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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 22 Dec 2010 16:35:26 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/22/t1293035622ip1x9e01xrm8rhl.htm/, Retrieved Mon, 06 May 2024 00:49:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114378, Retrieved Mon, 06 May 2024 00:49:50 +0000

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131

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-     [Univariate Data Series] [web server] [2010-10-19 15:51:23] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Pageviews] [2010-11-29 10:18:55] [b98453cac15ba1066b407e146608df68]
-   PD      [(Partial) Autocorrelation Function] [] [2010-12-22 16:35:26] [7b390cc0228d34e5578246b07143e3df] [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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114378&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114378&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114378&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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.089394	-0.7372	0.23178
2	0.012906	0.1064	0.457778
3	0.206123	1.6997	0.046876
4	-0.028703	-0.2367	0.406804
5	-0.171166	-1.4115	0.081332
6	0.03949	0.3256	0.372846
7	-0.204949	-1.6901	0.047798
8	-0.134776	-1.1114	0.135157
9	-0.059457	-0.4903	0.312751
10	-0.151087	-1.2459	0.108539
11	-0.109763	-0.9051	0.184297
12	0.224057	1.8476	0.034504
13	-0.064981	-0.5358	0.296906
14	0.03136	0.2586	0.398361
15	0.128539	1.06	0.146457
16	0.000204	0.0017	0.499332
17	0.034331	0.2831	0.38898
18	-0.031629	-0.2608	0.397509

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.089394 & -0.7372 & 0.23178 \tabularnewline
2 & 0.012906 & 0.1064 & 0.457778 \tabularnewline
3 & 0.206123 & 1.6997 & 0.046876 \tabularnewline
4 & -0.028703 & -0.2367 & 0.406804 \tabularnewline
5 & -0.171166 & -1.4115 & 0.081332 \tabularnewline
6 & 0.03949 & 0.3256 & 0.372846 \tabularnewline
7 & -0.204949 & -1.6901 & 0.047798 \tabularnewline
8 & -0.134776 & -1.1114 & 0.135157 \tabularnewline
9 & -0.059457 & -0.4903 & 0.312751 \tabularnewline
10 & -0.151087 & -1.2459 & 0.108539 \tabularnewline
11 & -0.109763 & -0.9051 & 0.184297 \tabularnewline
12 & 0.224057 & 1.8476 & 0.034504 \tabularnewline
13 & -0.064981 & -0.5358 & 0.296906 \tabularnewline
14 & 0.03136 & 0.2586 & 0.398361 \tabularnewline
15 & 0.128539 & 1.06 & 0.146457 \tabularnewline
16 & 0.000204 & 0.0017 & 0.499332 \tabularnewline
17 & 0.034331 & 0.2831 & 0.38898 \tabularnewline
18 & -0.031629 & -0.2608 & 0.397509 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114378&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]-0.089394[/C][C]-0.7372[/C][C]0.23178[/C][/ROW]
[ROW][C]2[/C][C]0.012906[/C][C]0.1064[/C][C]0.457778[/C][/ROW]
[ROW][C]3[/C][C]0.206123[/C][C]1.6997[/C][C]0.046876[/C][/ROW]
[ROW][C]4[/C][C]-0.028703[/C][C]-0.2367[/C][C]0.406804[/C][/ROW]
[ROW][C]5[/C][C]-0.171166[/C][C]-1.4115[/C][C]0.081332[/C][/ROW]
[ROW][C]6[/C][C]0.03949[/C][C]0.3256[/C][C]0.372846[/C][/ROW]
[ROW][C]7[/C][C]-0.204949[/C][C]-1.6901[/C][C]0.047798[/C][/ROW]
[ROW][C]8[/C][C]-0.134776[/C][C]-1.1114[/C][C]0.135157[/C][/ROW]
[ROW][C]9[/C][C]-0.059457[/C][C]-0.4903[/C][C]0.312751[/C][/ROW]
[ROW][C]10[/C][C]-0.151087[/C][C]-1.2459[/C][C]0.108539[/C][/ROW]
[ROW][C]11[/C][C]-0.109763[/C][C]-0.9051[/C][C]0.184297[/C][/ROW]
[ROW][C]12[/C][C]0.224057[/C][C]1.8476[/C][C]0.034504[/C][/ROW]
[ROW][C]13[/C][C]-0.064981[/C][C]-0.5358[/C][C]0.296906[/C][/ROW]
[ROW][C]14[/C][C]0.03136[/C][C]0.2586[/C][C]0.398361[/C][/ROW]
[ROW][C]15[/C][C]0.128539[/C][C]1.06[/C][C]0.146457[/C][/ROW]
[ROW][C]16[/C][C]0.000204[/C][C]0.0017[/C][C]0.499332[/C][/ROW]
[ROW][C]17[/C][C]0.034331[/C][C]0.2831[/C][C]0.38898[/C][/ROW]
[ROW][C]18[/C][C]-0.031629[/C][C]-0.2608[/C][C]0.397509[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114378&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114378&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	-0.089394	-0.7372	0.23178
2	0.012906	0.1064	0.457778
3	0.206123	1.6997	0.046876
4	-0.028703	-0.2367	0.406804
5	-0.171166	-1.4115	0.081332
6	0.03949	0.3256	0.372846
7	-0.204949	-1.6901	0.047798
8	-0.134776	-1.1114	0.135157
9	-0.059457	-0.4903	0.312751
10	-0.151087	-1.2459	0.108539
11	-0.109763	-0.9051	0.184297
12	0.224057	1.8476	0.034504
13	-0.064981	-0.5358	0.296906
14	0.03136	0.2586	0.398361
15	0.128539	1.06	0.146457
16	0.000204	0.0017	0.499332
17	0.034331	0.2831	0.38898
18	-0.031629	-0.2608	0.397509

