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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 16 Nov 2015 09:59:43 +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/Nov/16/t1447668014847qn1mk9521loj.htm/, Retrieved Wed, 15 May 2024 14:48:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283357, Retrieved Wed, 15 May 2024 14:48:38 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

123

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

-       [(Partial) Autocorrelation Function] [] [2015-11-16 09:59:43] [663b8bcb3523d59827bca0af0b37f04c] [Current]
- R PD    [(Partial) Autocorrelation Function] [] [2015-12-30 12:35:04] [1abbea75cc6be7d57004024c66566ad0] 

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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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283357&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283357&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283357&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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.968957	10.0697	0
2	0.936417	9.7315	0
3	0.904633	9.4012	0
4	0.87548	9.0983	0
5	0.84715	8.8038	0
6	0.81803	8.5012	0
7	0.78985	8.2084	0
8	0.761009	7.9086	0
9	0.734535	7.6335	0
10	0.711978	7.3991	0
11	0.689383	7.1643	0
12	0.665107	6.912	0
13	0.635433	6.6036	0
14	0.604084	6.2778	0
15	0.572803	5.9527	0
16	0.546277	5.6771	0
17	0.521977	5.4245	0
18	0.497433	5.1695	1e-06
19	0.473961	4.9255	2e-06
20	0.449451	4.6708	4e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.968957 & 10.0697 & 0 \tabularnewline
2 & 0.936417 & 9.7315 & 0 \tabularnewline
3 & 0.904633 & 9.4012 & 0 \tabularnewline
4 & 0.87548 & 9.0983 & 0 \tabularnewline
5 & 0.84715 & 8.8038 & 0 \tabularnewline
6 & 0.81803 & 8.5012 & 0 \tabularnewline
7 & 0.78985 & 8.2084 & 0 \tabularnewline
8 & 0.761009 & 7.9086 & 0 \tabularnewline
9 & 0.734535 & 7.6335 & 0 \tabularnewline
10 & 0.711978 & 7.3991 & 0 \tabularnewline
11 & 0.689383 & 7.1643 & 0 \tabularnewline
12 & 0.665107 & 6.912 & 0 \tabularnewline
13 & 0.635433 & 6.6036 & 0 \tabularnewline
14 & 0.604084 & 6.2778 & 0 \tabularnewline
15 & 0.572803 & 5.9527 & 0 \tabularnewline
16 & 0.546277 & 5.6771 & 0 \tabularnewline
17 & 0.521977 & 5.4245 & 0 \tabularnewline
18 & 0.497433 & 5.1695 & 1e-06 \tabularnewline
19 & 0.473961 & 4.9255 & 2e-06 \tabularnewline
20 & 0.449451 & 4.6708 & 4e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283357&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]0.968957[/C][C]10.0697[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.936417[/C][C]9.7315[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.904633[/C][C]9.4012[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.87548[/C][C]9.0983[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.84715[/C][C]8.8038[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.81803[/C][C]8.5012[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.78985[/C][C]8.2084[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.761009[/C][C]7.9086[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.734535[/C][C]7.6335[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.711978[/C][C]7.3991[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.689383[/C][C]7.1643[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.665107[/C][C]6.912[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.635433[/C][C]6.6036[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.604084[/C][C]6.2778[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.572803[/C][C]5.9527[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.546277[/C][C]5.6771[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.521977[/C][C]5.4245[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.497433[/C][C]5.1695[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]0.473961[/C][C]4.9255[/C][C]2e-06[/C][/ROW]
[ROW][C]20[/C][C]0.449451[/C][C]4.6708[/C][C]4e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283357&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283357&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	0.968957	10.0697	0
2	0.936417	9.7315	0
3	0.904633	9.4012	0
4	0.87548	9.0983	0
5	0.84715	8.8038	0
6	0.81803	8.5012	0
7	0.78985	8.2084	0
8	0.761009	7.9086	0
9	0.734535	7.6335	0
10	0.711978	7.3991	0
11	0.689383	7.1643	0
12	0.665107	6.912	0
13	0.635433	6.6036	0
14	0.604084	6.2778	0
15	0.572803	5.9527	0
16	0.546277	5.6771	0
17	0.521977	5.4245	0
18	0.497433	5.1695	1e-06
19	0.473961	4.9255	2e-06
20	0.449451	4.6708	4e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.968957	10.0697	0
2	-0.040263	-0.4184	0.338234
3	-0.003842	-0.0399	0.484111
4	0.025819	0.2683	0.394483
5	-0.003982	-0.0414	0.483533
6	-0.027977	-0.2907	0.385903
7	0.002018	0.021	0.491655
8	-0.026656	-0.277	0.391148
9	0.022468	0.2335	0.407908
10	0.047915	0.4979	0.309767
11	-0.016794	-0.1745	0.430887
12	-0.037606	-0.3908	0.348353
13	-0.095939	-0.997	0.160489
14	-0.042533	-0.442	0.329681
15	-0.020917	-0.2174	0.414162
16	0.053367	0.5546	0.290156
17	0.013919	0.1447	0.442628
18	-0.014994	-0.1558	0.438234
19	0.008973	0.0933	0.462939
20	-0.032247	-0.3351	0.369092

