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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 04 Dec 2007 09:00:54 -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/04/t1196783344r0cs3quasf0n2ci.htm/, Retrieved Thu, 02 May 2024 07:07:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2406, Retrieved Thu, 02 May 2024 07:07:12 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

212

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

-       [(Partial) Autocorrelation Function] [ACF en PACF] [2007-12-04 16:00:54] [ca5e0f9f346e091f4d0fe7e17f7dba21] [Current]

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Dataseries X:

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Histogram

Boxplots

16.4
-8.5
0.2
-7.8
-0.1
9.1
-2.7
-6.1
7.9
-14.3
-5
22.6
2.4
-13.5
-6
5
1
14.7
-6.5
-6.6
11.3
-12
-6.6
22.3
-4.2
-5.6
-10.7
0.3
-0.2
7.2
-0.8
-3.8
13
-24.8
4.7
16.6
-6.1
2.6
-11
6.7
-1.6
14.4
-11.5
5.7
3.7
-20.5
5.2
15.9
1.6
-5.5
-11.6
10.4
-1.1
12
-10.3
1.3
1.8
-13.9
4.5

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=2406&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=2406&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2406&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	7.6811	0
1	-0.30887	-2.3725	0.989526
2	-0.270969	-2.0813	0.979125
3	0.062185	0.4777	0.317332
4	-0.106359	-0.817	0.79138
5	0.095434	0.733	0.233218
6	0.116725	0.8966	0.186792
7	0.039778	0.3055	0.380515
8	-0.114972	-0.8831	0.809621
9	0.112441	0.8637	0.195631
10	-0.363895	-2.7951	0.996505
11	-0.038338	-0.2945	0.615287
12	0.662612	5.0896	2e-06
13	-0.308823	-2.3721	0.989516
14	-0.146512	-1.1254	0.867507
15	0.055089	0.4231	0.336863
16	-0.106261	-0.8162	0.791168

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & -0.30887 & -2.3725 & 0.989526 \tabularnewline
2 & -0.270969 & -2.0813 & 0.979125 \tabularnewline
3 & 0.062185 & 0.4777 & 0.317332 \tabularnewline
4 & -0.106359 & -0.817 & 0.79138 \tabularnewline
5 & 0.095434 & 0.733 & 0.233218 \tabularnewline
6 & 0.116725 & 0.8966 & 0.186792 \tabularnewline
7 & 0.039778 & 0.3055 & 0.380515 \tabularnewline
8 & -0.114972 & -0.8831 & 0.809621 \tabularnewline
9 & 0.112441 & 0.8637 & 0.195631 \tabularnewline
10 & -0.363895 & -2.7951 & 0.996505 \tabularnewline
11 & -0.038338 & -0.2945 & 0.615287 \tabularnewline
12 & 0.662612 & 5.0896 & 2e-06 \tabularnewline
13 & -0.308823 & -2.3721 & 0.989516 \tabularnewline
14 & -0.146512 & -1.1254 & 0.867507 \tabularnewline
15 & 0.055089 & 0.4231 & 0.336863 \tabularnewline
16 & -0.106261 & -0.8162 & 0.791168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2406&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]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.30887[/C][C]-2.3725[/C][C]0.989526[/C][/ROW]
[ROW][C]2[/C][C]-0.270969[/C][C]-2.0813[/C][C]0.979125[/C][/ROW]
[ROW][C]3[/C][C]0.062185[/C][C]0.4777[/C][C]0.317332[/C][/ROW]
[ROW][C]4[/C][C]-0.106359[/C][C]-0.817[/C][C]0.79138[/C][/ROW]
[ROW][C]5[/C][C]0.095434[/C][C]0.733[/C][C]0.233218[/C][/ROW]
[ROW][C]6[/C][C]0.116725[/C][C]0.8966[/C][C]0.186792[/C][/ROW]
[ROW][C]7[/C][C]0.039778[/C][C]0.3055[/C][C]0.380515[/C][/ROW]
[ROW][C]8[/C][C]-0.114972[/C][C]-0.8831[/C][C]0.809621[/C][/ROW]
[ROW][C]9[/C][C]0.112441[/C][C]0.8637[/C][C]0.195631[/C][/ROW]
[ROW][C]10[/C][C]-0.363895[/C][C]-2.7951[/C][C]0.996505[/C][/ROW]
[ROW][C]11[/C][C]-0.038338[/C][C]-0.2945[/C][C]0.615287[/C][/ROW]
[ROW][C]12[/C][C]0.662612[/C][C]5.0896[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.308823[/C][C]-2.3721[/C][C]0.989516[/C][/ROW]
[ROW][C]14[/C][C]-0.146512[/C][C]-1.1254[/C][C]0.867507[/C][/ROW]
[ROW][C]15[/C][C]0.055089[/C][C]0.4231[/C][C]0.336863[/C][/ROW]
[ROW][C]16[/C][C]-0.106261[/C][C]-0.8162[/C][C]0.791168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2406&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2406&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	7.6811	0
1	-0.30887	-2.3725	0.989526
2	-0.270969	-2.0813	0.979125
3	0.062185	0.4777	0.317332
4	-0.106359	-0.817	0.79138
5	0.095434	0.733	0.233218
6	0.116725	0.8966	0.186792
7	0.039778	0.3055	0.380515
8	-0.114972	-0.8831	0.809621
9	0.112441	0.8637	0.195631
10	-0.363895	-2.7951	0.996505
11	-0.038338	-0.2945	0.615287
12	0.662612	5.0896	2e-06
13	-0.308823	-2.3721	0.989516
14	-0.146512	-1.1254	0.867507
15	0.055089	0.4231	0.336863
16	-0.106261	-0.8162	0.791168

