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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

Sat, 11 Aug 2012 09:42:51 -0400

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/2012/Aug/11/t1344692775g4i4o193mgwfqj5.htm/, Retrieved Mon, 06 May 2024 15:08:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169216, Retrieved Mon, 06 May 2024 15:08:42 +0000

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Original text written by user:

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No (this computation is public)

User-defined keywords

Estimated Impact

182

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

-     [Univariate Data Series] [Workshop 6: Run s...] [2010-12-14 12:57:17] [b9eaf9df71639055b3e2389f5099ca2c]
- RMPD    [(Partial) Autocorrelation Function] [Berekening 8] [2012-08-11 13:42:51] [0b94335bf72158573fe52322b9537409] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169216&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169216&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169216&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.876329	6.4397	0
2	0.772541	5.677	0
3	0.670864	4.9298	4e-06
4	0.541464	3.9789	0.000104
5	0.444865	3.2691	0.00094
6	0.309354	2.2733	0.013505
7	0.203274	1.4938	0.07053
8	0.080614	0.5924	0.27803
9	-0.055189	-0.4056	0.343337
10	-0.083378	-0.6127	0.271324
11	-0.124485	-0.9148	0.182189
12	-0.166086	-1.2205	0.113793
13	-0.191377	-1.4063	0.082678
14	-0.222734	-1.6368	0.053749
15	-0.25117	-1.8457	0.035209
16	-0.303308	-2.2289	0.015003
17	-0.30638	-2.2514	0.014225

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.876329 & 6.4397 & 0 \tabularnewline
2 & 0.772541 & 5.677 & 0 \tabularnewline
3 & 0.670864 & 4.9298 & 4e-06 \tabularnewline
4 & 0.541464 & 3.9789 & 0.000104 \tabularnewline
5 & 0.444865 & 3.2691 & 0.00094 \tabularnewline
6 & 0.309354 & 2.2733 & 0.013505 \tabularnewline
7 & 0.203274 & 1.4938 & 0.07053 \tabularnewline
8 & 0.080614 & 0.5924 & 0.27803 \tabularnewline
9 & -0.055189 & -0.4056 & 0.343337 \tabularnewline
10 & -0.083378 & -0.6127 & 0.271324 \tabularnewline
11 & -0.124485 & -0.9148 & 0.182189 \tabularnewline
12 & -0.166086 & -1.2205 & 0.113793 \tabularnewline
13 & -0.191377 & -1.4063 & 0.082678 \tabularnewline
14 & -0.222734 & -1.6368 & 0.053749 \tabularnewline
15 & -0.25117 & -1.8457 & 0.035209 \tabularnewline
16 & -0.303308 & -2.2289 & 0.015003 \tabularnewline
17 & -0.30638 & -2.2514 & 0.014225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169216&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]0.876329[/C][C]6.4397[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.772541[/C][C]5.677[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.670864[/C][C]4.9298[/C][C]4e-06[/C][/ROW]
[ROW][C]4[/C][C]0.541464[/C][C]3.9789[/C][C]0.000104[/C][/ROW]
[ROW][C]5[/C][C]0.444865[/C][C]3.2691[/C][C]0.00094[/C][/ROW]
[ROW][C]6[/C][C]0.309354[/C][C]2.2733[/C][C]0.013505[/C][/ROW]
[ROW][C]7[/C][C]0.203274[/C][C]1.4938[/C][C]0.07053[/C][/ROW]
[ROW][C]8[/C][C]0.080614[/C][C]0.5924[/C][C]0.27803[/C][/ROW]
[ROW][C]9[/C][C]-0.055189[/C][C]-0.4056[/C][C]0.343337[/C][/ROW]
[ROW][C]10[/C][C]-0.083378[/C][C]-0.6127[/C][C]0.271324[/C][/ROW]
[ROW][C]11[/C][C]-0.124485[/C][C]-0.9148[/C][C]0.182189[/C][/ROW]
[ROW][C]12[/C][C]-0.166086[/C][C]-1.2205[/C][C]0.113793[/C][/ROW]
[ROW][C]13[/C][C]-0.191377[/C][C]-1.4063[/C][C]0.082678[/C][/ROW]
[ROW][C]14[/C][C]-0.222734[/C][C]-1.6368[/C][C]0.053749[/C][/ROW]
[ROW][C]15[/C][C]-0.25117[/C][C]-1.8457[/C][C]0.035209[/C][/ROW]
[ROW][C]16[/C][C]-0.303308[/C][C]-2.2289[/C][C]0.015003[/C][/ROW]
[ROW][C]17[/C][C]-0.30638[/C][C]-2.2514[/C][C]0.014225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169216&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169216&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	0.876329	6.4397	0
2	0.772541	5.677	0
3	0.670864	4.9298	4e-06
4	0.541464	3.9789	0.000104
5	0.444865	3.2691	0.00094
6	0.309354	2.2733	0.013505
7	0.203274	1.4938	0.07053
8	0.080614	0.5924	0.27803
9	-0.055189	-0.4056	0.343337
10	-0.083378	-0.6127	0.271324
11	-0.124485	-0.9148	0.182189
12	-0.166086	-1.2205	0.113793
13	-0.191377	-1.4063	0.082678
14	-0.222734	-1.6368	0.053749
15	-0.25117	-1.8457	0.035209
16	-0.303308	-2.2289	0.015003
17	-0.30638	-2.2514	0.014225

