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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, 02 Mar 2015 08:13:43 +0000

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/2015/Mar/02/t1425284090hufq2wdl33hp0f4.htm/, Retrieved Tue, 21 May 2024 05:02:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277767, Retrieved Tue, 21 May 2024 05:02:59 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

121

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

-       [(Partial) Autocorrelation Function] [Auto Correlatie W...] [2015-03-02 08:13:43] [70d22f55a70f3427b60459805adf1606] [Current]

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Dataseries X:

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Histogram

Boxplots

7,8
8
8,1
8,2
8,1
7,7
6,9
6,6
6,7
7
7,1
7
6,9
6,8
6,8
7
7
6,8
6,7
6,6
6,4
6,4
6,4
6,5
6,6
6,5
6,3
6,2
6,1
6,5
7,1
7,2
6,9
6,2
6
6,2
6,9
7,4
7,8
7,8
7,7
7,7
7,6
7,6
7,7
8
8,2
8,4
8,2
8,1
8,1
8,2
8,3
8,4
8,5
8,3
8,1
7,9
7,7
7,6
7,4
7,3
7
6,8
6,8
6,9
7,3
7,5
7,5
7,2
7
6,9
7
7,1
7,1
7,2
7,3
7,3
7,2
7,5
8
8,7
9
9
8,8
8,5
8,5
8,5
8,5
8,6
8,7
8,8
8,8
8,7
8,7
8,8

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	'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277767&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277767&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277767&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.93856	9.196	0
2	0.822348	8.0573	0
3	0.702786	6.8859	0
4	0.619266	6.0675	0
5	0.575993	5.6436	0
6	0.549801	5.3869	0
7	0.513519	5.0314	1e-06
8	0.452235	4.431	1.2e-05
9	0.370405	3.6292	0.000229
10	0.2822	2.765	0.003413
11	0.20684	2.0266	0.022738
12	0.142311	1.3944	0.083214
13	0.088624	0.8683	0.193689
14	0.033612	0.3293	0.371314
15	-0.035394	-0.3468	0.364755
16	-0.114865	-1.1254	0.131603
17	-0.192782	-1.8889	0.030964
18	-0.249443	-2.444	0.008175
19	-0.279892	-2.7424	0.003639

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.93856 & 9.196 & 0 \tabularnewline
2 & 0.822348 & 8.0573 & 0 \tabularnewline
3 & 0.702786 & 6.8859 & 0 \tabularnewline
4 & 0.619266 & 6.0675 & 0 \tabularnewline
5 & 0.575993 & 5.6436 & 0 \tabularnewline
6 & 0.549801 & 5.3869 & 0 \tabularnewline
7 & 0.513519 & 5.0314 & 1e-06 \tabularnewline
8 & 0.452235 & 4.431 & 1.2e-05 \tabularnewline
9 & 0.370405 & 3.6292 & 0.000229 \tabularnewline
10 & 0.2822 & 2.765 & 0.003413 \tabularnewline
11 & 0.20684 & 2.0266 & 0.022738 \tabularnewline
12 & 0.142311 & 1.3944 & 0.083214 \tabularnewline
13 & 0.088624 & 0.8683 & 0.193689 \tabularnewline
14 & 0.033612 & 0.3293 & 0.371314 \tabularnewline
15 & -0.035394 & -0.3468 & 0.364755 \tabularnewline
16 & -0.114865 & -1.1254 & 0.131603 \tabularnewline
17 & -0.192782 & -1.8889 & 0.030964 \tabularnewline
18 & -0.249443 & -2.444 & 0.008175 \tabularnewline
19 & -0.279892 & -2.7424 & 0.003639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277767&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]0.93856[/C][C]9.196[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.822348[/C][C]8.0573[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.702786[/C][C]6.8859[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.619266[/C][C]6.0675[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.575993[/C][C]5.6436[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.549801[/C][C]5.3869[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.513519[/C][C]5.0314[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.452235[/C][C]4.431[/C][C]1.2e-05[/C][/ROW]
[ROW][C]9[/C][C]0.370405[/C][C]3.6292[/C][C]0.000229[/C][/ROW]
[ROW][C]10[/C][C]0.2822[/C][C]2.765[/C][C]0.003413[/C][/ROW]
[ROW][C]11[/C][C]0.20684[/C][C]2.0266[/C][C]0.022738[/C][/ROW]
[ROW][C]12[/C][C]0.142311[/C][C]1.3944[/C][C]0.083214[/C][/ROW]
[ROW][C]13[/C][C]0.088624[/C][C]0.8683[/C][C]0.193689[/C][/ROW]
[ROW][C]14[/C][C]0.033612[/C][C]0.3293[/C][C]0.371314[/C][/ROW]
[ROW][C]15[/C][C]-0.035394[/C][C]-0.3468[/C][C]0.364755[/C][/ROW]
[ROW][C]16[/C][C]-0.114865[/C][C]-1.1254[/C][C]0.131603[/C][/ROW]
[ROW][C]17[/C][C]-0.192782[/C][C]-1.8889[/C][C]0.030964[/C][/ROW]
[ROW][C]18[/C][C]-0.249443[/C][C]-2.444[/C][C]0.008175[/C][/ROW]
[ROW][C]19[/C][C]-0.279892[/C][C]-2.7424[/C][C]0.003639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277767&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277767&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	0.93856	9.196	0
2	0.822348	8.0573	0
3	0.702786	6.8859	0
4	0.619266	6.0675	0
5	0.575993	5.6436	0
6	0.549801	5.3869	0
7	0.513519	5.0314	1e-06
8	0.452235	4.431	1.2e-05
9	0.370405	3.6292	0.000229
10	0.2822	2.765	0.003413
11	0.20684	2.0266	0.022738
12	0.142311	1.3944	0.083214
13	0.088624	0.8683	0.193689
14	0.033612	0.3293	0.371314
15	-0.035394	-0.3468	0.364755
16	-0.114865	-1.1254	0.131603
17	-0.192782	-1.8889	0.030964
18	-0.249443	-2.444	0.008175
19	-0.279892	-2.7424	0.003639

