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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 21 May 2015 21:03:32 +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/2015/May/21/t1432238626nkl76jcbmu770oh.htm/, Retrieved Sat, 04 May 2024 05:46:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279208, Retrieved Sat, 04 May 2024 05:46:18 +0000

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No (this computation is public)

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Estimated Impact

138

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

-       [(Partial) Autocorrelation Function] [] [2015-05-21 20:03:32] [d87d05de12b09f00f3ae4d3dfdb2afe6] [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	1 seconds
R Server	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279208&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279208&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279208&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.407275	-3.7105	0.000187
2	0.214493	1.9541	0.027027
3	-0.186327	-1.6975	0.046672
4	0.12693	1.1564	0.125419
5	-0.24276	-2.2117	0.01487
6	0.162128	1.4771	0.071723
7	-0.214128	-1.9508	0.027228
8	0.034672	0.3159	0.376446
9	-0.109635	-0.9988	0.160391
10	0.059328	0.5405	0.29515
11	-0.029735	-0.2709	0.393569
12	0.287888	2.6228	0.005187
13	-0.203658	-1.8554	0.033543
14	0.203865	1.8573	0.033408
15	-0.021789	-0.1985	0.421567
16	0.036468	0.3322	0.370274
17	-0.104647	-0.9534	0.171583
18	0.032037	0.2919	0.385558
19	-0.242667	-2.2108	0.0149

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.407275 & -3.7105 & 0.000187 \tabularnewline
2 & 0.214493 & 1.9541 & 0.027027 \tabularnewline
3 & -0.186327 & -1.6975 & 0.046672 \tabularnewline
4 & 0.12693 & 1.1564 & 0.125419 \tabularnewline
5 & -0.24276 & -2.2117 & 0.01487 \tabularnewline
6 & 0.162128 & 1.4771 & 0.071723 \tabularnewline
7 & -0.214128 & -1.9508 & 0.027228 \tabularnewline
8 & 0.034672 & 0.3159 & 0.376446 \tabularnewline
9 & -0.109635 & -0.9988 & 0.160391 \tabularnewline
10 & 0.059328 & 0.5405 & 0.29515 \tabularnewline
11 & -0.029735 & -0.2709 & 0.393569 \tabularnewline
12 & 0.287888 & 2.6228 & 0.005187 \tabularnewline
13 & -0.203658 & -1.8554 & 0.033543 \tabularnewline
14 & 0.203865 & 1.8573 & 0.033408 \tabularnewline
15 & -0.021789 & -0.1985 & 0.421567 \tabularnewline
16 & 0.036468 & 0.3322 & 0.370274 \tabularnewline
17 & -0.104647 & -0.9534 & 0.171583 \tabularnewline
18 & 0.032037 & 0.2919 & 0.385558 \tabularnewline
19 & -0.242667 & -2.2108 & 0.0149 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279208&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]-0.407275[/C][C]-3.7105[/C][C]0.000187[/C][/ROW]
[ROW][C]2[/C][C]0.214493[/C][C]1.9541[/C][C]0.027027[/C][/ROW]
[ROW][C]3[/C][C]-0.186327[/C][C]-1.6975[/C][C]0.046672[/C][/ROW]
[ROW][C]4[/C][C]0.12693[/C][C]1.1564[/C][C]0.125419[/C][/ROW]
[ROW][C]5[/C][C]-0.24276[/C][C]-2.2117[/C][C]0.01487[/C][/ROW]
[ROW][C]6[/C][C]0.162128[/C][C]1.4771[/C][C]0.071723[/C][/ROW]
[ROW][C]7[/C][C]-0.214128[/C][C]-1.9508[/C][C]0.027228[/C][/ROW]
[ROW][C]8[/C][C]0.034672[/C][C]0.3159[/C][C]0.376446[/C][/ROW]
[ROW][C]9[/C][C]-0.109635[/C][C]-0.9988[/C][C]0.160391[/C][/ROW]
[ROW][C]10[/C][C]0.059328[/C][C]0.5405[/C][C]0.29515[/C][/ROW]
[ROW][C]11[/C][C]-0.029735[/C][C]-0.2709[/C][C]0.393569[/C][/ROW]
[ROW][C]12[/C][C]0.287888[/C][C]2.6228[/C][C]0.005187[/C][/ROW]
[ROW][C]13[/C][C]-0.203658[/C][C]-1.8554[/C][C]0.033543[/C][/ROW]
[ROW][C]14[/C][C]0.203865[/C][C]1.8573[/C][C]0.033408[/C][/ROW]
[ROW][C]15[/C][C]-0.021789[/C][C]-0.1985[/C][C]0.421567[/C][/ROW]
[ROW][C]16[/C][C]0.036468[/C][C]0.3322[/C][C]0.370274[/C][/ROW]
[ROW][C]17[/C][C]-0.104647[/C][C]-0.9534[/C][C]0.171583[/C][/ROW]
[ROW][C]18[/C][C]0.032037[/C][C]0.2919[/C][C]0.385558[/C][/ROW]
[ROW][C]19[/C][C]-0.242667[/C][C]-2.2108[/C][C]0.0149[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279208&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279208&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	-0.407275	-3.7105	0.000187
2	0.214493	1.9541	0.027027
3	-0.186327	-1.6975	0.046672
4	0.12693	1.1564	0.125419
5	-0.24276	-2.2117	0.01487
6	0.162128	1.4771	0.071723
7	-0.214128	-1.9508	0.027228
8	0.034672	0.3159	0.376446
9	-0.109635	-0.9988	0.160391
10	0.059328	0.5405	0.29515
11	-0.029735	-0.2709	0.393569
12	0.287888	2.6228	0.005187
13	-0.203658	-1.8554	0.033543
14	0.203865	1.8573	0.033408
15	-0.021789	-0.1985	0.421567
16	0.036468	0.3322	0.370274
17	-0.104647	-0.9534	0.171583
18	0.032037	0.2919	0.385558
19	-0.242667	-2.2108	0.0149

