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Paper: autocorrelation function

*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: Sun, 07 Dec 2008 09:35:18 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/07/t1228667777gjybo6hczkusgjo.htm/, Retrieved Sun, 07 Dec 2008 16:36:19 +0000

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/2008/Dec/07/t1228667777gjybo6hczkusgjo.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply] 
test

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

15107 15024 12083 15761 16943 15070 13660 14769 14725 15998 15371 14957 15470 15102 11704 16284 16727 14969 14861 14583 15306 17904 16379 15420 17871 15913 13867 17823 17872 17422 16705 15991 16584 19124 17839 17209 18587 16258 15142 19202 17747 19090 18040 17516 17752 21073 17170 19440 19795 17575 16165 19465 19932 19961 17343 18924 18574 21351 18595 19823 20844 19640 17735 19814 22239 20682 17819 21872 22117 21866

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	0.618216	5.1724	1e-06
2	0.474218	3.9676	8.7e-05
3	0.544136	4.5526	1.1e-05
4	0.599519	5.0159	2e-06
5	0.524804	4.3908	2e-05
6	0.557471	4.6641	7e-06
7	0.428535	3.5854	0.000309
8	0.493686	4.1305	4.9e-05
9	0.409971	3.4301	0.000508
10	0.280574	2.3475	0.010868
11	0.368158	3.0802	0.001478
12	0.573238	4.7961	4e-06
13	0.273734	2.2902	0.012513
14	0.203294	1.7009	0.046702
15	0.211741	1.7716	0.040411
16	0.252512	2.1127	0.019099
17	0.223181	1.8673	0.033026
18	0.20911	1.7495	0.04229
19	0.100275	0.839	0.202173
20	0.168217	1.4074	0.081866
21	0.08747	0.7318	0.233359
22	-0.010548	-0.0882	0.464966
23	0.089502	0.7488	0.228235
24	0.183067	1.5316	0.065058
25	-0.015617	-0.1307	0.44821
26	-0.05319	-0.445	0.32884
27	-0.083257	-0.6966	0.244187
28	-0.046886	-0.3923	0.348022
29	-0.067004	-0.5606	0.288431
30	-0.079477	-0.665	0.254133
31	-0.147043	-1.2303	0.11136
32	-0.088321	-0.7389	0.231205
33	-0.166055	-1.3893	0.08457
34	-0.215429	-1.8024	0.037893
35	-0.126775	-1.0607	0.146242
36	-0.076542	-0.6404	0.262004

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.618216	5.1724	1e-06
2	0.148956	1.2463	0.108412
3	0.33529	2.8052	0.003252
4	0.272562	2.2804	0.012816
5	0.078616	0.6577	0.256429
6	0.227547	1.9038	0.030524
7	-0.186271	-1.5585	0.061817
8	0.200368	1.6764	0.04906
9	-0.232394	-1.9443	0.027937
10	-0.22411	-1.875	0.032479
11	0.193961	1.6228	0.054565
12	0.318734	2.6667	0.004753
13	-0.368531	-3.0833	0.001464
14	0.010383	0.0869	0.465513
15	-0.175301	-1.4667	0.073472
16	0.004364	0.0365	0.485491
17	0.002327	0.0195	0.492262
18	-0.033937	-0.2839	0.388648
19	0.08978	0.7511	0.22754
20	-0.104549	-0.8747	0.192358
21	0.016806	0.1406	0.444291
22	-0.026032	-0.2178	0.414111
23	0.059126	0.4947	0.311187
24	-0.055547	-0.4647	0.321779
25	0.009957	0.0833	0.466924
26	-0.071246	-0.5961	0.276521
27	-0.088058	-0.7367	0.23187
28	-0.048462	-0.4055	0.343187
29	-0.12142	-1.0159	0.156593
30	0.10738	0.8984	0.186025
31	-0.036756	-0.3075	0.379679
32	0.047388	0.3965	0.34648
33	0.008647	0.0723	0.471265
34	-0.007666	-0.0641	0.474522
35	0.010211	0.0854	0.46608
36	-0.003823	-0.032	0.487286

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228667777gjybo6hczkusgjo/1z5dl1228667717.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228667777gjybo6hczkusgjo/1z5dl1228667717.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228667777gjybo6hczkusgjo/2s6d41228667717.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228667777gjybo6hczkusgjo/2s6d41228667717.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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