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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, 04 Dec 2009 05:09:12 -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/04/t1259928592d3w3bewkcyr06up.htm/, Retrieved Fri, 04 Dec 2009 13:09:55 +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/04/t1259928592d3w3bewkcyr06up.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 «

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 99 102.3 108.8 105.9 113.2 95.7 80.9 113.9 98.1 102.8 104.7 95.9 94.6 101.6 103.9 110.3 114.1

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	0.254372	1.9704	0.026708
2	0.005089	0.0394	0.484342
3	0.145643	1.1281	0.131874
4	0.059333	0.4596	0.323736
5	0.28178	2.1827	0.016493
6	0.309225	2.3952	0.009874
7	0.17275	1.3381	0.092954
8	-0.016668	-0.1291	0.448853
9	-0.095778	-0.7419	0.230522
10	-0.292433	-2.2652	0.013563
11	-0.007281	-0.0564	0.477607
12	0.426682	3.3051	0.000803
13	-0.055901	-0.433	0.33328
14	-0.265259	-2.0547	0.022136
15	-0.214391	-1.6607	0.050999
16	-0.137985	-1.0688	0.144714
17	0.039436	0.3055	0.380533
18	0.005957	0.0461	0.481675
19	0.002235	0.0173	0.493124
20	-0.15174	-1.1754	0.122245
21	-0.215518	-1.6694	0.050124
22	-0.260848	-2.0205	0.0239
23	-0.073796	-0.5716	0.284858
24	0.236133	1.8291	0.036179
25	-0.057526	-0.4456	0.328746
26	-0.275762	-2.136	0.018383
27	-0.19485	-1.5093	0.068235
28	-0.10784	-0.8353	0.203425
29	-0.02139	-0.1657	0.434481
30	-0.003039	-0.0235	0.490648
31	-0.012363	-0.0958	0.462014
32	-0.148007	-1.1465	0.128079
33	-0.160941	-1.2466	0.108687
34	-0.131768	-1.0207	0.155754
35	-0.080011	-0.6198	0.268882
36	0.185483	1.4367	0.077992

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.254372	1.9704	0.026708
2	-0.06374	-0.4937	0.31165
3	0.172282	1.3345	0.093543
4	-0.027591	-0.2137	0.415746
5	0.318227	2.465	0.008291
6	0.15323	1.1869	0.11997
7	0.128436	0.9949	0.1619
8	-0.156189	-1.2098	0.115544
9	-0.12208	-0.9456	0.174065
10	-0.494008	-3.8266	0.000156
11	0.015777	0.1222	0.45157
12	0.411537	3.1878	0.001139
13	-0.077934	-0.6037	0.274167
14	-0.175058	-1.356	0.090091
15	-0.108977	-0.8441	0.200974
16	0.191191	1.481	0.071925
17	-0.000164	-0.0013	0.499497
18	-0.20349	-1.5762	0.060116
19	-0.03327	-0.2577	0.398756
20	-0.089193	-0.6909	0.246151
21	0.022635	0.1753	0.430705
22	0.054443	0.4217	0.337369
23	-0.07424	-0.5751	0.283699
24	-0.075858	-0.5876	0.279506
25	-0.025453	-0.1972	0.422186
26	0.02063	0.1598	0.436789
27	0.049946	0.3869	0.350106
28	-0.167621	-1.2984	0.099561
29	-0.145929	-1.1304	0.131412
30	-0.001323	-0.0102	0.495929
31	0.046333	0.3589	0.360466
32	-0.054639	-0.4232	0.33682
33	-0.082532	-0.6393	0.262534
34	0.104584	0.8101	0.210541
35	-0.098081	-0.7597	0.225194
36	-0.012614	-0.0977	0.461244

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928592d3w3bewkcyr06up/1au8r1259928550.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928592d3w3bewkcyr06up/1au8r1259928550.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928592d3w3bewkcyr06up/2g3x71259928550.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259928592d3w3bewkcyr06up/2g3x71259928550.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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