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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 08 Dec 2008 11:34:40 -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/08/t1228761328yqa7wovdi55ppuh.htm/, Retrieved Thu, 16 May 2024 17:49:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30663, Retrieved Thu, 16 May 2024 17:49:32 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

166

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

-     [Univariate Data Series] [Run sequence plot...] [2008-12-02 22:19:27] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMPD  [Standard Deviation-Mean Plot] [SD mean plot] [2008-12-06 11:49:39] [ed2ba3b6182103c15c0ab511ae4e6284]
F RM      [Variance Reduction Matrix] [variance reduction] [2008-12-06 12:44:59] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMPD      [(Partial) Autocorrelation Function] [ACF] [2008-12-08 18:32:31] [077ffec662d24c06be4c491541a44245]
-   P           [(Partial) Autocorrelation Function] [ACF] [2008-12-08 18:34:40] [3817f5e632a8bfeb1be7b5e8c86bd450] [Current]
-   P             [(Partial) Autocorrelation Function] [ACF] [2008-12-08 18:36:48] [077ffec662d24c06be4c491541a44245] 

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30663&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30663&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30663&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.56399	4.3686	2.5e-05
2	0.411056	3.184	0.001152
3	0.510913	3.9575	0.000102
4	0.567087	4.3926	2.3e-05
5	0.438143	3.3938	0.000613
6	0.475338	3.6819	0.000249
7	0.349731	2.709	0.004391
8	0.424272	3.2864	0.000849
9	0.324218	2.5114	0.007368
10	0.167838	1.3001	0.099274
11	0.24374	1.888	0.031932
12	0.479042	3.7106	0.000227
13	0.163335	1.2652	0.105348
14	0.08711	0.6747	0.251213
15	0.13065	1.012	0.157799
16	0.179469	1.3902	0.084808
17	0.095788	0.742	0.230499

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.56399 & 4.3686 & 2.5e-05 \tabularnewline
2 & 0.411056 & 3.184 & 0.001152 \tabularnewline
3 & 0.510913 & 3.9575 & 0.000102 \tabularnewline
4 & 0.567087 & 4.3926 & 2.3e-05 \tabularnewline
5 & 0.438143 & 3.3938 & 0.000613 \tabularnewline
6 & 0.475338 & 3.6819 & 0.000249 \tabularnewline
7 & 0.349731 & 2.709 & 0.004391 \tabularnewline
8 & 0.424272 & 3.2864 & 0.000849 \tabularnewline
9 & 0.324218 & 2.5114 & 0.007368 \tabularnewline
10 & 0.167838 & 1.3001 & 0.099274 \tabularnewline
11 & 0.24374 & 1.888 & 0.031932 \tabularnewline
12 & 0.479042 & 3.7106 & 0.000227 \tabularnewline
13 & 0.163335 & 1.2652 & 0.105348 \tabularnewline
14 & 0.08711 & 0.6747 & 0.251213 \tabularnewline
15 & 0.13065 & 1.012 & 0.157799 \tabularnewline
16 & 0.179469 & 1.3902 & 0.084808 \tabularnewline
17 & 0.095788 & 0.742 & 0.230499 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30663&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]0.56399[/C][C]4.3686[/C][C]2.5e-05[/C][/ROW]
[ROW][C]2[/C][C]0.411056[/C][C]3.184[/C][C]0.001152[/C][/ROW]
[ROW][C]3[/C][C]0.510913[/C][C]3.9575[/C][C]0.000102[/C][/ROW]
[ROW][C]4[/C][C]0.567087[/C][C]4.3926[/C][C]2.3e-05[/C][/ROW]
[ROW][C]5[/C][C]0.438143[/C][C]3.3938[/C][C]0.000613[/C][/ROW]
[ROW][C]6[/C][C]0.475338[/C][C]3.6819[/C][C]0.000249[/C][/ROW]
[ROW][C]7[/C][C]0.349731[/C][C]2.709[/C][C]0.004391[/C][/ROW]
[ROW][C]8[/C][C]0.424272[/C][C]3.2864[/C][C]0.000849[/C][/ROW]
[ROW][C]9[/C][C]0.324218[/C][C]2.5114[/C][C]0.007368[/C][/ROW]
[ROW][C]10[/C][C]0.167838[/C][C]1.3001[/C][C]0.099274[/C][/ROW]
[ROW][C]11[/C][C]0.24374[/C][C]1.888[/C][C]0.031932[/C][/ROW]
[ROW][C]12[/C][C]0.479042[/C][C]3.7106[/C][C]0.000227[/C][/ROW]
[ROW][C]13[/C][C]0.163335[/C][C]1.2652[/C][C]0.105348[/C][/ROW]
[ROW][C]14[/C][C]0.08711[/C][C]0.6747[/C][C]0.251213[/C][/ROW]
[ROW][C]15[/C][C]0.13065[/C][C]1.012[/C][C]0.157799[/C][/ROW]
[ROW][C]16[/C][C]0.179469[/C][C]1.3902[/C][C]0.084808[/C][/ROW]
[ROW][C]17[/C][C]0.095788[/C][C]0.742[/C][C]0.230499[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30663&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30663&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	0.56399	4.3686	2.5e-05
2	0.411056	3.184	0.001152
3	0.510913	3.9575	0.000102
4	0.567087	4.3926	2.3e-05
5	0.438143	3.3938	0.000613
6	0.475338	3.6819	0.000249
7	0.349731	2.709	0.004391
8	0.424272	3.2864	0.000849
9	0.324218	2.5114	0.007368
10	0.167838	1.3001	0.099274
11	0.24374	1.888	0.031932
12	0.479042	3.7106	0.000227
13	0.163335	1.2652	0.105348
14	0.08711	0.6747	0.251213
15	0.13065	1.012	0.157799
16	0.179469	1.3902	0.084808
17	0.095788	0.742	0.230499

