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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, 29 Nov 2011 14:07:12 -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/Nov/29/t13225937242ij5nvqq1qzxiqv.htm/, Retrieved Fri, 19 Apr 2024 10:44:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148680, Retrieved Fri, 19 Apr 2024 10:44:55 +0000

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-     [Classical Decomposition] [HPC Retail Sales] [2008-03-02 16:19:32] [74be16979710d4c4e7c6647856088456]
-  M D  [Classical Decomposition] [Workshop 8, Class...] [2010-11-28 20:55:54] [d946de7cca328fbcf207448a112523ab]
- RMPD      [(Partial) Autocorrelation Function] [ws8 autocorrelati...] [2011-11-29 19:07:12] [635499bc27d9f41bf7bccae25a54e146] [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	'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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148680&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148680&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148680&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.426071	4.8952	1e-06
2	0.502397	5.7721	0
3	0.49896	5.7326	0
4	0.263079	3.0225	0.001506
5	0.330445	3.7965	0.000111
6	0.278938	3.2047	0.000848
7	0.263177	3.0237	0.001501
8	0.262196	3.0124	0.001554
9	0.428222	4.9199	1e-06
10	0.392143	4.5054	7e-06
11	0.34593	3.9744	5.8e-05
12	0.668004	7.6748	0
13	0.255093	2.9308	0.001993
14	0.378231	4.3455	1.4e-05
15	0.292332	3.3586	0.000512
16	0.155373	1.7851	0.038271
17	0.183501	2.1083	0.018449
18	0.122163	1.4035	0.081401
19	0.134502	1.5453	0.062332
20	0.10859	1.2476	0.107193
21	0.238852	2.7442	0.003455

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.426071 & 4.8952 & 1e-06 \tabularnewline
2 & 0.502397 & 5.7721 & 0 \tabularnewline
3 & 0.49896 & 5.7326 & 0 \tabularnewline
4 & 0.263079 & 3.0225 & 0.001506 \tabularnewline
5 & 0.330445 & 3.7965 & 0.000111 \tabularnewline
6 & 0.278938 & 3.2047 & 0.000848 \tabularnewline
7 & 0.263177 & 3.0237 & 0.001501 \tabularnewline
8 & 0.262196 & 3.0124 & 0.001554 \tabularnewline
9 & 0.428222 & 4.9199 & 1e-06 \tabularnewline
10 & 0.392143 & 4.5054 & 7e-06 \tabularnewline
11 & 0.34593 & 3.9744 & 5.8e-05 \tabularnewline
12 & 0.668004 & 7.6748 & 0 \tabularnewline
13 & 0.255093 & 2.9308 & 0.001993 \tabularnewline
14 & 0.378231 & 4.3455 & 1.4e-05 \tabularnewline
15 & 0.292332 & 3.3586 & 0.000512 \tabularnewline
16 & 0.155373 & 1.7851 & 0.038271 \tabularnewline