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.30887	-2.3725	0.989526
1	-0.405008	-3.1109	0.998564
2	-0.238689	-1.8334	0.964106
3	-0.399501	-3.0686	0.998377
4	-0.287659	-2.2095	0.984485
5	-0.195	-1.4978	0.930245
6	0.017981	0.1381	0.445311
7	0.010157	0.078	0.469038
8	0.368122	2.8276	0.003198
9	-0.200379	-1.5391	0.935442
10	-0.498968	-3.8326	0.999845
11	0.201011	1.544	0.063969
12	-0.071481	-0.5491	0.70748
13	-0.103349	-0.7938	0.784765
14	0.007575	0.0582	0.476899
15	-0.031875	-0.2448	0.596283
16	-0.023154	-0.1779	0.570276

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.30887 & -2.3725 & 0.989526 \tabularnewline
1 & -0.405008 & -3.1109 & 0.998564 \tabularnewline
2 & -0.238689 & -1.8334 & 0.964106 \tabularnewline
3 & -0.399501 & -3.0686 & 0.998377 \tabularnewline
4 & -0.287659 & -2.2095 & 0.984485 \tabularnewline
5 & -0.195 & -1.4978 & 0.930245 \tabularnewline
6 & 0.017981 & 0.1381 & 0.445311 \tabularnewline
7 & 0.010157 & 0.078 & 0.469038 \tabularnewline
8 & 0.368122 & 2.8276 & 0.003198 \tabularnewline
9 & -0.200379 & -1.5391 & 0.935442 \tabularnewline
10 & -0.498968 & -3.8326 & 0.999845 \tabularnewline
11 & 0.201011 & 1.544 & 0.063969 \tabularnewline
12 & -0.071481 & -0.5491 & 0.70748 \tabularnewline
13 & -0.103349 & -0.7938 & 0.784765 \tabularnewline
14 & 0.007575 & 0.0582 & 0.476899 \tabularnewline
15 & -0.031875 & -0.2448 & 0.596283 \tabularnewline
16 & -0.023154 & -0.1779 & 0.570276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2406&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]-0.30887[/C][C]-2.3725[/C][C]0.989526[/C][/ROW]
[ROW][C]1[/C][C]-0.405008[/C][C]-3.1109[/C][C]0.998564[/C][/ROW]
[ROW][C]2[/C][C]-0.238689[/C][C]-1.8334[/C][C]0.964106[/C][/ROW]
[ROW][C]3[/C][C]-0.399501[/C][C]-3.0686[/C][C]0.998377[/C][/ROW]
[ROW][C]4[/C][C]-0.287659[/C][C]-2.2095[/C][C]0.984485[/C][/ROW]
[ROW][C]5[/C][C]-0.195[/C][C]-1.4978[/C][C]0.930245[/C][/ROW]
[ROW][C]6[/C][C]0.017981[/C][C]0.1381[/C][C]0.445311[/C][/ROW]
[ROW][C]7[/C][C]0.010157[/C][C]0.078[/C][C]0.469038[/C][/ROW]
[ROW][C]8[/C][C]0.368122[/C][C]2.8276[/C][C]0.003198[/C][/ROW]
[ROW][C]9[/C][C]-0.200379[/C][C]-1.5391[/C][C]0.935442[/C][/ROW]
[ROW][C]10[/C][C]-0.498968[/C][C]-3.8326[/C][C]0.999845[/C][/ROW]
[ROW][C]11[/C][C]0.201011[/C][C]1.544[/C][C]0.063969[/C][/ROW]
[ROW][C]12[/C][C]-0.071481[/C][C]-0.5491[/C][C]0.70748[/C][/ROW]
[ROW][C]13[/C][C]-0.103349[/C][C]-0.7938[/C][C]0.784765[/C][/ROW]
[ROW][C]14[/C][C]0.007575[/C][C]0.0582[/C][C]0.476899[/C][/ROW]
[ROW][C]15[/C][C]-0.031875[/C][C]-0.2448[/C][C]0.596283[/C][/ROW]
[ROW][C]16[/C][C]-0.023154[/C][C]-0.1779[/C][C]0.570276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2406&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2406&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	-0.30887	-2.3725	0.989526
1	-0.405008	-3.1109	0.998564
2	-0.238689	-1.8334	0.964106
3	-0.399501	-3.0686	0.998377
4	-0.287659	-2.2095	0.984485
5	-0.195	-1.4978	0.930245
6	0.017981	0.1381	0.445311
7	0.010157	0.078	0.469038
8	0.368122	2.8276	0.003198
9	-0.200379	-1.5391	0.935442
10	-0.498968	-3.8326	0.999845
11	0.201011	1.544	0.063969
12	-0.071481	-0.5491	0.70748
13	-0.103349	-0.7938	0.784765
14	0.007575	0.0582	0.476899
15	-0.031875	-0.2448	0.596283
16	-0.023154	-0.1779	0.570276

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code