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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

Sat, 13 Dec 2008 05:16:36 -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/13/t1229170642zp67su6dmh1ovoh.htm/, Retrieved Sun, 19 May 2024 03:58:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33001, Retrieved Sun, 19 May 2024 03:58:21 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

jenske_cole@hotmail.com

Estimated Impact

193

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

F     [Bivariate Kernel Density Estimation] [Various EDA Topic...] [2008-11-12 13:37:39] [8094ad203a218aaca2d1cea2c78c2d6e]
F    D  [Bivariate Kernel Density Estimation] [opdracht3 blok8 q...] [2008-11-12 17:51:49] [975daa21de49eaf4d491226310243f5a]
- RMPD      [(Partial) Autocorrelation Function] [paper autocorrela...] [2008-12-13 12:16:36] [120dfa2440e51a0cfc0f5296bc5d7460] [Current]

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Dataseries X:

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Histogram

Boxplots

7.6
7.4
7.3
7.1
6.9
6.8
7.5
7.6
7.8
8
8.1
8.2
8.3
8.2
8
7.9
7.6
7.6
8.2
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
6.9
6.8
6.7

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=33001&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=33001&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33001&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	0.465646	3.8679	0.000123
2	-0.098028	-0.8143	0.209144
3	-0.546388	-4.5386	1.2e-05
4	-0.601195	-4.9939	2e-06
5	-0.20412	-1.6955	0.04724
6	0.166161	1.3802	0.085985
7	0.312156	2.593	0.005804
8	0.297469	2.471	0.007974
9	0.101087	0.8397	0.20199
10	-0.082585	-0.686	0.247505
11	-0.143481	-1.1918	0.118703
12	-0.229263	-1.9044	0.030514
13	-0.059504	-0.4943	0.31134
14	0.077653	0.645	0.260522
15	0.155358	1.2905	0.100593
16	0.098614	0.8192	0.20776
17	-0.075659	-0.6285	0.265885
18	-0.106422	-0.884	0.189881
19	-0.090723	-0.7536	0.226827