17 & 0.183501 & 2.1083 & 0.018449 \tabularnewline
18 & 0.122163 & 1.4035 & 0.081401 \tabularnewline
19 & 0.134502 & 1.5453 & 0.062332 \tabularnewline
20 & 0.10859 & 1.2476 & 0.107193 \tabularnewline
21 & 0.238852 & 2.7442 & 0.003455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148680&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]0.426071[/C][C]4.8952[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.502397[/C][C]5.7721[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.49896[/C][C]5.7326[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.263079[/C][C]3.0225[/C][C]0.001506[/C][/ROW]
[ROW][C]5[/C][C]0.330445[/C][C]3.7965[/C][C]0.000111[/C][/ROW]
[ROW][C]6[/C][C]0.278938[/C][C]3.2047[/C][C]0.000848[/C][/ROW]
[ROW][C]7[/C][C]0.263177[/C][C]3.0237[/C][C]0.001501[/C][/ROW]
[ROW][C]8[/C][C]0.262196[/C][C]3.0124[/C][C]0.001554[/C][/ROW]
[ROW][C]9[/C][C]0.428222[/C][C]4.9199[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.392143[/C][C]4.5054[/C][C]7e-06[/C][/ROW]
[ROW][C]11[/C][C]0.34593[/C][C]3.9744[/C][C]5.8e-05[/C][/ROW]
[ROW][C]12[/C][C]0.668004[/C][C]7.6748[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.255093[/C][C]2.9308[/C][C]0.001993[/C][/ROW]
[ROW][C]14[/C][C]0.378231[/C][C]4.3455[/C][C]1.4e-05[/C][/ROW]
[ROW][C]15[/C][C]0.292332[/C][C]3.3586[/C][C]0.000512[/C][/ROW]
[ROW][C]16[/C][C]0.155373[/C][C]1.7851[/C][C]0.038271[/C][/ROW]
[ROW][C]17[/C][C]0.183501[/C][C]2.1083[/C][C]0.018449[/C][/ROW]
[ROW][C]18[/C][C]0.122163[/C][C]1.4035[/C][C]0.081401[/C][/ROW]
[ROW][C]19[/C][C]0.134502[/C][C]1.5453[/C][C]0.062332[/C][/ROW]
[ROW][C]20[/C][C]0.10859[/C][C]1.2476[/C][C]0.107193[/C][/ROW]
[ROW][C]21[/C][C]0.238852[/C][C]2.7442[/C][C]0.003455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148680&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148680&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	0.426071	4.8952	1e-06
2	0.502397	5.7721	0
3	0.49896	5.7326	0
4	0.263079	3.0225	0.001506
5	0.330445	3.7965	0.000111
6	0.278938	3.2047	0.000848
7	0.263177	3.0237	0.001501
8	0.262196	3.0124	0.001554
9	0.428222	4.9199	1e-06
10	0.392143	4.5054	7e-06
11	0.34593	3.9744	5.8e-05
12	0.668004	7.6748	0
13	0.255093	2.9308	0.001993
14	0.378231	4.3455	1.4e-05
15	0.292332	3.3586	0.000512
16	0.155373	1.7851	0.038271
17	0.183501	2.1083	0.018449
18	0.122163	1.4035	0.081401
19	0.134502	1.5453	0.062332
20	0.10859	1.2476	0.107193
21	0.238852	2.7442	0.003455

