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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 05:56:20 -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/Nov/25/t1195994851d5iupcmjtp7jiai.htm/, Retrieved Sat, 04 May 2024 18:44:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6427, Retrieved Sat, 04 May 2024 18:44:47 +0000

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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] [Autocorrelation f...] [2007-11-25 12:56:20] [9fe578921d87f9af8e79a90d6142ba02] [Current]

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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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6427&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6427&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6427&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.8102	0
1	0.715386	5.5873	0
2	0.31412	2.4534	0.008513
3	-0.032114	-0.2508	0.5986
4	-0.265938	-2.077	0.978992
5	-0.339972	-2.6553	0.994952
6	-0.346009	-2.7024	0.995548
7	-0.32532	-2.5408	0.99319
8	-0.280506	-2.1908	0.983852
9	-0.126278	-0.9863	0.836049
10	0.086061	0.6722	0.252011
11	0.369233	2.8838	0.002711
12	0.541052	4.2257	4e-05
13	0.396515	3.0969	0.001477
14	0.131906	1.0302	0.153487
15	-0.100134	-0.7821	0.781401
16	-0.212547	-1.66	0.948981

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.8102 & 0 \tabularnewline
1 & 0.715386 & 5.5873 & 0 \tabularnewline
2 & 0.31412 & 2.4534 & 0.008513 \tabularnewline
3 & -0.032114 & -0.2508 & 0.5986 \tabularnewline
4 & -0.265938 & -2.077 & 0.978992 \tabularnewline
5 & -0.339972 & -2.6553 & 0.994952 \tabularnewline
6 & -0.346009 & -2.7024 & 0.995548 \tabularnewline
7 & -0.32532 & -2.5408 & 0.99319 \tabularnewline
8 & -0.280506 & -2.1908 & 0.983852 \tabularnewline
9 & -0.126278 & -0.9863 & 0.836049 \tabularnewline
10 & 0.086061 & 0.6722 & 0.252011 \tabularnewline
11 & 0.369233 & 2.8838 & 0.002711 \tabularnewline
12 & 0.541052 & 4.2257 & 4e-05 \tabularnewline
13 & 0.396515 & 3.0969 & 0.001477 \tabularnewline
14 & 0.131906 & 1.0302 & 0.153487 \tabularnewline
15 & -0.100134 & -0.7821 & 0.781401 \tabularnewline
16 & -0.212547 & -1.66 & 0.948981 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6427&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]7.8102[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.715386[/C][C]5.5873[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.31412[/C][C]2.4534[/C][C]0.008513[/C][/ROW]
[ROW][C]3[/C][C]-0.032114[/C][C]-0.2508[/C][C]0.5986[/C][/ROW]
[ROW][C]4[/C][C]-0.265938[/C][C]-2.077[/C][C]0.978992[/C][/ROW]
[ROW][C]5[/C][C]-0.339972[/C][C]-2.6553[/C][C]0.994952[/C][/ROW]
[ROW][C]6[/C][C]-0.346009[/C][C]-2.7024[/C][C]0.995548[/C][/ROW]
[ROW][C]7[/C][C]-0.32532[/C][C]-2.5408[/C][C]0.99319[/C][/ROW]
[ROW][C]8[/C][C]-0.280506[/C][C]-2.1908[/C][C]0.983852[/C][/ROW]
[ROW][C]9[/C][C]-0.126278[/C][C]-0.9863[/C][C]0.836049[/C][/ROW]
[ROW][C]10[/C][C]0.086061[/C][C]0.6722[/C][C]0.252011[/C][/ROW]
[ROW][C]11[/C][C]0.369233[/C][C]2.8838[/C][C]0.002711[/C][/ROW]
[ROW][C]12[/C][C]0.541052[/C][C]4.2257[/C][C]4e-05[/C][/ROW]
[ROW][C]13[/C][C]0.396515[/C][C]3.0969[/C][C]0.001477[/C][/ROW]
[ROW][C]14[/C][C]0.131906[/C][C]1.0302[/C][C]0.153487[/C][/ROW]
[ROW][C]15[/C][C]-0.100134[/C][C]-0.7821[/C][C]0.781401[/C][/ROW]
[ROW][C]16[/C][C]-0.212547[/C][C]-1.66[/C][C]0.948981[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6427&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6427&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	7.8102	0
1	0.715386	5.5873	0
2	0.31412	2.4534	0.008513
3	-0.032114	-0.2508	0.5986
4	-0.265938	-2.077	0.978992
5	-0.339972	-2.6553	0.994952
6	-0.346009	-2.7024	0.995548
7	-0.32532	-2.5408	0.99319
8	-0.280506	-2.1908	0.983852
9	-0.126278	-0.9863	0.836049
10	0.086061	0.6722	0.252011
11	0.369233	2.8838	0.002711
12	0.541052	4.2257	4e-05
13	0.396515	3.0969	0.001477
14	0.131906	1.0302	0.153487
15	-0.100134	-0.7821	0.781401
16	-0.212547	-1.66	0.948981