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.56399	4.3686	2.5e-05
2	0.136339	1.0561	0.147584
3	0.349346	2.706	0.004426
4	0.271349	2.1019	0.019886
5	0.014065	0.1089	0.456804
6	0.195869	1.5172	0.067234
7	-0.207778	-1.6094	0.056384
8	0.192274	1.4893	0.070817
9	-0.222269	-1.7217	0.045139
10	-0.245035	-1.898	0.031253
11	0.154836	1.1994	0.117553
12	0.303124	2.348	0.011095
13	-0.291908	-2.2611	0.013695
14	0.014807	0.1147	0.454536
15	-0.13895	-1.0763	0.14305
16	0.042663	0.3305	0.371098
17	-0.016952	-0.1313	0.447986

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.56399 & 4.3686 & 2.5e-05 \tabularnewline
2 & 0.136339 & 1.0561 & 0.147584 \tabularnewline
3 & 0.349346 & 2.706 & 0.004426 \tabularnewline
4 & 0.271349 & 2.1019 & 0.019886 \tabularnewline
5 & 0.014065 & 0.1089 & 0.456804 \tabularnewline
6 & 0.195869 & 1.5172 & 0.067234 \tabularnewline
7 & -0.207778 & -1.6094 & 0.056384 \tabularnewline
8 & 0.192274 & 1.4893 & 0.070817 \tabularnewline
9 & -0.222269 & -1.7217 & 0.045139 \tabularnewline
10 & -0.245035 & -1.898 & 0.031253 \tabularnewline
11 & 0.154836 & 1.1994 & 0.117553 \tabularnewline
12 & 0.303124 & 2.348 & 0.011095 \tabularnewline
13 & -0.291908 & -2.2611 & 0.013695 \tabularnewline
14 & 0.014807 & 0.1147 & 0.454536 \tabularnewline
15 & -0.13895 & -1.0763 & 0.14305 \tabularnewline
16 & 0.042663 & 0.3305 & 0.371098 \tabularnewline
17 & -0.016952 & -0.1313 & 0.447986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30663&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]0.56399[/C][C]4.3686[/C][C]2.5e-05[/C][/ROW]
[ROW][C]2[/C][C]0.136339[/C][C]1.0561[/C][C]0.147584[/C][/ROW]
[ROW][C]3[/C][C]0.349346[/C][C]2.706[/C][C]0.004426[/C][/ROW]
[ROW][C]4[/C][C]0.271349[/C][C]2.1019[/C][C]0.019886[/C][/ROW]
[ROW][C]5[/C][C]0.014065[/C][C]0.1089[/C][C]0.456804[/C][/ROW]
[ROW][C]6[/C][C]0.195869[/C][C]1.5172[/C][C]0.067234[/C][/ROW]
[ROW][C]7[/C][C]-0.207778[/C][C]-1.6094[/C][C]0.056384[/C][/ROW]
[ROW][C]8[/C][C]0.192274[/C][C]1.4893[/C][C]0.070817[/C][/ROW]
[ROW][C]9[/C][C]-0.222269[/C][C]-1.7217[/C][C]0.045139[/C][/ROW]
[ROW][C]10[/C][C]-0.245035[/C][C]-1.898[/C][C]0.031253[/C][/ROW]
[ROW][C]11[/C][C]0.154836[/C][C]1.1994[/C][C]0.117553[/C][/ROW]
[ROW][C]12[/C][C]0.303124[/C][C]2.348[/C][C]0.011095[/C][/ROW]
[ROW][C]13[/C][C]-0.291908[/C][C]-2.2611[/C][C]0.013695[/C][/ROW]
[ROW][C]14[/C][C]0.014807[/C][C]0.1147[/C][C]0.454536[/C][/ROW]
[ROW][C]15[/C][C]-0.13895[/C][C]-1.0763[/C][C]0.14305[/C][/ROW]
[ROW][C]16[/C][C]0.042663[/C][C]0.3305[/C][C]0.371098[/C][/ROW]
[ROW][C]17[/C][C]-0.016952[/C][C]-0.1313[/C][C]0.447986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30663&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30663&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	0.56399	4.3686	2.5e-05
2	0.136339	1.0561	0.147584
3	0.349346	2.706	0.004426
4	0.271349	2.1019	0.019886
5	0.014065	0.1089	0.456804
6	0.195869	1.5172	0.067234
7	-0.207778	-1.6094	0.056384
8	0.192274	1.4893	0.070817
9	-0.222269	-1.7217	0.045139
10	-0.245035	-1.898	0.031253
11	0.154836	1.1994	0.117553
12	0.303124	2.348	0.011095
13	-0.291908	-2.2611	0.013695
14	0.014807	0.1147	0.454536
15	-0.13895	-1.0763	0.14305
16	0.042663	0.3305	0.371098
17	-0.016952	-0.1313	0.447986

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.6 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.6 ; 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 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')

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Dataset

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