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.426071	4.8952	1e-06
2	0.392028	4.5041	7e-06
3	0.291316	3.347	0.000532
4	-0.145689	-1.6738	0.048265
5	0.008586	0.0986	0.460785
6	0.061161	0.7027	0.241744
7	0.116985	1.3441	0.090618
8	0.026311	0.3023	0.381454
9	0.320445	3.6816	0.000168
10	0.184066	2.1148	0.018165
11	-0.054994	-0.6318	0.264296
12	0.438681	5.0401	1e-06
13	-0.282981	-3.2512	0.000729
14	-0.088189	-1.0132	0.156407
15	-0.205961	-2.3663	0.00971
16	0.079673	0.9154	0.180832
17	-0.155973	-1.792	0.037712
18	-0.031635	-0.3635	0.358422
19	-0.012991	-0.1493	0.440789
20	-0.056763	-0.6522	0.257716
21	-0.037947	-0.436	0.331782

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.426071 & 4.8952 & 1e-06 \tabularnewline
2 & 0.392028 & 4.5041 & 7e-06 \tabularnewline
3 & 0.291316 & 3.347 & 0.000532 \tabularnewline
4 & -0.145689 & -1.6738 & 0.048265 \tabularnewline
5 & 0.008586 & 0.0986 & 0.460785 \tabularnewline
6 & 0.061161 & 0.7027 & 0.241744 \tabularnewline
7 & 0.116985 & 1.3441 & 0.090618 \tabularnewline
8 & 0.026311 & 0.3023 & 0.381454 \tabularnewline
9 & 0.320445 & 3.6816 & 0.000168 \tabularnewline
10 & 0.184066 & 2.1148 & 0.018165 \tabularnewline
11 & -0.054994 & -0.6318 & 0.264296 \tabularnewline
12 & 0.438681 & 5.0401 & 1e-06 \tabularnewline
13 & -0.282981 & -3.2512 & 0.000729 \tabularnewline
14 & -0.088189 & -1.0132 & 0.156407 \tabularnewline
15 & -0.205961 & -2.3663 & 0.00971 \tabularnewline
16 & 0.079673 & 0.9154 & 0.180832 \tabularnewline
17 & -0.155973 & -1.792 & 0.037712 \tabularnewline
18 & -0.031635 & -0.3635 & 0.358422 \tabularnewline
19 & -0.012991 & -0.1493 & 0.440789 \tabularnewline
20 & -0.056763 & -0.6522 & 0.257716 \tabularnewline
21 & -0.037947 & -0.436 & 0.331782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148680&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]0.426071[/C][C]4.8952[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.392028[/C][C]4.5041[/C][C]7e-06[/C][/ROW]
[ROW][C]3[/C][C]0.291316[/C][C]3.347[/C][C]0.000532[/C][/ROW]
[ROW][C]4[/C][C]-0.145689[/C][C]-1.6738[/C][C]0.048265[/C][/ROW]
[ROW][C]5[/C][C]0.008586[/C][C]0.0986[/C][C]0.460785[/C][/ROW]
[ROW][C]6[/C][C]0.061161[/C][C]0.7027[/C][C]0.241744[/C][/ROW]
[ROW][C]7[/C][C]0.116985[/C][C]1.3441[/C][C]0.090618[/C][/ROW]
[ROW][C]8[/C][C]0.026311[/C][C]0.3023[/C][C]0.381454[/C][/ROW]
[ROW][C]9[/C][C]0.320445[/C][C]3.6816[/C][C]0.000168[/C][/ROW]
[ROW][C]10[/C][C]0.184066[/C][C]2.1148[/C][C]0.018165[/C][/ROW]
[ROW][C]11[/C][C]-0.054994[/C][C]-0.6318[/C][C]0.264296[/C][/ROW]
[ROW][C]12[/C][C]0.438681[/C][C]5.0401[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.282981[/C][C]-3.2512[/C][C]0.000729[/C][/ROW]
[ROW][C]14[/C][C]-0.088189[/C][C]-1.0132[/C][C]0.156407[/C][/ROW]
[ROW][C]15[/C][C]-0.205961[/C][C]-2.3663[/C][C]0.00971[/C][/ROW]
[ROW][C]16[/C][C]0.079673[/C][C]0.9154[/C][C]0.180832[/C][/ROW]
[ROW][C]17[/C][C]-0.155973[/C][C]-1.792[/C][C]0.037712[/C][/ROW]
[ROW][C]18[/C][C]-0.031635[/C][C]-0.3635[/C][C]0.358422[/C][/ROW]
[ROW][C]19[/C][C]-0.012991[/C][C]-0.1493[/C][C]0.440789[/C][/ROW]
[ROW][C]20[/C][C]-0.056763[/C][C]-0.6522[/C][C]0.257716[/C][/ROW]
[ROW][C]21[/C][C]-0.037947[/C][C]-0.436[/C][C]0.331782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148680&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148680&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	0.426071	4.8952	1e-06
2	0.392028	4.5041	7e-06
3	0.291316	3.347	0.000532
4	-0.145689	-1.6738	0.048265
5	0.008586	0.0986	0.460785
6	0.061161	0.7027	0.241744
7	0.116985	1.3441	0.090618
8	0.026311	0.3023	0.381454
9	0.320445	3.6816	0.000168
10	0.184066	2.1148	0.018165
11	-0.054994	-0.6318	0.264296
12	0.438681	5.0401	1e-06
13	-0.282981	-3.2512	0.000729
14	-0.088189	-1.0132	0.156407
15	-0.205961	-2.3663	0.00971
16	0.079673	0.9154	0.180832
17	-0.155973	-1.792	0.037712
18	-0.031635	-0.3635	0.358422
19	-0.012991	-0.1493	0.440789
20	-0.056763	-0.6522	0.257716
21	-0.037947	-0.436	0.331782

Figure 1

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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