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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 03 Dec 2007 14:24:55 -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/2007/Dec/03/t1196716407uzl1svawpbenvw0.htm/, Retrieved Fri, 03 May 2024 20:15:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2361, Retrieved Fri, 03 May 2024 20:15:34 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

188

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

-       [(Partial) Autocorrelation Function] [workshop 9 - Q1 d...] [2007-12-03 21:24:55] [3463f71ebce131edf0c83e066f45702c] [Current]

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Dataseries X:

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Histogram

Boxplots

8.5
8.5
8.5
8.4
8.5
8.5
8.3
8.4
8.4
8.4
8.4
8.4
8.5
8.5
8.5
8.5
8.5
8.5
8.3
8.3
8.4
8.2
8.2
8.1
8.1
8
7.8
7.9
7.8
7.7
7.9
7.8
7.7
7.7
7.6
7.5

Summary of compuational 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 compuational 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=2361&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]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=2361&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2361&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	5.9161	0
1	-0.309961	-1.8338	0.962397
2	-0.174967	-1.0351	0.846144
3	0.473788	2.803	0.0041
4	-0.203145	-1.2018	0.88125
5	0.092398	0.5466	0.294048
6	-0.134993	-0.7986	0.785055
7	0.055046	0.3257	0.373312
8	0.222149	1.3143	0.098655
9	-0.271298	-1.605	0.941262
10	0.161861	0.9576	0.172421
11	-0.024246	-0.1434	0.556619
12	-0.068152	-0.4032	0.655371
13	0.066841	0.3954	0.347459
14	-0.224771	-1.3298	0.903901

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 5.9161 & 0 \tabularnewline
1 & -0.309961 & -1.8338 & 0.962397 \tabularnewline
2 & -0.174967 & -1.0351 & 0.846144 \tabularnewline
3 & 0.473788 & 2.803 & 0.0041 \tabularnewline
4 & -0.203145 & -1.2018 & 0.88125 \tabularnewline
5 & 0.092398 & 0.5466 & 0.294048 \tabularnewline
6 & -0.134993 & -0.7986 & 0.785055 \tabularnewline
7 & 0.055046 & 0.3257 & 0.373312 \tabularnewline
8 & 0.222149 & 1.3143 & 0.098655 \tabularnewline
9 & -0.271298 & -1.605 & 0.941262 \tabularnewline
10 & 0.161861 & 0.9576 & 0.172421 \tabularnewline
11 & -0.024246 & -0.1434 & 0.556619 \tabularnewline
12 & -0.068152 & -0.4032 & 0.655371 \tabularnewline
13 & 0.066841 & 0.3954 & 0.347459 \tabularnewline
14 & -0.224771 & -1.3298 & 0.903901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2361&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]5.9161[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.309961[/C][C]-1.8338[/C][C]0.962397[/C][/ROW]
[ROW][C]2[/C][C]-0.174967[/C][C]-1.0351[/C][C]0.846144[/C][/ROW]
[ROW][C]3[/C][C]0.473788[/C][C]2.803[/C][C]0.0041[/C][/ROW]
[ROW][C]4[/C][C]-0.203145[/C][C]-1.2018[/C][C]0.88125[/C][/ROW]
[ROW][C]5[/C][C]0.092398[/C][C]0.5466[/C][C]0.294048[/C][/ROW]
[ROW][C]6[/C][C]-0.134993[/C][C]-0.7986[/C][C]0.785055[/C][/ROW]
[ROW][C]7[/C][C]0.055046[/C][C]0.3257[/C][C]0.373312[/C][/ROW]
[ROW][C]8[/C][C]0.222149[/C][C]1.3143[/C][C]0.098655[/C][/ROW]
[ROW][C]9[/C][C]-0.271298[/C][C]-1.605[/C][C]0.941262[/C][/ROW]
[ROW][C]10[/C][C]0.161861[/C][C]0.9576[/C][C]0.172421[/C][/ROW]
[ROW][C]11[/C][C]-0.024246[/C][C]-0.1434[/C][C]0.556619[/C][/ROW]
[ROW][C]12[/C][C]-0.068152[/C][C]-0.4032[/C][C]0.655371[/C][/ROW]
[ROW][C]13[/C][C]0.066841[/C][C]0.3954[/C][C]0.347459[/C][/ROW]
[ROW][C]14[/C][C]-0.224771[/C][C]-1.3298[/C][C]0.903901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2361&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2361&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	5.9161	0
1	-0.309961	-1.8338	0.962397
2	-0.174967	-1.0351	0.846144
3	0.473788	2.803	0.0041
4	-0.203145	-1.2018	0.88125
5	0.092398	0.5466	0.294048
6	-0.134993	-0.7986	0.785055
7	0.055046	0.3257	0.373312
8	0.222149	1.3143	0.098655
9	-0.271298	-1.605	0.941262
10	0.161861	0.9576	0.172421
11	-0.024246	-0.1434	0.556619
12	-0.068152	-0.4032	0.655371
13	0.066841	0.3954	0.347459
14	-0.224771	-1.3298	0.903901

