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WS 8: ACF (Lambda 0 + D 1 + d 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: Thu, 26 Nov 2009 12:10:39 -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/t1259262674nlol1j54b1hx1ys.htm/, Retrieved Thu, 26 Nov 2009 20:11:16 +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/t1259262674nlol1j54b1hx1ys.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 «

79.8 83.4 113.6 112.9 104 109.9 99 106.3 128.9 111.1 102.9 130 87 87.5 117.6 103.4 110.8 112.6 102.5 112.4 135.6 105.1 127.7 137 91 90.5 122.4 123.3 124.3 120 118.1 119 142.7 123.6 129.6 151.6 110.4 99.2 130.5 136.2 129.7 128 121.6 135.8 143.8 147.5 136.2 156.6 123.3 104.5 139.8 136.5 112.1 118.5 94.4 102.3 111.4 99.2 87.8 115.8

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.669355	-4.5398	2e-05
2	0.115606	0.7841	0.218508
3	0.221211	1.5003	0.070182
4	-0.249051	-1.6891	0.04898
5	0.05298	0.3593	0.360497
6	0.22152	1.5024	0.069912
7	-0.360675	-2.4462	0.00916
8	0.300979	2.0413	0.023489
9	-0.175028	-1.1871	0.120642
10	0.033989	0.2305	0.409353
11	0.082184	0.5574	0.289979
12	-0.111711	-0.7577	0.226259
13	0.024946	0.1692	0.433193
14	0.065042	0.4411	0.330589
15	-0.04528	-0.3071	0.380075
16	-0.058098	-0.394	0.347687
17	0.109137	0.7402	0.231469
18	-0.038789	-0.2631	0.396832
19	-0.058615	-0.3975	0.346401
20	0.051511	0.3494	0.364204
21	0.109655	0.7437	0.230415
22	-0.318114	-2.1576	0.01811
23	0.366366	2.4848	0.008331
24	-0.200462	-1.3596	0.090292
25	-0.035537	-0.241	0.405304
26	0.139965	0.9493	0.173717
27	-0.068579	-0.4651	0.322017
28	-0.077	-0.5222	0.302004
29	0.20918	1.4187	0.08136
30	-0.254779	-1.728	0.045349
31	0.184578	1.2519	0.108472
32	-0.081145	-0.5503	0.292371
33	-0.030683	-0.2081	0.418033
34	0.117712	0.7984	0.214381
35	-0.076459	-0.5186	0.303273
36	-0.067761	-0.4596	0.323992

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.669355	-4.5398	2e-05
2	-0.602267	-4.0848	8.7e-05
3	-0.164702	-1.1171	0.134884
4	-0.029399	-0.1994	0.421416
5	-0.173497	-1.1767	0.122682
6	0.185508	1.2582	0.107339
7	0.011152	0.0756	0.470018
8	0.092808	0.6295	0.266082
9	-0.148587	-1.0078	0.159419
10	-0.116472	-0.79	0.216804
11	-0.006832	-0.0463	0.481621
12	-0.037811	-0.2564	0.399375
13	-0.061137	-0.4147	0.340162
14	-0.103587	-0.7026	0.242934
15	0.170591	1.157	0.126622
16	-0.081991	-0.5561	0.290422
17	-0.097052	-0.6582	0.256834
18	0.074731	0.5069	0.30734
19	0.059491	0.4035	0.344229
20	-0.134598	-0.9129	0.18303
21	0.174676	1.1847	0.121108
22	-0.124521	-0.8445	0.201368
23	-0.059398	-0.4029	0.344459
24	-0.005186	-0.0352	0.486046
25	-0.042259	-0.2866	0.387847
26	-0.093658	-0.6352	0.264216
27	0.023631	0.1603	0.436684
28	0.062812	0.426	0.336043
29	0.039426	0.2674	0.395178
30	0.049153	0.3334	0.370183
31	-0.025069	-0.17	0.432867
32	-0.155512	-1.0547	0.148527
33	-0.152205	-1.0323	0.153664
34	-0.004026	-0.0273	0.489167
35	0.074322	0.5041	0.308308
36	0.050158	0.3402	0.367631

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259262674nlol1j54b1hx1ys/1iofo1259262638.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259262674nlol1j54b1hx1ys/1iofo1259262638.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259262674nlol1j54b1hx1ys/2pz6d1259262638.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259262674nlol1j54b1hx1ys/2pz6d1259262638.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 0.0 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 0.0 ; par3 = 2 ; 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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