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Paper

*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, 26 Dec 2009 09:53:41 -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/26/t1261846494t5mhchx3cfcaenq.htm/, Retrieved Sat, 26 Dec 2009 17:54:57 +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/26/t1261846494t5mhchx3cfcaenq.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 «

1.2613 1.2646 1.2262 1.1985 1.2007 1.2138 1.2266 1.2176 1.2218 1.249 1.2991 1.3408 1.3119 1.3014 1.3201 1.2938 1.2694 1.2165 1.2037 1.2292 1.2256 1.2015 1.1786 1.1856 1.2103 1.1938 1.202 1.2271 1.277 1.265 1.2684 1.2811 1.2727 1.2611 1.2881 1.3213 1.2999 1.3074 1.3242 1.3516 1.3511 1.3419 1.3716 1.3622 1.3896 1.4227 1.4684 1.457 1.4718 1.4748 1.5527 1.5751 1.5557 1.5553 1.577 1.4975 1.437 1.3322 1.2732 1.3449

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.877366	6.0786	0
2	0.663755	4.5986	1.6e-05
3	0.485156	3.3613	0.000765
4	0.358654	2.4848	0.00825
5	0.247157	1.7124	0.046643
6	0.14331	0.9929	0.162874
7	0.054504	0.3776	0.353691
8	0.000737	0.0051	0.497972
9	-0.021061	-0.1459	0.442299
10	-0.048833	-0.3383	0.368297
11	-0.093928	-0.6508	0.259155
12	-0.128916	-0.8932	0.188116
13	-0.118151	-0.8186	0.208537
14	-0.07341	-0.5086	0.306681
15	-0.04656	-0.3226	0.374208
16	-0.056145	-0.389	0.349505
17	-0.079668	-0.552	0.291769
18	-0.107951	-0.7479	0.229082
19	-0.159154	-1.1027	0.137838
20	-0.20443	-1.4163	0.081568
21	-0.237719	-1.647	0.053048
22	-0.275846	-1.9111	0.030985
23	-0.311208	-2.1561	0.018058
24	-0.327803	-2.2711	0.013833
25	-0.319202	-2.2115	0.015898
26	-0.323957	-2.2444	0.014725
27	-0.34522	-2.3918	0.010367
28	-0.341702	-2.3674	0.010997
29	-0.284613	-1.9719	0.027202
30	-0.186081	-1.2892	0.101752
31	-0.081325	-0.5634	0.28788
32	0.005216	0.0361	0.485661
33	0.064798	0.4489	0.32775
34	0.120504	0.8349	0.203962
35	0.159438	1.1046	0.137415
36	0.156239	1.0825	0.142229

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.877366	6.0786	0
2	-0.460483	-3.1903	0.001253
3	0.213033	1.4759	0.073246
4	-0.061658	-0.4272	0.335578
5	-0.106005	-0.7344	0.233132
6	0.000286	0.002	0.499214
7	-0.04811	-0.3333	0.370175
8	0.064032	0.4436	0.329654
9	-0.006286	-0.0435	0.482722
10	-0.127989	-0.8867	0.189823
11	-0.022506	-0.1559	0.438371
12	0.023642	0.1638	0.435289
13	0.107359	0.7438	0.230311
14	0.013223	0.0916	0.463695
15	-0.110975	-0.7689	0.222873
16	-0.027758	-0.1923	0.424155
17	-0.029571	-0.2049	0.419267
18	-0.108719	-0.7532	0.227496
19	-0.145671	-1.0092	0.158961
20	0.107496	0.7448	0.230027
21	-0.105648	-0.7319	0.233879
22	-0.139132	-0.9639	0.169955
23	-0.019816	-0.1373	0.445688
24	-0.035523	-0.2461	0.403322
25	0.048108	0.3333	0.370178
26	-0.23106	-1.6008	0.057988
27	-0.052829	-0.366	0.357982
28	0.117464	0.8138	0.209885
29	0.046245	0.3204	0.37503
30	0.063607	0.4407	0.33071
31	-0.015925	-0.1103	0.456302
32	0.052901	0.3665	0.357797
33	0.01904	0.1319	0.447801
34	0.029616	0.2052	0.419147
35	-0.117561	-0.8145	0.209694
36	-0.02711	-0.1878	0.425904

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/26/t1261846494t5mhchx3cfcaenq/1hcrf1261846418.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/26/t1261846494t5mhchx3cfcaenq/1hcrf1261846418.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/26/t1261846494t5mhchx3cfcaenq/2txey1261846418.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/26/t1261846494t5mhchx3cfcaenq/2txey1261846418.ps (open in new window)

Parameters (Session):

par1 = 1 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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