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*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: Wed, 16 Dec 2009 09:40:14 -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/16/t1260981649xti3ph30e0094pi.htm/, Retrieved Wed, 16 Dec 2009 17:40:51 +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/16/t1260981649xti3ph30e0094pi.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 «

19915 19843 19761 20858 21968 23061 22661 22269 21857 21568 21274 20987 19683 19381 19071 20772 22485 24181 23479 22782 22067 21489 20903 20330 19736 19483 19242 20334 21423 22523 21986 21462 20908 20575 20237 19904 19610 19251 18941 20450 21946 23409 22741 22069 21539 21189 20960 20704 19697 19598 19456 20316 21083 22158 21469 20892 20578 20233 19947 20049

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	0.875934	6.0687	0
2	0.654299	4.5331	1.9e-05
3	0.437449	3.0307	0.001962
4	0.27272	1.8895	0.032439
5	0.141849	0.9828	0.165327
6	0.02692	0.1865	0.426416
7	-0.082722	-0.5731	0.284621
8	-0.18457	-1.2787	0.103568
9	-0.288955	-2.0019	0.02548
10	-0.437465	-3.0308	0.001961
11	-0.597859	-4.1421	6.9e-05
12	-0.691728	-4.7924	8e-06
13	-0.656982	-4.5517	1.8e-05
14	-0.549845	-3.8094	0.000198
15	-0.431586	-2.9901	0.002195
16	-0.345212	-2.3917	0.010368
17	-0.271231	-1.8791	0.033152
18	-0.18245	-1.264	0.106158
19	-0.06714	-0.4652	0.321959
20	0.036444	0.2525	0.400869
21	0.129248	0.8955	0.187506
22	0.230499	1.5969	0.058421
23	0.338661	2.3463	0.011568
24	0.400833	2.7771	0.003901
25	0.399055	2.7647	0.004029
26	0.335361	2.3235	0.012219
27	0.256283	1.7756	0.041071
28	0.210435	1.4579	0.075685
29	0.185504	1.2852	0.102443
30	0.146546	1.0153	0.157527
31	0.083126	0.5759	0.283682
32	0.031085	0.2154	0.415199
33	-0.015914	-0.1103	0.456332
34	-0.062829	-0.4353	0.33265
35	-0.120345	-0.8338	0.20427
36	-0.165987	-1.15	0.127922

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.875934	6.0687	0
2	-0.485362	-3.3627	0.000762
3	0.063512	0.44	0.330947
4	0.034343	0.2379	0.406472
5	-0.127505	-0.8834	0.190716
6	-0.070384	-0.4876	0.314015
7	-0.094982	-0.6581	0.256823
8	-0.089622	-0.6209	0.268795
9	-0.17928	-1.2421	0.11012
10	-0.406721	-2.8178	0.0035
11	-0.162379	-1.125	0.133093
12	0.036141	0.2504	0.401675
13	0.168801	1.1695	0.123992
14	-0.147929	-1.0249	0.155279
15	-0.080662	-0.5588	0.289433
16	-0.124043	-0.8594	0.197197
17	-0.010422	-0.0722	0.471369
18	0.012054	0.0835	0.466896
19	0.090464	0.6268	0.266895
20	-0.126047	-0.8733	0.19343
21	-0.04299	-0.2978	0.383555
22	-0.088991	-0.6166	0.270222
23	0.01101	0.0763	0.469758
24	-0.132877	-0.9206	0.180932
25	0.04153	0.2877	0.387398
26	-0.201813	-1.3982	0.08424
27	-0.067182	-0.4654	0.321858
28	-0.024369	-0.1688	0.433319
29	-0.000734	-0.0051	0.497982
30	-0.064638	-0.4478	0.328147
31	-0.010507	-0.0728	0.471136
32	0.009804	0.0679	0.473065
33	-0.034015	-0.2357	0.407349
34	-0.024861	-0.1722	0.431987
35	0.011324	0.0785	0.468897
36	-0.022271	-0.1543	0.43901

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260981649xti3ph30e0094pi/10d4z1260981611.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260981649xti3ph30e0094pi/10d4z1260981611.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260981649xti3ph30e0094pi/2gyey1260981611.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260981649xti3ph30e0094pi/2gyey1260981611.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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