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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 07 Dec 2008 06:30:19 -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/07/t12286566478rx9engstscm0eh.htm/, Retrieved Sun, 19 May 2024 12:19:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29963, Retrieved Sun, 19 May 2024 12:19:44 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

266

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Variance Reduction Matrix] [] [2008-11-30 18:13:06] [b745fd448f60064800b631a75a630267]
F RM D    [Standard Deviation-Mean Plot] [SMP Q1] [2008-12-07 13:12:10] [e5d91604aae608e98a8ea24759233f66]
F RM        [Variance Reduction Matrix] [VRM Q1] [2008-12-07 13:13:31] [e5d91604aae608e98a8ea24759233f66]
F RMP         [(Partial) Autocorrelation Function] [ACF Q2] [2008-12-07 13:20:49] [e5d91604aae608e98a8ea24759233f66]
F   P             [(Partial) Autocorrelation Function] [ACF Q3] [2008-12-07 13:30:19] [55ca0ca4a201c9689dcf5fae352c92eb] [Current]

Feedback Forum

2008-12-15 20:12:45 [Jeroen Aerts] [reply] 
Correct.

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Dataseries X:

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Boxplots

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=29963&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=29963&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29963&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	-0.179891	-1.9624	0.026026
2	0.069612	0.7594	0.224563
3	-0.086235	-0.9407	0.17438
4	-0.055653	-0.6071	0.272469
5	-0.085561	-0.9334	0.176261
6	0.027065	0.2952	0.384161
7	0.089087	0.9718	0.166556
8	0.030503	0.3327	0.369955
9	0.003628	0.0396	0.48425
10	-0.035916	-0.3918	0.347953
11	-0.078572	-0.8571	0.19655
12	-0.128894	-1.4061	0.081155
13	0.007338	0.08	0.468167
14	-0.059765	-0.652	0.257842
15	0.073565	0.8025	0.211933
16	0.012039	0.1313	0.447869
17	-0.063582	-0.6936	0.244645
18	-0.05824	-0.6353	0.263218
19	0.045312	0.4943	0.311004
20	-0.030714	-0.335	0.36909

