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Method 1

*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 08:05:01 -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/t1259248500s4tzqr31bpvr3fk.htm/, Retrieved Thu, 26 Nov 2009 16:15:03 +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/t1259248500s4tzqr31bpvr3fk.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 «

108.5 112.3 116.6 115.5 120.1 132.9 128.1 129.3 132.5 131 124.9 120.8 122 122.1 127.4 135.2 137.3 135 136 138.4 134.7 138.4 133.9 133.6 141.2 151.8 155.4 156.6 161.6 160.7 156 159.5 168.7 169.9 169.9 185.9 190.8 195.8 211.9 227.1 251.3 256.7 251.9 251.2 270.3 267.2 243 229.9 187.2 178.2 175.2 192.4 187 184 194.1 212.7 217.5 200.5 205.9 196.5 206.3

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.939167	6.5742	0
2	0.84169	5.8918	0
3	0.717593	5.0232	4e-06
4	0.58283	4.0798	8.3e-05
5	0.426941	2.9886	0.002186
6	0.253036	1.7713	0.041369
7	0.082193	0.5753	0.283844
8	-0.069728	-0.4881	0.313829
9	-0.178327	-1.2483	0.108928
10	-0.278444	-1.9491	0.028509
11	-0.35726	-2.5008	0.007892
12	-0.416491	-2.9154	0.002671
13	-0.425964	-2.9817	0.002227
14	-0.406504	-2.8455	0.003228
15	-0.3729	-2.6103	0.005984
16	-0.335079	-2.3456	0.011546
17	-0.302759	-2.1193	0.019578
18	-0.265033	-1.8552	0.034792
19	-0.22154	-1.5508	0.063695
20	-0.189317	-1.3252	0.095622
21	-0.176743	-1.2372	0.110955
22	-0.166327	-1.1643	0.124972
23	-0.155237	-1.0867	0.141252
24	-0.140231	-0.9816	0.165555
25	-0.116027	-0.8122	0.210305
26	-0.093938	-0.6576	0.256946
27	-0.078982	-0.5529	0.291431
28	-0.056036	-0.3923	0.348287
29	-0.032849	-0.2299	0.409548
30	-0.012525	-0.0877	0.465245
31	0.003096	0.0217	0.491398
32	0.016503	0.1155	0.454253
33	0.029836	0.2089	0.417714
34	0.043853	0.307	0.380083
35	0.058411	0.4089	0.342206
36	0.062882	0.4402	0.330873

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.939167	6.5742	0
2	-0.342011	-2.3941	0.010267
3	-0.211627	-1.4814	0.072453
4	-0.075872	-0.5311	0.298872
5	-0.247296	-1.7311	0.044866
6	-0.224507	-1.5716	0.061245
7	-0.024971	-0.1748	0.430979
8	0.032498	0.2275	0.410497
9	0.230084	1.6106	0.056847
10	-0.212315	-1.4862	0.071816
11	-0.015695	-0.1099	0.456483
12	-0.042043	-0.2943	0.384886
13	0.194926	1.3645	0.089325
14	-0.051283	-0.359	0.360575
15	-0.074808	-0.5237	0.301439
16	-0.068263	-0.4778	0.317444
17	-0.160194	-1.1214	0.133801
18	-0.145821	-1.0207	0.156194
19	0.085475	0.5983	0.276189
20	-0.136481	-0.9554	0.172041
21	0.013914	0.0974	0.461405
22	0.014455	0.1012	0.459908
23	0.000237	0.0017	0.499341
24	-0.008815	-0.0617	0.475525
25	0.171497	1.2005	0.117863
26	-0.026926	-0.1885	0.425638
27	-0.118065	-0.8265	0.206277
28	-0.028315	-0.1982	0.421852
29	-0.153146	-1.072	0.14448
30	-0.109799	-0.7686	0.222912
31	0.043071	0.3015	0.382155
32	-0.032655	-0.2286	0.410071
33	0.042562	0.2979	0.383508
34	0.027593	0.1932	0.423819
35	0.008787	0.0615	0.475601
36	-0.03368	-0.2358	0.407301

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259248500s4tzqr31bpvr3fk/1uud91259247899.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259248500s4tzqr31bpvr3fk/1uud91259247899.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259248500s4tzqr31bpvr3fk/2uic11259247899.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259248500s4tzqr31bpvr3fk/2uic11259247899.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; 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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