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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: Thu, 26 Nov 2009 11:27:38 -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/t1259260114ht34bmqf3g9jwd1.htm/, Retrieved Thu, 26 Nov 2009 19:28:36 +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/Nov/26/t1259260114ht34bmqf3g9jwd1.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 «

6.9 6.8 6.7 6.6 6.5 6.5 7.0 7.5 7.6 7.6 7.6 7.8 8.0 8.0 8.0 7.9 7.9 8.0 8.5 9.2 9.4 9.5 9.5 9.6 9.7 9.7 9.6 9.5 9.4 9.3 9.6 10.2 10.2 10.1 9.9 9.8 9.8 9.7 9.5 9.3 9.1 9.0 9.5 10.0 10.2 10.1 10.0 9.9 10.0 9.9 9.7 9.5 9.2 9.0 9.3 9.8 9.8 9.6 9.4 9.3 9.2 9.2 9.0 8.8 8.7 8.7 9.1 9.7 9.8 9.6 9.4 9.4 9.5 9.4 9.3 9.2 9.0 8.9 9.2 9.8 9.9 9.6 9.2 9.1 9.1 9.0 8.9 8.7 8.5 8.3 8.5 8.7 8.4 8.1 7.8 7.7 7.5 7.2 6.8 6.7 6.4 6.3 6.8 7.3 7.1 7.0 6.8 6.6 6.3 6.1 6.1 6.3 6.3 6.0 6.2 6.4 6.8 7.5 7.5 7.6 7.6 7.4 7.3 7.1 6.9 6.8 7.5 7.6 7.8 8.0 8.1 8.2 8.3 8.2 8.0 7.9 7.6 7.6 8.3 8.4 8.4 8.4 8.4 8.6 8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8.0 8.2 8.1 8.1 8.0 7.9 7.9

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	0.960651	12.8885	0
2	0.890796	11.9513	0
3	0.826001	11.082	0
4	0.784581	10.5263	0
5	0.760802	10.2072	0
6	0.737118	9.8895	0
7	0.704514	9.452	0
8	0.671031	9.0028	0
9	0.649015	8.7075	0
10	0.643722	8.6364	0
11	0.646861	8.6786	0
12	0.633949	8.5053	0
13	0.577998	7.7547	0
14	0.50224	6.7383	0
15	0.429951	5.7684	0
16	0.372745	5.0009	1e-06
17	0.329324	4.4183	9e-06
18	0.290144	3.8927	7e-05
19	0.250243	3.3574	0.00048
20	0.217994	2.9247	0.001946
21	0.19856	2.664	0.004212
22	0.194496	2.6094	0.004916
23	0.198045	2.6571	0.004296
24	0.188774	2.5327	0.006087
25	0.147213	1.9751	0.024894
26	0.09269	1.2436	0.107639
27	0.042161	0.5656	0.28617
28	0.00377	0.0506	0.479857
29	-0.022715	-0.3047	0.380455
30	-0.043697	-0.5863	0.279219
31	-0.061918	-0.8307	0.203619
32	-0.072095	-0.9673	0.167357
33	-0.074035	-0.9933	0.160953
34	-0.068514	-0.9192	0.179608
35	-0.059575	-0.7993	0.212591
36	-0.061769	-0.8287	0.20418

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.960651	12.8885	0
2	-0.415488	-5.5744	0
3	0.216897	2.91	0.002035
4	0.187978	2.522	0.006268
5	0.012229	0.1641	0.434931
6	-0.082446	-1.1061	0.135073
7	-0.019025	-0.2552	0.399414
8	0.102293	1.3724	0.085823
9	0.104749	1.4054	0.080819
10	0.086024	1.1541	0.124989
11	0.013243	0.1777	0.429589
12	-0.218285	-2.9286	0.001923
13	-0.440172	-5.9055	0
14	0.124684	1.6728	0.048051
15	-0.058216	-0.781	0.217901
16	-0.142904	-1.9173	0.028394
17	-0.005903	-0.0792	0.46848
18	0.058606	0.7863	0.216367
19	0.02523	0.3385	0.367694
20	0.097669	1.3104	0.095871
21	0.033157	0.4449	0.328481
22	0.069674	0.9348	0.175579
23	0.002726	0.0366	0.485433
24	-0.069174	-0.9281	0.177307
25	-0.120875	-1.6217	0.053308
26	0.089391	1.1993	0.115994
27	-0.044462	-0.5965	0.275789
28	-0.049123	-0.6591	0.25535
29	0.037655	0.5052	0.307022
30	0.051828	0.6954	0.243866
31	0.01181	0.1584	0.437141
32	-0.003913	-0.0525	0.479097
33	-0.03247	-0.4356	0.331812
34	-0.053018	-0.7113	0.238907
35	-0.022592	-0.3031	0.381079
36	-0.047389	-0.6358	0.26286

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259260114ht34bmqf3g9jwd1/1rqou1259260057.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259260114ht34bmqf3g9jwd1/1rqou1259260057.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259260114ht34bmqf3g9jwd1/2adjh1259260057.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259260114ht34bmqf3g9jwd1/2adjh1259260057.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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