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.93856	9.196	0
2	-0.491553	-4.8162	3e-06
3	0.143079	1.4019	0.082088
4	0.233436	2.2872	0.01219
5	0.052687	0.5162	0.303442
6	-0.083672	-0.8198	0.207177
7	-0.094998	-0.9308	0.17715
8	-0.086494	-0.8475	0.199422
9	-0.055312	-0.5419	0.294555
10	-0.061302	-0.6006	0.274748
11	0.01043	0.1022	0.45941
12	-0.133787	-1.3108	0.096519
13	0.00516	0.0506	0.479893
14	-0.092342	-0.9048	0.183928
15	-0.151495	-1.4843	0.070498
16	-0.0389	-0.3811	0.351971
17	-0.015666	-0.1535	0.439166
18	0.062097	0.6084	0.272172
19	-0.006786	-0.0665	0.473562

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.93856 & 9.196 & 0 \tabularnewline
2 & -0.491553 & -4.8162 & 3e-06 \tabularnewline
3 & 0.143079 & 1.4019 & 0.082088 \tabularnewline
4 & 0.233436 & 2.2872 & 0.01219 \tabularnewline
5 & 0.052687 & 0.5162 & 0.303442 \tabularnewline
6 & -0.083672 & -0.8198 & 0.207177 \tabularnewline
7 & -0.094998 & -0.9308 & 0.17715 \tabularnewline
8 & -0.086494 & -0.8475 & 0.199422 \tabularnewline
9 & -0.055312 & -0.5419 & 0.294555 \tabularnewline
10 & -0.061302 & -0.6006 & 0.274748 \tabularnewline
11 & 0.01043 & 0.1022 & 0.45941 \tabularnewline
12 & -0.133787 & -1.3108 & 0.096519 \tabularnewline
13 & 0.00516 & 0.0506 & 0.479893 \tabularnewline
14 & -0.092342 & -0.9048 & 0.183928 \tabularnewline
15 & -0.151495 & -1.4843 & 0.070498 \tabularnewline
16 & -0.0389 & -0.3811 & 0.351971 \tabularnewline
17 & -0.015666 & -0.1535 & 0.439166 \tabularnewline
18 & 0.062097 & 0.6084 & 0.272172 \tabularnewline
19 & -0.006786 & -0.0665 & 0.473562 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277767&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]0.93856[/C][C]9.196[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.491553[/C][C]-4.8162[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]0.143079[/C][C]1.4019[/C][C]0.082088[/C][/ROW]
[ROW][C]4[/C][C]0.233436[/C][C]2.2872[/C][C]0.01219[/C][/ROW]
[ROW][C]5[/C][C]0.052687[/C][C]0.5162[/C][C]0.303442[/C][/ROW]
[ROW][C]6[/C][C]-0.083672[/C][C]-0.8198[/C][C]0.207177[/C][/ROW]
[ROW][C]7[/C][C]-0.094998[/C][C]-0.9308[/C][C]0.17715[/C][/ROW]
[ROW][C]8[/C][C]-0.086494[/C][C]-0.8475[/C][C]0.199422[/C][/ROW]
[ROW][C]9[/C][C]-0.055312[/C][C]-0.5419[/C][C]0.294555[/C][/ROW]
[ROW][C]10[/C][C]-0.061302[/C][C]-0.6006[/C][C]0.274748[/C][/ROW]
[ROW][C]11[/C][C]0.01043[/C][C]0.1022[/C][C]0.45941[/C][/ROW]
[ROW][C]12[/C][C]-0.133787[/C][C]-1.3108[/C][C]0.096519[/C][/ROW]
[ROW][C]13[/C][C]0.00516[/C][C]0.0506[/C][C]0.479893[/C][/ROW]
[ROW][C]14[/C][C]-0.092342[/C][C]-0.9048[/C][C]0.183928[/C][/ROW]
[ROW][C]15[/C][C]-0.151495[/C][C]-1.4843[/C][C]0.070498[/C][/ROW]
[ROW][C]16[/C][C]-0.0389[/C][C]-0.3811[/C][C]0.351971[/C][/ROW]
[ROW][C]17[/C][C]-0.015666[/C][C]-0.1535[/C][C]0.439166[/C][/ROW]
[ROW][C]18[/C][C]0.062097[/C][C]0.6084[/C][C]0.272172[/C][/ROW]
[ROW][C]19[/C][C]-0.006786[/C][C]-0.0665[/C][C]0.473562[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277767&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277767&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	0.93856	9.196	0
2	-0.491553	-4.8162	3e-06
3	0.143079	1.4019	0.082088
4	0.233436	2.2872	0.01219
5	0.052687	0.5162	0.303442
6	-0.083672	-0.8198	0.207177
7	-0.094998	-0.9308	0.17715
8	-0.086494	-0.8475	0.199422
9	-0.055312	-0.5419	0.294555
10	-0.061302	-0.6006	0.274748
11	0.01043	0.1022	0.45941
12	-0.133787	-1.3108	0.096519
13	0.00516	0.0506	0.479893
14	-0.092342	-0.9048	0.183928
15	-0.151495	-1.4843	0.070498
16	-0.0389	-0.3811	0.351971
17	-0.015666	-0.1535	0.439166
18	0.062097	0.6084	0.272172
19	-0.006786	-0.0665	0.473562

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