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.309961	-1.8338	0.962397
1	-0.299851	-1.7739	0.957613
2	0.377257	2.2319	0.016062
3	0.035737	0.2114	0.416892
4	0.251517	1.488	0.072854
5	-0.390833	-2.3122	0.986615
6	0.101637	0.6013	0.275759
7	0.066631	0.3942	0.347914
8	0.166468	0.9848	0.165731
9	0.018827	0.1114	0.455975
10	-0.214079	-1.2665	0.893153
11	-0.029247	-0.173	0.568188
12	-0.101516	-0.6006	0.724004
13	-0.014215	-0.0841	0.53327
14	-0.048876	-0.2892	0.612916

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.309961 & -1.8338 & 0.962397 \tabularnewline
1 & -0.299851 & -1.7739 & 0.957613 \tabularnewline
2 & 0.377257 & 2.2319 & 0.016062 \tabularnewline
3 & 0.035737 & 0.2114 & 0.416892 \tabularnewline
4 & 0.251517 & 1.488 & 0.072854 \tabularnewline
5 & -0.390833 & -2.3122 & 0.986615 \tabularnewline
6 & 0.101637 & 0.6013 & 0.275759 \tabularnewline
7 & 0.066631 & 0.3942 & 0.347914 \tabularnewline
8 & 0.166468 & 0.9848 & 0.165731 \tabularnewline
9 & 0.018827 & 0.1114 & 0.455975 \tabularnewline
10 & -0.214079 & -1.2665 & 0.893153 \tabularnewline
11 & -0.029247 & -0.173 & 0.568188 \tabularnewline
12 & -0.101516 & -0.6006 & 0.724004 \tabularnewline
13 & -0.014215 & -0.0841 & 0.53327 \tabularnewline
14 & -0.048876 & -0.2892 & 0.612916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2361&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]-0.309961[/C][C]-1.8338[/C][C]0.962397[/C][/ROW]
[ROW][C]1[/C][C]-0.299851[/C][C]-1.7739[/C][C]0.957613[/C][/ROW]
[ROW][C]2[/C][C]0.377257[/C][C]2.2319[/C][C]0.016062[/C][/ROW]
[ROW][C]3[/C][C]0.035737[/C][C]0.2114[/C][C]0.416892[/C][/ROW]
[ROW][C]4[/C][C]0.251517[/C][C]1.488[/C][C]0.072854[/C][/ROW]
[ROW][C]5[/C][C]-0.390833[/C][C]-2.3122[/C][C]0.986615[/C][/ROW]
[ROW][C]6[/C][C]0.101637[/C][C]0.6013[/C][C]0.275759[/C][/ROW]
[ROW][C]7[/C][C]0.066631[/C][C]0.3942[/C][C]0.347914[/C][/ROW]
[ROW][C]8[/C][C]0.166468[/C][C]0.9848[/C][C]0.165731[/C][/ROW]
[ROW][C]9[/C][C]0.018827[/C][C]0.1114[/C][C]0.455975[/C][/ROW]
[ROW][C]10[/C][C]-0.214079[/C][C]-1.2665[/C][C]0.893153[/C][/ROW]
[ROW][C]11[/C][C]-0.029247[/C][C]-0.173[/C][C]0.568188[/C][/ROW]
[ROW][C]12[/C][C]-0.101516[/C][C]-0.6006[/C][C]0.724004[/C][/ROW]
[ROW][C]13[/C][C]-0.014215[/C][C]-0.0841[/C][C]0.53327[/C][/ROW]
[ROW][C]14[/C][C]-0.048876[/C][C]-0.2892[/C][C]0.612916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2361&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2361&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	-0.309961	-1.8338	0.962397
1	-0.299851	-1.7739	0.957613
2	0.377257	2.2319	0.016062
3	0.035737	0.2114	0.416892
4	0.251517	1.488	0.072854
5	-0.390833	-2.3122	0.986615
6	0.101637	0.6013	0.275759
7	0.066631	0.3942	0.347914
8	0.166468	0.9848	0.165731
9	0.018827	0.1114	0.455975
10	-0.214079	-1.2665	0.893153
11	-0.029247	-0.173	0.568188
12	-0.101516	-0.6006	0.724004
13	-0.014215	-0.0841	0.53327
14	-0.048876	-0.2892	0.612916

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 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; 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 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code