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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 06 Dec 2011 03:31:19 -0500

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/2011/Dec/06/t1323160341p77aw2sb7pf6801.htm/, Retrieved Sun, 28 Apr 2024 21:40:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151386, Retrieved Sun, 28 Apr 2024 21:40:35 +0000

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User-defined keywords

Estimated Impact

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

-     [Variance Reduction Matrix] [] [2011-12-06 08:04:41] [80bca13c5f9401fbb753952fd2952f4a]
- RMP   [(Partial) Autocorrelation Function] [] [2011-12-06 08:29:14] [80bca13c5f9401fbb753952fd2952f4a]
-   P       [(Partial) Autocorrelation Function] [] [2011-12-06 08:31:19] [204816f6f70a8d342ddc2b9d4f4a80d3] [Current]
- RMP         [Variance Reduction Matrix] [] [2011-12-06 08:45:18] [80bca13c5f9401fbb753952fd2952f4a] 
- RM            [ARIMA Backward Selection] [] [2011-12-06 09:03:08] [80bca13c5f9401fbb753952fd2952f4a] 
- RM              [ARIMA Forecasting] [] [2011-12-06 09:14:29] [80bca13c5f9401fbb753952fd2952f4a] 
-   PD              [ARIMA Forecasting] [Paper arima forec...] [2011-12-23 12:03:11] [805a2cd4f7b6665cd8870eed4006f53c] 

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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	'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151386&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151386&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151386&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.445679	4.3667	1.6e-05
2	0.238635	2.3381	0.010728
3	-0.010388	-0.1018	0.459571
4	-0.268135	-2.6272	0.005012
5	-0.352368	-3.4525	0.000414
6	-0.405123	-3.9694	7e-05
7	-0.32367	-3.1713	0.001019
8	-0.295987	-2.9001	0.002312
9	-0.014715	-0.1442	0.442833
10	0.160972	1.5772	0.05902
11	0.322334	3.1582	0.001061
12	0.644609	6.3159	0
13	0.31107	3.0478	0.001489
14	0.249792	2.4474	0.008102
15	0.033915	0.3323	0.370193
16	-0.170795	-1.6734	0.048748
17	-0.284227	-2.7848	0.003226
18	-0.361752	-3.5444	0.000305
19	-0.307704	-3.0149	0.001645

