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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 18 Dec 2007 08:23:00 -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/2007/Dec/18/t11979903830vbt7d8p4n3b8z5.htm/, Retrieved Sat, 04 May 2024 15:33:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4538, Retrieved Sat, 04 May 2024 15:33:51 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

tijdreeks met outliers

Estimated Impact

173

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

-       [(Partial) Autocorrelation Function] [Partial Autocorre...] [2007-12-18 15:23:00] [bebbf4ab6ac77d61a56e6916ab0650f9] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4538&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4538&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4538&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.124	0
1	0.026856	0.2182	0.413981
2	-0.226677	-1.8415	0.964981
3	-0.130377	-1.0592	0.853312
4	-0.008461	-0.0687	0.527296
5	0.252784	2.0536	0.021989
6	-0.119916	-0.9742	0.833243
7	-0.096452	-0.7836	0.781956
8	-0.219693	-1.7848	0.960555
9	-0.150509	-1.2227	0.887113
10	0.261016	2.1205	0.018863
11	0.101951	0.8283	0.205256
12	-0.038517	-0.3129	0.622335
13	-0.157538	-1.2798	0.89746
14	-0.007888	-0.0641	0.525451
15	0.179102	1.455	0.0752
16	-0.090341	-0.7339	0.767205
17	-0.037302	-0.303	0.618595

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.124 & 0 \tabularnewline
1 & 0.026856 & 0.2182 & 0.413981 \tabularnewline
2 & -0.226677 & -1.8415 & 0.964981 \tabularnewline
3 & -0.130377 & -1.0592 & 0.853312 \tabularnewline
4 & -0.008461 & -0.0687 & 0.527296 \tabularnewline
5 & 0.252784 & 2.0536 & 0.021989 \tabularnewline
6 & -0.119916 & -0.9742 & 0.833243 \tabularnewline
7 & -0.096452 & -0.7836 & 0.781956 \tabularnewline
8 & -0.219693 & -1.7848 & 0.960555 \tabularnewline
9 & -0.150509 & -1.2227 & 0.887113 \tabularnewline
10 & 0.261016 & 2.1205 & 0.018863 \tabularnewline
11 & 0.101951 & 0.8283 & 0.205256 \tabularnewline
12 & -0.038517 & -0.3129 & 0.622335 \tabularnewline
13 & -0.157538 & -1.2798 & 0.89746 \tabularnewline
14 & -0.007888 & -0.0641 & 0.525451 \tabularnewline
15 & 0.179102 & 1.455 & 0.0752 \tabularnewline
16 & -0.090341 & -0.7339 & 0.767205 \tabularnewline
17 & -0.037302 & -0.303 & 0.618595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4538&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]0[/C][C]1[/C][C]8.124[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.026856[/C][C]0.2182[/C][C]0.413981[/C][/ROW]
[ROW][C]2[/C][C]-0.226677[/C][C]-1.8415[/C][C]0.964981[/C][/ROW]
[ROW][C]3[/C][C]-0.130377[/C][C]-1.0592[/C][C]0.853312[/C][/ROW]
[ROW][C]4[/C][C]-0.008461[/C][C]-0.0687[/C][C]0.527296[/C][/ROW]
[ROW][C]5[/C][C]0.252784[/C][C]2.0536[/C][C]0.021989[/C][/ROW]
[ROW][C]6[/C][C]-0.119916[/C][C]-0.9742[/C][C]0.833243[/C][/ROW]
[ROW][C]7[/C][C]-0.096452[/C][C]-0.7836[/C][C]0.781956[/C][/ROW]
[ROW][C]8[/C][C]-0.219693[/C][C]-1.7848[/C][C]0.960555[/C][/ROW]
[ROW][C]9[/C][C]-0.150509[/C][C]-1.2227[/C][C]0.887113[/C][/ROW]
[ROW][C]10[/C][C]0.261016[/C][C]2.1205[/C][C]0.018863[/C][/ROW]
[ROW][C]11[/C][C]0.101951[/C][C]0.8283[/C][C]0.205256[/C][/ROW]
[ROW][C]12[/C][C]-0.038517[/C][C]-0.3129[/C][C]0.622335[/C][/ROW]
[ROW][C]13[/C][C]-0.157538[/C][C]-1.2798[/C][C]0.89746[/C][/ROW]
[ROW][C]14[/C][C]-0.007888[/C][C]-0.0641[/C][C]0.525451[/C][/ROW]
[ROW][C]15[/C][C]0.179102[/C][C]1.455[/C][C]0.0752[/C][/ROW]
[ROW][C]16[/C][C]-0.090341[/C][C]-0.7339[/C][C]0.767205[/C][/ROW]
[ROW][C]17[/C][C]-0.037302[/C][C]-0.303[/C][C]0.618595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4538&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4538&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
0	1	8.124	0
1	0.026856	0.2182	0.413981
2	-0.226677	-1.8415	0.964981
3	-0.130377	-1.0592	0.853312
4	-0.008461	-0.0687	0.527296
5	0.252784	2.0536	0.021989
6	-0.119916	-0.9742	0.833243
7	-0.096452	-0.7836	0.781956
8	-0.219693	-1.7848	0.960555
9	-0.150509	-1.2227	0.887113
10	0.261016	2.1205	0.018863
11	0.101951	0.8283	0.205256
12	-0.038517	-0.3129	0.622335
13	-0.157538	-1.2798	0.89746
14	-0.007888	-0.0641	0.525451
15	0.179102	1.455	0.0752
16	-0.090341	-0.7339	0.767205
17	-0.037302	-0.303	0.618595