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.465646 & 3.8679 & 0.000123 \tabularnewline
2 & -0.098028 & -0.8143 & 0.209144 \tabularnewline
3 & -0.546388 & -4.5386 & 1.2e-05 \tabularnewline
4 & -0.601195 & -4.9939 & 2e-06 \tabularnewline
5 & -0.20412 & -1.6955 & 0.04724 \tabularnewline
6 & 0.166161 & 1.3802 & 0.085985 \tabularnewline
7 & 0.312156 & 2.593 & 0.005804 \tabularnewline
8 & 0.297469 & 2.471 & 0.007974 \tabularnewline
9 & 0.101087 & 0.8397 & 0.20199 \tabularnewline
10 & -0.082585 & -0.686 & 0.247505 \tabularnewline
11 & -0.143481 & -1.1918 & 0.118703 \tabularnewline
12 & -0.229263 & -1.9044 & 0.030514 \tabularnewline
13 & -0.059504 & -0.4943 & 0.31134 \tabularnewline
14 & 0.077653 & 0.645 & 0.260522 \tabularnewline
15 & 0.155358 & 1.2905 & 0.100593 \tabularnewline
16 & 0.098614 & 0.8192 & 0.20776 \tabularnewline
17 & -0.075659 & -0.6285 & 0.265885 \tabularnewline
18 & -0.106422 & -0.884 & 0.189881 \tabularnewline
19 & -0.090723 & -0.7536 & 0.226827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33001&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]0.465646[/C][C]3.8679[/C][C]0.000123[/C][/ROW]
[ROW][C]2[/C][C]-0.098028[/C][C]-0.8143[/C][C]0.209144[/C][/ROW]
[ROW][C]3[/C][C]-0.546388[/C][C]-4.5386[/C][C]1.2e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.601195[/C][C]-4.9939[/C][C]2e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.20412[/C][C]-1.6955[/C][C]0.04724[/C][/ROW]
[ROW][C]6[/C][C]0.166161[/C][C]1.3802[/C][C]0.085985[/C][/ROW]
[ROW][C]7[/C][C]0.312156[/C][C]2.593[/C][C]0.005804[/C][/ROW]
[ROW][C]8[/C][C]0.297469[/C][C]2.471[/C][C]0.007974[/C][/ROW]
[ROW][C]9[/C][C]0.101087[/C][C]0.8397[/C][C]0.20199[/C][/ROW]
[ROW][C]10[/C][C]-0.082585[/C][C]-0.686[/C][C]0.247505[/C][/ROW]
[ROW][C]11[/C][C]-0.143481[/C][C]-1.1918[/C][C]0.118703[/C][/ROW]
[ROW][C]12[/C][C]-0.229263[/C][C]-1.9044[/C][C]0.030514[/C][/ROW]
[ROW][C]13[/C][C]-0.059504[/C][C]-0.4943[/C][C]0.31134[/C][/ROW]
[ROW][C]14[/C][C]0.077653[/C][C]0.645[/C][C]0.260522[/C][/ROW]
[ROW][C]15[/C][C]0.155358[/C][C]1.2905[/C][C]0.100593[/C][/ROW]
[ROW][C]16[/C][C]0.098614[/C][C]0.8192[/C][C]0.20776[/C][/ROW]
[ROW][C]17[/C][C]-0.075659[/C][C]-0.6285[/C][C]0.265885[/C][/ROW]
[ROW][C]18[/C][C]-0.106422[/C][C]-0.884[/C][C]0.189881[/C][/ROW]
[ROW][C]19[/C][C]-0.090723[/C][C]-0.7536[/C][C]0.226827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33001&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33001&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	0.465646	3.8679	0.000123
2	-0.098028	-0.8143	0.209144
3	-0.546388	-4.5386	1.2e-05
4	-0.601195	-4.9939	2e-06
5	-0.20412	-1.6955	0.04724
6	0.166161	1.3802	0.085985
7	0.312156	2.593	0.005804
8	0.297469	2.471	0.007974
9	0.101087	0.8397	0.20199
10	-0.082585	-0.686	0.247505
11	-0.143481	-1.1918	0.118703
12	-0.229263	-1.9044	0.030514
13	-0.059504	-0.4943	0.31134
14	0.077653	0.645	0.260522
15	0.155358	1.2905	0.100593
16	0.098614	0.8192	0.20776
17	-0.075659	-0.6285	0.265885
18	-0.106422	-0.884	0.189881
19	-0.090723	-0.7536	0.226827

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.465646	3.8679	0.000123
2	-0.402023	-3.3395	0.000678
3	-0.449577	-3.7345	0.000192
4	-0.275893	-2.2917	0.012489
5	0.055067	0.4574	0.324404
6	-0.11861	-0.9852	0.163973
7	-0.199527	-1.6574	0.05099
8	0.056074	0.4658	0.321418
9	0.040875	0.3395	0.367619
10	-0.032764	-0.2722	0.393158
11	0.035512	0.295	0.384447
12	-0.156036	-1.2961	0.099624
13	0.156	1.2958	0.099676
14	0.034511	0.2867	0.387612
15	-0.007566	-0.0629	0.475033
16	-0.120533	-1.0012	0.160108
17	-0.079342	-0.6591	0.256024
18	0.117601	0.9769	0.166024
19	-0.114271	-0.9492	0.172915

