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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 03 Sep 2015 08:37:12 +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/Sep/03/t1441265838sr344a82ccopp2c.htm/, Retrieved Thu, 16 May 2024 16:21:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280520, Retrieved Thu, 16 May 2024 16:21:18 +0000

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

-       [(Partial) Autocorrelation Function] [] [2015-09-03 07:37:12] [6aaa86d036131c368c5c53235820ac38] [Current]

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1.4
1.5
1.8
1.8
1.8
1.7
1.5
1.1
1.3
1.6
1.9
1.9
2
2.2
2.2
2
2.3
2.6
3.2
3.2
3.1
2.8
2.3
1.9
1.9
2
2
1.8
1.6
1.4
0.2
0.3
0.4
0.7
1
1.1
0.8
0.8
1
1.1
1
0.8
1.6
1.5
1.6
1.6
1.6
1.9
2
1.9
2
2.1
2.3
2.3
2.6
2.6
2.7
2.6
2.6
2.4
2.5
2.5
2.5
2.4
2.1
2.1
2.3
2.3
2.3
2.9
2.8
2.9
3
3
2.9
2.6
2.8
2.9
3.1
2.8
2.4
1.6
1.5
1.7

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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280520&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280520&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280520&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.921523	8.4459	0
2	0.807459	7.4005	0
3	0.690555	6.329	0
4	0.601376	5.5117	0
5	0.533037	4.8854	2e-06
6	0.479241	4.3923	1.6e-05
7	0.414404	3.7981	0.000137
8	0.318675	2.9207	0.002242
9	0.19726	1.8079	0.037099
10	0.072641	0.6658	0.253692
11	-0.032089	-0.2941	0.384704
12	-0.11229	-1.0292	0.153181
13	-0.131503	-1.2052	0.115746
14	-0.128618	-1.1788	0.120903
15	-0.119034	-1.091	0.139204
16	-0.132233	-1.2119	0.114467
17	-0.162274	-1.4873	0.070345
18	-0.190328	-1.7444	0.042375
19	-0.208084	-1.9071	0.029961

