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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Dec 2010 16:15:04 +0000

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/2010/Dec/19/t1292775181pvu0scycwckns4r.htm/, Retrieved Sun, 05 May 2024 01:07:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112554, Retrieved Sun, 05 May 2024 01:07:55 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

140

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D    [(Partial) Autocorrelation Function] [Autocorrelation WS9] [2010-12-06 11:15:00] [f4dc4aa51d65be851b8508203d9f6001]
-    D      [(Partial) Autocorrelation Function] [Autocorrelation B...] [2010-12-19 15:56:02] [f4dc4aa51d65be851b8508203d9f6001]
-   P         [(Partial) Autocorrelation Function] [Autocorrelation B...] [2010-12-19 16:00:59] [f4dc4aa51d65be851b8508203d9f6001]
-   P             [(Partial) Autocorrelation Function] [Autocorrelation B...] [2010-12-19 16:15:04] [7a87ed98a7b21a29d6a45388a9b7b229] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112554&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112554&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112554&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.02433	-0.1668	0.434122
2	-0.065708	-0.4505	0.327221
3	0.176737	1.2116	0.115852
4	0.268319	1.8395	0.036081
5	-0.131177	-0.8993	0.186537
6	0.019368	0.1328	0.447468
7	0.132944	0.9114	0.183363
8	0.045258	0.3103	0.378861
9	-0.21524	-1.4756	0.073358
10	-0.096106	-0.6589	0.256598
11	0.02353	0.1613	0.436269
12	-0.310238	-2.1269	0.019354
13	-0.220042	-1.5085	0.069056
14	0.09018	0.6182	0.2697
15	-0.196727	-1.3487	0.091949
16	-0.064681	-0.4434	0.329745
17	-0.100953	-0.6921	0.246141

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.02433 & -0.1668 & 0.434122 \tabularnewline
2 & -0.065708 & -0.4505 & 0.327221 \tabularnewline
3 & 0.176737 & 1.2116 & 0.115852 \tabularnewline
4 & 0.268319 & 1.8395 & 0.036081 \tabularnewline
5 & -0.131177 & -0.8993 & 0.186537 \tabularnewline
6 & 0.019368 & 0.1328 & 0.447468 \tabularnewline
7 & 0.132944 & 0.9114 & 0.183363 \tabularnewline
8 & 0.045258 & 0.3103 & 0.378861 \tabularnewline
9 & -0.21524 & -1.4756 & 0.073358 \tabularnewline
10 & -0.096106 & -0.6589 & 0.256598 \tabularnewline
11 & 0.02353 & 0.1613 & 0.436269 \tabularnewline
12 & -0.310238 & -2.1269 & 0.019354 \tabularnewline
13 & -0.220042 & -1.5085 & 0.069056 \tabularnewline
14 & 0.09018 & 0.6182 & 0.2697 \tabularnewline
15 & -0.196727 & -1.3487 & 0.091949 \tabularnewline
16 & -0.064681 & -0.4434 & 0.329745 \tabularnewline
17 & -0.100953 & -0.6921 & 0.246141 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112554&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]-0.02433[/C][C]-0.1668[/C][C]0.434122[/C][/ROW]
[ROW][C]2[/C][C]-0.065708[/C][C]-0.4505[/C][C]0.327221[/C][/ROW]
[ROW][C]3[/C][C]0.176737[/C][C]1.2116[/C][C]0.115852[/C][/ROW]
[ROW][C]4[/C][C]0.268319[/C][C]1.8395[/C][C]0.036081[/C][/ROW]
[ROW][C]5[/C][C]-0.131177[/C][C]-0.8993[/C][C]0.186537[/C][/ROW]
[ROW][C]6[/C][C]0.019368[/C][C]0.1328[/C][C]0.447468[/C][/ROW]
[ROW][C]7[/C][C]0.132944[/C][C]0.9114[/C][C]0.183363[/C][/ROW]
[ROW][C]8[/C][C]0.045258[/C][C]0.3103[/C][C]0.378861[/C][/ROW]
[ROW][C]9[/C][C]-0.21524[/C][C]-1.4756[/C][C]0.073358[/C][/ROW]
[ROW][C]10[/C][C]-0.096106[/C][C]-0.6589[/C][C]0.256598[/C][/ROW]
[ROW][C]11[/C][C]0.02353[/C][C]0.1613[/C][C]0.436269[/C][/ROW]
[ROW][C]12[/C][C]-0.310238[/C][C]-2.1269[/C][C]0.019354[/C][/ROW]
[ROW][C]13[/C][C]-0.220042[/C][C]-1.5085[/C][C]0.069056[/C][/ROW]
[ROW][C]14[/C][C]0.09018[/C][C]0.6182[/C][C]0.2697[/C][/ROW]
[ROW][C]15[/C][C]-0.196727[/C][C]-1.3487[/C][C]0.091949[/C][/ROW]
[ROW][C]16[/C][C]-0.064681[/C][C]-0.4434[/C][C]0.329745[/C][/ROW]
[ROW][C]17[/C][C]-0.100953[/C][C]-0.6921[/C][C]0.246141[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112554&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112554&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	-0.02433	-0.1668	0.434122
2	-0.065708	-0.4505	0.327221
3	0.176737	1.2116	0.115852
4	0.268319	1.8395	0.036081
5	-0.131177	-0.8993	0.186537
6	0.019368	0.1328	0.447468
7	0.132944	0.9114	0.183363
8	0.045258	0.3103	0.378861
9	-0.21524	-1.4756	0.073358
10	-0.096106	-0.6589	0.256598
11	0.02353	0.1613	0.436269
12	-0.310238	-2.1269	0.019354
13	-0.220042	-1.5085	0.069056
14	0.09018	0.6182	0.2697
15	-0.196727	-1.3487	0.091949
16	-0.064681	-0.4434	0.329745
17	-0.100953	-0.6921	0.246141