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.465646 & 3.8679 & 0.000123 \tabularnewline
2 & -0.402023 & -3.3395 & 0.000678 \tabularnewline
3 & -0.449577 & -3.7345 & 0.000192 \tabularnewline
4 & -0.275893 & -2.2917 & 0.012489 \tabularnewline
5 & 0.055067 & 0.4574 & 0.324404 \tabularnewline
6 & -0.11861 & -0.9852 & 0.163973 \tabularnewline
7 & -0.199527 & -1.6574 & 0.05099 \tabularnewline
8 & 0.056074 & 0.4658 & 0.321418 \tabularnewline
9 & 0.040875 & 0.3395 & 0.367619 \tabularnewline
10 & -0.032764 & -0.2722 & 0.393158 \tabularnewline
11 & 0.035512 & 0.295 & 0.384447 \tabularnewline
12 & -0.156036 & -1.2961 & 0.099624 \tabularnewline
13 & 0.156 & 1.2958 & 0.099676 \tabularnewline
14 & 0.034511 & 0.2867 & 0.387612 \tabularnewline
15 & -0.007566 & -0.0629 & 0.475033 \tabularnewline
16 & -0.120533 & -1.0012 & 0.160108 \tabularnewline
17 & -0.079342 & -0.6591 & 0.256024 \tabularnewline
18 & 0.117601 & 0.9769 & 0.166024 \tabularnewline
19 & -0.114271 & -0.9492 & 0.172915 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33001&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]0.465646[/C][C]3.8679[/C][C]0.000123[/C][/ROW]
[ROW][C]2[/C][C]-0.402023[/C][C]-3.3395[/C][C]0.000678[/C][/ROW]
[ROW][C]3[/C][C]-0.449577[/C][C]-3.7345[/C][C]0.000192[/C][/ROW]
[ROW][C]4[/C][C]-0.275893[/C][C]-2.2917[/C][C]0.012489[/C][/ROW]
[ROW][C]5[/C][C]0.055067[/C][C]0.4574[/C][C]0.324404[/C][/ROW]
[ROW][C]6[/C][C]-0.11861[/C][C]-0.9852[/C][C]0.163973[/C][/ROW]
[ROW][C]7[/C][C]-0.199527[/C][C]-1.6574[/C][C]0.05099[/C][/ROW]
[ROW][C]8[/C][C]0.056074[/C][C]0.4658[/C][C]0.321418[/C][/ROW]
[ROW][C]9[/C][C]0.040875[/C][C]0.3395[/C][C]0.367619[/C][/ROW]
[ROW][C]10[/C][C]-0.032764[/C][C]-0.2722[/C][C]0.393158[/C][/ROW]
[ROW][C]11[/C][C]0.035512[/C][C]0.295[/C][C]0.384447[/C][/ROW]
[ROW][C]12[/C][C]-0.156036[/C][C]-1.2961[/C][C]0.099624[/C][/ROW]
[ROW][C]13[/C][C]0.156[/C][C]1.2958[/C][C]0.099676[/C][/ROW]
[ROW][C]14[/C][C]0.034511[/C][C]0.2867[/C][C]0.387612[/C][/ROW]
[ROW][C]15[/C][C]-0.007566[/C][C]-0.0629[/C][C]0.475033[/C][/ROW]
[ROW][C]16[/C][C]-0.120533[/C][C]-1.0012[/C][C]0.160108[/C][/ROW]
[ROW][C]17[/C][C]-0.079342[/C][C]-0.6591[/C][C]0.256024[/C][/ROW]
[ROW][C]18[/C][C]0.117601[/C][C]0.9769[/C][C]0.166024[/C][/ROW]
[ROW][C]19[/C][C]-0.114271[/C][C]-0.9492[/C][C]0.172915[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33001&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33001&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	0.465646	3.8679	0.000123
2	-0.402023	-3.3395	0.000678
3	-0.449577	-3.7345	0.000192
4	-0.275893	-2.2917	0.012489
5	0.055067	0.4574	0.324404
6	-0.11861	-0.9852	0.163973
7	-0.199527	-1.6574	0.05099
8	0.056074	0.4658	0.321418
9	0.040875	0.3395	0.367619
10	-0.032764	-0.2722	0.393158
11	0.035512	0.295	0.384447
12	-0.156036	-1.2961	0.099624
13	0.156	1.2958	0.099676
14	0.034511	0.2867	0.387612
15	-0.007566	-0.0629	0.475033
16	-0.120533	-1.0012	0.160108
17	-0.079342	-0.6591	0.256024
18	0.117601	0.9769	0.166024
19	-0.114271	-0.9492	0.172915

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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