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Workshop 8, methode 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 13:14:44 -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/t1259266541c3infeseh9v78g8.htm/, Retrieved Thu, 26 Nov 2009 21:15:43 +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/t1259266541c3infeseh9v78g8.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 «

25.6 23.7 22 21.3 20.7 20.4 20.3 20.4 19.8 19.5 23.1 23.5 23.5 22.9 21.9 21.5 20.5 20.2 19.4 19.2 18.8 18.8 22.6 23.3 23 21.4 19.9 18.8 18.6 18.4 18.6 19.9 19.2 18.4 21.1 20.5 19.1 18.1 17 17.1 17.4 16.8 15.3 14.3 13.4 15.3 22.1 23.7 22.2 19.5 16.6 17.3 19.8 21.2 21.5 20.6 19.1 19.6 23.5 24

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	0.872386	6.0441	0
2	0.599051	4.1503	6.8e-05
3	0.325993	2.2585	0.014247
4	0.178007	1.2333	0.111741
5	0.182384	1.2636	0.106239
6	0.264897	1.8353	0.036334
7	0.310993	2.1546	0.018119
8	0.246587	1.7084	0.047011
9	0.073704	0.5106	0.305972
10	-0.142354	-0.9863	0.164476
11	-0.310378	-2.1504	0.018296
12	-0.371414	-2.5732	0.00661
13	-0.312545	-2.1654	0.01768
14	-0.193944	-1.3437	0.092684
15	-0.093012	-0.6444	0.261191
16	-0.06577	-0.4557	0.325343
17	-0.102183	-0.7079	0.241201
18	-0.174757	-1.2108	0.115959
19	-0.230655	-1.598	0.0583
20	-0.223979	-1.5518	0.063643
21	-0.16583	-1.1489	0.128144
22	-0.078725	-0.5454	0.293995
23	-0.005624	-0.039	0.48454
24	0.019232	0.1332	0.447279
25	-0.01437	-0.0996	0.460554
26	-0.079082	-0.5479	0.29315
27	-0.145724	-1.0096	0.158873
28	-0.170082	-1.1784	0.122231
29	-0.147558	-1.0223	0.155879
30	-0.091969	-0.6372	0.263518
31	-0.030816	-0.2135	0.41592
32	-0.004336	-0.03	0.488081
33	-0.016523	-0.1145	0.45467
34	-0.048325	-0.3348	0.369615
35	-0.067566	-0.4681	0.320913
36	-0.062543	-0.4333	0.333364

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.872386	6.0441	0
2	-0.678018	-4.6974	1.1e-05
3	0.314084	2.176	0.017253
4	0.334881	2.3201	0.012316
5	0.052411	0.3631	0.359056
6	-0.149421	-1.0352	0.152877
7	-0.175773	-1.2178	0.114628
8	-0.100555	-0.6967	0.244686
9	-0.119562	-0.8284	0.205786
10	-0.150093	-1.0399	0.151804
11	-0.035204	-0.2439	0.404173
12	0.002417	0.0167	0.493354
13	0.169171	1.172	0.123481
14	-0.048594	-0.3367	0.368916
15	0.020407	0.1414	0.44408
16	0.02132	0.1477	0.441595
17	0.14957	1.0363	0.152638
18	-0.233067	-1.6147	0.056461
19	-0.072798	-0.5044	0.308157
20	0.103643	0.7181	0.2381
21	-0.184568	-1.2787	0.103571
22	0.053265	0.369	0.356864
23	-0.032944	-0.2282	0.410213
24	-0.037133	-0.2573	0.399037
25	-0.026386	-0.1828	0.427859
26	0.017958	0.1244	0.450754
27	-0.129985	-0.9006	0.186158
28	0.105981	0.7343	0.233182
29	-0.043316	-0.3001	0.382697
30	-0.030155	-0.2089	0.417697
31	0.046613	0.3229	0.374069
32	-0.102509	-0.7102	0.240506
33	0.111294	0.7711	0.222222
34	0.00852	0.059	0.476588
35	-0.011794	-0.0817	0.467608
36	-0.06229	-0.4316	0.333996

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266541c3infeseh9v78g8/1h5gx1259266483.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266541c3infeseh9v78g8/1h5gx1259266483.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266541c3infeseh9v78g8/2bhfi1259266483.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266541c3infeseh9v78g8/2bhfi1259266483.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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