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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 21 Dec 2008 15:24:49 -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/2008/Dec/21/t12298983317d28k3fc8fij2c6.htm/, Retrieved Fri, 17 May 2024 03:20:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35884, Retrieved Fri, 17 May 2024 03:20:21 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

162

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

-     [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:13:26] [4ddbf81f78ea7c738951638c7e93f6ee]
-   P   [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:16:00] [4ddbf81f78ea7c738951638c7e93f6ee]
-   PD    [(Partial) Autocorrelation Function] [autocorrelation v...] [2008-12-21 22:17:35] [4ddbf81f78ea7c738951638c7e93f6ee]
-   PD      [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:19:34] [4ddbf81f78ea7c738951638c7e93f6ee]
-             [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:20:27] [4ddbf81f78ea7c738951638c7e93f6ee]
-   P           [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:22:06] [4ddbf81f78ea7c738951638c7e93f6ee]
-   PD            [(Partial) Autocorrelation Function] [autocorrelation t...] [2008-12-21 22:23:36] [4ddbf81f78ea7c738951638c7e93f6ee]
-   PD                [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:24:49] [e8f764b122b426f433a1e1038b457077] [Current]
-   P                   [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:26:12] [4ddbf81f78ea7c738951638c7e93f6ee] 

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Dataseries X:

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Histogram

Boxplots

8.3
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35884&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35884&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35884&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.362729	2.7862	0.003581
2	-0.208153	-1.5989	0.057598
3	-0.565384	-4.3428	2.8e-05
4	-0.438653	-3.3694	0.000666
5	0.006844	0.0526	0.479128
6	0.360153	2.7664	0.003778
7	0.256599	1.971	0.026712
8	-0.018005	-0.1383	0.445238
9	-0.23547	-1.8087	0.037799
10	-0.165086	-1.2681	0.10488
11	0.065882	0.506	0.307355
12	0.364908	2.8029	0.003421
13	0.064789	0.4977	0.310289
14	-0.067504	-0.5185	0.303022
15	-0.197731	-1.5188	0.067076
16	-0.11691	-0.898	0.186416
17	0.022747	0.1747	0.430946

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.362729 & 2.7862 & 0.003581 \tabularnewline
2 & -0.208153 & -1.5989 & 0.057598 \tabularnewline
3 & -0.565384 & -4.3428 & 2.8e-05 \tabularnewline
4 & -0.438653 & -3.3694 & 0.000666 \tabularnewline
5 & 0.006844 & 0.0526 & 0.479128 \tabularnewline
6 & 0.360153 & 2.7664 & 0.003778 \tabularnewline
7 & 0.256599 & 1.971 & 0.026712 \tabularnewline
8 & -0.018005 & -0.1383 & 0.445238 \tabularnewline
9 & -0.23547 & -1.8087 & 0.037799 \tabularnewline
10 & -0.165086 & -1.2681 & 0.10488 \tabularnewline
11 & 0.065882 & 0.506 & 0.307355 \tabularnewline
12 & 0.364908 & 2.8029 & 0.003421 \tabularnewline
13 & 0.064789 & 0.4977 & 0.310289 \tabularnewline
14 & -0.067504 & -0.5185 & 0.303022 \tabularnewline
15 & -0.197731 & -1.5188 & 0.067076 \tabularnewline
16 & -0.11691 & -0.898 & 0.186416 \tabularnewline
17 & 0.022747 & 0.1747 & 0.430946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35884&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]0.362729[/C][C]2.7862[/C][C]0.003581[/C][/ROW]
[ROW][C]2[/C][C]-0.208153[/C][C]-1.5989[/C][C]0.057598[/C][/ROW]
[ROW][C]3[/C][C]-0.565384[/C][C]-4.3428[/C][C]2.8e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.438653[/C][C]-3.3694[/C][C]0.000666[/C][/ROW]
[ROW][C]5[/C][C]0.006844[/C][C]0.0526[/C][C]0.479128[/C][/ROW]
[ROW][C]6[/C][C]0.360153[/C][C]2.7664[/C][C]0.003778[/C][/ROW]
[ROW][C]7[/C][C]0.256599[/C][C]1.971[/C][C]0.026712[/C][/ROW]
[ROW][C]8[/C][C]-0.018005[/C][C]-0.1383[/C][C]0.445238[/C][/ROW]
[ROW][C]9[/C][C]-0.23547[/C][C]-1.8087[/C][C]0.037799[/C][/ROW]
[ROW][C]10[/C][C]-0.165086[/C][C]-1.2681[/C][C]0.10488[/C][/ROW]
[ROW][C]11[/C][C]0.065882[/C][C]0.506[/C][C]0.307355[/C][/ROW]
[ROW][C]12[/C][C]0.364908[/C][C]2.8029[/C][C]0.003421[/C][/ROW]
[ROW][C]13[/C][C]0.064789[/C][C]0.4977[/C][C]0.310289[/C][/ROW]
[ROW][C]14[/C][C]-0.067504[/C][C]-0.5185[/C][C]0.303022[/C][/ROW]
[ROW][C]15[/C][C]-0.197731[/C][C]-1.5188[/C][C]0.067076[/C][/ROW]
[ROW][C]16[/C][C]-0.11691[/C][C]-0.898[/C][C]0.186416[/C][/ROW]
[ROW][C]17[/C][C]0.022747[/C][C]0.1747[/C][C]0.430946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35884&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35884&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	0.362729	2.7862	0.003581
2	-0.208153	-1.5989	0.057598
3	-0.565384	-4.3428	2.8e-05
4	-0.438653	-3.3694	0.000666
5	0.006844	0.0526	0.479128
6	0.360153	2.7664	0.003778
7	0.256599	1.971	0.026712
8	-0.018005	-0.1383	0.445238
9	-0.23547	-1.8087	0.037799
10	-0.165086	-1.2681	0.10488
11	0.065882	0.506	0.307355
12	0.364908	2.8029	0.003421
13	0.064789	0.4977	0.310289
14	-0.067504	-0.5185	0.303022
15	-0.197731	-1.5188	0.067076
16	-0.11691	-0.898	0.186416
17	0.022747	0.1747	0.430946