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.089394	-0.7372	0.23178
2	0.004954	0.0409	0.483765
3	0.209392	1.7267	0.044382
4	0.008708	0.0718	0.471482
5	-0.190373	-1.5699	0.060545
6	-0.038582	-0.3182	0.375671
7	-0.201113	-1.6584	0.05092
8	-0.112062	-0.9241	0.179354
9	-0.085602	-0.7059	0.241335
10	-0.128071	-1.0561	0.147331
11	-0.111888	-0.9226	0.179726
12	0.188161	1.5516	0.062698
13	-0.003371	-0.0278	0.488952
14	-0.011088	-0.0914	0.46371
15	-0.03785	-0.3121	0.377953
16	-0.068189	-0.5623	0.28788
17	0.014319	0.1181	0.453179
18	-0.156501	-1.2905	0.100618

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.089394 & -0.7372 & 0.23178 \tabularnewline
2 & 0.004954 & 0.0409 & 0.483765 \tabularnewline
3 & 0.209392 & 1.7267 & 0.044382 \tabularnewline
4 & 0.008708 & 0.0718 & 0.471482 \tabularnewline
5 & -0.190373 & -1.5699 & 0.060545 \tabularnewline
6 & -0.038582 & -0.3182 & 0.375671 \tabularnewline
7 & -0.201113 & -1.6584 & 0.05092 \tabularnewline
8 & -0.112062 & -0.9241 & 0.179354 \tabularnewline
9 & -0.085602 & -0.7059 & 0.241335 \tabularnewline
10 & -0.128071 & -1.0561 & 0.147331 \tabularnewline
11 & -0.111888 & -0.9226 & 0.179726 \tabularnewline
12 & 0.188161 & 1.5516 & 0.062698 \tabularnewline
13 & -0.003371 & -0.0278 & 0.488952 \tabularnewline
14 & -0.011088 & -0.0914 & 0.46371 \tabularnewline
15 & -0.03785 & -0.3121 & 0.377953 \tabularnewline
16 & -0.068189 & -0.5623 & 0.28788 \tabularnewline
17 & 0.014319 & 0.1181 & 0.453179 \tabularnewline
18 & -0.156501 & -1.2905 & 0.100618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114378&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]-0.089394[/C][C]-0.7372[/C][C]0.23178[/C][/ROW]
[ROW][C]2[/C][C]0.004954[/C][C]0.0409[/C][C]0.483765[/C][/ROW]
[ROW][C]3[/C][C]0.209392[/C][C]1.7267[/C][C]0.044382[/C][/ROW]
[ROW][C]4[/C][C]0.008708[/C][C]0.0718[/C][C]0.471482[/C][/ROW]
[ROW][C]5[/C][C]-0.190373[/C][C]-1.5699[/C][C]0.060545[/C][/ROW]
[ROW][C]6[/C][C]-0.038582[/C][C]-0.3182[/C][C]0.375671[/C][/ROW]
[ROW][C]7[/C][C]-0.201113[/C][C]-1.6584[/C][C]0.05092[/C][/ROW]
[ROW][C]8[/C][C]-0.112062[/C][C]-0.9241[/C][C]0.179354[/C][/ROW]
[ROW][C]9[/C][C]-0.085602[/C][C]-0.7059[/C][C]0.241335[/C][/ROW]
[ROW][C]10[/C][C]-0.128071[/C][C]-1.0561[/C][C]0.147331[/C][/ROW]
[ROW][C]11[/C][C]-0.111888[/C][C]-0.9226[/C][C]0.179726[/C][/ROW]
[ROW][C]12[/C][C]0.188161[/C][C]1.5516[/C][C]0.062698[/C][/ROW]
[ROW][C]13[/C][C]-0.003371[/C][C]-0.0278[/C][C]0.488952[/C][/ROW]
[ROW][C]14[/C][C]-0.011088[/C][C]-0.0914[/C][C]0.46371[/C][/ROW]
[ROW][C]15[/C][C]-0.03785[/C][C]-0.3121[/C][C]0.377953[/C][/ROW]
[ROW][C]16[/C][C]-0.068189[/C][C]-0.5623[/C][C]0.28788[/C][/ROW]
[ROW][C]17[/C][C]0.014319[/C][C]0.1181[/C][C]0.453179[/C][/ROW]
[ROW][C]18[/C][C]-0.156501[/C][C]-1.2905[/C][C]0.100618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114378&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114378&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	-0.089394	-0.7372	0.23178
2	0.004954	0.0409	0.483765
3	0.209392	1.7267	0.044382
4	0.008708	0.0718	0.471482
5	-0.190373	-1.5699	0.060545
6	-0.038582	-0.3182	0.375671
7	-0.201113	-1.6584	0.05092
8	-0.112062	-0.9241	0.179354
9	-0.085602	-0.7059	0.241335
10	-0.128071	-1.0561	0.147331
11	-0.111888	-0.9226	0.179726
12	0.188161	1.5516	0.062698
13	-0.003371	-0.0278	0.488952
14	-0.011088	-0.0914	0.46371
15	-0.03785	-0.3121	0.377953
16	-0.068189	-0.5623	0.28788
17	0.014319	0.1181	0.453179
18	-0.156501	-1.2905	0.100618

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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):

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 <- 7
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code