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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

Tue, 27 Nov 2007 12:58:38 -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/Nov/27/t1196192948d1axwvimcjbaase.htm/, Retrieved Sun, 05 May 2024 18:12:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6933, Retrieved Sun, 05 May 2024 18:12:57 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

autocorrelatie bedrijfstak met niet seizoenale differentiatie Tinne Van der Eycken

Estimated Impact

174

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

-       [(Partial) Autocorrelation Function] [Workshop 3] [2007-11-27 19:58:38] [c8635c97647ba59406cb570a9fab7b02] [Current]

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Dataseries X:

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Boxplots

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=6933&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=6933&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6933&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	7	0
1	0.893258	6.2528	0
2	0.787973	5.5158	1e-06
3	0.700877	4.9061	5e-06
4	0.589777	4.1284	7.1e-05
5	0.474083	3.3186	0.000856
6	0.404414	2.8309	0.003357
7	0.334026	2.3382	0.011752
8	0.245693	1.7198	0.045886
9	0.18569	1.2998	0.099871
10	0.128295	0.8981	0.186771
11	0.084694	0.5929	0.278002
12	0.049646	0.3475	0.364845
13	0.044116	0.3088	0.379386
14	0.042715	0.299	0.3831
15	0.039836	0.2789	0.390766
16	0.037745	0.2642	0.39636

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7 & 0 \tabularnewline
1 & 0.893258 & 6.2528 & 0 \tabularnewline
2 & 0.787973 & 5.5158 & 1e-06 \tabularnewline
3 & 0.700877 & 4.9061 & 5e-06 \tabularnewline
4 & 0.589777 & 4.1284 & 7.1e-05 \tabularnewline
5 & 0.474083 & 3.3186 & 0.000856 \tabularnewline
6 & 0.404414 & 2.8309 & 0.003357 \tabularnewline
7 & 0.334026 & 2.3382 & 0.011752 \tabularnewline
8 & 0.245693 & 1.7198 & 0.045886 \tabularnewline
9 & 0.18569 & 1.2998 & 0.099871 \tabularnewline
10 & 0.128295 & 0.8981 & 0.186771 \tabularnewline
11 & 0.084694 & 0.5929 & 0.278002 \tabularnewline
12 & 0.049646 & 0.3475 & 0.364845 \tabularnewline
13 & 0.044116 & 0.3088 & 0.379386 \tabularnewline
14 & 0.042715 & 0.299 & 0.3831 \tabularnewline
15 & 0.039836 & 0.2789 & 0.390766 \tabularnewline
16 & 0.037745 & 0.2642 & 0.39636 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6933&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[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.893258[/C][C]6.2528[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.787973[/C][C]5.5158[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.700877[/C][C]4.9061[/C][C]5e-06[/C][/ROW]
[ROW][C]4[/C][C]0.589777[/C][C]4.1284[/C][C]7.1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.474083[/C][C]3.3186[/C][C]0.000856[/C][/ROW]
[ROW][C]6[/C][C]0.404414[/C][C]2.8309[/C][C]0.003357[/C][/ROW]
[ROW][C]7[/C][C]0.334026[/C][C]2.3382[/C][C]0.011752[/C][/ROW]
[ROW][C]8[/C][C]0.245693[/C][C]1.7198[/C][C]0.045886[/C][/ROW]
[ROW][C]9[/C][C]0.18569[/C][C]1.2998[/C][C]0.099871[/C][/ROW]
[ROW][C]10[/C][C]0.128295[/C][C]0.8981[/C][C]0.186771[/C][/ROW]
[ROW][C]11[/C][C]0.084694[/C][C]0.5929[/C][C]0.278002[/C][/ROW]
[ROW][C]12[/C][C]0.049646[/C][C]0.3475[/C][C]0.364845[/C][/ROW]
[ROW][C]13[/C][C]0.044116[/C][C]0.3088[/C][C]0.379386[/C][/ROW]
[ROW][C]14[/C][C]0.042715[/C][C]0.299[/C][C]0.3831[/C][/ROW]
[ROW][C]15[/C][C]0.039836[/C][C]0.2789[/C][C]0.390766[/C][/ROW]
[ROW][C]16[/C][C]0.037745[/C][C]0.2642[/C][C]0.39636[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6933&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6933&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	0
1	0.893258	6.2528	0
2	0.787973	5.5158	1e-06
3	0.700877	4.9061	5e-06
4	0.589777	4.1284	7.1e-05
5	0.474083	3.3186	0.000856
6	0.404414	2.8309	0.003357
7	0.334026	2.3382	0.011752
8	0.245693	1.7198	0.045886
9	0.18569	1.2998	0.099871
10	0.128295	0.8981	0.186771
11	0.084694	0.5929	0.278002
12	0.049646	0.3475	0.364845
13	0.044116	0.3088	0.379386
14	0.042715	0.299	0.3831
15	0.039836	0.2789	0.390766
16	0.037745	0.2642	0.39636