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.968957 & 10.0697 & 0 \tabularnewline
2 & -0.040263 & -0.4184 & 0.338234 \tabularnewline
3 & -0.003842 & -0.0399 & 0.484111 \tabularnewline
4 & 0.025819 & 0.2683 & 0.394483 \tabularnewline
5 & -0.003982 & -0.0414 & 0.483533 \tabularnewline
6 & -0.027977 & -0.2907 & 0.385903 \tabularnewline
7 & 0.002018 & 0.021 & 0.491655 \tabularnewline
8 & -0.026656 & -0.277 & 0.391148 \tabularnewline
9 & 0.022468 & 0.2335 & 0.407908 \tabularnewline
10 & 0.047915 & 0.4979 & 0.309767 \tabularnewline
11 & -0.016794 & -0.1745 & 0.430887 \tabularnewline
12 & -0.037606 & -0.3908 & 0.348353 \tabularnewline
13 & -0.095939 & -0.997 & 0.160489 \tabularnewline
14 & -0.042533 & -0.442 & 0.329681 \tabularnewline
15 & -0.020917 & -0.2174 & 0.414162 \tabularnewline
16 & 0.053367 & 0.5546 & 0.290156 \tabularnewline
17 & 0.013919 & 0.1447 & 0.442628 \tabularnewline
18 & -0.014994 & -0.1558 & 0.438234 \tabularnewline
19 & 0.008973 & 0.0933 & 0.462939 \tabularnewline
20 & -0.032247 & -0.3351 & 0.369092 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283357&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]0.968957[/C][C]10.0697[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.040263[/C][C]-0.4184[/C][C]0.338234[/C][/ROW]
[ROW][C]3[/C][C]-0.003842[/C][C]-0.0399[/C][C]0.484111[/C][/ROW]
[ROW][C]4[/C][C]0.025819[/C][C]0.2683[/C][C]0.394483[/C][/ROW]
[ROW][C]5[/C][C]-0.003982[/C][C]-0.0414[/C][C]0.483533[/C][/ROW]
[ROW][C]6[/C][C]-0.027977[/C][C]-0.2907[/C][C]0.385903[/C][/ROW]
[ROW][C]7[/C][C]0.002018[/C][C]0.021[/C][C]0.491655[/C][/ROW]
[ROW][C]8[/C][C]-0.026656[/C][C]-0.277[/C][C]0.391148[/C][/ROW]
[ROW][C]9[/C][C]0.022468[/C][C]0.2335[/C][C]0.407908[/C][/ROW]
[ROW][C]10[/C][C]0.047915[/C][C]0.4979[/C][C]0.309767[/C][/ROW]
[ROW][C]11[/C][C]-0.016794[/C][C]-0.1745[/C][C]0.430887[/C][/ROW]
[ROW][C]12[/C][C]-0.037606[/C][C]-0.3908[/C][C]0.348353[/C][/ROW]
[ROW][C]13[/C][C]-0.095939[/C][C]-0.997[/C][C]0.160489[/C][/ROW]
[ROW][C]14[/C][C]-0.042533[/C][C]-0.442[/C][C]0.329681[/C][/ROW]
[ROW][C]15[/C][C]-0.020917[/C][C]-0.2174[/C][C]0.414162[/C][/ROW]
[ROW][C]16[/C][C]0.053367[/C][C]0.5546[/C][C]0.290156[/C][/ROW]
[ROW][C]17[/C][C]0.013919[/C][C]0.1447[/C][C]0.442628[/C][/ROW]
[ROW][C]18[/C][C]-0.014994[/C][C]-0.1558[/C][C]0.438234[/C][/ROW]
[ROW][C]19[/C][C]0.008973[/C][C]0.0933[/C][C]0.462939[/C][/ROW]
[ROW][C]20[/C][C]-0.032247[/C][C]-0.3351[/C][C]0.369092[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283357&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283357&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	0.968957	10.0697	0
2	-0.040263	-0.4184	0.338234
3	-0.003842	-0.0399	0.484111
4	0.025819	0.2683	0.394483
5	-0.003982	-0.0414	0.483533
6	-0.027977	-0.2907	0.385903
7	0.002018	0.021	0.491655
8	-0.026656	-0.277	0.391148
9	0.022468	0.2335	0.407908
10	0.047915	0.4979	0.309767
11	-0.016794	-0.1745	0.430887
12	-0.037606	-0.3908	0.348353
13	-0.095939	-0.997	0.160489
14	-0.042533	-0.442	0.329681
15	-0.020917	-0.2174	0.414162
16	0.053367	0.5546	0.290156
17	0.013919	0.1447	0.442628
18	-0.014994	-0.1558	0.438234
19	0.008973	0.0933	0.462939
20	-0.032247	-0.3351	0.369092

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