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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2011 17:28:13 -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/Dec/21/t1324506508m5b57udy8gd9r77.htm/, Retrieved Tue, 23 Apr 2024 17:56:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159102, Retrieved Tue, 23 Apr 2024 17:56:41 +0000

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User-defined keywords

Estimated Impact

103

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

F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Univariate Data Series] [] [2011-11-25 14:57:13] [493236dcc414c5f9e1823f06b33a5ad6]
- RMPD    [(Partial) Autocorrelation Function] [] [2011-12-05 14:06:22] [493236dcc414c5f9e1823f06b33a5ad6]
- R         [(Partial) Autocorrelation Function] [] [2011-12-21 22:08:52] [493236dcc414c5f9e1823f06b33a5ad6]
-               [(Partial) Autocorrelation Function] [] [2011-12-21 22:28:13] [75a32e1bc492240bc1028714aca23077] [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=159102&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=159102&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159102&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	0.872672	6.7597	0
2	0.722669	5.5978	0
3	0.60438	4.6815	8e-06
4	0.509363	3.9455	0.000106
5	0.443807	3.4377	0.000536
6	0.371875	2.8805	0.002749
7	0.316274	2.4498	0.008613
8	0.242439	1.8779	0.032627
9	0.164801	1.2765	0.103341
10	0.111622	0.8646	0.195346
11	0.063437	0.4914	0.312474
12	0.039156	0.3033	0.381353
13	0.02024	0.1568	0.437973
14	0.017467	0.1353	0.446414
15	-0.002539	-0.0197	0.492187
16	-0.03922	-0.3038	0.381167
17	-0.069962	-0.5419	0.29494

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.872672 & 6.7597 & 0 \tabularnewline
2 & 0.722669 & 5.5978 & 0 \tabularnewline
3 & 0.60438 & 4.6815 & 8e-06 \tabularnewline
4 & 0.509363 & 3.9455 & 0.000106 \tabularnewline
5 & 0.443807 & 3.4377 & 0.000536 \tabularnewline
6 & 0.371875 & 2.8805 & 0.002749 \tabularnewline
7 & 0.316274 & 2.4498 & 0.008613 \tabularnewline
8 & 0.242439 & 1.8779 & 0.032627 \tabularnewline
9 & 0.164801 & 1.2765 & 0.103341 \tabularnewline
10 & 0.111622 & 0.8646 & 0.195346 \tabularnewline
11 & 0.063437 & 0.4914 & 0.312474 \tabularnewline
12 & 0.039156 & 0.3033 & 0.381353 \tabularnewline
13 & 0.02024 & 0.1568 & 0.437973 \tabularnewline
14 & 0.017467 & 0.1353 & 0.446414 \tabularnewline
15 & -0.002539 & -0.0197 & 0.492187 \tabularnewline
16 & -0.03922 & -0.3038 & 0.381167 \tabularnewline
17 & -0.069962 & -0.5419 & 0.29494 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159102&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]0.872672[/C][C]6.7597[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.722669[/C][C]5.5978[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.60438[/C][C]4.6815[/C][C]8e-06[/C][/ROW]
[ROW][C]4[/C][C]0.509363[/C][C]3.9455[/C][C]0.000106[/C][/ROW]
[ROW][C]5[/C][C]0.443807[/C][C]3.4377[/C][C]0.000536[/C][/ROW]
[ROW][C]6[/C][C]0.371875[/C][C]2.8805[/C][C]0.002749[/C][/ROW]
[ROW][C]7[/C][C]0.316274[/C][C]2.4498[/C][C]0.008613[/C][/ROW]
[ROW][C]8[/C][C]0.242439[/C][C]1.8779[/C][C]0.032627[/C][/ROW]
[ROW][C]9[/C][C]0.164801[/C][C]1.2765[/C][C]0.103341[/C][/ROW]
[ROW][C]10[/C][C]0.111622[/C][C]0.8646[/C][C]0.195346[/C][/ROW]
[ROW][C]11[/C][C]0.063437[/C][C]0.4914[/C][C]0.312474[/C][/ROW]
[ROW][C]12[/C][C]0.039156[/C][C]0.3033[/C][C]0.381353[/C][/ROW]
[ROW][C]13[/C][C]0.02024[/C][C]0.1568[/C][C]0.437973[/C][/ROW]
[ROW][C]14[/C][C]0.017467[/C][C]0.1353[/C][C]0.446414[/C][/ROW]
[ROW][C]15[/C][C]-0.002539[/C][C]-0.0197[/C][C]0.492187[/C][/ROW]
[ROW][C]16[/C][C]-0.03922[/C][C]-0.3038[/C][C]0.381167[/C][/ROW]
[ROW][C]17[/C][C]-0.069962[/C][C]-0.5419[/C][C]0.29494[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159102&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159102&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	0.872672	6.7597	0
2	0.722669	5.5978	0
3	0.60438	4.6815	8e-06
4	0.509363	3.9455	0.000106
5	0.443807	3.4377	0.000536
6	0.371875	2.8805	0.002749
7	0.316274	2.4498	0.008613
8	0.242439	1.8779	0.032627
9	0.164801	1.2765	0.103341
10	0.111622	0.8646	0.195346
11	0.063437	0.4914	0.312474
12	0.039156	0.3033	0.381353
13	0.02024	0.1568	0.437973
14	0.017467	0.1353	0.446414
15	-0.002539	-0.0197	0.492187
16	-0.03922	-0.3038	0.381167
17	-0.069962	-0.5419	0.29494

