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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 01 Dec 2007 05:17:39 -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/01/t1196510822wjuxnrmsdlnysqk.htm/, Retrieved Sun, 19 May 2024 19:03:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2227, Retrieved Sun, 19 May 2024 19:03:22 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

227

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

-       [(Partial) Autocorrelation Function] [Autocorrelation i...] [2007-12-01 12:17:39] [bd02e85be52eb1cb060a2c60779eb820] [Current]

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Dataseries X:

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Histogram

Boxplots

9,1
11,2
7,7
7,9
-2,4
-2,8
-4,9
2,3
7,9
6,7
6
3,8
4,7
6,4
9,3
11
8,5
8,8
10
16,8
11,6
11,5
6
2,9
2,1
2,7
11,2
7,3
11,6
4,6
6
-0,5
1,8
3,7
8,3
8,3
12
7,8
5,3
1
-0,3
2,4
2,7
5,7
3,5
0,6
5,2
2,9
1
-5,5
-7,1
-7,9
-8,8
-7
-5,5
-7,3
-7,5
-3,5
2,2
3,1
4,1
4,2
6
5,5
5,1
5,5
1
1,5
1,2
1,7
-8,6
-11,2
-12,7
-3,1
-1
0,3
-2,9
-2,2
3,2
5,9
13,3
7,3
6,9
8,3
11,8
9,2
5,8
8,8
14,6
28,1
19,7
16,5
-5,3
-2,4
1,9
1,6
-0,1
-1,9
3,4
3,3
3,3
-9,8
-4,6
-6,1
10,6
8,8
10,7
11,7

Summary of compuational 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 compuational 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=2227&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]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=2227&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2227&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	10.3923	0
1	0.739822	7.6885	0
2	0.506657	5.2653	0
3	0.223485	2.3225	0.01104
4	0.186046	1.9334	0.027899
5	0.186345	1.9366	0.027707
6	0.153888	1.5993	0.056343
7	0.10794	1.1217	0.13223
8	0.028157	0.2926	0.38519
9	0.032682	0.3396	0.367392
10	-0.045667	-0.4746	0.681979
11	-0.112466	-1.1688	0.877468
12	-0.279831	-2.9081	0.997793
13	-0.254244	-2.6422	0.99527
14	-0.165944	-1.7245	0.956264
15	-0.008886	-0.0923	0.536703
16	0.069811	0.7255	0.234859
17	0.042278	0.4394	0.330635
18	0.050991	0.5299	0.298628
19	0.046473	0.483	0.31505