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.179891 & -1.9624 & 0.026026 \tabularnewline
2 & 0.069612 & 0.7594 & 0.224563 \tabularnewline
3 & -0.086235 & -0.9407 & 0.17438 \tabularnewline
4 & -0.055653 & -0.6071 & 0.272469 \tabularnewline
5 & -0.085561 & -0.9334 & 0.176261 \tabularnewline
6 & 0.027065 & 0.2952 & 0.384161 \tabularnewline
7 & 0.089087 & 0.9718 & 0.166556 \tabularnewline
8 & 0.030503 & 0.3327 & 0.369955 \tabularnewline
9 & 0.003628 & 0.0396 & 0.48425 \tabularnewline
10 & -0.035916 & -0.3918 & 0.347953 \tabularnewline
11 & -0.078572 & -0.8571 & 0.19655 \tabularnewline
12 & -0.128894 & -1.4061 & 0.081155 \tabularnewline
13 & 0.007338 & 0.08 & 0.468167 \tabularnewline
14 & -0.059765 & -0.652 & 0.257842 \tabularnewline
15 & 0.073565 & 0.8025 & 0.211933 \tabularnewline
16 & 0.012039 & 0.1313 & 0.447869 \tabularnewline
17 & -0.063582 & -0.6936 & 0.244645 \tabularnewline
18 & -0.05824 & -0.6353 & 0.263218 \tabularnewline
19 & 0.045312 & 0.4943 & 0.311004 \tabularnewline
20 & -0.030714 & -0.335 & 0.36909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29963&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]-0.179891[/C][C]-1.9624[/C][C]0.026026[/C][/ROW]
[ROW][C]2[/C][C]0.069612[/C][C]0.7594[/C][C]0.224563[/C][/ROW]
[ROW][C]3[/C][C]-0.086235[/C][C]-0.9407[/C][C]0.17438[/C][/ROW]
[ROW][C]4[/C][C]-0.055653[/C][C]-0.6071[/C][C]0.272469[/C][/ROW]
[ROW][C]5[/C][C]-0.085561[/C][C]-0.9334[/C][C]0.176261[/C][/ROW]
[ROW][C]6[/C][C]0.027065[/C][C]0.2952[/C][C]0.384161[/C][/ROW]
[ROW][C]7[/C][C]0.089087[/C][C]0.9718[/C][C]0.166556[/C][/ROW]
[ROW][C]8[/C][C]0.030503[/C][C]0.3327[/C][C]0.369955[/C][/ROW]
[ROW][C]9[/C][C]0.003628[/C][C]0.0396[/C][C]0.48425[/C][/ROW]
[ROW][C]10[/C][C]-0.035916[/C][C]-0.3918[/C][C]0.347953[/C][/ROW]
[ROW][C]11[/C][C]-0.078572[/C][C]-0.8571[/C][C]0.19655[/C][/ROW]
[ROW][C]12[/C][C]-0.128894[/C][C]-1.4061[/C][C]0.081155[/C][/ROW]
[ROW][C]13[/C][C]0.007338[/C][C]0.08[/C][C]0.468167[/C][/ROW]
[ROW][C]14[/C][C]-0.059765[/C][C]-0.652[/C][C]0.257842[/C][/ROW]
[ROW][C]15[/C][C]0.073565[/C][C]0.8025[/C][C]0.211933[/C][/ROW]
[ROW][C]16[/C][C]0.012039[/C][C]0.1313[/C][C]0.447869[/C][/ROW]
[ROW][C]17[/C][C]-0.063582[/C][C]-0.6936[/C][C]0.244645[/C][/ROW]
[ROW][C]18[/C][C]-0.05824[/C][C]-0.6353[/C][C]0.263218[/C][/ROW]
[ROW][C]19[/C][C]0.045312[/C][C]0.4943[/C][C]0.311004[/C][/ROW]
[ROW][C]20[/C][C]-0.030714[/C][C]-0.335[/C][C]0.36909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29963&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29963&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	-0.179891	-1.9624	0.026026
2	0.069612	0.7594	0.224563
3	-0.086235	-0.9407	0.17438
4	-0.055653	-0.6071	0.272469
5	-0.085561	-0.9334	0.176261
6	0.027065	0.2952	0.384161
7	0.089087	0.9718	0.166556
8	0.030503	0.3327	0.369955
9	0.003628	0.0396	0.48425
10	-0.035916	-0.3918	0.347953
11	-0.078572	-0.8571	0.19655
12	-0.128894	-1.4061	0.081155
13	0.007338	0.08	0.468167
14	-0.059765	-0.652	0.257842
15	0.073565	0.8025	0.211933
16	0.012039	0.1313	0.447869
17	-0.063582	-0.6936	0.244645
18	-0.05824	-0.6353	0.263218
19	0.045312	0.4943	0.311004
20	-0.030714	-0.335	0.36909

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.179891	-1.9624	0.026026
2	0.038497	0.42	0.337637
3	-0.069622	-0.7595	0.224533
4	-0.088093	-0.961	0.169255
5	-0.107806	-1.176	0.120966
6	-0.007121	-0.0777	0.469107
7	0.093622	1.0213	0.154594
8	0.044027	0.4803	0.315954
9	-0.004082	-0.0445	0.482278
10	-0.033517	-0.3656	0.357646
11	-0.072479	-0.7907	0.21536
12	-0.140665	-1.5345	0.063784
13	-0.042288	-0.4613	0.322709
14	-0.089213	-0.9732	0.166216
15	0.002653	0.0289	0.48848
16	-0.003376	-0.0368	0.485342
17	-0.100906	-1.1008	0.136611
18	-0.086825	-0.9471	0.172742
19	0.049908	0.5444	0.293582
20	-0.000416	-0.0045	0.498192

