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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 06 Dec 2008 07:15:12 -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/06/t1228572940rrftoszxa5r09nt.htm/, Retrieved Sun, 19 May 2024 11:32:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29625, Retrieved Sun, 19 May 2024 11:32:39 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

186

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

F     [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-02 21:04:58] [1a98f534d827b920a5783bf87d2d3cce]
- RMP     [(Partial) Autocorrelation Function] [] [2008-12-06 14:15:12] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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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=29625&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=29625&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29625&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	0.964268	7.5312	0
2	0.89526	6.9922	0
3	0.808092	6.3114	0
4	0.716243	5.594	0
5	0.622617	4.8628	4e-06
6	0.529679	4.1369	5.5e-05
7	0.44196	3.4518	0.000509
8	0.361875	2.8263	0.003179
9	0.289746	2.263	0.013604
10	0.227012	1.773	0.040609
11	0.176226	1.3764	0.08687
12	0.132849	1.0376	0.151779
13	0.084927	0.6633	0.254819
14	0.039199	0.3062	0.380264
15	-0.005661	-0.0442	0.482439
16	-0.047502	-0.371	0.355959
17	-0.087694	-0.6849	0.247997

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.964268 & 7.5312 & 0 \tabularnewline
2 & 0.89526 & 6.9922 & 0 \tabularnewline
3 & 0.808092 & 6.3114 & 0 \tabularnewline
4 & 0.716243 & 5.594 & 0 \tabularnewline
5 & 0.622617 & 4.8628 & 4e-06 \tabularnewline
6 & 0.529679 & 4.1369 & 5.5e-05 \tabularnewline
7 & 0.44196 & 3.4518 & 0.000509 \tabularnewline
8 & 0.361875 & 2.8263 & 0.003179 \tabularnewline
9 & 0.289746 & 2.263 & 0.013604 \tabularnewline
10 & 0.227012 & 1.773 & 0.040609 \tabularnewline
11 & 0.176226 & 1.3764 & 0.08687 \tabularnewline
12 & 0.132849 & 1.0376 & 0.151779 \tabularnewline
13 & 0.084927 & 0.6633 & 0.254819 \tabularnewline
14 & 0.039199 & 0.3062 & 0.380264 \tabularnewline
15 & -0.005661 & -0.0442 & 0.482439 \tabularnewline
16 & -0.047502 & -0.371 & 0.355959 \tabularnewline
17 & -0.087694 & -0.6849 & 0.247997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29625&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]0.964268[/C][C]7.5312[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.89526[/C][C]6.9922[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.808092[/C][C]6.3114[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.716243[/C][C]5.594[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.622617[/C][C]4.8628[/C][C]4e-06[/C][/ROW]
[ROW][C]6[/C][C]0.529679[/C][C]4.1369[/C][C]5.5e-05[/C][/ROW]
[ROW][C]7[/C][C]0.44196[/C][C]3.4518[/C][C]0.000509[/C][/ROW]
[ROW][C]8[/C][C]0.361875[/C][C]2.8263[/C][C]0.003179[/C][/ROW]
[ROW][C]9[/C][C]0.289746[/C][C]2.263[/C][C]0.013604[/C][/ROW]
[ROW][C]10[/C][C]0.227012[/C][C]1.773[/C][C]0.040609[/C][/ROW]
[ROW][C]11[/C][C]0.176226[/C][C]1.3764[/C][C]0.08687[/C][/ROW]
[ROW][C]12[/C][C]0.132849[/C][C]1.0376[/C][C]0.151779[/C][/ROW]
[ROW][C]13[/C][C]0.084927[/C][C]0.6633[/C][C]0.254819[/C][/ROW]
[ROW][C]14[/C][C]0.039199[/C][C]0.3062[/C][C]0.380264[/C][/ROW]
[ROW][C]15[/C][C]-0.005661[/C][C]-0.0442[/C][C]0.482439[/C][/ROW]
[ROW][C]16[/C][C]-0.047502[/C][C]-0.371[/C][C]0.355959[/C][/ROW]
[ROW][C]17[/C][C]-0.087694[/C][C]-0.6849[/C][C]0.247997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29625&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29625&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	0.964268	7.5312	0
2	0.89526	6.9922	0
3	0.808092	6.3114	0
4	0.716243	5.594	0
5	0.622617	4.8628	4e-06
6	0.529679	4.1369	5.5e-05
7	0.44196	3.4518	0.000509
8	0.361875	2.8263	0.003179
9	0.289746	2.263	0.013604
10	0.227012	1.773	0.040609
11	0.176226	1.3764	0.08687
12	0.132849	1.0376	0.151779
13	0.084927	0.6633	0.254819
14	0.039199	0.3062	0.380264
15	-0.005661	-0.0442	0.482439
16	-0.047502	-0.371	0.355959
17	-0.087694	-0.6849	0.247997

