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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2011 05:37:20 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/20/t1324377812ezafn6vcx3v2rzp.htm/, Retrieved Mon, 06 May 2024 07:41:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157907, Retrieved Mon, 06 May 2024 07:41:53 +0000

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156

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

-     [(Partial) Autocorrelation Function] [] [2011-12-03 13:49:01] [06c08141d7d783218a8164fd2ea166f2]
- R PD    [(Partial) Autocorrelation Function] [] [2011-12-20 10:37:20] [ce4468323d272130d499477f5e05a6d2] [Current]
-   P       [(Partial) Autocorrelation Function] [] [2011-12-20 10:45:04] [06c08141d7d783218a8164fd2ea166f2] 
-   P         [(Partial) Autocorrelation Function] [] [2011-12-20 18:20:49] [06c08141d7d783218a8164fd2ea166f2] 
-               [(Partial) Autocorrelation Function] [] [2011-12-20 18:26:39] [06c08141d7d783218a8164fd2ea166f2] 

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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=157907&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=157907&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157907&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	-0.141297	-0.9373	0.176871
2	-0.052078	-0.3454	0.365703
3	0.081689	0.5419	0.295323
4	-0.019003	-0.1261	0.450133
5	-0.109997	-0.7296	0.23474
6	0.074124	0.4917	0.312695
7	-0.029542	-0.196	0.422772
8	0.048342	0.3207	0.374992
9	0.224242	1.4875	0.072013
10	0.059573	0.3952	0.347316
11	0.139988	0.9286	0.179088
12	-0.2179	-1.4454	0.077717
13	-0.054488	-0.3614	0.359753
14	0.046894	0.3111	0.378613
15	-0.030217	-0.2004	0.421031
16	-0.206422	-1.3693	0.088935
17	0.213026	1.4131	0.082338

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.141297 & -0.9373 & 0.176871 \tabularnewline
2 & -0.052078 & -0.3454 & 0.365703 \tabularnewline
3 & 0.081689 & 0.5419 & 0.295323 \tabularnewline
4 & -0.019003 & -0.1261 & 0.450133 \tabularnewline
5 & -0.109997 & -0.7296 & 0.23474 \tabularnewline
6 & 0.074124 & 0.4917 & 0.312695 \tabularnewline
7 & -0.029542 & -0.196 & 0.422772 \tabularnewline
8 & 0.048342 & 0.3207 & 0.374992 \tabularnewline
9 & 0.224242 & 1.4875 & 0.072013 \tabularnewline
10 & 0.059573 & 0.3952 & 0.347316 \tabularnewline
11 & 0.139988 & 0.9286 & 0.179088 \tabularnewline
12 & -0.2179 & -1.4454 & 0.077717 \tabularnewline
13 & -0.054488 & -0.3614 & 0.359753 \tabularnewline
14 & 0.046894 & 0.3111 & 0.378613 \tabularnewline
15 & -0.030217 & -0.2004 & 0.421031 \tabularnewline
16 & -0.206422 & -1.3693 & 0.088935 \tabularnewline
17 & 0.213026 & 1.4131 & 0.082338 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157907&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]-0.141297[/C][C]-0.9373[/C][C]0.176871[/C][/ROW]
[ROW][C]2[/C][C]-0.052078[/C][C]-0.3454[/C][C]0.365703[/C][/ROW]
[ROW][C]3[/C][C]0.081689[/C][C]0.5419[/C][C]0.295323[/C][/ROW]
[ROW][C]4[/C][C]-0.019003[/C][C]-0.1261[/C][C]0.450133[/C][/ROW]
[ROW][C]5[/C][C]-0.109997[/C][C]-0.7296[/C][C]0.23474[/C][/ROW]
[ROW][C]6[/C][C]0.074124[/C][C]0.4917[/C][C]0.312695[/C][/ROW]
[ROW][C]7[/C][C]-0.029542[/C][C]-0.196[/C][C]0.422772[/C][/ROW]
[ROW][C]8[/C][C]0.048342[/C][C]0.3207[/C][C]0.374992[/C][/ROW]
[ROW][C]9[/C][C]0.224242[/C][C]1.4875[/C][C]0.072013[/C][/ROW]
[ROW][C]10[/C][C]0.059573[/C][C]0.3952[/C][C]0.347316[/C][/ROW]
[ROW][C]11[/C][C]0.139988[/C][C]0.9286[/C][C]0.179088[/C][/ROW]
[ROW][C]12[/C][C]-0.2179[/C][C]-1.4454[/C][C]0.077717[/C][/ROW]
[ROW][C]13[/C][C]-0.054488[/C][C]-0.3614[/C][C]0.359753[/C][/ROW]
[ROW][C]14[/C][C]0.046894[/C][C]0.3111[/C][C]0.378613[/C][/ROW]
[ROW][C]15[/C][C]-0.030217[/C][C]-0.2004[/C][C]0.421031[/C][/ROW]
[ROW][C]16[/C][C]-0.206422[/C][C]-1.3693[/C][C]0.088935[/C][/ROW]
[ROW][C]17[/C][C]0.213026[/C][C]1.4131[/C][C]0.082338[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157907&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157907&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	-0.141297	-0.9373	0.176871
2	-0.052078	-0.3454	0.365703
3	0.081689	0.5419	0.295323
4	-0.019003	-0.1261	0.450133
5	-0.109997	-0.7296	0.23474
6	0.074124	0.4917	0.312695
7	-0.029542	-0.196	0.422772
8	0.048342	0.3207	0.374992
9	0.224242	1.4875	0.072013
10	0.059573	0.3952	0.347316
11	0.139988	0.9286	0.179088
12	-0.2179	-1.4454	0.077717
13	-0.054488	-0.3614	0.359753
14	0.046894	0.3111	0.378613
15	-0.030217	-0.2004	0.421031
16	-0.206422	-1.3693	0.088935
17	0.213026	1.4131	0.082338

