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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

Thu, 07 Aug 2014 16:54:36 +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/07/t1407426947l1khmqqlym9xvan.htm/, Retrieved Thu, 16 May 2024 15:05:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235421, Retrieved Thu, 16 May 2024 15:05:52 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Daemen Wout

Estimated Impact

169

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

-     [Histogram] [Tijdreeks 1 - Stap 3] [2014-07-16 17:55:19] [db363657be53a1294332fdf107f4512c]
- RMP   [Kernel Density Estimation] [Tijdreeks 1 - Stap 6] [2014-07-26 16:09:14] [74be16979710d4c4e7c6647856088456]
- RM      [Central Tendency] [Tijdreeks 1 - Sta...] [2014-07-26 17:27:42] [db363657be53a1294332fdf107f4512c]
- RMP         [(Partial) Autocorrelation Function] [Tijdreeks  - Stap 17] [2014-08-07 15:54:36] [a3f6f3ab25c27d7686091f6989fa462a] [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	2 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235421&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235421&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235421&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	'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.018818	0.2053	0.418852
2	-0.301952	-3.2939	0.000651
3	-0.309555	-3.3768	0.000496
4	-0.140993	-1.538	0.063346
5	0.190834	2.0818	0.019754
6	0.300912	3.2826	0.000675
7	0.175894	1.9188	0.028704
8	-0.089058	-0.9715	0.166632
9	-0.332198	-3.6239	0.000214
10	-0.286088	-3.1209	0.001132
11	0.065212	0.7114	0.23912
12	0.798033	8.7055	0
13	0.003691	0.0403	0.483975
14	-0.253091	-2.7609	0.003339
15	-0.24486	-2.6711	0.004309
16	-0.117948	-1.2867	0.100355
17	0.127764	1.3937	0.082997
18	0.273751	2.9863	0.001715
19	0.152463	1.6632	0.049454
20	-0.087046	-0.9496	0.172131

