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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: Fri, 27 Nov 2009 09:20:57 -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/27/t12593391251rgqlc7avqxk7ap.htm/, Retrieved Fri, 27 Nov 2009 17:25:28 +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/27/t12593391251rgqlc7avqxk7ap.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 «

92.9 107.7 103.5 91.1 79.8 71.9 82.9 90.1 100.7 90.7 108.8 44.1 93.6 107.4 96.5 93.6 76.5 76.7 84 103.3 88.5 99 105.9 44.7 94 107.1 104.8 102.5 77.7 85.2 91.3 106.5 92.4 97.5 107 51.1 98.6 102.2 114.3 99.4 72.5 92.3 99.4 85.9 109.4 97.6 104.7 56.9 86.7 108.5 103.4 86.2 71 75.9 87.1 102 88.5 87.8 100.8 50.6 85.9

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	-0.054723	-0.4274	0.335296
2	-0.221632	-1.731	0.044254
3	-0.242414	-1.8933	0.031531
4	-0.169728	-1.3256	0.094954
5	0.230998	1.8042	0.038072
6	0.224371	1.7524	0.042366
7	0.217414	1.6981	0.047297
8	-0.109349	-0.854	0.198212
9	-0.225849	-1.7639	0.041375
10	-0.271821	-2.123	0.01891
11	-0.011271	-0.088	0.465072
12	0.679856	5.3098	1e-06
13	-0.051633	-0.4033	0.344082
14	-0.199969	-1.5618	0.061753
15	-0.278212	-2.1729	0.016841
16	-0.123269	-0.9628	0.169734
17	0.186504	1.4566	0.075172
18	0.123336	0.9633	0.169604
19	0.156375	1.2213	0.113331
20	-0.104702	-0.8177	0.208343
21	-0.238808	-1.8652	0.033486
22	-0.205734	-1.6068	0.056627
23	-0.039742	-0.3104	0.378661
24	0.487933	3.8109	0.000162
25	-0.037195	-0.2905	0.386208
26	-0.159275	-1.244	0.109133
27	-0.192795	-1.5058	0.068642
28	-0.087445	-0.683	0.248608
29	0.133164	1.04	0.151212
30	0.109037	0.8516	0.198881
31	0.089044	0.6955	0.244704
32	-0.071939	-0.5619	0.288135
33	-0.161985	-1.2651	0.105315
34	-0.117733	-0.9195	0.180722
35	-0.034561	-0.2699	0.394064
36	0.351871	2.7482	0.003935

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.054723	-0.4274	0.335296
2	-0.225301	-1.7597	0.04174
3	-0.284875	-2.2249	0.014897
4	-0.311983	-2.4367	0.008878
5	0.033919	0.2649	0.395985
6	0.099793	0.7794	0.219377
7	0.299965	2.3428	0.011209
8	0.156559	1.2228	0.113061
9	0.090498	0.7068	0.241188
10	-0.228672	-1.786	0.039536
11	-0.26877	-2.0992	0.019974
12	0.484454	3.7837	0.000177
13	-0.102253	-0.7986	0.213805
14	-0.172175	-1.3447	0.091846
15	-0.171085	-1.3362	0.093221
16	0.050721	0.3961	0.346692
17	-0.018063	-0.1411	0.444138
18	-0.143615	-1.1217	0.1332
19	-0.07734	-0.604	0.274027
20	-0.018905	-0.1477	0.441552
21	-0.079114	-0.6179	0.26947
22	0.045299	0.3538	0.362357
23	-0.15138	-1.1823	0.120834
24	-0.068228	-0.5329	0.298027
25	-0.100539	-0.7852	0.217678
26	-0.003393	-0.0265	0.489472
27	0.081146	0.6338	0.264299
28	-0.016744	-0.1308	0.448193
29	-0.06336	-0.4949	0.311238
30	0.076444	0.5971	0.276342
31	-0.045725	-0.3571	0.361116
32	-0.038222	-0.2985	0.383159
33	-0.063272	-0.4942	0.31148
34	0.007428	0.058	0.476964
35	-0.098812	-0.7717	0.221623
36	-0.109973	-0.8589	0.196875

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593391251rgqlc7avqxk7ap/1f7o01259338855.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593391251rgqlc7avqxk7ap/1f7o01259338855.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593391251rgqlc7avqxk7ap/2ixp01259338855.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593391251rgqlc7avqxk7ap/2ixp01259338855.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; 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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