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.141297	-0.9373	0.176871
2	-0.07351	-0.4876	0.314123
3	0.065046	0.4315	0.334118
4	-0.00116	-0.0077	0.496947
5	-0.107527	-0.7133	0.239728
6	0.037592	0.2494	0.402123
7	-0.02385	-0.1582	0.43751
8	0.063901	0.4239	0.336862
9	0.237399	1.5747	0.061241
10	0.13949	0.9253	0.179936
11	0.224699	1.4905	0.071616
12	-0.206472	-1.3696	0.088884
13	-0.12453	-0.826	0.206619
14	0.004269	0.0283	0.488768
15	0.000719	0.0048	0.498109
16	-0.200561	-1.3304	0.095125
17	0.060132	0.3989	0.345958

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.141297 & -0.9373 & 0.176871 \tabularnewline
2 & -0.07351 & -0.4876 & 0.314123 \tabularnewline
3 & 0.065046 & 0.4315 & 0.334118 \tabularnewline
4 & -0.00116 & -0.0077 & 0.496947 \tabularnewline
5 & -0.107527 & -0.7133 & 0.239728 \tabularnewline
6 & 0.037592 & 0.2494 & 0.402123 \tabularnewline
7 & -0.02385 & -0.1582 & 0.43751 \tabularnewline
8 & 0.063901 & 0.4239 & 0.336862 \tabularnewline
9 & 0.237399 & 1.5747 & 0.061241 \tabularnewline
10 & 0.13949 & 0.9253 & 0.179936 \tabularnewline
11 & 0.224699 & 1.4905 & 0.071616 \tabularnewline
12 & -0.206472 & -1.3696 & 0.088884 \tabularnewline
13 & -0.12453 & -0.826 & 0.206619 \tabularnewline
14 & 0.004269 & 0.0283 & 0.488768 \tabularnewline
15 & 0.000719 & 0.0048 & 0.498109 \tabularnewline
16 & -0.200561 & -1.3304 & 0.095125 \tabularnewline
17 & 0.060132 & 0.3989 & 0.345958 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157907&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]-0.141297[/C][C]-0.9373[/C][C]0.176871[/C][/ROW]
[ROW][C]2[/C][C]-0.07351[/C][C]-0.4876[/C][C]0.314123[/C][/ROW]
[ROW][C]3[/C][C]0.065046[/C][C]0.4315[/C][C]0.334118[/C][/ROW]
[ROW][C]4[/C][C]-0.00116[/C][C]-0.0077[/C][C]0.496947[/C][/ROW]
[ROW][C]5[/C][C]-0.107527[/C][C]-0.7133[/C][C]0.239728[/C][/ROW]
[ROW][C]6[/C][C]0.037592[/C][C]0.2494[/C][C]0.402123[/C][/ROW]
[ROW][C]7[/C][C]-0.02385[/C][C]-0.1582[/C][C]0.43751[/C][/ROW]
[ROW][C]8[/C][C]0.063901[/C][C]0.4239[/C][C]0.336862[/C][/ROW]
[ROW][C]9[/C][C]0.237399[/C][C]1.5747[/C][C]0.061241[/C][/ROW]
[ROW][C]10[/C][C]0.13949[/C][C]0.9253[/C][C]0.179936[/C][/ROW]
[ROW][C]11[/C][C]0.224699[/C][C]1.4905[/C][C]0.071616[/C][/ROW]
[ROW][C]12[/C][C]-0.206472[/C][C]-1.3696[/C][C]0.088884[/C][/ROW]
[ROW][C]13[/C][C]-0.12453[/C][C]-0.826[/C][C]0.206619[/C][/ROW]
[ROW][C]14[/C][C]0.004269[/C][C]0.0283[/C][C]0.488768[/C][/ROW]
[ROW][C]15[/C][C]0.000719[/C][C]0.0048[/C][C]0.498109[/C][/ROW]
[ROW][C]16[/C][C]-0.200561[/C][C]-1.3304[/C][C]0.095125[/C][/ROW]
[ROW][C]17[/C][C]0.060132[/C][C]0.3989[/C][C]0.345958[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157907&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157907&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	-0.141297	-0.9373	0.176871
2	-0.07351	-0.4876	0.314123
3	0.065046	0.4315	0.334118
4	-0.00116	-0.0077	0.496947
5	-0.107527	-0.7133	0.239728
6	0.037592	0.2494	0.402123
7	-0.02385	-0.1582	0.43751
8	0.063901	0.4239	0.336862
9	0.237399	1.5747	0.061241
10	0.13949	0.9253	0.179936
11	0.224699	1.4905	0.071616
12	-0.206472	-1.3696	0.088884
13	-0.12453	-0.826	0.206619
14	0.004269	0.0283	0.488768
15	0.000719	0.0048	0.498109
16	-0.200561	-1.3304	0.095125
17	0.060132	0.3989	0.345958

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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')

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Dataset

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Figures (Output of Computation)

Input Parameters & R Code