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WS 9 (P)ACF 2

*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 03:02:05 -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/t1259921014zj9tlgnll8u2g2w.htm/, Retrieved Fri, 04 Dec 2009 11:03:36 +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/t1259921014zj9tlgnll8u2g2w.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 «

98.8 100.5 110.4 96.4 101.9 106.2 81 94.7 101 109.4 102.3 90.7 96.2 96.1 106 103.1 102 104.7 86 92.1 106.9 112.6 101.7 92 97.4 97 105.4 102.7 98.1 104.5 87.4 89.9 109.8 111.7 98.6 96.9 95.1 97 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3

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	0.011365	0.1042	0.458644
2	0.158487	1.4526	0.075036
3	0.325112	2.9797	0.001886
4	-0.048166	-0.4415	0.33001
5	0.163633	1.4997	0.068718
6	0.159183	1.4589	0.074156
7	-0.171681	-1.5735	0.059683
8	0.010163	0.0931	0.463003
9	0.102843	0.9426	0.174301
10	-0.193869	-1.7768	0.039608
11	0.005393	0.0494	0.480348
12	-0.013936	-0.1277	0.449334
13	-0.15033	-1.3778	0.085963
14	0.011299	0.1036	0.458882
15	0.028021	0.2568	0.398975
16	-0.208438	-1.9104	0.029749
17	0.063268	0.5799	0.28178
18	0.033047	0.3029	0.381364
19	-0.161705	-1.482	0.071035
20	0.068285	0.6258	0.266557
21	0.029543	0.2708	0.393618
22	-0.20456	-1.8748	0.032146
23	0.280195	2.568	0.005999
24	-0.192466	-1.764	0.040685
25	-0.110532	-1.013	0.156974
26	0.158139	1.4494	0.075479
27	-0.129719	-1.1889	0.118916
28	-0.049121	-0.4502	0.326862
29	-0.002291	-0.021	0.491647
30	-0.220606	-2.0219	0.023186
31	-0.046484	-0.426	0.335588
32	0.021756	0.1994	0.421217
33	-0.261841	-2.3998	0.009307
34	-0.036364	-0.3333	0.369877
35	-0.036307	-0.3328	0.370074
36	-0.073275	-0.6716	0.251848

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.011365	0.1042	0.458644
2	0.158378	1.4516	0.075174
3	0.330118	3.0256	0.001646
4	-0.072108	-0.6609	0.255248
5	0.066672	0.6111	0.271405
6	0.088596	0.812	0.209543
7	-0.19203	-1.76	0.041025
8	-0.127806	-1.1714	0.122382
9	0.120008	1.0999	0.137261
10	-0.08956	-0.8208	0.207033
11	-0.063872	-0.5854	0.279926
12	0.015643	0.1434	0.443169
13	0.005429	0.0498	0.480216
14	-0.052085	-0.4774	0.31717
15	0.070975	0.6505	0.258573
16	-0.108815	-0.9973	0.160739
17	0.012071	0.1106	0.456084
18	0.066667	0.611	0.271421
19	-0.062617	-0.5739	0.283788
20	-0.046198	-0.4234	0.336538
21	0.096485	0.8843	0.189529
22	-0.148426	-1.3604	0.088679
23	0.213067	1.9528	0.027087
24	-0.216097	-1.9806	0.025457
25	-0.026621	-0.244	0.403918
26	0.009545	0.0875	0.46525
27	0.044853	0.4111	0.341029
28	-0.096312	-0.8827	0.189956
29	-0.087291	-0.8	0.212974
30	-0.119273	-1.0932	0.138726
31	0.033292	0.3051	0.380514
32	-0.080913	-0.7416	0.230206
33	-0.070865	-0.6495	0.258897
34	-0.029781	-0.273	0.392781
35	0.024031	0.2202	0.413107
36	0.047896	0.439	0.330904

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259921014zj9tlgnll8u2g2w/1x8181259920923.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259921014zj9tlgnll8u2g2w/1x8181259920923.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259921014zj9tlgnll8u2g2w/2ngly1259920923.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259921014zj9tlgnll8u2g2w/2ngly1259920923.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = 0.0 ; par3 = 0 ; 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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