0.380883
46	-0.036288	-0.2764	0.391627
47	-0.032215	-0.2453	0.403528
48	0.128786	0.9808	0.165382

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.311548	2.3727	0.010498
2	-0.061081	-0.4652	0.321774
3	0.255671	1.9471	0.028183
4	0.009218	0.0702	0.472138
5	0.40883	3.1136	0.001435
6	0.182819	1.3923	0.084572
7	0.263632	2.0078	0.024667
8	-0.10971	-0.8355	0.203425
9	-0.120972	-0.9213	0.180357
10	-0.479683	-3.6532	0.000279
11	-0.136586	-1.0402	0.151279
12	0.294945	2.2462	0.014256
13	-0.196605	-1.4973	0.069869
14	-0.104869	-0.7987	0.213873
15	-0.194308	-1.4798	0.072168
16	0.166222	1.2659	0.105304
17	-0.023375	-0.178	0.429664
18	0.010683	0.0814	0.467717
19	-0.012731	-0.097	0.461548
20	0.037586	0.2862	0.387854
21	0.060515	0.4609	0.323309
22	-0.059396	-0.4523	0.326353
23	-0.015369	-0.117	0.453613
24	-0.120293	-0.9161	0.181697
25	-0.00759	-0.0578	0.477051
26	-0.103515	-0.7883	0.216853
27	0.01321	0.1006	0.460105
28	0.010909	0.0831	0.467037
29	-0.016028	-0.1221	0.451636
30	0.075656	0.5762	0.283361
31	0.047773	0.3638	0.358654
32	-0.067814	-0.5165	0.303751
33	0.119142	0.9074	0.183986
34	-0.060601	-0.4615	0.323076
35	-0.101768	-0.775	0.220732
36	-0.052226	-0.3977	0.34614
37	-0.105087	-0.8003	0.213396
38	0.024664	0.1878	0.425832
39	0.054955	0.4185	0.338554
40	-0.078641	-0.5989	0.275783
41	-0.026416	-0.2012	0.42063
42	0.09471	0.7213	0.236815
43	0.026848	0.2045	0.419351
44	-0.00199	-0.0152	0.493981
45	-0.043047	-0.3278	0.372108
46	0.006411	0.0488	0.480614
47	-0.041914	-0.3192	0.375357
48	-0.099252	-0.7559	0.22639

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292231904ztks9401q4e3gg8/16wm81292231976.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292231904ztks9401q4e3gg8/16wm81292231976.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292231904ztks9401q4e3gg8/26wm81292231976.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292231904ztks9401q4e3gg8/26wm81292231976.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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