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(Partial) Autocorrelation Function

*Unverified author*

R Software Module: rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 21 Dec 2008 09:05:06 -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/21/t1229875541vg2g2jk4bkumg48.htm/, Retrieved Sun, 21 Dec 2008 17:05:43 +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/2008/Dec/21/t1229875541vg2g2jk4bkumg48.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},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

67.8 66.9 71.5 75.9 71.9 70.7 73.5 76.1 82.5 87.1 83.2 86.1 85.9 77.4 74.4 69.9 73.8 69.2 69.7 71 71.2 75.8 73 66.4 58.6 55.5 52.6 54.9 54.6 51.2 50.9 49.6 53.4 52 47.5 42.1 44.5 43.2 51.4 59.4 60.3 61.4 68.8 73.6 81.8 79.6 85.8 88.1 89.1 95 96.2 84.2 96.9 103.1 99.3 103.5 112.4 111.1 113.7 92 93 98.4 92.6 94.6 99.5 97.6 91.3 93.6 93.1 78.4 70.2 69.3 71.1 73.5 85.9 91.5 91.8 88.3 91.3 94 99.3 96.7 88 96.7 106.8 114.3 105.7 90.1 91.6 97.7 100.8 104.6 95.9 102.7 104 107.9 113.8 113.8 123.1 125.1 137.6 134 140.3 152.1 150.6 167.3 153.2 142 154.4 158.5 180.9 181.3 172.4 192 199.3 215.4 214.3 201.5 190.5 196 215.7 209.4 214.1 237.8 239 237.8 251.5 248.8 215.4 201.2 203.1 214.2 188.9 203 213.3 228.5 228.2 240.9 258.8 248.5 269.2 289.6 323.4 317.2 322.8 340.9 368.2 388.5 441.2 474.3 483.9 417.9 365.9 263 199.4

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	-0.372854	-4.612	4e-06
2	-0.11203	-1.3857	0.083922
3	0.018984	0.2348	0.407331
4	-0.040083	-0.4958	0.310374
5	0.070132	0.8675	0.193518
6	0.008939	0.1106	0.456054
7	-0.039906	-0.4936	0.311143
8	0.008742	0.1081	0.457015
9	-0.14165	-1.7521	0.040879
10	0.125624	1.5539	0.061139
11	0.123768	1.5309	0.063926
12	-0.010032	-0.1241	0.450705
13	-0.181875	-2.2497	0.012948
14	0.08962	1.1085	0.134685
15	-0.003877	-0.048	0.480906
16	-0.049769	-0.6156	0.269532
17	0.049826	0.6163	0.269302
18	-0.020025	-0.2477	0.402353
19	-0.019529	-0.2416	0.404721
20	0.067131	0.8304	0.203813
21	-0.137921	-1.706	0.04502
22	0.182534	2.2578	0.012686
23	-0.137393	-1.6995	0.045633
24	-0.055077	-0.6813	0.248368
25	0.204627	2.5311	0.00619
26	-0.081436	-1.0073	0.157687
27	-0.067372	-0.8333	0.202974
28	0.094183	1.165	0.12292
29	-0.102319	-1.2656	0.103787
30	0.072184	0.8929	0.186666
31	0.012946	0.1601	0.436494
32	-0.044362	-0.5487	0.291995
33	0.017324	0.2143	0.415305
34	-0.128645	-1.5913	0.056808
35	0.097038	1.2003	0.115941
36	0.100089	1.238	0.1088

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.372854	-4.612	4e-06
2	-0.291587	-3.6067	0.00021
3	-0.182395	-2.2561	0.012741
4	-0.184415	-2.2811	0.011962
5	-0.060301	-0.7459	0.228442
6	-0.013978	-0.1729	0.431482
7	-0.031277	-0.3869	0.349695
8	-0.014913	-0.1845	0.426946
9	-0.203048	-2.5116	0.006529
10	-0.066134	-0.818	0.207304
11	0.110097	1.3618	0.087628
12	0.176998	2.1893	0.015043
13	-0.058175	-0.7196	0.236438
14	0.036444	0.4508	0.32639
15	0.002923	0.0362	0.485601
16	-0.095492	-1.1812	0.119683
17	-0.05442	-0.6731	0.250939
18	-0.041665	-0.5154	0.30352
19	-0.012549	-0.1552	0.438426
20	0.093877	1.1612	0.123686
21	-0.126377	-1.5632	0.060036
22	0.016051	0.1985	0.421442
23	-0.108492	-1.342	0.090796
24	-0.141258	-1.7473	0.041298
25	0.102538	1.2683	0.103304
26	0.075291	0.9313	0.176582
27	0.009452	0.1169	0.453538
28	0.092689	1.1465	0.126688
29	-0.06028	-0.7456	0.228522
30	-0.049101	-0.6073	0.272261
31	0.028822	0.3565	0.360978
32	-0.013196	-0.1632	0.435277
33	0.032805	0.4058	0.342739
34	-0.1414	-1.749	0.041146
35	-0.03244	-0.4013	0.344395
36	-0.01029	-0.1273	0.449442

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229875541vg2g2jk4bkumg48/1vvyf1229875504.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229875541vg2g2jk4bkumg48/1vvyf1229875504.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229875541vg2g2jk4bkumg48/24kt41229875504.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229875541vg2g2jk4bkumg48/24kt41229875504.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = -0.1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = -0.1 ; par3 = 2 ; 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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