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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 16 Jan 2008 10:16:50 -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/Jan/16/t1200503558bhipddeph94jh7m.htm/, Retrieved Wed, 15 May 2024 15:33:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7997, Retrieved Wed, 15 May 2024 15:33:34 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

279

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

-     [Hierarchical Clustering] [paper] [2007-12-05 22:51:14] [8d3192ea84fef628e5e980e3df2ac42d]
- RMPD    [(Partial) Autocorrelation Function] [] [2008-01-16 17:16:50] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

0.88
0.87
0.88
0.89
0.92
0.96
0.99
0.98
0.98
0.98
1.00
1.02
1.06
1.08
1.08
1.08
1.16
1.17
1.14
1.11
1.12
1.17
1.17
1.23
1.26
1.26
1.23
1.20
1.20
1.21
1.23
1.22
1.22
1.25
1.30
1.34
1.31
1.30
1.32
1.29
1.27
1.22
1.20
1.23
1.23
1.20
1.18
1.19
1.21
1.19
1.20
1.23
1.28
1.27
1.27
1.28
1.27
1.26
1.29
1.32

Summary of compuational 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 compuational 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=7997&T=0

[TABLE]
[ROW][C]Summary of compuational 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=7997&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7997&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 compuational 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
0	1	7.746	0
1	0.92292	7.1489	0
2	0.832824	6.451	0
3	0.755278	5.8504	0
4	0.682997	5.2905	1e-06
5	0.611925	4.74	7e-06
6	0.549061	4.253	3.7e-05
7	0.499792	3.8714	0.000135
8	0.444723	3.4448	0.000524
9	0.391716	3.0342	0.001781
10	0.337855	2.617	0.005604
11	0.287248	2.225	0.014926
12	0.237124	1.8368	0.0356
13	0.198377	1.5366	0.064822
14	0.16454	1.2745	0.103696
15	0.124472	0.9642	0.169418
16	0.084016	0.6508	0.258835

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.92292 & 7.1489 & 0 \tabularnewline
2 & 0.832824 & 6.451 & 0 \tabularnewline
3 & 0.755278 & 5.8504 & 0 \tabularnewline
4 & 0.682997 & 5.2905 & 1e-06 \tabularnewline
5 & 0.611925 & 4.74 & 7e-06 \tabularnewline
6 & 0.549061 & 4.253 & 3.7e-05 \tabularnewline
7 & 0.499792 & 3.8714 & 0.000135 \tabularnewline
8 & 0.444723 & 3.4448 & 0.000524 \tabularnewline
9 & 0.391716 & 3.0342 & 0.001781 \tabularnewline
10 & 0.337855 & 2.617 & 0.005604 \tabularnewline
11 & 0.287248 & 2.225 & 0.014926 \tabularnewline
12 & 0.237124 & 1.8368 & 0.0356 \tabularnewline
13 & 0.198377 & 1.5366 & 0.064822 \tabularnewline
14 & 0.16454 & 1.2745 & 0.103696 \tabularnewline
15 & 0.124472 & 0.9642 & 0.169418 \tabularnewline
16 & 0.084016 & 0.6508 & 0.258835 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7997&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]0[/C][C]1[/C][C]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.92292[/C][C]7.1489[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.832824[/C][C]6.451[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.755278[/C][C]5.8504[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.682997[/C][C]5.2905[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.611925[/C][C]4.74[/C][C]7e-06[/C][/ROW]
[ROW][C]6[/C][C]0.549061[/C][C]4.253[/C][C]3.7e-05[/C][/ROW]
[ROW][C]7[/C][C]0.499792[/C][C]3.8714[/C][C]0.000135[/C][/ROW]
[ROW][C]8[/C][C]0.444723[/C][C]3.4448[/C][C]0.000524[/C][/ROW]
[ROW][C]9[/C][C]0.391716[/C][C]3.0342[/C][C]0.001781[/C][/ROW]
[ROW][C]10[/C][C]0.337855[/C][C]2.617[/C][C]0.005604[/C][/ROW]
[ROW][C]11[/C][C]0.287248[/C][C]2.225[/C][C]0.014926[/C][/ROW]
[ROW][C]12[/C][C]0.237124[/C][C]1.8368[/C][C]0.0356[/C][/ROW]
[ROW][C]13[/C][C]0.198377[/C][C]1.5366[/C][C]0.064822[/C][/ROW]
[ROW][C]14[/C][C]0.16454[/C][C]1.2745[/C][C]0.103696[/C][/ROW]
[ROW][C]15[/C][C]0.124472[/C][C]0.9642[/C][C]0.169418[/C][/ROW]
[ROW][C]16[/C][C]0.084016[/C][C]0.6508[/C][C]0.258835[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7997&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7997&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
0	1	7.746	0
1	0.92292	7.1489	0
2	0.832824	6.451	0
3	0.755278	5.8504	0
4	0.682997	5.2905	1e-06
5	0.611925	4.74	7e-06
6	0.549061	4.253	3.7e-05
7	0.499792	3.8714	0.000135
8	0.444723	3.4448	0.000524
9	0.391716	3.0342	0.001781
10	0.337855	2.617	0.005604
11	0.287248	2.225	0.014926
12	0.237124	1.8368	0.0356
13	0.198377	1.5366	0.064822
14	0.16454	1.2745	0.103696
15	0.124472	0.9642	0.169418
16	0.084016	0.6508	0.258835

