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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 09:13:28 -0700

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/2009/Nov/27/t125933853806mcd5ki0rxce4q.htm/, Retrieved Sun, 28 Apr 2024 22:58:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60944, Retrieved Sun, 28 Apr 2024 22:58:23 +0000

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User-defined keywords

Estimated Impact

163

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-    D        [(Partial) Autocorrelation Function] [Model 1 (d = 0, D...] [2009-11-24 17:27:24] [ee7c2e7343f5b1451e62c5c16ec521f1]
-    D          [(Partial) Autocorrelation Function] [Methode 1 (D=0, d=0)] [2009-11-27 12:01:23] [76ab39dc7a55316678260825bd5ad46c]
-   P               [(Partial) Autocorrelation Function] [Methode 1 (d=1, D=0)] [2009-11-27 16:13:28] [d79e31a57591875d497c91f296c77132] [Current]
-   P                 [(Partial) Autocorrelation Function] [Methode 1 (d=1,D=1)] [2009-11-27 16:26:44] [76ab39dc7a55316678260825bd5ad46c] 
-    D                  [(Partial) Autocorrelation Function] [methode 1 ( d=1 D...] [2009-11-27 20:29:59] [4b453aa14d54730625f8d3de5f1f6d82] 
-    D                [(Partial) Autocorrelation Function] [methode 1 (d= 1 D...] [2009-11-27 20:25:46] [4b453aa14d54730625f8d3de5f1f6d82] 

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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=60944&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=60944&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60944&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	-0.449973	-3.4563	0.000511
2	0.081351	0.6249	0.267234
3	0.00216	0.0166	0.49341
4	0.065084	0.4999	0.309496
5	-0.441406	-3.3905	0.000625
6	0.738521	5.6727	0
7	-0.434862	-3.3402	0.000728
8	0.04824	0.3705	0.356155
9	-0.021884	-0.1681	0.433541
10	0.006876	0.0528	0.479029
11	-0.345973	-2.6575	0.005057
12	0.659486	5.0656	2e-06
13	-0.402704	-3.0932	0.001512
14	0.031321	0.2406	0.405357
15	0.012192	0.0937	0.462851
16	-0.014659	-0.1126	0.455365
17	-0.346393	-2.6607	0.005014

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.449973 & -3.4563 & 0.000511 \tabularnewline
2 & 0.081351 & 0.6249 & 0.267234 \tabularnewline
3 & 0.00216 & 0.0166 & 0.49341 \tabularnewline
4 & 0.065084 & 0.4999 & 0.309496 \tabularnewline
5 & -0.441406 & -3.3905 & 0.000625 \tabularnewline
6 & 0.738521 & 5.6727 & 0 \tabularnewline
7 & -0.434862 & -3.3402 & 0.000728 \tabularnewline
8 & 0.04824 & 0.3705 & 0.356155 \tabularnewline
9 & -0.021884 & -0.1681 & 0.433541 \tabularnewline
10 & 0.006876 & 0.0528 & 0.479029 \tabularnewline
11 & -0.345973 & -2.6575 & 0.005057 \tabularnewline
12 & 0.659486 & 5.0656 & 2e-06 \tabularnewline
13 & -0.402704 & -3.0932 & 0.001512 \tabularnewline
14 & 0.031321 & 0.2406 & 0.405357 \tabularnewline
15 & 0.012192 & 0.0937 & 0.462851 \tabularnewline
16 & -0.014659 & -0.1126 & 0.455365 \tabularnewline
17 & -0.346393 & -2.6607 & 0.005014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60944&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]-0.449973[/C][C]-3.4563[/C][C]0.000511[/C][/ROW]
[ROW][C]2[/C][C]0.081351[/C][C]0.6249[/C][C]0.267234[/C][/ROW]
[ROW][C]3[/C][C]0.00216[/C][C]0.0166[/C][C]0.49341[/C][/ROW]
[ROW][C]4[/C][C]0.065084[/C][C]0.4999[/C][C]0.309496[/C][/ROW]
[ROW][C]5[/C][C]-0.441406[/C][C]-3.3905[/C][C]0.000625[/C][/ROW]
[ROW][C]6[/C][C]0.738521[/C][C]5.6727[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.434862[/C][C]-3.3402[/C][C]0.000728[/C][/ROW]
[ROW][C]8[/C][C]0.04824[/C][C]0.3705[/C][C]0.356155[/C][/ROW]
[ROW][C]9[/C][C]-0.021884[/C][C]-0.1681[/C][C]0.433541[/C][/ROW]
[ROW][C]10[/C][C]0.006876[/C][C]0.0528[/C][C]0.479029[/C][/ROW]
[ROW][C]11[/C][C]-0.345973[/C][C]-2.6575[/C][C]0.005057[/C][/ROW]
[ROW][C]12[/C][C]0.659486[/C][C]5.0656[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.402704[/C][C]-3.0932[/C][C]0.001512[/C][/ROW]
[ROW][C]14[/C][C]0.031321[/C][C]0.2406[/C][C]0.405357[/C][/ROW]
[ROW][C]15[/C][C]0.012192[/C][C]0.0937[/C][C]0.462851[/C][/ROW]
[ROW][C]16[/C][C]-0.014659[/C][C]-0.1126[/C][C]0.455365[/C][/ROW]
[ROW][C]17[/C][C]-0.346393[/C][C]-2.6607[/C][C]0.005014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60944&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60944&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	-0.449973	-3.4563	0.000511
2	0.081351	0.6249	0.267234
3	0.00216	0.0166	0.49341
4	0.065084	0.4999	0.309496
5	-0.441406	-3.3905	0.000625
6	0.738521	5.6727	0
7	-0.434862	-3.3402	0.000728
8	0.04824	0.3705	0.356155
9	-0.021884	-0.1681	0.433541
10	0.006876	0.0528	0.479029
11	-0.345973	-2.6575	0.005057
12	0.659486	5.0656	2e-06
13	-0.402704	-3.0932	0.001512
14	0.031321	0.2406	0.405357
15	0.012192	0.0937	0.462851
16	-0.014659	-0.1126	0.455365
17	-0.346393	-2.6607	0.005014