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.018818 & 0.2053 & 0.418852 \tabularnewline
2 & -0.301952 & -3.2939 & 0.000651 \tabularnewline
3 & -0.309555 & -3.3768 & 0.000496 \tabularnewline
4 & -0.140993 & -1.538 & 0.063346 \tabularnewline
5 & 0.190834 & 2.0818 & 0.019754 \tabularnewline
6 & 0.300912 & 3.2826 & 0.000675 \tabularnewline
7 & 0.175894 & 1.9188 & 0.028704 \tabularnewline
8 & -0.089058 & -0.9715 & 0.166632 \tabularnewline
9 & -0.332198 & -3.6239 & 0.000214 \tabularnewline
10 & -0.286088 & -3.1209 & 0.001132 \tabularnewline
11 & 0.065212 & 0.7114 & 0.23912 \tabularnewline
12 & 0.798033 & 8.7055 & 0 \tabularnewline
13 & 0.003691 & 0.0403 & 0.483975 \tabularnewline
14 & -0.253091 & -2.7609 & 0.003339 \tabularnewline
15 & -0.24486 & -2.6711 & 0.004309 \tabularnewline
16 & -0.117948 & -1.2867 & 0.100355 \tabularnewline
17 & 0.127764 & 1.3937 & 0.082997 \tabularnewline
18 & 0.273751 & 2.9863 & 0.001715 \tabularnewline
19 & 0.152463 & 1.6632 & 0.049454 \tabularnewline
20 & -0.087046 & -0.9496 & 0.172131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235421&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]0.018818[/C][C]0.2053[/C][C]0.418852[/C][/ROW]
[ROW][C]2[/C][C]-0.301952[/C][C]-3.2939[/C][C]0.000651[/C][/ROW]
[ROW][C]3[/C][C]-0.309555[/C][C]-3.3768[/C][C]0.000496[/C][/ROW]
[ROW][C]4[/C][C]-0.140993[/C][C]-1.538[/C][C]0.063346[/C][/ROW]
[ROW][C]5[/C][C]0.190834[/C][C]2.0818[/C][C]0.019754[/C][/ROW]
[ROW][C]6[/C][C]0.300912[/C][C]3.2826[/C][C]0.000675[/C][/ROW]
[ROW][C]7[/C][C]0.175894[/C][C]1.9188[/C][C]0.028704[/C][/ROW]
[ROW][C]8[/C][C]-0.089058[/C][C]-0.9715[/C][C]0.166632[/C][/ROW]
[ROW][C]9[/C][C]-0.332198[/C][C]-3.6239[/C][C]0.000214[/C][/ROW]
[ROW][C]10[/C][C]-0.286088[/C][C]-3.1209[/C][C]0.001132[/C][/ROW]
[ROW][C]11[/C][C]0.065212[/C][C]0.7114[/C][C]0.23912[/C][/ROW]
[ROW][C]12[/C][C]0.798033[/C][C]8.7055[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.003691[/C][C]0.0403[/C][C]0.483975[/C][/ROW]
[ROW][C]14[/C][C]-0.253091[/C][C]-2.7609[/C][C]0.003339[/C][/ROW]
[ROW][C]15[/C][C]-0.24486[/C][C]-2.6711[/C][C]0.004309[/C][/ROW]
[ROW][C]16[/C][C]-0.117948[/C][C]-1.2867[/C][C]0.100355[/C][/ROW]
[ROW][C]17[/C][C]0.127764[/C][C]1.3937[/C][C]0.082997[/C][/ROW]
[ROW][C]18[/C][C]0.273751[/C][C]2.9863[/C][C]0.001715[/C][/ROW]
[ROW][C]19[/C][C]0.152463[/C][C]1.6632[/C][C]0.049454[/C][/ROW]
[ROW][C]20[/C][C]-0.087046[/C][C]-0.9496[/C][C]0.172131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235421&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235421&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	0.018818	0.2053	0.418852
2	-0.301952	-3.2939	0.000651
3	-0.309555	-3.3768	0.000496
4	-0.140993	-1.538	0.063346
5	0.190834	2.0818	0.019754
6	0.300912	3.2826	0.000675
7	0.175894	1.9188	0.028704
8	-0.089058	-0.9715	0.166632
9	-0.332198	-3.6239	0.000214
10	-0.286088	-3.1209	0.001132
11	0.065212	0.7114	0.23912
12	0.798033	8.7055	0
13	0.003691	0.0403	0.483975
14	-0.253091	-2.7609	0.003339
15	-0.24486	-2.6711	0.004309
16	-0.117948	-1.2867	0.100355
17	0.127764	1.3937	0.082997
18	0.273751	2.9863	0.001715
19	0.152463	1.6632	0.049454
20	-0.087046	-0.9496	0.172131

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.018818	0.2053	0.418852
2	-0.302413	-3.2989	0.00064
3	-0.326421	-3.5608	0.000266
4	-0.304046	-3.3167	0.000604
5	-0.070776	-0.7721	0.220801
6	0.095371	1.0404	0.150138
7	0.211231	2.3043	0.011471
8	0.185049	2.0187	0.022886
9	-0.031134	-0.3396	0.367367
10	-0.240332	-2.6217	0.004946
11	-0.235164	-2.5653	0.005775
12	0.676212	7.3766	0
13	-0.030315	-0.3307	0.370729
14	0.081387	0.8878	0.188212
15	0.126621	1.3813	0.084892
16	0.182846	1.9946	0.024185
17	-0.10257	-1.1189	0.132717
18	0.015194	0.1657	0.434321
19	-0.03566	-0.389	0.348984
20	-0.122823	-1.3398	0.091425

