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workshop 3

*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: Thu, 26 Nov 2009 03:51:55 -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/26/t12592329319k1kvaeye8aurlx.htm/, Retrieved Thu, 26 Nov 2009 11:55:33 +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/26/t12592329319k1kvaeye8aurlx.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 «

108.2 108.8 110.2 109.5 109.5 116 111.2 112.1 114 119.1 114.1 115.1 115.4 110.8 116 119.2 126.5 127.8 131.3 140.3 137.3 143 134.5 139.9 159.3 170.4 175 175.8 180.9 180.3 169.6 172.3 184.8 177.7 184.6 211.4 215.3 215.9 244.7 259.3 289 310.9 321 315.1 333.2 314.1 284.7 273.9 216 196.4 190.9 206.4 196.3 199.5 198.9 214.4 214.2 187.6 180.6 172.2

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	0.964801	7.4733	0
2	0.911722	7.0622	0
3	0.845657	6.5504	0
4	0.76794	5.9484	0
5	0.686562	5.3181	1e-06
6	0.610431	4.7284	7e-06
7	0.537753	4.1654	5.1e-05
8	0.474303	3.6739	0.000255
9	0.424098	3.285	0.000853
10	0.372945	2.8888	0.002686
11	0.325641	2.5224	0.007163
12	0.276911	2.1449	0.018008
13	0.227994	1.766	0.041239
14	0.181231	1.4038	0.082765
15	0.137946	1.0685	0.144782
16	0.091483	0.7086	0.240651
17	0.042902	0.3323	0.370404
18	-0.00446	-0.0345	0.486277
19	-0.04944	-0.383	0.35155
20	-0.091798	-0.7111	0.2399
21	-0.136726	-1.0591	0.146904
22	-0.177424	-1.3743	0.087227
23	-0.214345	-1.6603	0.051035
24	-0.247879	-1.9201	0.029804
25	-0.271674	-2.1044	0.019772
26	-0.28865	-2.2359	0.014546
27	-0.306727	-2.3759	0.010358
28	-0.325066	-2.5179	0.007245
29	-0.341279	-2.6435	0.005226
30	-0.354345	-2.7447	0.003989
31	-0.370102	-2.8668	0.002856
32	-0.383186	-2.9681	0.00215
33	-0.389943	-3.0205	0.001852
34	-0.39569	-3.065	0.00163
35	-0.396309	-3.0698	0.001608
36	-0.391117	-3.0296	0.001805

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.964801	7.4733	0
2	-0.276453	-2.1414	0.018156
3	-0.163256	-1.2646	0.105456
4	-0.14615	-1.1321	0.131054
5	-0.022101	-0.1712	0.432325
6	0.080282	0.6219	0.268194
7	-0.011778	-0.0912	0.463807
8	0.060715	0.4703	0.319924
9	0.084271	0.6528	0.258203
10	-0.168211	-1.303	0.098784
11	-0.017354	-0.1344	0.446759
12	-0.107585	-0.8333	0.203977
13	-0.004481	-0.0347	0.486212
14	0.036519	0.2829	0.389123
15	0.010911	0.0845	0.466463
16	-0.09022	-0.6988	0.243675
17	-0.092895	-0.7196	0.237294
18	-0.049197	-0.3811	0.352245
19	0.01935	0.1499	0.440681
20	-0.021723	-0.1683	0.433471
21	-0.100985	-0.7822	0.218578
22	0.031119	0.241	0.40517
23	-0.015365	-0.119	0.452829
24	-0.047195	-0.3656	0.357985
25	0.080214	0.6213	0.268368
26	-0.011914	-0.0923	0.46339
27	-0.106422	-0.8243	0.206505
28	-0.086086	-0.6668	0.253721
29	-0.035426	-0.2744	0.392356
30	0.06609	0.5119	0.30529
31	-0.102327	-0.7926	0.21556
32	0.03755	0.2909	0.386079
33	0.0907	0.7026	0.242523
34	-0.115925	-0.898	0.1864
35	-0.018166	-0.1407	0.444284
36	0.01281	0.0992	0.460644

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592329319k1kvaeye8aurlx/1oyr51259232714.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592329319k1kvaeye8aurlx/1oyr51259232714.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592329319k1kvaeye8aurlx/210j91259232714.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592329319k1kvaeye8aurlx/210j91259232714.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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