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.715386	5.5873	0
1	-0.40485	-3.162	0.998779
2	-0.142536	-1.1132	0.865014
3	-0.128466	-1.0034	0.840173
4	-0.010039	-0.0784	0.531121
5	-0.166137	-1.2976	0.90034
6	-0.134037	-1.0469	0.850352
7	-0.104775	-0.8183	0.79182
8	0.156044	1.2187	0.113816
9	0.077552	0.6057	0.27348
10	0.334464	2.6122	0.005655
11	0.042551	0.3323	0.370388
12	-0.325782	-2.5444	0.993254
13	-0.029117	-0.2274	0.589568
14	0.080088	0.6255	0.266985
15	0.091427	0.7141	0.238954
16	-0.046091	-0.36	0.639947

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.715386 & 5.5873 & 0 \tabularnewline
1 & -0.40485 & -3.162 & 0.998779 \tabularnewline
2 & -0.142536 & -1.1132 & 0.865014 \tabularnewline
3 & -0.128466 & -1.0034 & 0.840173 \tabularnewline
4 & -0.010039 & -0.0784 & 0.531121 \tabularnewline
5 & -0.166137 & -1.2976 & 0.90034 \tabularnewline
6 & -0.134037 & -1.0469 & 0.850352 \tabularnewline
7 & -0.104775 & -0.8183 & 0.79182 \tabularnewline
8 & 0.156044 & 1.2187 & 0.113816 \tabularnewline
9 & 0.077552 & 0.6057 & 0.27348 \tabularnewline
10 & 0.334464 & 2.6122 & 0.005655 \tabularnewline
11 & 0.042551 & 0.3323 & 0.370388 \tabularnewline
12 & -0.325782 & -2.5444 & 0.993254 \tabularnewline
13 & -0.029117 & -0.2274 & 0.589568 \tabularnewline
14 & 0.080088 & 0.6255 & 0.266985 \tabularnewline
15 & 0.091427 & 0.7141 & 0.238954 \tabularnewline
16 & -0.046091 & -0.36 & 0.639947 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6427&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]0.715386[/C][C]5.5873[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.40485[/C][C]-3.162[/C][C]0.998779[/C][/ROW]
[ROW][C]2[/C][C]-0.142536[/C][C]-1.1132[/C][C]0.865014[/C][/ROW]
[ROW][C]3[/C][C]-0.128466[/C][C]-1.0034[/C][C]0.840173[/C][/ROW]
[ROW][C]4[/C][C]-0.010039[/C][C]-0.0784[/C][C]0.531121[/C][/ROW]
[ROW][C]5[/C][C]-0.166137[/C][C]-1.2976[/C][C]0.90034[/C][/ROW]
[ROW][C]6[/C][C]-0.134037[/C][C]-1.0469[/C][C]0.850352[/C][/ROW]
[ROW][C]7[/C][C]-0.104775[/C][C]-0.8183[/C][C]0.79182[/C][/ROW]
[ROW][C]8[/C][C]0.156044[/C][C]1.2187[/C][C]0.113816[/C][/ROW]
[ROW][C]9[/C][C]0.077552[/C][C]0.6057[/C][C]0.27348[/C][/ROW]
[ROW][C]10[/C][C]0.334464[/C][C]2.6122[/C][C]0.005655[/C][/ROW]
[ROW][C]11[/C][C]0.042551[/C][C]0.3323[/C][C]0.370388[/C][/ROW]
[ROW][C]12[/C][C]-0.325782[/C][C]-2.5444[/C][C]0.993254[/C][/ROW]
[ROW][C]13[/C][C]-0.029117[/C][C]-0.2274[/C][C]0.589568[/C][/ROW]
[ROW][C]14[/C][C]0.080088[/C][C]0.6255[/C][C]0.266985[/C][/ROW]
[ROW][C]15[/C][C]0.091427[/C][C]0.7141[/C][C]0.238954[/C][/ROW]
[ROW][C]16[/C][C]-0.046091[/C][C]-0.36[/C][C]0.639947[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6427&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6427&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	0.715386	5.5873	0
1	-0.40485	-3.162	0.998779
2	-0.142536	-1.1132	0.865014
3	-0.128466	-1.0034	0.840173
4	-0.010039	-0.0784	0.531121
5	-0.166137	-1.2976	0.90034
6	-0.134037	-1.0469	0.850352
7	-0.104775	-0.8183	0.79182
8	0.156044	1.2187	0.113816
9	0.077552	0.6057	0.27348
10	0.334464	2.6122	0.005655
11	0.042551	0.3323	0.370388
12	-0.325782	-2.5444	0.993254
13	-0.029117	-0.2274	0.589568
14	0.080088	0.6255	0.266985
15	0.091427	0.7141	0.238954
16	-0.046091	-0.36	0.639947

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 = 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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Dataset

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Input Parameters & R Code