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.026856	0.2182	0.413981
1	-0.227563	-1.8487	0.965512
2	-0.12326	-1.0014	0.839847
3	-0.059125	-0.4803	0.68371
4	0.210368	1.709	0.046071
5	-0.171846	-1.3961	0.916317
6	0.005258	0.0427	0.483027
7	-0.269427	-2.1888	0.983924
8	-0.195151	-1.5854	0.941174
9	0.107719	0.8751	0.192343
10	0.051669	0.4198	0.338011
11	-0.01463	-0.1189	0.547126
12	-0.047287	-0.3842	0.648953
13	1.1e-05	1e-04	0.499964
14	-0.019597	-0.1592	0.563003
15	-0.176891	-1.4371	0.922288
16	-0.037232	-0.3025	0.618381
17	-0.121024	-0.9832	0.83545

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.026856 & 0.2182 & 0.413981 \tabularnewline
1 & -0.227563 & -1.8487 & 0.965512 \tabularnewline
2 & -0.12326 & -1.0014 & 0.839847 \tabularnewline
3 & -0.059125 & -0.4803 & 0.68371 \tabularnewline
4 & 0.210368 & 1.709 & 0.046071 \tabularnewline
5 & -0.171846 & -1.3961 & 0.916317 \tabularnewline
6 & 0.005258 & 0.0427 & 0.483027 \tabularnewline
7 & -0.269427 & -2.1888 & 0.983924 \tabularnewline
8 & -0.195151 & -1.5854 & 0.941174 \tabularnewline
9 & 0.107719 & 0.8751 & 0.192343 \tabularnewline
10 & 0.051669 & 0.4198 & 0.338011 \tabularnewline
11 & -0.01463 & -0.1189 & 0.547126 \tabularnewline
12 & -0.047287 & -0.3842 & 0.648953 \tabularnewline
13 & 1.1e-05 & 1e-04 & 0.499964 \tabularnewline
14 & -0.019597 & -0.1592 & 0.563003 \tabularnewline
15 & -0.176891 & -1.4371 & 0.922288 \tabularnewline
16 & -0.037232 & -0.3025 & 0.618381 \tabularnewline
17 & -0.121024 & -0.9832 & 0.83545 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4538&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]0[/C][C]0.026856[/C][C]0.2182[/C][C]0.413981[/C][/ROW]
[ROW][C]1[/C][C]-0.227563[/C][C]-1.8487[/C][C]0.965512[/C][/ROW]
[ROW][C]2[/C][C]-0.12326[/C][C]-1.0014[/C][C]0.839847[/C][/ROW]
[ROW][C]3[/C][C]-0.059125[/C][C]-0.4803[/C][C]0.68371[/C][/ROW]
[ROW][C]4[/C][C]0.210368[/C][C]1.709[/C][C]0.046071[/C][/ROW]
[ROW][C]5[/C][C]-0.171846[/C][C]-1.3961[/C][C]0.916317[/C][/ROW]
[ROW][C]6[/C][C]0.005258[/C][C]0.0427[/C][C]0.483027[/C][/ROW]
[ROW][C]7[/C][C]-0.269427[/C][C]-2.1888[/C][C]0.983924[/C][/ROW]
[ROW][C]8[/C][C]-0.195151[/C][C]-1.5854[/C][C]0.941174[/C][/ROW]
[ROW][C]9[/C][C]0.107719[/C][C]0.8751[/C][C]0.192343[/C][/ROW]
[ROW][C]10[/C][C]0.051669[/C][C]0.4198[/C][C]0.338011[/C][/ROW]
[ROW][C]11[/C][C]-0.01463[/C][C]-0.1189[/C][C]0.547126[/C][/ROW]
[ROW][C]12[/C][C]-0.047287[/C][C]-0.3842[/C][C]0.648953[/C][/ROW]
[ROW][C]13[/C][C]1.1e-05[/C][C]1e-04[/C][C]0.499964[/C][/ROW]
[ROW][C]14[/C][C]-0.019597[/C][C]-0.1592[/C][C]0.563003[/C][/ROW]
[ROW][C]15[/C][C]-0.176891[/C][C]-1.4371[/C][C]0.922288[/C][/ROW]
[ROW][C]16[/C][C]-0.037232[/C][C]-0.3025[/C][C]0.618381[/C][/ROW]
[ROW][C]17[/C][C]-0.121024[/C][C]-0.9832[/C][C]0.83545[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4538&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4538&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
0	0.026856	0.2182	0.413981
1	-0.227563	-1.8487	0.965512
2	-0.12326	-1.0014	0.839847
3	-0.059125	-0.4803	0.68371
4	0.210368	1.709	0.046071
5	-0.171846	-1.3961	0.916317
6	0.005258	0.0427	0.483027
7	-0.269427	-2.1888	0.983924
8	-0.195151	-1.5854	0.941174
9	0.107719	0.8751	0.192343
10	0.051669	0.4198	0.338011
11	-0.01463	-0.1189	0.547126
12	-0.047287	-0.3842	0.648953
13	1.1e-05	1e-04	0.499964
14	-0.019597	-0.1592	0.563003
15	-0.176891	-1.4371	0.922288
16	-0.037232	-0.3025	0.618381
17	-0.121024	-0.9832	0.83545

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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