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 10.3923 & 0 \tabularnewline
1 & 0.739822 & 7.6885 & 0 \tabularnewline
2 & 0.506657 & 5.2653 & 0 \tabularnewline
3 & 0.223485 & 2.3225 & 0.01104 \tabularnewline
4 & 0.186046 & 1.9334 & 0.027899 \tabularnewline
5 & 0.186345 & 1.9366 & 0.027707 \tabularnewline
6 & 0.153888 & 1.5993 & 0.056343 \tabularnewline
7 & 0.10794 & 1.1217 & 0.13223 \tabularnewline
8 & 0.028157 & 0.2926 & 0.38519 \tabularnewline
9 & 0.032682 & 0.3396 & 0.367392 \tabularnewline
10 & -0.045667 & -0.4746 & 0.681979 \tabularnewline
11 & -0.112466 & -1.1688 & 0.877468 \tabularnewline
12 & -0.279831 & -2.9081 & 0.997793 \tabularnewline
13 & -0.254244 & -2.6422 & 0.99527 \tabularnewline
14 & -0.165944 & -1.7245 & 0.956264 \tabularnewline
15 & -0.008886 & -0.0923 & 0.536703 \tabularnewline
16 & 0.069811 & 0.7255 & 0.234859 \tabularnewline
17 & 0.042278 & 0.4394 & 0.330635 \tabularnewline
18 & 0.050991 & 0.5299 & 0.298628 \tabularnewline
19 & 0.046473 & 0.483 & 0.31505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2227&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]10.3923[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.739822[/C][C]7.6885[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.506657[/C][C]5.2653[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.223485[/C][C]2.3225[/C][C]0.01104[/C][/ROW]
[ROW][C]4[/C][C]0.186046[/C][C]1.9334[/C][C]0.027899[/C][/ROW]
[ROW][C]5[/C][C]0.186345[/C][C]1.9366[/C][C]0.027707[/C][/ROW]
[ROW][C]6[/C][C]0.153888[/C][C]1.5993[/C][C]0.056343[/C][/ROW]
[ROW][C]7[/C][C]0.10794[/C][C]1.1217[/C][C]0.13223[/C][/ROW]
[ROW][C]8[/C][C]0.028157[/C][C]0.2926[/C][C]0.38519[/C][/ROW]
[ROW][C]9[/C][C]0.032682[/C][C]0.3396[/C][C]0.367392[/C][/ROW]
[ROW][C]10[/C][C]-0.045667[/C][C]-0.4746[/C][C]0.681979[/C][/ROW]
[ROW][C]11[/C][C]-0.112466[/C][C]-1.1688[/C][C]0.877468[/C][/ROW]
[ROW][C]12[/C][C]-0.279831[/C][C]-2.9081[/C][C]0.997793[/C][/ROW]
[ROW][C]13[/C][C]-0.254244[/C][C]-2.6422[/C][C]0.99527[/C][/ROW]
[ROW][C]14[/C][C]-0.165944[/C][C]-1.7245[/C][C]0.956264[/C][/ROW]
[ROW][C]15[/C][C]-0.008886[/C][C]-0.0923[/C][C]0.536703[/C][/ROW]
[ROW][C]16[/C][C]0.069811[/C][C]0.7255[/C][C]0.234859[/C][/ROW]
[ROW][C]17[/C][C]0.042278[/C][C]0.4394[/C][C]0.330635[/C][/ROW]
[ROW][C]18[/C][C]0.050991[/C][C]0.5299[/C][C]0.298628[/C][/ROW]
[ROW][C]19[/C][C]0.046473[/C][C]0.483[/C][C]0.31505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2227&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2227&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	10.3923	0
1	0.739822	7.6885	0
2	0.506657	5.2653	0
3	0.223485	2.3225	0.01104
4	0.186046	1.9334	0.027899
5	0.186345	1.9366	0.027707
6	0.153888	1.5993	0.056343
7	0.10794	1.1217	0.13223
8	0.028157	0.2926	0.38519
9	0.032682	0.3396	0.367392
10	-0.045667	-0.4746	0.681979
11	-0.112466	-1.1688	0.877468
12	-0.279831	-2.9081	0.997793
13	-0.254244	-2.6422	0.99527
14	-0.165944	-1.7245	0.956264
15	-0.008886	-0.0923	0.536703
16	0.069811	0.7255	0.234859
17	0.042278	0.4394	0.330635
18	0.050991	0.5299	0.298628
19	0.046473	0.483	0.31505

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.739822	7.6885	0
1	-0.089866	-0.9339	0.823783
2	-0.264028	-2.7439	0.996444
3	0.34511	3.5865	0.000252
4	0.057287	0.5953	0.27643
5	-0.26557	-2.7599	0.996603
6	0.134148	1.3941	0.083073
7	0.004576	0.0476	0.481079
8	-0.021232	-0.2207	0.58711
9	-0.201358	-2.0926	0.980635
10	-0.084252	-0.8756	0.808397
11	-0.19483	-2.0247	0.977319
12	0.269301	2.7987	0.003039
13	0.113401	1.1785	0.120593
14	-0.114039	-1.1851	0.880716
15	0.133277	1.3851	0.084445
16	0.015464	0.1607	0.436312
17	0.047886	0.4976	0.309872
18	0.042974	0.4466	0.328028
19	-0.017672	-0.1837	0.572686

