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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 02 Dec 2008 09:21:43 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/02/t1228234973lsdidywmegipit7.htm/, Retrieved Sun, 19 May 2024 09:22:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28024, Retrieved Sun, 19 May 2024 09:22:29 +0000

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No (this computation is public)

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Estimated Impact

147

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

-       [(Partial) Autocorrelation Function] [Non Stationary Ti...] [2008-12-02 16:21:43] [b72e060d4eaf5aae1831b15bc791ef7e] [Current]

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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	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28024&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28024&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28024&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.412367	-3.4747	0.000438
2	-0.13267	-1.1179	0.13369
3	0.081856	0.6897	0.246305
4	0.018434	0.1553	0.438501
5	0.046565	0.3924	0.347981
6	-0.023705	-0.1997	0.421126
7	-0.02154	-0.1815	0.428247
8	-0.05322	-0.4484	0.327601
9	0.051173	0.4312	0.333816
10	-0.060675	-0.5113	0.305379
11	0.13281	1.1191	0.13344
12	-0.247896	-2.0888	0.020155
13	0.055088	0.4642	0.32197
14	0.093826	0.7906	0.215908
15	-0.014472	-0.1219	0.451644
16	0.030547	0.2574	0.39881
17	-0.155356	-1.309	0.097369
18	0.127531	1.0746	0.143097
19	-0.043196	-0.364	0.35848

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.412367 & -3.4747 & 0.000438 \tabularnewline
2 & -0.13267 & -1.1179 & 0.13369 \tabularnewline
3 & 0.081856 & 0.6897 & 0.246305 \tabularnewline
4 & 0.018434 & 0.1553 & 0.438501 \tabularnewline
5 & 0.046565 & 0.3924 & 0.347981 \tabularnewline
6 & -0.023705 & -0.1997 & 0.421126 \tabularnewline
7 & -0.02154 & -0.1815 & 0.428247 \tabularnewline
8 & -0.05322 & -0.4484 & 0.327601 \tabularnewline
9 & 0.051173 & 0.4312 & 0.333816 \tabularnewline
10 & -0.060675 & -0.5113 & 0.305379 \tabularnewline
11 & 0.13281 & 1.1191 & 0.13344 \tabularnewline
12 & -0.247896 & -2.0888 & 0.020155 \tabularnewline
13 & 0.055088 & 0.4642 & 0.32197 \tabularnewline
14 & 0.093826 & 0.7906 & 0.215908 \tabularnewline
15 & -0.014472 & -0.1219 & 0.451644 \tabularnewline
16 & 0.030547 & 0.2574 & 0.39881 \tabularnewline
17 & -0.155356 & -1.309 & 0.097369 \tabularnewline
18 & 0.127531 & 1.0746 & 0.143097 \tabularnewline
19 & -0.043196 & -0.364 & 0.35848 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28024&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.412367[/C][C]-3.4747[/C][C]0.000438[/C][/ROW]
[ROW][C]2[/C][C]-0.13267[/C][C]-1.1179[/C][C]0.13369[/C][/ROW]
[ROW][C]3[/C][C]0.081856[/C][C]0.6897[/C][C]0.246305[/C][/ROW]
[ROW][C]4[/C][C]0.018434[/C][C]0.1553[/C][C]0.438501[/C][/ROW]
[ROW][C]5[/C][C]0.046565[/C][C]0.3924[/C][C]0.347981[/C][/ROW]
[ROW][C]6[/C][C]-0.023705[/C][C]-0.1997[/C][C]0.421126[/C][/ROW]
[ROW][C]7[/C][C]-0.02154[/C][C]-0.1815[/C][C]0.428247[/C][/ROW]
[ROW][C]8[/C][C]-0.05322[/C][C]-0.4484[/C][C]0.327601[/C][/ROW]
[ROW][C]9[/C][C]0.051173[/C][C]0.4312[/C][C]0.333816[/C][/ROW]
[ROW][C]10[/C][C]-0.060675[/C][C]-0.5113[/C][C]0.305379[/C][/ROW]
[ROW][C]11[/C][C]0.13281[/C][C]1.1191[/C][C]0.13344[/C][/ROW]
[ROW][C]12[/C][C]-0.247896[/C][C]-2.0888[/C][C]0.020155[/C][/ROW]
[ROW][C]13[/C][C]0.055088[/C][C]0.4642[/C][C]0.32197[/C][/ROW]
[ROW][C]14[/C][C]0.093826[/C][C]0.7906[/C][C]0.215908[/C][/ROW]
[ROW][C]15[/C][C]-0.014472[/C][C]-0.1219[/C][C]0.451644[/C][/ROW]
[ROW][C]16[/C][C]0.030547[/C][C]0.2574[/C][C]0.39881[/C][/ROW]
[ROW][C]17[/C][C]-0.155356[/C][C]-1.309[/C][C]0.097369[/C][/ROW]
[ROW][C]18[/C][C]0.127531[/C][C]1.0746[/C][C]0.143097[/C][/ROW]
[ROW][C]19[/C][C]-0.043196[/C][C]-0.364[/C][C]0.35848[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28024&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28024&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.412367	-3.4747	0.000438
2	-0.13267	-1.1179	0.13369
3	0.081856	0.6897	0.246305
4	0.018434	0.1553	0.438501
5	0.046565	0.3924	0.347981
6	-0.023705	-0.1997	0.421126
7	-0.02154	-0.1815	0.428247
8	-0.05322	-0.4484	0.327601
9	0.051173	0.4312	0.333816
10	-0.060675	-0.5113	0.305379
11	0.13281	1.1191	0.13344
12	-0.247896	-2.0888	0.020155
13	0.055088	0.4642	0.32197
14	0.093826	0.7906	0.215908
15	-0.014472	-0.1219	0.451644
16	0.030547	0.2574	0.39881
17	-0.155356	-1.309	0.097369
18	0.127531	1.0746	0.143097
19	-0.043196	-0.364	0.35848