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.876329	6.4397	0
2	0.019773	0.1453	0.442508
3	-0.043443	-0.3192	0.375389
4	-0.178904	-1.3147	0.097088
5	0.043891	0.3225	0.374149
6	-0.22558	-1.6577	0.051591
7	0.030062	0.2209	0.412998
8	-0.190575	-1.4004	0.083552
9	-0.123958	-0.9109	0.183198
10	0.310284	2.2801	0.013287
11	-0.018667	-0.1372	0.445701
12	-0.098344	-0.7227	0.236497
13	-0.057665	-0.4238	0.336715
14	-0.005925	-0.0435	0.482717
15	-0.187811	-1.3801	0.086619
16	-0.133981	-0.9846	0.164616
17	0.094314	0.6931	0.24562

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.876329 & 6.4397 & 0 \tabularnewline
2 & 0.019773 & 0.1453 & 0.442508 \tabularnewline
3 & -0.043443 & -0.3192 & 0.375389 \tabularnewline
4 & -0.178904 & -1.3147 & 0.097088 \tabularnewline
5 & 0.043891 & 0.3225 & 0.374149 \tabularnewline
6 & -0.22558 & -1.6577 & 0.051591 \tabularnewline
7 & 0.030062 & 0.2209 & 0.412998 \tabularnewline
8 & -0.190575 & -1.4004 & 0.083552 \tabularnewline
9 & -0.123958 & -0.9109 & 0.183198 \tabularnewline
10 & 0.310284 & 2.2801 & 0.013287 \tabularnewline
11 & -0.018667 & -0.1372 & 0.445701 \tabularnewline
12 & -0.098344 & -0.7227 & 0.236497 \tabularnewline
13 & -0.057665 & -0.4238 & 0.336715 \tabularnewline
14 & -0.005925 & -0.0435 & 0.482717 \tabularnewline
15 & -0.187811 & -1.3801 & 0.086619 \tabularnewline
16 & -0.133981 & -0.9846 & 0.164616 \tabularnewline
17 & 0.094314 & 0.6931 & 0.24562 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169216&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]0.876329[/C][C]6.4397[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.019773[/C][C]0.1453[/C][C]0.442508[/C][/ROW]
[ROW][C]3[/C][C]-0.043443[/C][C]-0.3192[/C][C]0.375389[/C][/ROW]
[ROW][C]4[/C][C]-0.178904[/C][C]-1.3147[/C][C]0.097088[/C][/ROW]
[ROW][C]5[/C][C]0.043891[/C][C]0.3225[/C][C]0.374149[/C][/ROW]
[ROW][C]6[/C][C]-0.22558[/C][C]-1.6577[/C][C]0.051591[/C][/ROW]
[ROW][C]7[/C][C]0.030062[/C][C]0.2209[/C][C]0.412998[/C][/ROW]
[ROW][C]8[/C][C]-0.190575[/C][C]-1.4004[/C][C]0.083552[/C][/ROW]
[ROW][C]9[/C][C]-0.123958[/C][C]-0.9109[/C][C]0.183198[/C][/ROW]
[ROW][C]10[/C][C]0.310284[/C][C]2.2801[/C][C]0.013287[/C][/ROW]
[ROW][C]11[/C][C]-0.018667[/C][C]-0.1372[/C][C]0.445701[/C][/ROW]
[ROW][C]12[/C][C]-0.098344[/C][C]-0.7227[/C][C]0.236497[/C][/ROW]
[ROW][C]13[/C][C]-0.057665[/C][C]-0.4238[/C][C]0.336715[/C][/ROW]
[ROW][C]14[/C][C]-0.005925[/C][C]-0.0435[/C][C]0.482717[/C][/ROW]
[ROW][C]15[/C][C]-0.187811[/C][C]-1.3801[/C][C]0.086619[/C][/ROW]
[ROW][C]16[/C][C]-0.133981[/C][C]-0.9846[/C][C]0.164616[/C][/ROW]
[ROW][C]17[/C][C]0.094314[/C][C]0.6931[/C][C]0.24562[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169216&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169216&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	0.876329	6.4397	0
2	0.019773	0.1453	0.442508
3	-0.043443	-0.3192	0.375389
4	-0.178904	-1.3147	0.097088
5	0.043891	0.3225	0.374149
6	-0.22558	-1.6577	0.051591
7	0.030062	0.2209	0.412998
8	-0.190575	-1.4004	0.083552
9	-0.123958	-0.9109	0.183198
10	0.310284	2.2801	0.013287
11	-0.018667	-0.1372	0.445701
12	-0.098344	-0.7227	0.236497
13	-0.057665	-0.4238	0.336715
14	-0.005925	-0.0435	0.482717
15	-0.187811	-1.3801	0.086619
16	-0.133981	-0.9846	0.164616
17	0.094314	0.6931	0.24562

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