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.018818 & 0.2053 & 0.418852 \tabularnewline
2 & -0.302413 & -3.2989 & 0.00064 \tabularnewline
3 & -0.326421 & -3.5608 & 0.000266 \tabularnewline
4 & -0.304046 & -3.3167 & 0.000604 \tabularnewline
5 & -0.070776 & -0.7721 & 0.220801 \tabularnewline
6 & 0.095371 & 1.0404 & 0.150138 \tabularnewline
7 & 0.211231 & 2.3043 & 0.011471 \tabularnewline
8 & 0.185049 & 2.0187 & 0.022886 \tabularnewline
9 & -0.031134 & -0.3396 & 0.367367 \tabularnewline
10 & -0.240332 & -2.6217 & 0.004946 \tabularnewline
11 & -0.235164 & -2.5653 & 0.005775 \tabularnewline
12 & 0.676212 & 7.3766 & 0 \tabularnewline
13 & -0.030315 & -0.3307 & 0.370729 \tabularnewline
14 & 0.081387 & 0.8878 & 0.188212 \tabularnewline
15 & 0.126621 & 1.3813 & 0.084892 \tabularnewline
16 & 0.182846 & 1.9946 & 0.024185 \tabularnewline
17 & -0.10257 & -1.1189 & 0.132717 \tabularnewline
18 & 0.015194 & 0.1657 & 0.434321 \tabularnewline
19 & -0.03566 & -0.389 & 0.348984 \tabularnewline
20 & -0.122823 & -1.3398 & 0.091425 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235421&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]0.018818[/C][C]0.2053[/C][C]0.418852[/C][/ROW]
[ROW][C]2[/C][C]-0.302413[/C][C]-3.2989[/C][C]0.00064[/C][/ROW]
[ROW][C]3[/C][C]-0.326421[/C][C]-3.5608[/C][C]0.000266[/C][/ROW]
[ROW][C]4[/C][C]-0.304046[/C][C]-3.3167[/C][C]0.000604[/C][/ROW]
[ROW][C]5[/C][C]-0.070776[/C][C]-0.7721[/C][C]0.220801[/C][/ROW]
[ROW][C]6[/C][C]0.095371[/C][C]1.0404[/C][C]0.150138[/C][/ROW]
[ROW][C]7[/C][C]0.211231[/C][C]2.3043[/C][C]0.011471[/C][/ROW]
[ROW][C]8[/C][C]0.185049[/C][C]2.0187[/C][C]0.022886[/C][/ROW]
[ROW][C]9[/C][C]-0.031134[/C][C]-0.3396[/C][C]0.367367[/C][/ROW]
[ROW][C]10[/C][C]-0.240332[/C][C]-2.6217[/C][C]0.004946[/C][/ROW]
[ROW][C]11[/C][C]-0.235164[/C][C]-2.5653[/C][C]0.005775[/C][/ROW]
[ROW][C]12[/C][C]0.676212[/C][C]7.3766[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.030315[/C][C]-0.3307[/C][C]0.370729[/C][/ROW]
[ROW][C]14[/C][C]0.081387[/C][C]0.8878[/C][C]0.188212[/C][/ROW]
[ROW][C]15[/C][C]0.126621[/C][C]1.3813[/C][C]0.084892[/C][/ROW]
[ROW][C]16[/C][C]0.182846[/C][C]1.9946[/C][C]0.024185[/C][/ROW]
[ROW][C]17[/C][C]-0.10257[/C][C]-1.1189[/C][C]0.132717[/C][/ROW]
[ROW][C]18[/C][C]0.015194[/C][C]0.1657[/C][C]0.434321[/C][/ROW]
[ROW][C]19[/C][C]-0.03566[/C][C]-0.389[/C][C]0.348984[/C][/ROW]
[ROW][C]20[/C][C]-0.122823[/C][C]-1.3398[/C][C]0.091425[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235421&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235421&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	0.018818	0.2053	0.418852
2	-0.302413	-3.2989	0.00064
3	-0.326421	-3.5608	0.000266
4	-0.304046	-3.3167	0.000604
5	-0.070776	-0.7721	0.220801
6	0.095371	1.0404	0.150138
7	0.211231	2.3043	0.011471
8	0.185049	2.0187	0.022886
9	-0.031134	-0.3396	0.367367
10	-0.240332	-2.6217	0.004946
11	-0.235164	-2.5653	0.005775
12	0.676212	7.3766	0
13	-0.030315	-0.3307	0.370729
14	0.081387	0.8878	0.188212
15	0.126621	1.3813	0.084892
16	0.182846	1.9946	0.024185
17	-0.10257	-1.1189	0.132717
18	0.015194	0.1657	0.434321
19	-0.03566	-0.389	0.348984
20	-0.122823	-1.3398	0.091425

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '1'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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