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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

Wed, 13 Aug 2014 10:41:06 +0100

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/2014/Aug/13/t1407922936fnasac6wbt86vtm.htm/, Retrieved Fri, 01 Nov 2024 00:59:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235495, Retrieved Fri, 01 Nov 2024 00:59:35 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

145

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

-       [(Partial) Autocorrelation Function] [] [2014-08-13 09:41:06] [b3e3d38149b35cb70244b37a39776b3a] [Current]
- RMP     [Standard Deviation Plot] [] [2014-08-13 09:51:12] [ba0170e6f15797e8c541ec0953bc1848] 
- RMP     [Standard Deviation-Mean Plot] [] [2014-08-13 09:59:59] [ba0170e6f15797e8c541ec0953bc1848] 
- RMP     [Classical Decomposition] [] [2014-08-13 10:04:03] [ba0170e6f15797e8c541ec0953bc1848] 
- RMP     [Exponential Smoothing] [] [2014-08-13 10:15:04] [ba0170e6f15797e8c541ec0953bc1848] 
- RMPD    [Univariate Data Series] [] [2014-08-13 10:18:26] [f85cc8f00ef4b762f0a6fdfddc793773] 
- RMPD    [Histogram] [] [2014-08-13 10:20:32] [f85cc8f00ef4b762f0a6fdfddc793773] 
- RMPD    [Kernel Density Estimation] [] [2014-08-13 10:21:53] [ba0170e6f15797e8c541ec0953bc1848] 
- RMPD    [Notched Boxplots] [] [2014-08-13 10:26:48] [ba0170e6f15797e8c541ec0953bc1848] 
- RMPD    [Harrell-Davis Quantiles] [] [2014-08-13 10:28:23] [ba0170e6f15797e8c541ec0953bc1848] 
- RMPD    [Harrell-Davis Quantiles] [] [2014-08-13 10:30:20] [ba0170e6f15797e8c541ec0953bc1848] 
- RMPD    [Central Tendency] [] [2014-08-13 10:32:56] [ba0170e6f15797e8c541ec0953bc1848] 

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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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235495&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235495&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235495&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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.974725	10.6776	0
2	0.950404	10.4112	0
3	0.923525	10.1167	0
4	0.895883	9.8139	0
5	0.869079	9.5203	0
6	0.842321	9.2272	0
7	0.816459	8.9439	0
8	0.789809	8.6519	0
9	0.766726	8.3991	0
10	0.743594	8.1457	0
11	0.722908	7.9191	0
12	0.700636	7.6751	0
13	0.67518	7.3962	0
14	0.649832	7.1185	0
15	0.622241	6.8163	0
16	0.594464	6.512	0
17	0.567805	6.22	0
18	0.541505	5.9319	0
19	0.515616	5.6483	0
20	0.489252	5.3595	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.974725 & 10.6776 & 0 \tabularnewline
2 & 0.950404 & 10.4112 & 0 \tabularnewline
3 & 0.923525 & 10.1167 & 0 \tabularnewline
4 & 0.895883 & 9.8139 & 0 \tabularnewline
5 & 0.869079 & 9.5203 & 0 \tabularnewline
6 & 0.842321 & 9.2272 & 0 \tabularnewline
7 & 0.816459 & 8.9439 & 0 \tabularnewline
8 & 0.789809 & 8.6519 & 0 \tabularnewline
9 & 0.766726 & 8.3991 & 0 \tabularnewline
10 & 0.743594 & 8.1457 & 0 \tabularnewline
11 & 0.722908 & 7.9191 & 0 \tabularnewline
12 & 0.700636 & 7.6751 & 0 \tabularnewline
13 & 0.67518 & 7.3962 & 0 \tabularnewline
14 & 0.649832 & 7.1185 & 0 \tabularnewline
15 & 0.622241 & 6.8163 & 0 \tabularnewline
16 & 0.594464 & 6.512 & 0 \tabularnewline
17 & 0.567805 & 6.22 & 0 \tabularnewline
18 & 0.541505 & 5.9319 & 0 \tabularnewline
19 & 0.515616 & 5.6483 & 0 \tabularnewline
20 & 0.489252 & 5.3595 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235495&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]0.974725[/C][C]10.6776[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.950404[/C][C]10.4112[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.923525[/C][C]10.1167[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.895883[/C][C]9.8139[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.869079[/C][C]9.5203[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.842321[/C][C]9.2272[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.816459[/C][C]8.9439[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.789809[/C][C]8.6519[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.766726[/C][C]8.3991[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.743594[/C][C]8.1457[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.722908[/C][C]7.9191[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.700636[/C][C]7.6751[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.67518[/C][C]7.3962[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.649832[/C][C]7.1185[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.622241[/C][C]6.8163[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.594464[/C][C]6.512[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.567805[/C][C]6.22[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.541505[/C][C]5.9319[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.515616[/C][C]5.6483[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.489252[/C][C]5.3595[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235495&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235495&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	0.974725	10.6776	0
2	0.950404	10.4112	0
3	0.923525	10.1167	0
4	0.895883	9.8139	0
5	0.869079	9.5203	0
6	0.842321	9.2272	0
7	0.816459	8.9439	0
8	0.789809	8.6519	0
9	0.766726	8.3991	0
10	0.743594	8.1457	0
11	0.722908	7.9191	0
12	0.700636	7.6751	0
13	0.67518	7.3962	0
14	0.649832	7.1185	0
15	0.622241	6.8163	0
16	0.594464	6.512	0
17	0.567805	6.22	0
18	0.541505	5.9319	0
19	0.515616	5.6483	0
20	0.489252	5.3595	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.974725	10.6776	0
2	0.006301	0.069	0.472544
3	-0.063351	-0.694	0.24452
4	-0.03124	-0.3422	0.366393
5	0.004176	0.0458	0.481793
6	-0.011124	-0.1219	0.451609
7	0.002095	0.0229	0.490866
8	-0.030227	-0.3311	0.370564
9	0.054912	0.6015	0.274312
10	-0.01044	-0.1144	0.454572
11	0.030124	0.33	0.370993
12	-0.045644	-0.5	0.308992
13	-0.080847	-0.8856	0.188792
14	-0.014102	-0.1545	0.438746
15	-0.049519	-0.5425	0.294256
16	-0.023094	-0.253	0.400355
17	0.012892	0.1412	0.443966
18	-0.008893	-0.0974	0.461277
19	-0.006015	-0.0659	0.473785
20	-0.030322	-0.3322	0.370175

