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tutorial 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: Mon, 13 Dec 2010 19:20:33 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/13/t1292267978xq6vorc16ijc52t.htm/, Retrieved Mon, 13 Dec 2010 20:19:38 +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/2010/Dec/13/t1292267978xq6vorc16ijc52t.htm/},
    year = {2010},
}
@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 = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

workshop 6

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1,2998 1,3146 1,3225 1,3321 1,3339 1,3496 1,3647 1,3674 1,3647 1,3481 1,3612 1,3626 1,3711 1,37 1,377 1,3945 1,3917 1,4084 1,4244 1,4014 1,4018 1,3926 1,3857 1,3857 1,3803 1,3912 1,4031 1,3934 1,4016 1,3861 1,3859 1,3896 1,4089 1,4101 1,3958 1,3833 1,3936 1,3874 1,397 1,3856 1,378 1,3705 1,3726 1,3648 1,3611 1,346 1,3477 1,3412 1,3323 1,3364 1,312 1,3074 1,306 1,3078 1,2989 1,285 1,2801 1,2725 1,2715 1,2697 1,2744 1,2874 1,2834 1,2818 1,28 1,268 1,27 1,2713 1,2693 1,2613 1,2611 1,2704 1,2711 1,2836 1,288 1,286 1,282 1,2799 1,279 1,3016 1,3133 1,3253 1,3176 1,3184 1,3206 1,3221 1,3073 1,3028 1,3069 1,2992 1,3033 1,2931 1,2897 1,285 1,2817 1,2844 1,2957 1,3 1,2828 1,2703 1,2569 1,2572 1,2637 1,266 1,2567 1,2579 1,2531 1,2548 1,2328 1,2271 1,2198 1,2339 1,2294 1,2262 1,2271 1,2258 1,2391 1,2372 1,2363 1,2277 1,2258 1,2249 1,2127 1,2045 1,201 1,1942 1,1959 1,206 1,2268 1,2218 1,2155 1 etc...

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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.990176	21.9408	0
2	0.981015	21.7378	0
3	0.972838	21.5567	0
4	0.965112	21.3854	0
5	0.958127	21.2307	0
6	0.949942	21.0493	0
7	0.941492	20.8621	0
8	0.932852	20.6706	0
9	0.923266	20.4582	0
10	0.913187	20.2349	0
11	0.902438	19.9967	0
12	0.892361	19.7734	0
13	0.881145	19.5249	0
14	0.869388	19.2644	0
15	0.857295	18.9964	0
16	0.845578	18.7368	0
17	0.834653	18.4947	0
18	0.824232	18.2638	0
19	0.813963	18.0362	0
20	0.802938	17.7919	0
21	0.791685	17.5426	0
22	0.780115	17.2862	0
23	0.768375	17.0261	0
24	0.756937	16.7726	0
25	0.746513	16.5416	0
26	0.736408	16.3177	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.990176	21.9408	0
2	0.028971	0.642	0.260601
3	0.046889	1.039	0.149659
4	0.022419	0.4968	0.309783
5	0.038508	0.8533	0.196958
6	-0.059854	-1.3263	0.092683
7	-0.017272	-0.3827	0.35105
8	-0.019268	-0.4269	0.334805
9	-0.056911	-1.2611	0.103941
10	-0.040713	-0.9021	0.18371
11	-0.045973	-1.0187	0.154425
12	0.021103	0.4676	0.320136
13	-0.069953	-1.5501	0.060886
14	-0.033588	-0.7443	0.228536
15	-0.029111	-0.6451	0.259597
16	0.0141	0.3124	0.377419
17	0.028711	0.6362	0.262476
18	0.03282	0.7272	0.233715
19	0.018256	0.4045	0.343
20	-0.032309	-0.7159	0.237189
21	-0.008992	-0.1993	0.421072
22	-0.0241	-0.534	0.296788
23	-0.01442	-0.3195	0.374733
24	-0.003157	-0.0699	0.472132
25	0.045942	1.018	0.154587
26	0.010902	0.2416	0.404603

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292267978xq6vorc16ijc52t/121yx1292268030.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292267978xq6vorc16ijc52t/121yx1292268030.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292267978xq6vorc16ijc52t/2vbf01292268030.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292267978xq6vorc16ijc52t/2vbf01292268030.ps (open in new window)

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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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