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.179891 & -1.9624 & 0.026026 \tabularnewline
2 & 0.038497 & 0.42 & 0.337637 \tabularnewline
3 & -0.069622 & -0.7595 & 0.224533 \tabularnewline
4 & -0.088093 & -0.961 & 0.169255 \tabularnewline
5 & -0.107806 & -1.176 & 0.120966 \tabularnewline
6 & -0.007121 & -0.0777 & 0.469107 \tabularnewline
7 & 0.093622 & 1.0213 & 0.154594 \tabularnewline
8 & 0.044027 & 0.4803 & 0.315954 \tabularnewline
9 & -0.004082 & -0.0445 & 0.482278 \tabularnewline
10 & -0.033517 & -0.3656 & 0.357646 \tabularnewline
11 & -0.072479 & -0.7907 & 0.21536 \tabularnewline
12 & -0.140665 & -1.5345 & 0.063784 \tabularnewline
13 & -0.042288 & -0.4613 & 0.322709 \tabularnewline
14 & -0.089213 & -0.9732 & 0.166216 \tabularnewline
15 & 0.002653 & 0.0289 & 0.48848 \tabularnewline
16 & -0.003376 & -0.0368 & 0.485342 \tabularnewline
17 & -0.100906 & -1.1008 & 0.136611 \tabularnewline
18 & -0.086825 & -0.9471 & 0.172742 \tabularnewline
19 & 0.049908 & 0.5444 & 0.293582 \tabularnewline
20 & -0.000416 & -0.0045 & 0.498192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29963&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]-0.179891[/C][C]-1.9624[/C][C]0.026026[/C][/ROW]
[ROW][C]2[/C][C]0.038497[/C][C]0.42[/C][C]0.337637[/C][/ROW]
[ROW][C]3[/C][C]-0.069622[/C][C]-0.7595[/C][C]0.224533[/C][/ROW]
[ROW][C]4[/C][C]-0.088093[/C][C]-0.961[/C][C]0.169255[/C][/ROW]
[ROW][C]5[/C][C]-0.107806[/C][C]-1.176[/C][C]0.120966[/C][/ROW]
[ROW][C]6[/C][C]-0.007121[/C][C]-0.0777[/C][C]0.469107[/C][/ROW]
[ROW][C]7[/C][C]0.093622[/C][C]1.0213[/C][C]0.154594[/C][/ROW]
[ROW][C]8[/C][C]0.044027[/C][C]0.4803[/C][C]0.315954[/C][/ROW]
[ROW][C]9[/C][C]-0.004082[/C][C]-0.0445[/C][C]0.482278[/C][/ROW]
[ROW][C]10[/C][C]-0.033517[/C][C]-0.3656[/C][C]0.357646[/C][/ROW]
[ROW][C]11[/C][C]-0.072479[/C][C]-0.7907[/C][C]0.21536[/C][/ROW]
[ROW][C]12[/C][C]-0.140665[/C][C]-1.5345[/C][C]0.063784[/C][/ROW]
[ROW][C]13[/C][C]-0.042288[/C][C]-0.4613[/C][C]0.322709[/C][/ROW]
[ROW][C]14[/C][C]-0.089213[/C][C]-0.9732[/C][C]0.166216[/C][/ROW]
[ROW][C]15[/C][C]0.002653[/C][C]0.0289[/C][C]0.48848[/C][/ROW]
[ROW][C]16[/C][C]-0.003376[/C][C]-0.0368[/C][C]0.485342[/C][/ROW]
[ROW][C]17[/C][C]-0.100906[/C][C]-1.1008[/C][C]0.136611[/C][/ROW]
[ROW][C]18[/C][C]-0.086825[/C][C]-0.9471[/C][C]0.172742[/C][/ROW]
[ROW][C]19[/C][C]0.049908[/C][C]0.5444[/C][C]0.293582[/C][/ROW]
[ROW][C]20[/C][C]-0.000416[/C][C]-0.0045[/C][C]0.498192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29963&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29963&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	-0.179891	-1.9624	0.026026
2	0.038497	0.42	0.337637
3	-0.069622	-0.7595	0.224533
4	-0.088093	-0.961	0.169255
5	-0.107806	-1.176	0.120966
6	-0.007121	-0.0777	0.469107
7	0.093622	1.0213	0.154594
8	0.044027	0.4803	0.315954
9	-0.004082	-0.0445	0.482278
10	-0.033517	-0.3656	0.357646
11	-0.072479	-0.7907	0.21536
12	-0.140665	-1.5345	0.063784
13	-0.042288	-0.4613	0.322709
14	-0.089213	-0.9732	0.166216
15	0.002653	0.0289	0.48848
16	-0.003376	-0.0368	0.485342
17	-0.100906	-1.1008	0.136611
18	-0.086825	-0.9471	0.172742
19	0.049908	0.5444	0.293582
20	-0.000416	-0.0045	0.498192

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1.3 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1.3 ; par3 = 1 ; 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('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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code