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.92292	7.1489	0
1	-0.127903	-0.9907	0.837102
2	0.043775	0.3391	0.367866
3	-0.02322	-0.1799	0.571068
4	-0.03282	-0.2542	0.599904
5	0.014943	0.1157	0.454121
6	0.043971	0.3406	0.367298
7	-0.081766	-0.6334	0.735546
8	-0.000711	-0.0055	0.502187
9	-0.051566	-0.3994	0.654502
10	-0.011799	-0.0914	0.536258
11	-0.034293	-0.2656	0.604284
12	0.043789	0.3392	0.367826
13	-0.021015	-0.1628	0.564383
14	-0.06398	-0.4956	0.689001
15	-0.029217	-0.2263	0.589136
16	0.17248	1.336	0.093293

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.92292 & 7.1489 & 0 \tabularnewline
1 & -0.127903 & -0.9907 & 0.837102 \tabularnewline
2 & 0.043775 & 0.3391 & 0.367866 \tabularnewline
3 & -0.02322 & -0.1799 & 0.571068 \tabularnewline
4 & -0.03282 & -0.2542 & 0.599904 \tabularnewline
5 & 0.014943 & 0.1157 & 0.454121 \tabularnewline
6 & 0.043971 & 0.3406 & 0.367298 \tabularnewline
7 & -0.081766 & -0.6334 & 0.735546 \tabularnewline
8 & -0.000711 & -0.0055 & 0.502187 \tabularnewline
9 & -0.051566 & -0.3994 & 0.654502 \tabularnewline
10 & -0.011799 & -0.0914 & 0.536258 \tabularnewline
11 & -0.034293 & -0.2656 & 0.604284 \tabularnewline
12 & 0.043789 & 0.3392 & 0.367826 \tabularnewline
13 & -0.021015 & -0.1628 & 0.564383 \tabularnewline
14 & -0.06398 & -0.4956 & 0.689001 \tabularnewline
15 & -0.029217 & -0.2263 & 0.589136 \tabularnewline
16 & 0.17248 & 1.336 & 0.093293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7997&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]0[/C][C]0.92292[/C][C]7.1489[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.127903[/C][C]-0.9907[/C][C]0.837102[/C][/ROW]
[ROW][C]2[/C][C]0.043775[/C][C]0.3391[/C][C]0.367866[/C][/ROW]
[ROW][C]3[/C][C]-0.02322[/C][C]-0.1799[/C][C]0.571068[/C][/ROW]
[ROW][C]4[/C][C]-0.03282[/C][C]-0.2542[/C][C]0.599904[/C][/ROW]
[ROW][C]5[/C][C]0.014943[/C][C]0.1157[/C][C]0.454121[/C][/ROW]
[ROW][C]6[/C][C]0.043971[/C][C]0.3406[/C][C]0.367298[/C][/ROW]
[ROW][C]7[/C][C]-0.081766[/C][C]-0.6334[/C][C]0.735546[/C][/ROW]
[ROW][C]8[/C][C]-0.000711[/C][C]-0.0055[/C][C]0.502187[/C][/ROW]
[ROW][C]9[/C][C]-0.051566[/C][C]-0.3994[/C][C]0.654502[/C][/ROW]
[ROW][C]10[/C][C]-0.011799[/C][C]-0.0914[/C][C]0.536258[/C][/ROW]
[ROW][C]11[/C][C]-0.034293[/C][C]-0.2656[/C][C]0.604284[/C][/ROW]
[ROW][C]12[/C][C]0.043789[/C][C]0.3392[/C][C]0.367826[/C][/ROW]
[ROW][C]13[/C][C]-0.021015[/C][C]-0.1628[/C][C]0.564383[/C][/ROW]
[ROW][C]14[/C][C]-0.06398[/C][C]-0.4956[/C][C]0.689001[/C][/ROW]
[ROW][C]15[/C][C]-0.029217[/C][C]-0.2263[/C][C]0.589136[/C][/ROW]
[ROW][C]16[/C][C]0.17248[/C][C]1.336[/C][C]0.093293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7997&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7997&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
0	0.92292	7.1489	0
1	-0.127903	-0.9907	0.837102
2	0.043775	0.3391	0.367866
3	-0.02322	-0.1799	0.571068
4	-0.03282	-0.2542	0.599904
5	0.014943	0.1157	0.454121
6	0.043971	0.3406	0.367298
7	-0.081766	-0.6334	0.735546
8	-0.000711	-0.0055	0.502187
9	-0.051566	-0.3994	0.654502
10	-0.011799	-0.0914	0.536258
11	-0.034293	-0.2656	0.604284
12	0.043789	0.3392	0.367826
13	-0.021015	-0.1628	0.564383
14	-0.06398	-0.4956	0.689001
15	-0.029217	-0.2263	0.589136
16	0.17248	1.336	0.093293

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; 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('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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Input Parameters & R Code