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921523 & 8.4459 & 0 \tabularnewline
2 & 0.807459 & 7.4005 & 0 \tabularnewline
3 & 0.690555 & 6.329 & 0 \tabularnewline
4 & 0.601376 & 5.5117 & 0 \tabularnewline
5 & 0.533037 & 4.8854 & 2e-06 \tabularnewline
6 & 0.479241 & 4.3923 & 1.6e-05 \tabularnewline
7 & 0.414404 & 3.7981 & 0.000137 \tabularnewline
8 & 0.318675 & 2.9207 & 0.002242 \tabularnewline
9 & 0.19726 & 1.8079 & 0.037099 \tabularnewline
10 & 0.072641 & 0.6658 & 0.253692 \tabularnewline
11 & -0.032089 & -0.2941 & 0.384704 \tabularnewline
12 & -0.11229 & -1.0292 & 0.153181 \tabularnewline
13 & -0.131503 & -1.2052 & 0.115746 \tabularnewline
14 & -0.128618 & -1.1788 & 0.120903 \tabularnewline
15 & -0.119034 & -1.091 & 0.139204 \tabularnewline
16 & -0.132233 & -1.2119 & 0.114467 \tabularnewline
17 & -0.162274 & -1.4873 & 0.070345 \tabularnewline
18 & -0.190328 & -1.7444 & 0.042375 \tabularnewline
19 & -0.208084 & -1.9071 & 0.029961 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280520&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]0.921523[/C][C]8.4459[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.807459[/C][C]7.4005[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.690555[/C][C]6.329[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.601376[/C][C]5.5117[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.533037[/C][C]4.8854[/C][C]2e-06[/C][/ROW]
[ROW][C]6[/C][C]0.479241[/C][C]4.3923[/C][C]1.6e-05[/C][/ROW]
[ROW][C]7[/C][C]0.414404[/C][C]3.7981[/C][C]0.000137[/C][/ROW]
[ROW][C]8[/C][C]0.318675[/C][C]2.9207[/C][C]0.002242[/C][/ROW]
[ROW][C]9[/C][C]0.19726[/C][C]1.8079[/C][C]0.037099[/C][/ROW]
[ROW][C]10[/C][C]0.072641[/C][C]0.6658[/C][C]0.253692[/C][/ROW]
[ROW][C]11[/C][C]-0.032089[/C][C]-0.2941[/C][C]0.384704[/C][/ROW]
[ROW][C]12[/C][C]-0.11229[/C][C]-1.0292[/C][C]0.153181[/C][/ROW]
[ROW][C]13[/C][C]-0.131503[/C][C]-1.2052[/C][C]0.115746[/C][/ROW]
[ROW][C]14[/C][C]-0.128618[/C][C]-1.1788[/C][C]0.120903[/C][/ROW]
[ROW][C]15[/C][C]-0.119034[/C][C]-1.091[/C][C]0.139204[/C][/ROW]
[ROW][C]16[/C][C]-0.132233[/C][C]-1.2119[/C][C]0.114467[/C][/ROW]
[ROW][C]17[/C][C]-0.162274[/C][C]-1.4873[/C][C]0.070345[/C][/ROW]
[ROW][C]18[/C][C]-0.190328[/C][C]-1.7444[/C][C]0.042375[/C][/ROW]
[ROW][C]19[/C][C]-0.208084[/C][C]-1.9071[/C][C]0.029961[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280520&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280520&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	0.921523	8.4459	0
2	0.807459	7.4005	0
3	0.690555	6.329	0
4	0.601376	5.5117	0
5	0.533037	4.8854	2e-06
6	0.479241	4.3923	1.6e-05
7	0.414404	3.7981	0.000137
8	0.318675	2.9207	0.002242
9	0.19726	1.8079	0.037099
10	0.072641	0.6658	0.253692
11	-0.032089	-0.2941	0.384704
12	-0.11229	-1.0292	0.153181
13	-0.131503	-1.2052	0.115746
14	-0.128618	-1.1788	0.120903
15	-0.119034	-1.091	0.139204
16	-0.132233	-1.2119	0.114467
17	-0.162274	-1.4873	0.070345
18	-0.190328	-1.7444	0.042375
19	-0.208084	-1.9071	0.029961

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.921523	8.4459	0
2	-0.276835	-2.5372	0.006511
3	-0.031726	-0.2908	0.385971
4	0.126078	1.1555	0.125576
5	0.008611	0.0789	0.46864
6	0.00641	0.0588	0.476644
7	-0.12756	-1.1691	0.122835
8	-0.213554	-1.9573	0.026819
9	-0.15116	-1.3854	0.084798
10	-0.072231	-0.662	0.25489
11	-0.01212	-0.1111	0.455909
12	-0.035379	-0.3243	0.373275
13	0.293381	2.6889	0.004322
14	0.005655	0.0518	0.479393
15	0.053356	0.489	0.313051
16	-0.062456	-0.5724	0.284285
17	-0.070062	-0.6421	0.261268
18	0.018301	0.1677	0.433598
19	-0.09611	-0.8809	0.190453