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.407275	-3.7105	0.000187
2	0.058288	0.531	0.298408
3	-0.096623	-0.8803	0.190625
4	0.015313	0.1395	0.444693
5	-0.200847	-1.8298	0.035435
6	-0.017535	-0.1598	0.436731
7	-0.146009	-1.3302	0.093546
8	-0.179399	-1.6344	0.052981
9	-0.156132	-1.4224	0.079324
10	-0.130352	-1.1876	0.119196
11	-0.063327	-0.5769	0.282771
12	0.235559	2.146	0.017395
13	-0.051032	-0.4649	0.321603
14	0.04795	0.4368	0.331678
15	0.150938	1.3751	0.086399
16	0.041918	0.3819	0.351759
17	0.004692	0.0427	0.483003
18	-0.057354	-0.5225	0.301349
19	-0.192676	-1.7554	0.041444

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.407275 & -3.7105 & 0.000187 \tabularnewline
2 & 0.058288 & 0.531 & 0.298408 \tabularnewline
3 & -0.096623 & -0.8803 & 0.190625 \tabularnewline
4 & 0.015313 & 0.1395 & 0.444693 \tabularnewline
5 & -0.200847 & -1.8298 & 0.035435 \tabularnewline
6 & -0.017535 & -0.1598 & 0.436731 \tabularnewline
7 & -0.146009 & -1.3302 & 0.093546 \tabularnewline
8 & -0.179399 & -1.6344 & 0.052981 \tabularnewline
9 & -0.156132 & -1.4224 & 0.079324 \tabularnewline
10 & -0.130352 & -1.1876 & 0.119196 \tabularnewline
11 & -0.063327 & -0.5769 & 0.282771 \tabularnewline
12 & 0.235559 & 2.146 & 0.017395 \tabularnewline
13 & -0.051032 & -0.4649 & 0.321603 \tabularnewline
14 & 0.04795 & 0.4368 & 0.331678 \tabularnewline
15 & 0.150938 & 1.3751 & 0.086399 \tabularnewline
16 & 0.041918 & 0.3819 & 0.351759 \tabularnewline
17 & 0.004692 & 0.0427 & 0.483003 \tabularnewline
18 & -0.057354 & -0.5225 & 0.301349 \tabularnewline
19 & -0.192676 & -1.7554 & 0.041444 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279208&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]-0.407275[/C][C]-3.7105[/C][C]0.000187[/C][/ROW]
[ROW][C]2[/C][C]0.058288[/C][C]0.531[/C][C]0.298408[/C][/ROW]
[ROW][C]3[/C][C]-0.096623[/C][C]-0.8803[/C][C]0.190625[/C][/ROW]
[ROW][C]4[/C][C]0.015313[/C][C]0.1395[/C][C]0.444693[/C][/ROW]
[ROW][C]5[/C][C]-0.200847[/C][C]-1.8298[/C][C]0.035435[/C][/ROW]
[ROW][C]6[/C][C]-0.017535[/C][C]-0.1598[/C][C]0.436731[/C][/ROW]
[ROW][C]7[/C][C]-0.146009[/C][C]-1.3302[/C][C]0.093546[/C][/ROW]
[ROW][C]8[/C][C]-0.179399[/C][C]-1.6344[/C][C]0.052981[/C][/ROW]
[ROW][C]9[/C][C]-0.156132[/C][C]-1.4224[/C][C]0.079324[/C][/ROW]
[ROW][C]10[/C][C]-0.130352[/C][C]-1.1876[/C][C]0.119196[/C][/ROW]
[ROW][C]11[/C][C]-0.063327[/C][C]-0.5769[/C][C]0.282771[/C][/ROW]
[ROW][C]12[/C][C]0.235559[/C][C]2.146[/C][C]0.017395[/C][/ROW]
[ROW][C]13[/C][C]-0.051032[/C][C]-0.4649[/C][C]0.321603[/C][/ROW]
[ROW][C]14[/C][C]0.04795[/C][C]0.4368[/C][C]0.331678[/C][/ROW]
[ROW][C]15[/C][C]0.150938[/C][C]1.3751[/C][C]0.086399[/C][/ROW]
[ROW][C]16[/C][C]0.041918[/C][C]0.3819[/C][C]0.351759[/C][/ROW]
[ROW][C]17[/C][C]0.004692[/C][C]0.0427[/C][C]0.483003[/C][/ROW]
[ROW][C]18[/C][C]-0.057354[/C][C]-0.5225[/C][C]0.301349[/C][/ROW]
[ROW][C]19[/C][C]-0.192676[/C][C]-1.7554[/C][C]0.041444[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279208&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279208&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	-0.407275	-3.7105	0.000187
2	0.058288	0.531	0.298408
3	-0.096623	-0.8803	0.190625
4	0.015313	0.1395	0.444693
5	-0.200847	-1.8298	0.035435
6	-0.017535	-0.1598	0.436731
7	-0.146009	-1.3302	0.093546
8	-0.179399	-1.6344	0.052981
9	-0.156132	-1.4224	0.079324
10	-0.130352	-1.1876	0.119196
11	-0.063327	-0.5769	0.282771
12	0.235559	2.146	0.017395
13	-0.051032	-0.4649	0.321603
14	0.04795	0.4368	0.331678
15	0.150938	1.3751	0.086399
16	0.041918	0.3819	0.351759
17	0.004692	0.0427	0.483003
18	-0.057354	-0.5225	0.301349
19	-0.192676	-1.7554	0.041444

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 <- '0'
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