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workshop 8

*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, 28 Nov 2009 01:54:14 -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/28/t1259398497gy1ufh3cvxzybz2.htm/, Retrieved Sat, 28 Nov 2009 09:54:59 +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/28/t1259398497gy1ufh3cvxzybz2.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 «

130 136.7 138.1 139.5 140.4 144.6 151.4 147.9 141.5 143.8 143.6 150.5 150.1 154.9 162.1 176.7 186.6 194.8 196.3 228.8 267.2 237.2 254.7 258.2 257.9 269.6 266.9 269.6 253.9 258.6 274.2 301.5 304.5 285.1 287.7 265.5 264.1 276.1 258.9 239.1 250.1 276.8 297.6 295.4 283 275.8 279.7 254.6 234.6 176.9 148.1 122.7 124.9 121.6 128.4 144.5 151.8 167.1 173.8 203.7 199.8

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	0 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.220798	1.5297	0.066323
2	-0.030553	-0.2117	0.416627
3	0.103615	0.7179	0.238161
4	0.183743	1.273	0.104573
5	0.150256	1.041	0.151545
6	-0.08204	-0.5684	0.286209
7	-0.133889	-0.9276	0.179126
8	-0.240114	-1.6636	0.051359
9	-0.193472	-1.3404	0.093211
10	-0.071987	-0.4987	0.31012
11	0.076486	0.5299	0.299309
12	-0.181056	-1.2544	0.107886
13	-0.168017	-1.1641	0.125077
14	0.107142	0.7423	0.230761
15	0.062434	0.4326	0.333638
16	-0.063226	-0.438	0.33166
17	0.097089	0.6727	0.252197
18	0.081489	0.5646	0.287497
19	-0.049045	-0.3398	0.367748
20	-0.045231	-0.3134	0.37768
21	0.093769	0.6496	0.259508
22	0.097694	0.6768	0.250878
23	-0.054526	-0.3778	0.353635
24	-0.195211	-1.3525	0.091283
25	-0.017637	-0.1222	0.451628
26	0.093331	0.6466	0.260481
27	-0.109388	-0.7579	0.226119
28	-0.046214	-0.3202	0.375111
29	-0.182165	-1.2621	0.10651
30	-0.133677	-0.9261	0.179504
31	-0.08941	-0.6194	0.269275
32	-0.055327	-0.3833	0.351589
33	-0.11045	-0.7652	0.223944
34	-0.124688	-0.8639	0.195979
35	-0.007327	-0.0508	0.479864
36	0.028921	0.2004	0.421019

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.220798	1.5297	0.066323
2	-0.083369	-0.5776	0.283117
3	0.136911	0.9485	0.173802
4	0.133772	0.9268	0.179333
5	0.100638	0.6972	0.244507
6	-0.138869	-0.9621	0.170407
7	-0.112412	-0.7788	0.219957
8	-0.286401	-1.9842	0.026481
9	-0.155739	-1.079	0.142992
10	-0.017438	-0.1208	0.452172
11	0.24284	1.6824	0.049489
12	-0.094875	-0.6573	0.25706
13	0.038328	0.2655	0.395864
14	0.09679	0.6706	0.25285
15	-0.093644	-0.6488	0.259785
16	-0.196411	-1.3608	0.08997
17	0.160862	1.1145	0.13531
18	-0.03969	-0.275	0.392256
19	-0.059235	-0.4104	0.341671
20	-0.019151	-0.1327	0.4475
21	0.109346	0.7576	0.226205
22	-0.032413	-0.2246	0.411636
23	0.05006	0.3468	0.36512
24	-0.231687	-1.6052	0.057508
25	-0.022363	-0.1549	0.438762
26	0.085106	0.5896	0.279102
27	-0.065863	-0.4563	0.325111
28	-0.056338	-0.3903	0.349012
29	-0.121841	-0.8441	0.20139
30	-0.025218	-0.1747	0.431018
31	-0.203998	-1.4133	0.082004
32	-0.114681	-0.7945	0.215397
33	-0.066677	-0.462	0.323102
34	0.064662	0.448	0.328087
35	0.076712	0.5315	0.298771
36	-0.005401	-0.0374	0.485154

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259398497gy1ufh3cvxzybz2/17dp31259398451.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259398497gy1ufh3cvxzybz2/17dp31259398451.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259398497gy1ufh3cvxzybz2/29omu1259398451.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259398497gy1ufh3cvxzybz2/29omu1259398451.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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