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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

Fri, 27 Nov 2009 12:51:06 -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/2009/Nov/27/t1259351500xlu0o75ttml27nr.htm/, Retrieved Sun, 28 Apr 2024 23:33:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61199, Retrieved Sun, 28 Apr 2024 23:33:57 +0000

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User-defined keywords

Estimated Impact

113

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:26:39] [b98453cac15ba1066b407e146608df68]
-   PD        [(Partial) Autocorrelation Function] [] [2009-11-26 20:28:54] [6998f38352c0f6bc3cf32a17448703fc]
- R               [(Partial) Autocorrelation Function] [] [2009-11-27 19:51:06] [85bc2b59254337d32abe63c415a20c60] [Current]

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Boxplots

8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.2

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

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61199&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]1 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=61199&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61199&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.51492	3.5301	0.000471
2	-0.114891	-0.7877	0.217426
3	-0.510343	-3.4987	0.000517
4	-0.514217	-3.5253	0.000478
5	-0.149333	-1.0238	0.155591
6	0.227943	1.5627	0.062416
7	0.45221	3.1002	0.001632
8	0.335569	2.3005	0.012951
9	0.013924	0.0955	0.462178
10	-0.192895	-1.3224	0.096213
11	-0.284478	-1.9503	0.02856
12	-0.262972	-1.8028	0.038913
13	-0.046388	-0.318	0.37594
14	0.176142	1.2076	0.116628
15	0.202997	1.3917	0.085285
16	0.04113	0.282	0.389602
17	-0.075009	-0.5142	0.304748

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.51492 & 3.5301 & 0.000471 \tabularnewline
2 & -0.114891 & -0.7877 & 0.217426 \tabularnewline
3 & -0.510343 & -3.4987 & 0.000517 \tabularnewline
4 & -0.514217 & -3.5253 & 0.000478 \tabularnewline
5 & -0.149333 & -1.0238 & 0.155591 \tabularnewline
6 & 0.227943 & 1.5627 & 0.062416 \tabularnewline
7 & 0.45221 & 3.1002 & 0.001632 \tabularnewline
8 & 0.335569 & 2.3005 & 0.012951 \tabularnewline
9 & 0.013924 & 0.0955 & 0.462178 \tabularnewline
10 & -0.192895 & -1.3224 & 0.096213 \tabularnewline
11 & -0.284478 & -1.9503 & 0.02856 \tabularnewline
12 & -0.262972 & -1.8028 & 0.038913 \tabularnewline
13 & -0.046388 & -0.318 & 0.37594 \tabularnewline
14 & 0.176142 & 1.2076 & 0.116628 \tabularnewline
15 & 0.202997 & 1.3917 & 0.085285 \tabularnewline
16 & 0.04113 & 0.282 & 0.389602 \tabularnewline
17 & -0.075009 & -0.5142 & 0.304748 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61199&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]0.51492[/C][C]3.5301[/C][C]0.000471[/C][/ROW]
[ROW][C]2[/C][C]-0.114891[/C][C]-0.7877[/C][C]0.217426[/C][/ROW]
[ROW][C]3[/C][C]-0.510343[/C][C]-3.4987[/C][C]0.000517[/C][/ROW]
[ROW][C]4[/C][C]-0.514217[/C][C]-3.5253[/C][C]0.000478[/C][/ROW]
[ROW][C]5[/C][C]-0.149333[/C][C]-1.0238[/C][C]0.155591[/C][/ROW]
[ROW][C]6[/C][C]0.227943[/C][C]1.5627[/C][C]0.062416[/C][/ROW]
[ROW][C]7[/C][C]0.45221[/C][C]3.1002[/C][C]0.001632[/C][/ROW]
[ROW][C]8[/C][C]0.335569[/C][C]2.3005[/C][C]0.012951[/C][/ROW]
[ROW][C]9[/C][C]0.013924[/C][C]0.0955[/C][C]0.462178[/C][/ROW]
[ROW][C]10[/C][C]-0.192895[/C][C]-1.3224[/C][C]0.096213[/C][/ROW]
[ROW][C]11[/C][C]-0.284478[/C][C]-1.9503[/C][C]0.02856[/C][/ROW]
[ROW][C]12[/C][C]-0.262972[/C][C]-1.8028[/C][C]0.038913[/C][/ROW]
[ROW][C]13[/C][C]-0.046388[/C][C]-0.318[/C][C]0.37594[/C][/ROW]
[ROW][C]14[/C][C]0.176142[/C][C]1.2076[/C][C]0.116628[/C][/ROW]
[ROW][C]15[/C][C]0.202997[/C][C]1.3917[/C][C]0.085285[/C][/ROW]
[ROW][C]16[/C][C]0.04113[/C][C]0.282[/C][C]0.389602[/C][/ROW]
[ROW][C]17[/C][C]-0.075009[/C][C]-0.5142[/C][C]0.304748[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61199&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61199&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	0.51492	3.5301	0.000471
2	-0.114891	-0.7877	0.217426
3	-0.510343	-3.4987	0.000517
4	-0.514217	-3.5253	0.000478
5	-0.149333	-1.0238	0.155591
6	0.227943	1.5627	0.062416
7	0.45221	3.1002	0.001632
8	0.335569	2.3005	0.012951
9	0.013924	0.0955	0.462178
10	-0.192895	-1.3224	0.096213
11	-0.284478	-1.9503	0.02856
12	-0.262972	-1.8028	0.038913
13	-0.046388	-0.318	0.37594
14	0.176142	1.2076	0.116628
15	0.202997	1.3917	0.085285
16	0.04113	0.282	0.389602
17	-0.075009	-0.5142	0.304748