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.974725 & 10.6776 & 0 \tabularnewline
2 & 0.006301 & 0.069 & 0.472544 \tabularnewline
3 & -0.063351 & -0.694 & 0.24452 \tabularnewline
4 & -0.03124 & -0.3422 & 0.366393 \tabularnewline
5 & 0.004176 & 0.0458 & 0.481793 \tabularnewline
6 & -0.011124 & -0.1219 & 0.451609 \tabularnewline
7 & 0.002095 & 0.0229 & 0.490866 \tabularnewline
8 & -0.030227 & -0.3311 & 0.370564 \tabularnewline
9 & 0.054912 & 0.6015 & 0.274312 \tabularnewline
10 & -0.01044 & -0.1144 & 0.454572 \tabularnewline
11 & 0.030124 & 0.33 & 0.370993 \tabularnewline
12 & -0.045644 & -0.5 & 0.308992 \tabularnewline
13 & -0.080847 & -0.8856 & 0.188792 \tabularnewline
14 & -0.014102 & -0.1545 & 0.438746 \tabularnewline
15 & -0.049519 & -0.5425 & 0.294256 \tabularnewline
16 & -0.023094 & -0.253 & 0.400355 \tabularnewline
17 & 0.012892 & 0.1412 & 0.443966 \tabularnewline
18 & -0.008893 & -0.0974 & 0.461277 \tabularnewline
19 & -0.006015 & -0.0659 & 0.473785 \tabularnewline
20 & -0.030322 & -0.3322 & 0.370175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235495&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]0.974725[/C][C]10.6776[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.006301[/C][C]0.069[/C][C]0.472544[/C][/ROW]
[ROW][C]3[/C][C]-0.063351[/C][C]-0.694[/C][C]0.24452[/C][/ROW]
[ROW][C]4[/C][C]-0.03124[/C][C]-0.3422[/C][C]0.366393[/C][/ROW]
[ROW][C]5[/C][C]0.004176[/C][C]0.0458[/C][C]0.481793[/C][/ROW]
[ROW][C]6[/C][C]-0.011124[/C][C]-0.1219[/C][C]0.451609[/C][/ROW]
[ROW][C]7[/C][C]0.002095[/C][C]0.0229[/C][C]0.490866[/C][/ROW]
[ROW][C]8[/C][C]-0.030227[/C][C]-0.3311[/C][C]0.370564[/C][/ROW]
[ROW][C]9[/C][C]0.054912[/C][C]0.6015[/C][C]0.274312[/C][/ROW]
[ROW][C]10[/C][C]-0.01044[/C][C]-0.1144[/C][C]0.454572[/C][/ROW]
[ROW][C]11[/C][C]0.030124[/C][C]0.33[/C][C]0.370993[/C][/ROW]
[ROW][C]12[/C][C]-0.045644[/C][C]-0.5[/C][C]0.308992[/C][/ROW]
[ROW][C]13[/C][C]-0.080847[/C][C]-0.8856[/C][C]0.188792[/C][/ROW]
[ROW][C]14[/C][C]-0.014102[/C][C]-0.1545[/C][C]0.438746[/C][/ROW]
[ROW][C]15[/C][C]-0.049519[/C][C]-0.5425[/C][C]0.294256[/C][/ROW]
[ROW][C]16[/C][C]-0.023094[/C][C]-0.253[/C][C]0.400355[/C][/ROW]
[ROW][C]17[/C][C]0.012892[/C][C]0.1412[/C][C]0.443966[/C][/ROW]
[ROW][C]18[/C][C]-0.008893[/C][C]-0.0974[/C][C]0.461277[/C][/ROW]
[ROW][C]19[/C][C]-0.006015[/C][C]-0.0659[/C][C]0.473785[/C][/ROW]
[ROW][C]20[/C][C]-0.030322[/C][C]-0.3322[/C][C]0.370175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235495&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235495&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	0.974725	10.6776	0
2	0.006301	0.069	0.472544
3	-0.063351	-0.694	0.24452
4	-0.03124	-0.3422	0.366393
5	0.004176	0.0458	0.481793
6	-0.011124	-0.1219	0.451609
7	0.002095	0.0229	0.490866
8	-0.030227	-0.3311	0.370564
9	0.054912	0.6015	0.274312
10	-0.01044	-0.1144	0.454572
11	0.030124	0.33	0.370993
12	-0.045644	-0.5	0.308992
13	-0.080847	-0.8856	0.188792
14	-0.014102	-0.1545	0.438746
15	-0.049519	-0.5425	0.294256
16	-0.023094	-0.253	0.400355
17	0.012892	0.1412	0.443966
18	-0.008893	-0.0974	0.461277
19	-0.006015	-0.0659	0.473785
20	-0.030322	-0.3322	0.370175

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code