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.449973	-3.4563	0.000511
2	-0.151877	-1.1666	0.124036
3	-0.030823	-0.2368	0.406832
4	0.084789	0.6513	0.258698
5	-0.478981	-3.6791	0.000254
6	0.56139	4.3121	3.1e-05
7	-0.077893	-0.5983	0.275962
8	-0.147541	-1.1333	0.130839
9	-0.12417	-0.9538	0.172047
10	-0.212937	-1.6356	0.053624
11	0.007473	0.0574	0.477209
12	0.204802	1.5731	0.06052
13	-0.029957	-0.2301	0.409403
14	-0.14977	-1.1504	0.127309
15	-0.075215	-0.5777	0.282819
16	-0.058112	-0.4464	0.328484
17	-0.18545	-1.4245	0.07979

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.449973 & -3.4563 & 0.000511 \tabularnewline
2 & -0.151877 & -1.1666 & 0.124036 \tabularnewline
3 & -0.030823 & -0.2368 & 0.406832 \tabularnewline
4 & 0.084789 & 0.6513 & 0.258698 \tabularnewline
5 & -0.478981 & -3.6791 & 0.000254 \tabularnewline
6 & 0.56139 & 4.3121 & 3.1e-05 \tabularnewline
7 & -0.077893 & -0.5983 & 0.275962 \tabularnewline
8 & -0.147541 & -1.1333 & 0.130839 \tabularnewline
9 & -0.12417 & -0.9538 & 0.172047 \tabularnewline
10 & -0.212937 & -1.6356 & 0.053624 \tabularnewline
11 & 0.007473 & 0.0574 & 0.477209 \tabularnewline
12 & 0.204802 & 1.5731 & 0.06052 \tabularnewline
13 & -0.029957 & -0.2301 & 0.409403 \tabularnewline
14 & -0.14977 & -1.1504 & 0.127309 \tabularnewline
15 & -0.075215 & -0.5777 & 0.282819 \tabularnewline
16 & -0.058112 & -0.4464 & 0.328484 \tabularnewline
17 & -0.18545 & -1.4245 & 0.07979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60944&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]-0.449973[/C][C]-3.4563[/C][C]0.000511[/C][/ROW]
[ROW][C]2[/C][C]-0.151877[/C][C]-1.1666[/C][C]0.124036[/C][/ROW]
[ROW][C]3[/C][C]-0.030823[/C][C]-0.2368[/C][C]0.406832[/C][/ROW]
[ROW][C]4[/C][C]0.084789[/C][C]0.6513[/C][C]0.258698[/C][/ROW]
[ROW][C]5[/C][C]-0.478981[/C][C]-3.6791[/C][C]0.000254[/C][/ROW]
[ROW][C]6[/C][C]0.56139[/C][C]4.3121[/C][C]3.1e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.077893[/C][C]-0.5983[/C][C]0.275962[/C][/ROW]
[ROW][C]8[/C][C]-0.147541[/C][C]-1.1333[/C][C]0.130839[/C][/ROW]
[ROW][C]9[/C][C]-0.12417[/C][C]-0.9538[/C][C]0.172047[/C][/ROW]
[ROW][C]10[/C][C]-0.212937[/C][C]-1.6356[/C][C]0.053624[/C][/ROW]
[ROW][C]11[/C][C]0.007473[/C][C]0.0574[/C][C]0.477209[/C][/ROW]
[ROW][C]12[/C][C]0.204802[/C][C]1.5731[/C][C]0.06052[/C][/ROW]
[ROW][C]13[/C][C]-0.029957[/C][C]-0.2301[/C][C]0.409403[/C][/ROW]
[ROW][C]14[/C][C]-0.14977[/C][C]-1.1504[/C][C]0.127309[/C][/ROW]
[ROW][C]15[/C][C]-0.075215[/C][C]-0.5777[/C][C]0.282819[/C][/ROW]
[ROW][C]16[/C][C]-0.058112[/C][C]-0.4464[/C][C]0.328484[/C][/ROW]
[ROW][C]17[/C][C]-0.18545[/C][C]-1.4245[/C][C]0.07979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60944&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60944&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	-0.449973	-3.4563	0.000511
2	-0.151877	-1.1666	0.124036
3	-0.030823	-0.2368	0.406832
4	0.084789	0.6513	0.258698
5	-0.478981	-3.6791	0.000254
6	0.56139	4.3121	3.1e-05
7	-0.077893	-0.5983	0.275962
8	-0.147541	-1.1333	0.130839
9	-0.12417	-0.9538	0.172047
10	-0.212937	-1.6356	0.053624
11	0.007473	0.0574	0.477209
12	0.204802	1.5731	0.06052
13	-0.029957	-0.2301	0.409403
14	-0.14977	-1.1504	0.127309
15	-0.075215	-0.5777	0.282819
16	-0.058112	-0.4464	0.328484
17	-0.18545	-1.4245	0.07979

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 ;

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code