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.445679 & 4.3667 & 1.6e-05 \tabularnewline
2 & 0.238635 & 2.3381 & 0.010728 \tabularnewline
3 & -0.010388 & -0.1018 & 0.459571 \tabularnewline
4 & -0.268135 & -2.6272 & 0.005012 \tabularnewline
5 & -0.352368 & -3.4525 & 0.000414 \tabularnewline
6 & -0.405123 & -3.9694 & 7e-05 \tabularnewline
7 & -0.32367 & -3.1713 & 0.001019 \tabularnewline
8 & -0.295987 & -2.9001 & 0.002312 \tabularnewline
9 & -0.014715 & -0.1442 & 0.442833 \tabularnewline
10 & 0.160972 & 1.5772 & 0.05902 \tabularnewline
11 & 0.322334 & 3.1582 & 0.001061 \tabularnewline
12 & 0.644609 & 6.3159 & 0 \tabularnewline
13 & 0.31107 & 3.0478 & 0.001489 \tabularnewline
14 & 0.249792 & 2.4474 & 0.008102 \tabularnewline
15 & 0.033915 & 0.3323 & 0.370193 \tabularnewline
16 & -0.170795 & -1.6734 & 0.048748 \tabularnewline
17 & -0.284227 & -2.7848 & 0.003226 \tabularnewline
18 & -0.361752 & -3.5444 & 0.000305 \tabularnewline
19 & -0.307704 & -3.0149 & 0.001645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151386&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]0.445679[/C][C]4.3667[/C][C]1.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.238635[/C][C]2.3381[/C][C]0.010728[/C][/ROW]
[ROW][C]3[/C][C]-0.010388[/C][C]-0.1018[/C][C]0.459571[/C][/ROW]
[ROW][C]4[/C][C]-0.268135[/C][C]-2.6272[/C][C]0.005012[/C][/ROW]
[ROW][C]5[/C][C]-0.352368[/C][C]-3.4525[/C][C]0.000414[/C][/ROW]
[ROW][C]6[/C][C]-0.405123[/C][C]-3.9694[/C][C]7e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.32367[/C][C]-3.1713[/C][C]0.001019[/C][/ROW]
[ROW][C]8[/C][C]-0.295987[/C][C]-2.9001[/C][C]0.002312[/C][/ROW]
[ROW][C]9[/C][C]-0.014715[/C][C]-0.1442[/C][C]0.442833[/C][/ROW]
[ROW][C]10[/C][C]0.160972[/C][C]1.5772[/C][C]0.05902[/C][/ROW]
[ROW][C]11[/C][C]0.322334[/C][C]3.1582[/C][C]0.001061[/C][/ROW]
[ROW][C]12[/C][C]0.644609[/C][C]6.3159[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.31107[/C][C]3.0478[/C][C]0.001489[/C][/ROW]
[ROW][C]14[/C][C]0.249792[/C][C]2.4474[/C][C]0.008102[/C][/ROW]
[ROW][C]15[/C][C]0.033915[/C][C]0.3323[/C][C]0.370193[/C][/ROW]
[ROW][C]16[/C][C]-0.170795[/C][C]-1.6734[/C][C]0.048748[/C][/ROW]
[ROW][C]17[/C][C]-0.284227[/C][C]-2.7848[/C][C]0.003226[/C][/ROW]
[ROW][C]18[/C][C]-0.361752[/C][C]-3.5444[/C][C]0.000305[/C][/ROW]
[ROW][C]19[/C][C]-0.307704[/C][C]-3.0149[/C][C]0.001645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151386&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151386&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	0.445679	4.3667	1.6e-05
2	0.238635	2.3381	0.010728
3	-0.010388	-0.1018	0.459571
4	-0.268135	-2.6272	0.005012
5	-0.352368	-3.4525	0.000414
6	-0.405123	-3.9694	7e-05
7	-0.32367	-3.1713	0.001019
8	-0.295987	-2.9001	0.002312
9	-0.014715	-0.1442	0.442833
10	0.160972	1.5772	0.05902
11	0.322334	3.1582	0.001061
12	0.644609	6.3159	0
13	0.31107	3.0478	0.001489
14	0.249792	2.4474	0.008102
15	0.033915	0.3323	0.370193
16	-0.170795	-1.6734	0.048748
17	-0.284227	-2.7848	0.003226
18	-0.361752	-3.5444	0.000305
19	-0.307704	-3.0149	0.001645

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.445679	4.3667	1.6e-05
2	0.049921	0.4891	0.312935
3	-0.167234	-1.6385	0.05229
4	-0.280467	-2.748	0.003581
5	-0.155827	-1.5268	0.065051
6	-0.176867	-1.7329	0.043159
7	-0.097218	-0.9525	0.171608
8	-0.225464	-2.2091	0.014774
9	0.091048	0.8921	0.187288
10	0.056648	0.555	0.290082
11	0.110086	1.0786	0.14173
12	0.47152	4.6199	6e-06
13	-0.230962	-2.263	0.012946
14	0.11336	1.1107	0.134736
15	0.02576	0.2524	0.400637
16	-0.005459	-0.0535	0.478729
17	0.018341	0.1797	0.428881
18	-0.056239	-0.551	0.291447
19	-0.017588	-0.1723	0.431773