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.739822 & 7.6885 & 0 \tabularnewline
1 & -0.089866 & -0.9339 & 0.823783 \tabularnewline
2 & -0.264028 & -2.7439 & 0.996444 \tabularnewline
3 & 0.34511 & 3.5865 & 0.000252 \tabularnewline
4 & 0.057287 & 0.5953 & 0.27643 \tabularnewline
5 & -0.26557 & -2.7599 & 0.996603 \tabularnewline
6 & 0.134148 & 1.3941 & 0.083073 \tabularnewline
7 & 0.004576 & 0.0476 & 0.481079 \tabularnewline
8 & -0.021232 & -0.2207 & 0.58711 \tabularnewline
9 & -0.201358 & -2.0926 & 0.980635 \tabularnewline
10 & -0.084252 & -0.8756 & 0.808397 \tabularnewline
11 & -0.19483 & -2.0247 & 0.977319 \tabularnewline
12 & 0.269301 & 2.7987 & 0.003039 \tabularnewline
13 & 0.113401 & 1.1785 & 0.120593 \tabularnewline
14 & -0.114039 & -1.1851 & 0.880716 \tabularnewline
15 & 0.133277 & 1.3851 & 0.084445 \tabularnewline
16 & 0.015464 & 0.1607 & 0.436312 \tabularnewline
17 & 0.047886 & 0.4976 & 0.309872 \tabularnewline
18 & 0.042974 & 0.4466 & 0.328028 \tabularnewline
19 & -0.017672 & -0.1837 & 0.572686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2227&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]0.739822[/C][C]7.6885[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.089866[/C][C]-0.9339[/C][C]0.823783[/C][/ROW]
[ROW][C]2[/C][C]-0.264028[/C][C]-2.7439[/C][C]0.996444[/C][/ROW]
[ROW][C]3[/C][C]0.34511[/C][C]3.5865[/C][C]0.000252[/C][/ROW]
[ROW][C]4[/C][C]0.057287[/C][C]0.5953[/C][C]0.27643[/C][/ROW]
[ROW][C]5[/C][C]-0.26557[/C][C]-2.7599[/C][C]0.996603[/C][/ROW]
[ROW][C]6[/C][C]0.134148[/C][C]1.3941[/C][C]0.083073[/C][/ROW]
[ROW][C]7[/C][C]0.004576[/C][C]0.0476[/C][C]0.481079[/C][/ROW]
[ROW][C]8[/C][C]-0.021232[/C][C]-0.2207[/C][C]0.58711[/C][/ROW]
[ROW][C]9[/C][C]-0.201358[/C][C]-2.0926[/C][C]0.980635[/C][/ROW]
[ROW][C]10[/C][C]-0.084252[/C][C]-0.8756[/C][C]0.808397[/C][/ROW]
[ROW][C]11[/C][C]-0.19483[/C][C]-2.0247[/C][C]0.977319[/C][/ROW]
[ROW][C]12[/C][C]0.269301[/C][C]2.7987[/C][C]0.003039[/C][/ROW]
[ROW][C]13[/C][C]0.113401[/C][C]1.1785[/C][C]0.120593[/C][/ROW]
[ROW][C]14[/C][C]-0.114039[/C][C]-1.1851[/C][C]0.880716[/C][/ROW]
[ROW][C]15[/C][C]0.133277[/C][C]1.3851[/C][C]0.084445[/C][/ROW]
[ROW][C]16[/C][C]0.015464[/C][C]0.1607[/C][C]0.436312[/C][/ROW]
[ROW][C]17[/C][C]0.047886[/C][C]0.4976[/C][C]0.309872[/C][/ROW]
[ROW][C]18[/C][C]0.042974[/C][C]0.4466[/C][C]0.328028[/C][/ROW]
[ROW][C]19[/C][C]-0.017672[/C][C]-0.1837[/C][C]0.572686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2227&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2227&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	0.739822	7.6885	0
1	-0.089866	-0.9339	0.823783
2	-0.264028	-2.7439	0.996444
3	0.34511	3.5865	0.000252
4	0.057287	0.5953	0.27643
5	-0.26557	-2.7599	0.996603
6	0.134148	1.3941	0.083073
7	0.004576	0.0476	0.481079
8	-0.021232	-0.2207	0.58711
9	-0.201358	-2.0926	0.980635
10	-0.084252	-0.8756	0.808397
11	-0.19483	-2.0247	0.977319
12	0.269301	2.7987	0.003039
13	0.113401	1.1785	0.120593
14	-0.114039	-1.1851	0.880716
15	0.133277	1.3851	0.084445
16	0.015464	0.1607	0.436312
17	0.047886	0.4976	0.309872
18	0.042974	0.4466	0.328028
19	-0.017672	-0.1837	0.572686

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code