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.02433	-0.1668	0.434122
2	-0.066339	-0.4548	0.325674
3	0.174288	1.1949	0.119069
4	0.280932	1.926	0.030084
5	-0.098771	-0.6771	0.250819
6	0.007731	0.053	0.478978
7	0.032553	0.2232	0.412185
8	0.020768	0.1424	0.443694
9	-0.171494	-1.1757	0.122817
10	-0.181637	-1.2452	0.109608
11	-0.060156	-0.4124	0.340957
12	-0.312854	-2.1448	0.018584
13	-0.167401	-1.1476	0.128462
14	0.076844	0.5268	0.3004
15	-0.166863	-1.144	0.129217
16	0.203407	1.3945	0.084864
17	-0.06079	-0.4168	0.339378

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.02433 & -0.1668 & 0.434122 \tabularnewline
2 & -0.066339 & -0.4548 & 0.325674 \tabularnewline
3 & 0.174288 & 1.1949 & 0.119069 \tabularnewline
4 & 0.280932 & 1.926 & 0.030084 \tabularnewline
5 & -0.098771 & -0.6771 & 0.250819 \tabularnewline
6 & 0.007731 & 0.053 & 0.478978 \tabularnewline
7 & 0.032553 & 0.2232 & 0.412185 \tabularnewline
8 & 0.020768 & 0.1424 & 0.443694 \tabularnewline
9 & -0.171494 & -1.1757 & 0.122817 \tabularnewline
10 & -0.181637 & -1.2452 & 0.109608 \tabularnewline
11 & -0.060156 & -0.4124 & 0.340957 \tabularnewline
12 & -0.312854 & -2.1448 & 0.018584 \tabularnewline
13 & -0.167401 & -1.1476 & 0.128462 \tabularnewline
14 & 0.076844 & 0.5268 & 0.3004 \tabularnewline
15 & -0.166863 & -1.144 & 0.129217 \tabularnewline
16 & 0.203407 & 1.3945 & 0.084864 \tabularnewline
17 & -0.06079 & -0.4168 & 0.339378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112554&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]-0.02433[/C][C]-0.1668[/C][C]0.434122[/C][/ROW]
[ROW][C]2[/C][C]-0.066339[/C][C]-0.4548[/C][C]0.325674[/C][/ROW]
[ROW][C]3[/C][C]0.174288[/C][C]1.1949[/C][C]0.119069[/C][/ROW]
[ROW][C]4[/C][C]0.280932[/C][C]1.926[/C][C]0.030084[/C][/ROW]
[ROW][C]5[/C][C]-0.098771[/C][C]-0.6771[/C][C]0.250819[/C][/ROW]
[ROW][C]6[/C][C]0.007731[/C][C]0.053[/C][C]0.478978[/C][/ROW]
[ROW][C]7[/C][C]0.032553[/C][C]0.2232[/C][C]0.412185[/C][/ROW]
[ROW][C]8[/C][C]0.020768[/C][C]0.1424[/C][C]0.443694[/C][/ROW]
[ROW][C]9[/C][C]-0.171494[/C][C]-1.1757[/C][C]0.122817[/C][/ROW]
[ROW][C]10[/C][C]-0.181637[/C][C]-1.2452[/C][C]0.109608[/C][/ROW]
[ROW][C]11[/C][C]-0.060156[/C][C]-0.4124[/C][C]0.340957[/C][/ROW]
[ROW][C]12[/C][C]-0.312854[/C][C]-2.1448[/C][C]0.018584[/C][/ROW]
[ROW][C]13[/C][C]-0.167401[/C][C]-1.1476[/C][C]0.128462[/C][/ROW]
[ROW][C]14[/C][C]0.076844[/C][C]0.5268[/C][C]0.3004[/C][/ROW]
[ROW][C]15[/C][C]-0.166863[/C][C]-1.144[/C][C]0.129217[/C][/ROW]
[ROW][C]16[/C][C]0.203407[/C][C]1.3945[/C][C]0.084864[/C][/ROW]
[ROW][C]17[/C][C]-0.06079[/C][C]-0.4168[/C][C]0.339378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112554&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112554&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	-0.02433	-0.1668	0.434122
2	-0.066339	-0.4548	0.325674
3	0.174288	1.1949	0.119069
4	0.280932	1.926	0.030084
5	-0.098771	-0.6771	0.250819
6	0.007731	0.053	0.478978
7	0.032553	0.2232	0.412185
8	0.020768	0.1424	0.443694
9	-0.171494	-1.1757	0.122817
10	-0.181637	-1.2452	0.109608
11	-0.060156	-0.4124	0.340957
12	-0.312854	-2.1448	0.018584
13	-0.167401	-1.1476	0.128462
14	0.076844	0.5268	0.3004
15	-0.166863	-1.144	0.129217
16	0.203407	1.3945	0.084864
17	-0.06079	-0.4168	0.339378

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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 (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