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.893258	6.2528	0
1	-0.049175	-0.3442	0.633926
2	0.031387	0.2197	0.413505
3	-0.170136	-1.1909	0.880294
4	-0.086198	-0.6034	0.725481
5	0.13846	0.9692	0.168598
6	-0.048582	-0.3401	0.632373
7	-0.113386	-0.7937	0.784401
8	0.035153	0.2461	0.403327
9	-0.064028	-0.4482	0.672007
10	0.087877	0.6151	0.270654
11	-0.025253	-0.1768	0.569791
12	0.08619	0.6033	0.274536
13	0.019225	0.1346	0.44675
14	-0.024296	-0.1701	0.567173
15	-0.018831	-0.1318	0.552167
16	0.079967	0.5598	0.289093

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.893258 & 6.2528 & 0 \tabularnewline
1 & -0.049175 & -0.3442 & 0.633926 \tabularnewline
2 & 0.031387 & 0.2197 & 0.413505 \tabularnewline
3 & -0.170136 & -1.1909 & 0.880294 \tabularnewline
4 & -0.086198 & -0.6034 & 0.725481 \tabularnewline
5 & 0.13846 & 0.9692 & 0.168598 \tabularnewline
6 & -0.048582 & -0.3401 & 0.632373 \tabularnewline
7 & -0.113386 & -0.7937 & 0.784401 \tabularnewline
8 & 0.035153 & 0.2461 & 0.403327 \tabularnewline
9 & -0.064028 & -0.4482 & 0.672007 \tabularnewline
10 & 0.087877 & 0.6151 & 0.270654 \tabularnewline
11 & -0.025253 & -0.1768 & 0.569791 \tabularnewline
12 & 0.08619 & 0.6033 & 0.274536 \tabularnewline
13 & 0.019225 & 0.1346 & 0.44675 \tabularnewline
14 & -0.024296 & -0.1701 & 0.567173 \tabularnewline
15 & -0.018831 & -0.1318 & 0.552167 \tabularnewline
16 & 0.079967 & 0.5598 & 0.289093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6933&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]0.893258[/C][C]6.2528[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.049175[/C][C]-0.3442[/C][C]0.633926[/C][/ROW]
[ROW][C]2[/C][C]0.031387[/C][C]0.2197[/C][C]0.413505[/C][/ROW]
[ROW][C]3[/C][C]-0.170136[/C][C]-1.1909[/C][C]0.880294[/C][/ROW]
[ROW][C]4[/C][C]-0.086198[/C][C]-0.6034[/C][C]0.725481[/C][/ROW]
[ROW][C]5[/C][C]0.13846[/C][C]0.9692[/C][C]0.168598[/C][/ROW]
[ROW][C]6[/C][C]-0.048582[/C][C]-0.3401[/C][C]0.632373[/C][/ROW]
[ROW][C]7[/C][C]-0.113386[/C][C]-0.7937[/C][C]0.784401[/C][/ROW]
[ROW][C]8[/C][C]0.035153[/C][C]0.2461[/C][C]0.403327[/C][/ROW]
[ROW][C]9[/C][C]-0.064028[/C][C]-0.4482[/C][C]0.672007[/C][/ROW]
[ROW][C]10[/C][C]0.087877[/C][C]0.6151[/C][C]0.270654[/C][/ROW]
[ROW][C]11[/C][C]-0.025253[/C][C]-0.1768[/C][C]0.569791[/C][/ROW]
[ROW][C]12[/C][C]0.08619[/C][C]0.6033[/C][C]0.274536[/C][/ROW]
[ROW][C]13[/C][C]0.019225[/C][C]0.1346[/C][C]0.44675[/C][/ROW]
[ROW][C]14[/C][C]-0.024296[/C][C]-0.1701[/C][C]0.567173[/C][/ROW]
[ROW][C]15[/C][C]-0.018831[/C][C]-0.1318[/C][C]0.552167[/C][/ROW]
[ROW][C]16[/C][C]0.079967[/C][C]0.5598[/C][C]0.289093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6933&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6933&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	0.893258	6.2528	0
1	-0.049175	-0.3442	0.633926
2	0.031387	0.2197	0.413505
3	-0.170136	-1.1909	0.880294
4	-0.086198	-0.6034	0.725481
5	0.13846	0.9692	0.168598
6	-0.048582	-0.3401	0.632373
7	-0.113386	-0.7937	0.784401
8	0.035153	0.2461	0.403327
9	-0.064028	-0.4482	0.672007
10	0.087877	0.6151	0.270654
11	-0.025253	-0.1768	0.569791
12	0.08619	0.6033	0.274536
13	0.019225	0.1346	0.44675
14	-0.024296	-0.1701	0.567173
15	-0.018831	-0.1318	0.552167
16	0.079967	0.5598	0.289093

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code