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Review workshop 5

*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: Mon, 07 Dec 2009 06:35:00 -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/07/t1260193911w4p0t81jdx41y9j.htm/, Retrieved Mon, 07 Dec 2009 14:51:53 +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/07/t1260193911w4p0t81jdx41y9j.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 «

17 14 15 16 16 15 13 12 13 13 12 10 14 14 15 16 16 15 15 13 15 15 15 13 16 16 14 16 15 14 15 15 14 13 12 13 12 9 10 8 11 8 8 8 4 6 8 10 5 6 5 9 8 6 9 11 11 8 11 11 13

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.273759	-2.1205	0.019052
2	-0.106841	-0.8276	0.205591
3	-0.038567	-0.2987	0.383085
4	0.142151	1.1011	0.137626
5	0.071261	0.552	0.291504
6	-0.047808	-0.3703	0.356224
7	-0.033005	-0.2557	0.399547
8	-0.050574	-0.3917	0.348317
9	0.12827	0.9936	0.16221
10	-0.070509	-0.5462	0.29349
11	-0.003087	-0.0239	0.490501
12	0.059003	0.457	0.324647
13	-0.000501	-0.0039	0.498458
14	-0.216519	-1.6772	0.049358
15	0.100307	0.777	0.220114
16	0.137681	1.0665	0.145241
17	-0.256861	-1.9896	0.025598
18	0.121765	0.9432	0.174683
19	-0.139896	-1.0836	0.141432
20	0.09309	0.7211	0.236832
21	-0.150831	-1.1683	0.123647
22	0.102622	0.7949	0.214901
23	-0.103574	-0.8023	0.212778
24	-0.089943	-0.6967	0.244341
25	0.070239	0.5441	0.294206
26	-0.080161	-0.6209	0.2685
27	0.095867	0.7426	0.230317
28	0.011015	0.0853	0.466145
29	-0.136498	-1.0573	0.147304
30	0.005292	0.041	0.483719
31	0.192866	1.4939	0.070217
32	-0.085714	-0.6639	0.254637
33	0.012939	0.1002	0.460249
34	0.03118	0.2415	0.404987
35	0.01306	0.1012	0.459881
36	0.006795	0.0526	0.479098

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.273759	-2.1205	0.019052
2	-0.196513	-1.5222	0.066609
3	-0.143209	-1.1093	0.135865
4	0.072576	0.5622	0.288046
5	0.137294	1.0635	0.145915
6	0.063965	0.4955	0.311038
7	0.019281	0.1494	0.440889
8	-0.079408	-0.6151	0.270411
9	0.054603	0.423	0.336921
10	-0.049202	-0.3811	0.352232
11	-0.010199	-0.079	0.468648
12	0.084287	0.6529	0.258163
13	0.034914	0.2704	0.393873
14	-0.233297	-1.8071	0.037879
15	-0.042371	-0.3282	0.371951
16	0.104657	0.8107	0.210379
17	-0.231487	-1.7931	0.039
18	0.08163	0.6323	0.264797
19	-0.102932	-0.7973	0.214208
20	-0.02841	-0.2201	0.413286
21	-0.189488	-1.4678	0.073695
22	0.035786	0.2772	0.391292
23	-0.058781	-0.4553	0.325262
24	-0.200221	-1.5509	0.063092
25	-0.024902	-0.1929	0.423848
26	-0.039431	-0.3054	0.380546
27	0.003342	0.0259	0.489715
28	0.046398	0.3594	0.360279
29	-0.071188	-0.5514	0.291697
30	0.000771	0.006	0.497627
31	0.043232	0.3349	0.369445
32	0.001739	0.0135	0.494648
33	0.097367	0.7542	0.22684
34	0.028945	0.2242	0.411679
35	0.03728	0.2888	0.386876
36	-0.035392	-0.2741	0.392457

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260193911w4p0t81jdx41y9j/1uxop1260192895.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260193911w4p0t81jdx41y9j/1uxop1260192895.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260193911w4p0t81jdx41y9j/2f0a41260192895.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260193911w4p0t81jdx41y9j/2f0a41260192895.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 2.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 2.0 ; par3 = 1 ; 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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