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921523 & 8.4459 & 0 \tabularnewline
2 & -0.276835 & -2.5372 & 0.006511 \tabularnewline
3 & -0.031726 & -0.2908 & 0.385971 \tabularnewline
4 & 0.126078 & 1.1555 & 0.125576 \tabularnewline
5 & 0.008611 & 0.0789 & 0.46864 \tabularnewline
6 & 0.00641 & 0.0588 & 0.476644 \tabularnewline
7 & -0.12756 & -1.1691 & 0.122835 \tabularnewline
8 & -0.213554 & -1.9573 & 0.026819 \tabularnewline
9 & -0.15116 & -1.3854 & 0.084798 \tabularnewline
10 & -0.072231 & -0.662 & 0.25489 \tabularnewline
11 & -0.01212 & -0.1111 & 0.455909 \tabularnewline
12 & -0.035379 & -0.3243 & 0.373275 \tabularnewline
13 & 0.293381 & 2.6889 & 0.004322 \tabularnewline
14 & 0.005655 & 0.0518 & 0.479393 \tabularnewline
15 & 0.053356 & 0.489 & 0.313051 \tabularnewline
16 & -0.062456 & -0.5724 & 0.284285 \tabularnewline
17 & -0.070062 & -0.6421 & 0.261268 \tabularnewline
18 & 0.018301 & 0.1677 & 0.433598 \tabularnewline
19 & -0.09611 & -0.8809 & 0.190453 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280520&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]0.921523[/C][C]8.4459[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.276835[/C][C]-2.5372[/C][C]0.006511[/C][/ROW]
[ROW][C]3[/C][C]-0.031726[/C][C]-0.2908[/C][C]0.385971[/C][/ROW]
[ROW][C]4[/C][C]0.126078[/C][C]1.1555[/C][C]0.125576[/C][/ROW]
[ROW][C]5[/C][C]0.008611[/C][C]0.0789[/C][C]0.46864[/C][/ROW]
[ROW][C]6[/C][C]0.00641[/C][C]0.0588[/C][C]0.476644[/C][/ROW]
[ROW][C]7[/C][C]-0.12756[/C][C]-1.1691[/C][C]0.122835[/C][/ROW]
[ROW][C]8[/C][C]-0.213554[/C][C]-1.9573[/C][C]0.026819[/C][/ROW]
[ROW][C]9[/C][C]-0.15116[/C][C]-1.3854[/C][C]0.084798[/C][/ROW]
[ROW][C]10[/C][C]-0.072231[/C][C]-0.662[/C][C]0.25489[/C][/ROW]
[ROW][C]11[/C][C]-0.01212[/C][C]-0.1111[/C][C]0.455909[/C][/ROW]
[ROW][C]12[/C][C]-0.035379[/C][C]-0.3243[/C][C]0.373275[/C][/ROW]
[ROW][C]13[/C][C]0.293381[/C][C]2.6889[/C][C]0.004322[/C][/ROW]
[ROW][C]14[/C][C]0.005655[/C][C]0.0518[/C][C]0.479393[/C][/ROW]
[ROW][C]15[/C][C]0.053356[/C][C]0.489[/C][C]0.313051[/C][/ROW]
[ROW][C]16[/C][C]-0.062456[/C][C]-0.5724[/C][C]0.284285[/C][/ROW]
[ROW][C]17[/C][C]-0.070062[/C][C]-0.6421[/C][C]0.261268[/C][/ROW]
[ROW][C]18[/C][C]0.018301[/C][C]0.1677[/C][C]0.433598[/C][/ROW]
[ROW][C]19[/C][C]-0.09611[/C][C]-0.8809[/C][C]0.190453[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280520&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280520&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	0.921523	8.4459	0
2	-0.276835	-2.5372	0.006511
3	-0.031726	-0.2908	0.385971
4	0.126078	1.1555	0.125576
5	0.008611	0.0789	0.46864
6	0.00641	0.0588	0.476644
7	-0.12756	-1.1691	0.122835
8	-0.213554	-1.9573	0.026819
9	-0.15116	-1.3854	0.084798
10	-0.072231	-0.662	0.25489
11	-0.01212	-0.1111	0.455909
12	-0.035379	-0.3243	0.373275
13	0.293381	2.6889	0.004322
14	0.005655	0.0518	0.479393
15	0.053356	0.489	0.313051
16	-0.062456	-0.5724	0.284285
17	-0.070062	-0.6421	0.261268
18	0.018301	0.1677	0.433598
19	-0.09611	-0.8809	0.190453

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 = 1.2 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1.2 ; par3 = 0 ; 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 <- '2'
par2 <- '1.2'
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