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.412367	-3.4747	0.000438
2	-0.364738	-3.0733	0.001501
3	-0.199033	-1.6771	0.048962
4	-0.10836	-0.9131	0.18215
5	0.031783	0.2678	0.394812
6	0.05623	0.4738	0.318547
7	0.041646	0.3509	0.363347
8	-0.069168	-0.5828	0.28093
9	-0.047364	-0.3991	0.34551
10	-0.140623	-1.1849	0.120003
11	0.068742	0.5792	0.282135
12	-0.229745	-1.9359	0.028433
13	-0.187829	-1.5827	0.05897
14	-0.126336	-1.0645	0.145348
15	-0.031499	-0.2654	0.39573
16	0.088175	0.743	0.229975
17	-0.081109	-0.6834	0.248279
18	0.016961	0.1429	0.443381
19	-0.093009	-0.7837	0.21791

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.412367 & -3.4747 & 0.000438 \tabularnewline
2 & -0.364738 & -3.0733 & 0.001501 \tabularnewline
3 & -0.199033 & -1.6771 & 0.048962 \tabularnewline
4 & -0.10836 & -0.9131 & 0.18215 \tabularnewline
5 & 0.031783 & 0.2678 & 0.394812 \tabularnewline
6 & 0.05623 & 0.4738 & 0.318547 \tabularnewline
7 & 0.041646 & 0.3509 & 0.363347 \tabularnewline
8 & -0.069168 & -0.5828 & 0.28093 \tabularnewline
9 & -0.047364 & -0.3991 & 0.34551 \tabularnewline
10 & -0.140623 & -1.1849 & 0.120003 \tabularnewline
11 & 0.068742 & 0.5792 & 0.282135 \tabularnewline
12 & -0.229745 & -1.9359 & 0.028433 \tabularnewline
13 & -0.187829 & -1.5827 & 0.05897 \tabularnewline
14 & -0.126336 & -1.0645 & 0.145348 \tabularnewline
15 & -0.031499 & -0.2654 & 0.39573 \tabularnewline
16 & 0.088175 & 0.743 & 0.229975 \tabularnewline
17 & -0.081109 & -0.6834 & 0.248279 \tabularnewline
18 & 0.016961 & 0.1429 & 0.443381 \tabularnewline
19 & -0.093009 & -0.7837 & 0.21791 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28024&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.412367[/C][C]-3.4747[/C][C]0.000438[/C][/ROW]
[ROW][C]2[/C][C]-0.364738[/C][C]-3.0733[/C][C]0.001501[/C][/ROW]
[ROW][C]3[/C][C]-0.199033[/C][C]-1.6771[/C][C]0.048962[/C][/ROW]
[ROW][C]4[/C][C]-0.10836[/C][C]-0.9131[/C][C]0.18215[/C][/ROW]
[ROW][C]5[/C][C]0.031783[/C][C]0.2678[/C][C]0.394812[/C][/ROW]
[ROW][C]6[/C][C]0.05623[/C][C]0.4738[/C][C]0.318547[/C][/ROW]
[ROW][C]7[/C][C]0.041646[/C][C]0.3509[/C][C]0.363347[/C][/ROW]
[ROW][C]8[/C][C]-0.069168[/C][C]-0.5828[/C][C]0.28093[/C][/ROW]
[ROW][C]9[/C][C]-0.047364[/C][C]-0.3991[/C][C]0.34551[/C][/ROW]
[ROW][C]10[/C][C]-0.140623[/C][C]-1.1849[/C][C]0.120003[/C][/ROW]
[ROW][C]11[/C][C]0.068742[/C][C]0.5792[/C][C]0.282135[/C][/ROW]
[ROW][C]12[/C][C]-0.229745[/C][C]-1.9359[/C][C]0.028433[/C][/ROW]
[ROW][C]13[/C][C]-0.187829[/C][C]-1.5827[/C][C]0.05897[/C][/ROW]
[ROW][C]14[/C][C]-0.126336[/C][C]-1.0645[/C][C]0.145348[/C][/ROW]
[ROW][C]15[/C][C]-0.031499[/C][C]-0.2654[/C][C]0.39573[/C][/ROW]
[ROW][C]16[/C][C]0.088175[/C][C]0.743[/C][C]0.229975[/C][/ROW]
[ROW][C]17[/C][C]-0.081109[/C][C]-0.6834[/C][C]0.248279[/C][/ROW]
[ROW][C]18[/C][C]0.016961[/C][C]0.1429[/C][C]0.443381[/C][/ROW]
[ROW][C]19[/C][C]-0.093009[/C][C]-0.7837[/C][C]0.21791[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28024&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28024&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.412367	-3.4747	0.000438
2	-0.364738	-3.0733	0.001501
3	-0.199033	-1.6771	0.048962
4	-0.10836	-0.9131	0.18215
5	0.031783	0.2678	0.394812
6	0.05623	0.4738	0.318547
7	0.041646	0.3509	0.363347
8	-0.069168	-0.5828	0.28093
9	-0.047364	-0.3991	0.34551
10	-0.140623	-1.1849	0.120003
11	0.068742	0.5792	0.282135
12	-0.229745	-1.9359	0.028433
13	-0.187829	-1.5827	0.05897
14	-0.126336	-1.0645	0.145348
15	-0.031499	-0.2654	0.39573
16	0.088175	0.743	0.229975
17	-0.081109	-0.6834	0.248279
18	0.016961	0.1429	0.443381
19	-0.093009	-0.7837	0.21791

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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('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('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')

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