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.964268	7.5312	0
2	-0.492287	-3.8449	0.000145
3	-0.102644	-0.8017	0.212927
4	0.032904	0.257	0.399027
5	-0.074185	-0.5794	0.282225
6	-0.0451	-0.3522	0.362936
7	0.026933	0.2104	0.417048
8	-2e-05	-2e-04	0.499939
9	-0.022484	-0.1756	0.430593
10	0.022201	0.1734	0.431456
11	0.053319	0.4164	0.339276
12	-0.073245	-0.5721	0.284692
13	-0.217271	-1.6969	0.047403
14	0.114562	0.8948	0.187217
15	-0.054926	-0.429	0.334722
16	-0.045634	-0.3564	0.36138
17	-0.019062	-0.1489	0.441072

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.964268 & 7.5312 & 0 \tabularnewline
2 & -0.492287 & -3.8449 & 0.000145 \tabularnewline
3 & -0.102644 & -0.8017 & 0.212927 \tabularnewline
4 & 0.032904 & 0.257 & 0.399027 \tabularnewline
5 & -0.074185 & -0.5794 & 0.282225 \tabularnewline
6 & -0.0451 & -0.3522 & 0.362936 \tabularnewline
7 & 0.026933 & 0.2104 & 0.417048 \tabularnewline
8 & -2e-05 & -2e-04 & 0.499939 \tabularnewline
9 & -0.022484 & -0.1756 & 0.430593 \tabularnewline
10 & 0.022201 & 0.1734 & 0.431456 \tabularnewline
11 & 0.053319 & 0.4164 & 0.339276 \tabularnewline
12 & -0.073245 & -0.5721 & 0.284692 \tabularnewline
13 & -0.217271 & -1.6969 & 0.047403 \tabularnewline
14 & 0.114562 & 0.8948 & 0.187217 \tabularnewline
15 & -0.054926 & -0.429 & 0.334722 \tabularnewline
16 & -0.045634 & -0.3564 & 0.36138 \tabularnewline
17 & -0.019062 & -0.1489 & 0.441072 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29625&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]0.964268[/C][C]7.5312[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.492287[/C][C]-3.8449[/C][C]0.000145[/C][/ROW]
[ROW][C]3[/C][C]-0.102644[/C][C]-0.8017[/C][C]0.212927[/C][/ROW]
[ROW][C]4[/C][C]0.032904[/C][C]0.257[/C][C]0.399027[/C][/ROW]
[ROW][C]5[/C][C]-0.074185[/C][C]-0.5794[/C][C]0.282225[/C][/ROW]
[ROW][C]6[/C][C]-0.0451[/C][C]-0.3522[/C][C]0.362936[/C][/ROW]
[ROW][C]7[/C][C]0.026933[/C][C]0.2104[/C][C]0.417048[/C][/ROW]
[ROW][C]8[/C][C]-2e-05[/C][C]-2e-04[/C][C]0.499939[/C][/ROW]
[ROW][C]9[/C][C]-0.022484[/C][C]-0.1756[/C][C]0.430593[/C][/ROW]
[ROW][C]10[/C][C]0.022201[/C][C]0.1734[/C][C]0.431456[/C][/ROW]
[ROW][C]11[/C][C]0.053319[/C][C]0.4164[/C][C]0.339276[/C][/ROW]
[ROW][C]12[/C][C]-0.073245[/C][C]-0.5721[/C][C]0.284692[/C][/ROW]
[ROW][C]13[/C][C]-0.217271[/C][C]-1.6969[/C][C]0.047403[/C][/ROW]
[ROW][C]14[/C][C]0.114562[/C][C]0.8948[/C][C]0.187217[/C][/ROW]
[ROW][C]15[/C][C]-0.054926[/C][C]-0.429[/C][C]0.334722[/C][/ROW]
[ROW][C]16[/C][C]-0.045634[/C][C]-0.3564[/C][C]0.36138[/C][/ROW]
[ROW][C]17[/C][C]-0.019062[/C][C]-0.1489[/C][C]0.441072[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29625&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29625&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	0.964268	7.5312	0
2	-0.492287	-3.8449	0.000145
3	-0.102644	-0.8017	0.212927
4	0.032904	0.257	0.399027
5	-0.074185	-0.5794	0.282225
6	-0.0451	-0.3522	0.362936
7	0.026933	0.2104	0.417048
8	-2e-05	-2e-04	0.499939
9	-0.022484	-0.1756	0.430593
10	0.022201	0.1734	0.431456
11	0.053319	0.4164	0.339276
12	-0.073245	-0.5721	0.284692
13	-0.217271	-1.6969	0.047403
14	0.114562	0.8948	0.187217
15	-0.054926	-0.429	0.334722
16	-0.045634	-0.3564	0.36138
17	-0.019062	-0.1489	0.441072

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 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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code