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.872672	6.7597	0
2	-0.163089	-1.2633	0.105688
3	0.056862	0.4405	0.330596
4	0.00113	0.0088	0.496522
5	0.061253	0.4745	0.318445
6	-0.083858	-0.6496	0.259226
7	0.054297	0.4206	0.337781
8	-0.137614	-1.066	0.145358
9	-0.027892	-0.2161	0.41484
10	0.022813	0.1767	0.430167
11	-0.038946	-0.3017	0.381971
12	0.046889	0.3632	0.358866
13	-0.011265	-0.0873	0.465379
14	0.062432	0.4836	0.315216
15	-0.105111	-0.8142	0.209379
16	-0.030772	-0.2384	0.406207
17	-0.035403	-0.2742	0.392426

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.872672 & 6.7597 & 0 \tabularnewline
2 & -0.163089 & -1.2633 & 0.105688 \tabularnewline
3 & 0.056862 & 0.4405 & 0.330596 \tabularnewline
4 & 0.00113 & 0.0088 & 0.496522 \tabularnewline
5 & 0.061253 & 0.4745 & 0.318445 \tabularnewline
6 & -0.083858 & -0.6496 & 0.259226 \tabularnewline
7 & 0.054297 & 0.4206 & 0.337781 \tabularnewline
8 & -0.137614 & -1.066 & 0.145358 \tabularnewline
9 & -0.027892 & -0.2161 & 0.41484 \tabularnewline
10 & 0.022813 & 0.1767 & 0.430167 \tabularnewline
11 & -0.038946 & -0.3017 & 0.381971 \tabularnewline
12 & 0.046889 & 0.3632 & 0.358866 \tabularnewline
13 & -0.011265 & -0.0873 & 0.465379 \tabularnewline
14 & 0.062432 & 0.4836 & 0.315216 \tabularnewline
15 & -0.105111 & -0.8142 & 0.209379 \tabularnewline
16 & -0.030772 & -0.2384 & 0.406207 \tabularnewline
17 & -0.035403 & -0.2742 & 0.392426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159102&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]0.872672[/C][C]6.7597[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.163089[/C][C]-1.2633[/C][C]0.105688[/C][/ROW]
[ROW][C]3[/C][C]0.056862[/C][C]0.4405[/C][C]0.330596[/C][/ROW]
[ROW][C]4[/C][C]0.00113[/C][C]0.0088[/C][C]0.496522[/C][/ROW]
[ROW][C]5[/C][C]0.061253[/C][C]0.4745[/C][C]0.318445[/C][/ROW]
[ROW][C]6[/C][C]-0.083858[/C][C]-0.6496[/C][C]0.259226[/C][/ROW]
[ROW][C]7[/C][C]0.054297[/C][C]0.4206[/C][C]0.337781[/C][/ROW]
[ROW][C]8[/C][C]-0.137614[/C][C]-1.066[/C][C]0.145358[/C][/ROW]
[ROW][C]9[/C][C]-0.027892[/C][C]-0.2161[/C][C]0.41484[/C][/ROW]
[ROW][C]10[/C][C]0.022813[/C][C]0.1767[/C][C]0.430167[/C][/ROW]
[ROW][C]11[/C][C]-0.038946[/C][C]-0.3017[/C][C]0.381971[/C][/ROW]
[ROW][C]12[/C][C]0.046889[/C][C]0.3632[/C][C]0.358866[/C][/ROW]
[ROW][C]13[/C][C]-0.011265[/C][C]-0.0873[/C][C]0.465379[/C][/ROW]
[ROW][C]14[/C][C]0.062432[/C][C]0.4836[/C][C]0.315216[/C][/ROW]
[ROW][C]15[/C][C]-0.105111[/C][C]-0.8142[/C][C]0.209379[/C][/ROW]
[ROW][C]16[/C][C]-0.030772[/C][C]-0.2384[/C][C]0.406207[/C][/ROW]
[ROW][C]17[/C][C]-0.035403[/C][C]-0.2742[/C][C]0.392426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159102&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159102&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	0.872672	6.7597	0
2	-0.163089	-1.2633	0.105688
3	0.056862	0.4405	0.330596
4	0.00113	0.0088	0.496522
5	0.061253	0.4745	0.318445
6	-0.083858	-0.6496	0.259226
7	0.054297	0.4206	0.337781
8	-0.137614	-1.066	0.145358
9	-0.027892	-0.2161	0.41484
10	0.022813	0.1767	0.430167
11	-0.038946	-0.3017	0.381971
12	0.046889	0.3632	0.358866
13	-0.011265	-0.0873	0.465379
14	0.062432	0.4836	0.315216
15	-0.105111	-0.8142	0.209379
16	-0.030772	-0.2384	0.406207
17	-0.035403	-0.2742	0.392426

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 = additive ; par2 = 12 ;

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code