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.362729	2.7862	0.003581
2	-0.391196	-3.0048	0.001948
3	-0.432948	-3.3255	0.000761
4	-0.214189	-1.6452	0.052621
5	-0.004945	-0.038	0.484916
6	0.032296	0.2481	0.40247
7	-0.199582	-1.533	0.065308
8	-0.121814	-0.9357	0.176628
9	-0.073354	-0.5634	0.287635
10	0.018834	0.1447	0.442735
11	0.024339	0.187	0.426169
12	0.284615	2.1862	0.016391
13	-0.282223	-2.1678	0.01711
14	0.221731	1.7031	0.046902
15	0.099833	0.7668	0.22312
16	0.084451	0.6487	0.259532
17	-0.072327	-0.5556	0.290308

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.362729 & 2.7862 & 0.003581 \tabularnewline
2 & -0.391196 & -3.0048 & 0.001948 \tabularnewline
3 & -0.432948 & -3.3255 & 0.000761 \tabularnewline
4 & -0.214189 & -1.6452 & 0.052621 \tabularnewline
5 & -0.004945 & -0.038 & 0.484916 \tabularnewline
6 & 0.032296 & 0.2481 & 0.40247 \tabularnewline
7 & -0.199582 & -1.533 & 0.065308 \tabularnewline
8 & -0.121814 & -0.9357 & 0.176628 \tabularnewline
9 & -0.073354 & -0.5634 & 0.287635 \tabularnewline
10 & 0.018834 & 0.1447 & 0.442735 \tabularnewline
11 & 0.024339 & 0.187 & 0.426169 \tabularnewline
12 & 0.284615 & 2.1862 & 0.016391 \tabularnewline
13 & -0.282223 & -2.1678 & 0.01711 \tabularnewline
14 & 0.221731 & 1.7031 & 0.046902 \tabularnewline
15 & 0.099833 & 0.7668 & 0.22312 \tabularnewline
16 & 0.084451 & 0.6487 & 0.259532 \tabularnewline
17 & -0.072327 & -0.5556 & 0.290308 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35884&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]0.362729[/C][C]2.7862[/C][C]0.003581[/C][/ROW]
[ROW][C]2[/C][C]-0.391196[/C][C]-3.0048[/C][C]0.001948[/C][/ROW]
[ROW][C]3[/C][C]-0.432948[/C][C]-3.3255[/C][C]0.000761[/C][/ROW]
[ROW][C]4[/C][C]-0.214189[/C][C]-1.6452[/C][C]0.052621[/C][/ROW]
[ROW][C]5[/C][C]-0.004945[/C][C]-0.038[/C][C]0.484916[/C][/ROW]
[ROW][C]6[/C][C]0.032296[/C][C]0.2481[/C][C]0.40247[/C][/ROW]
[ROW][C]7[/C][C]-0.199582[/C][C]-1.533[/C][C]0.065308[/C][/ROW]
[ROW][C]8[/C][C]-0.121814[/C][C]-0.9357[/C][C]0.176628[/C][/ROW]
[ROW][C]9[/C][C]-0.073354[/C][C]-0.5634[/C][C]0.287635[/C][/ROW]
[ROW][C]10[/C][C]0.018834[/C][C]0.1447[/C][C]0.442735[/C][/ROW]
[ROW][C]11[/C][C]0.024339[/C][C]0.187[/C][C]0.426169[/C][/ROW]
[ROW][C]12[/C][C]0.284615[/C][C]2.1862[/C][C]0.016391[/C][/ROW]
[ROW][C]13[/C][C]-0.282223[/C][C]-2.1678[/C][C]0.01711[/C][/ROW]
[ROW][C]14[/C][C]0.221731[/C][C]1.7031[/C][C]0.046902[/C][/ROW]
[ROW][C]15[/C][C]0.099833[/C][C]0.7668[/C][C]0.22312[/C][/ROW]
[ROW][C]16[/C][C]0.084451[/C][C]0.6487[/C][C]0.259532[/C][/ROW]
[ROW][C]17[/C][C]-0.072327[/C][C]-0.5556[/C][C]0.290308[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35884&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35884&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	0.362729	2.7862	0.003581
2	-0.391196	-3.0048	0.001948
3	-0.432948	-3.3255	0.000761
4	-0.214189	-1.6452	0.052621
5	-0.004945	-0.038	0.484916
6	0.032296	0.2481	0.40247
7	-0.199582	-1.533	0.065308
8	-0.121814	-0.9357	0.176628
9	-0.073354	-0.5634	0.287635
10	0.018834	0.1447	0.442735
11	0.024339	0.187	0.426169
12	0.284615	2.1862	0.016391
13	-0.282223	-2.1678	0.01711
14	0.221731	1.7031	0.046902
15	0.099833	0.7668	0.22312
16	0.084451	0.6487	0.259532
17	-0.072327	-0.5556	0.290308

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; 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 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