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.51492	3.5301	0.000471
2	-0.517154	-3.5454	0.00045
3	-0.286622	-1.965	0.027671
4	-0.156408	-1.0723	0.144535
5	0.080969	0.5551	0.29073
6	0.008837	0.0606	0.475973
7	0.182048	1.2481	0.109096
8	-0.004477	-0.0307	0.487821
9	0.015259	0.1046	0.458566
10	0.136366	0.9349	0.177314
11	-0.079273	-0.5435	0.294689
12	-0.191873	-1.3154	0.097376
13	0.069717	0.478	0.31745
14	0.000314	0.0021	0.499147
15	-0.168257	-1.1535	0.127267
16	-0.128268	-0.8794	0.191841
17	0.10828	0.7423	0.230791

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.51492 & 3.5301 & 0.000471 \tabularnewline
2 & -0.517154 & -3.5454 & 0.00045 \tabularnewline
3 & -0.286622 & -1.965 & 0.027671 \tabularnewline
4 & -0.156408 & -1.0723 & 0.144535 \tabularnewline
5 & 0.080969 & 0.5551 & 0.29073 \tabularnewline
6 & 0.008837 & 0.0606 & 0.475973 \tabularnewline
7 & 0.182048 & 1.2481 & 0.109096 \tabularnewline
8 & -0.004477 & -0.0307 & 0.487821 \tabularnewline
9 & 0.015259 & 0.1046 & 0.458566 \tabularnewline
10 & 0.136366 & 0.9349 & 0.177314 \tabularnewline
11 & -0.079273 & -0.5435 & 0.294689 \tabularnewline
12 & -0.191873 & -1.3154 & 0.097376 \tabularnewline
13 & 0.069717 & 0.478 & 0.31745 \tabularnewline
14 & 0.000314 & 0.0021 & 0.499147 \tabularnewline
15 & -0.168257 & -1.1535 & 0.127267 \tabularnewline
16 & -0.128268 & -0.8794 & 0.191841 \tabularnewline
17 & 0.10828 & 0.7423 & 0.230791 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61199&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]0.51492[/C][C]3.5301[/C][C]0.000471[/C][/ROW]
[ROW][C]2[/C][C]-0.517154[/C][C]-3.5454[/C][C]0.00045[/C][/ROW]
[ROW][C]3[/C][C]-0.286622[/C][C]-1.965[/C][C]0.027671[/C][/ROW]
[ROW][C]4[/C][C]-0.156408[/C][C]-1.0723[/C][C]0.144535[/C][/ROW]
[ROW][C]5[/C][C]0.080969[/C][C]0.5551[/C][C]0.29073[/C][/ROW]
[ROW][C]6[/C][C]0.008837[/C][C]0.0606[/C][C]0.475973[/C][/ROW]
[ROW][C]7[/C][C]0.182048[/C][C]1.2481[/C][C]0.109096[/C][/ROW]
[ROW][C]8[/C][C]-0.004477[/C][C]-0.0307[/C][C]0.487821[/C][/ROW]
[ROW][C]9[/C][C]0.015259[/C][C]0.1046[/C][C]0.458566[/C][/ROW]
[ROW][C]10[/C][C]0.136366[/C][C]0.9349[/C][C]0.177314[/C][/ROW]
[ROW][C]11[/C][C]-0.079273[/C][C]-0.5435[/C][C]0.294689[/C][/ROW]
[ROW][C]12[/C][C]-0.191873[/C][C]-1.3154[/C][C]0.097376[/C][/ROW]
[ROW][C]13[/C][C]0.069717[/C][C]0.478[/C][C]0.31745[/C][/ROW]
[ROW][C]14[/C][C]0.000314[/C][C]0.0021[/C][C]0.499147[/C][/ROW]
[ROW][C]15[/C][C]-0.168257[/C][C]-1.1535[/C][C]0.127267[/C][/ROW]
[ROW][C]16[/C][C]-0.128268[/C][C]-0.8794[/C][C]0.191841[/C][/ROW]
[ROW][C]17[/C][C]0.10828[/C][C]0.7423[/C][C]0.230791[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61199&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61199&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	0.51492	3.5301	0.000471
2	-0.517154	-3.5454	0.00045
3	-0.286622	-1.965	0.027671
4	-0.156408	-1.0723	0.144535
5	0.080969	0.5551	0.29073
6	0.008837	0.0606	0.475973
7	0.182048	1.2481	0.109096
8	-0.004477	-0.0307	0.487821
9	0.015259	0.1046	0.458566
10	0.136366	0.9349	0.177314
11	-0.079273	-0.5435	0.294689
12	-0.191873	-1.3154	0.097376
13	0.069717	0.478	0.31745
14	0.000314	0.0021	0.499147
15	-0.168257	-1.1535	0.127267
16	-0.128268	-0.8794	0.191841
17	0.10828	0.7423	0.230791

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 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

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