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.445679 & 4.3667 & 1.6e-05 \tabularnewline
2 & 0.049921 & 0.4891 & 0.312935 \tabularnewline
3 & -0.167234 & -1.6385 & 0.05229 \tabularnewline
4 & -0.280467 & -2.748 & 0.003581 \tabularnewline
5 & -0.155827 & -1.5268 & 0.065051 \tabularnewline
6 & -0.176867 & -1.7329 & 0.043159 \tabularnewline
7 & -0.097218 & -0.9525 & 0.171608 \tabularnewline
8 & -0.225464 & -2.2091 & 0.014774 \tabularnewline
9 & 0.091048 & 0.8921 & 0.187288 \tabularnewline
10 & 0.056648 & 0.555 & 0.290082 \tabularnewline
11 & 0.110086 & 1.0786 & 0.14173 \tabularnewline
12 & 0.47152 & 4.6199 & 6e-06 \tabularnewline
13 & -0.230962 & -2.263 & 0.012946 \tabularnewline
14 & 0.11336 & 1.1107 & 0.134736 \tabularnewline
15 & 0.02576 & 0.2524 & 0.400637 \tabularnewline
16 & -0.005459 & -0.0535 & 0.478729 \tabularnewline
17 & 0.018341 & 0.1797 & 0.428881 \tabularnewline
18 & -0.056239 & -0.551 & 0.291447 \tabularnewline
19 & -0.017588 & -0.1723 & 0.431773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151386&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]0.445679[/C][C]4.3667[/C][C]1.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.049921[/C][C]0.4891[/C][C]0.312935[/C][/ROW]
[ROW][C]3[/C][C]-0.167234[/C][C]-1.6385[/C][C]0.05229[/C][/ROW]
[ROW][C]4[/C][C]-0.280467[/C][C]-2.748[/C][C]0.003581[/C][/ROW]
[ROW][C]5[/C][C]-0.155827[/C][C]-1.5268[/C][C]0.065051[/C][/ROW]
[ROW][C]6[/C][C]-0.176867[/C][C]-1.7329[/C][C]0.043159[/C][/ROW]
[ROW][C]7[/C][C]-0.097218[/C][C]-0.9525[/C][C]0.171608[/C][/ROW]
[ROW][C]8[/C][C]-0.225464[/C][C]-2.2091[/C][C]0.014774[/C][/ROW]
[ROW][C]9[/C][C]0.091048[/C][C]0.8921[/C][C]0.187288[/C][/ROW]
[ROW][C]10[/C][C]0.056648[/C][C]0.555[/C][C]0.290082[/C][/ROW]
[ROW][C]11[/C][C]0.110086[/C][C]1.0786[/C][C]0.14173[/C][/ROW]
[ROW][C]12[/C][C]0.47152[/C][C]4.6199[/C][C]6e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.230962[/C][C]-2.263[/C][C]0.012946[/C][/ROW]
[ROW][C]14[/C][C]0.11336[/C][C]1.1107[/C][C]0.134736[/C][/ROW]
[ROW][C]15[/C][C]0.02576[/C][C]0.2524[/C][C]0.400637[/C][/ROW]
[ROW][C]16[/C][C]-0.005459[/C][C]-0.0535[/C][C]0.478729[/C][/ROW]
[ROW][C]17[/C][C]0.018341[/C][C]0.1797[/C][C]0.428881[/C][/ROW]
[ROW][C]18[/C][C]-0.056239[/C][C]-0.551[/C][C]0.291447[/C][/ROW]
[ROW][C]19[/C][C]-0.017588[/C][C]-0.1723[/C][C]0.431773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151386&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151386&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	0.445679	4.3667	1.6e-05
2	0.049921	0.4891	0.312935
3	-0.167234	-1.6385	0.05229
4	-0.280467	-2.748	0.003581
5	-0.155827	-1.5268	0.065051
6	-0.176867	-1.7329	0.043159
7	-0.097218	-0.9525	0.171608
8	-0.225464	-2.2091	0.014774
9	0.091048	0.8921	0.187288
10	0.056648	0.555	0.290082
11	0.110086	1.0786	0.14173
12	0.47152	4.6199	6e-06
13	-0.230962	-2.263	0.012946
14	0.11336	1.1107	0.134736
15	0.02576	0.2524	0.400637
16	-0.005459	-0.0535	0.478729
17	0.018341	0.1797	0.428881
18	-0.056239	-0.551	0.291447
19	-0.017588	-0.1723	0.431773

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