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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

Wed, 08 Dec 2010 16:30:25 +0000

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/2010/Dec/08/t1291825717kuxurpauv8kmt0q.htm/, Retrieved Fri, 03 May 2024 04:13:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106990, Retrieved Fri, 03 May 2024 04:13:07 +0000

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Original text written by user:

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No (this computation is public)

User-defined keywords

Estimated Impact

186

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

F       [(Partial) Autocorrelation Function] [WS9] [2010-12-08 16:30:25] [4c92126b39409bf78ea2674c8170c829] [Current]
-   P     [(Partial) Autocorrelation Function] [ws 10 verbetering] [2010-12-14 08:26:44] [05ab9592748364013445d860bb938e43] 
-    D    [(Partial) Autocorrelation Function] [Workshop 6 (1)] [2010-12-16 15:58:47] [34b8ec63a78ce61b49b6bd4fc5a61e1c] 
-   P       [(Partial) Autocorrelation Function] [workshop 6 (2)] [2010-12-16 16:26:48] [34b8ec63a78ce61b49b6bd4fc5a61e1c] 
- R  D    [(Partial) Autocorrelation Function] [] [2011-12-06 13:43:04] [74be16979710d4c4e7c6647856088456] 
-    D      [(Partial) Autocorrelation Function] [] [2011-12-06 14:36:38] [74be16979710d4c4e7c6647856088456] 

Feedback Forum

2010-12-10 10:25:39 [48eb36e2c01435ad7e4ea7854a9d98fe] [reply] 
De student heeft hier wel gebruik gemaakt van de correcte softwaremodule, maar het aantal 'lags' werd te laag ingesteld. Het is beter dit in de software aan te passen naar bijvoorbeeld 48. Op die manier is een eventuele seizoenaliteit ook beter te detecteren. 
 
Aangezien ik zelf met dezelfde gegevens werk dan deze student (maar niet samen) beschik ik hierbij over een voorbeeld met 48 lags: http://www.freestatistics.org/blog/index.php?v=date/2010/Dec/08/t1291830387e2h3ysryba7mzua.htm/ 
 
Wanneer we deze autocorrelatiefunctie bekijken, zien we veel duidelijker een langetermijntrend. De seizoenaliteit blijft wel twijfelachtig, hoewel er een duidelijke - negatieve - uitschieter te zien is bij 'lag' 12.

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	27 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 & 27 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106990&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]27 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=106990&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106990&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	27 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.530773	3.9363	0.000117
2	0.361681	2.6823	0.004818
3	0.492013	3.6489	0.000293
4	0.428335	3.1766	0.001222
5	0.293715	2.1782	0.016846
6	0.253013	1.8764	0.032955
7	0.093812	0.6957	0.244765
8	0.13625	1.0105	0.158351
9	-0.028809	-0.2137	0.415804
10	-0.242793	-1.8006	0.038625
11	-0.12828	-0.9514	0.172794
12	0.062062	0.4603	0.32357
13	-0.212876	-1.5787	0.060067
14	-0.344768	-2.5569	0.006676
15	-0.260041	-1.9285	0.029479
16	-0.2122	-1.5737	0.060644
17	-0.232678	-1.7256	0.045018

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.530773 & 3.9363 & 0.000117 \tabularnewline
2 & 0.361681 & 2.6823 & 0.004818 \tabularnewline
3 & 0.492013 & 3.6489 & 0.000293 \tabularnewline
4 & 0.428335 & 3.1766 & 0.001222 \tabularnewline
5 & 0.293715 & 2.1782 & 0.016846 \tabularnewline
6 & 0.253013 & 1.8764 & 0.032955 \tabularnewline
7 & 0.093812 & 0.6957 & 0.244765 \tabularnewline
8 & 0.13625 & 1.0105 & 0.158351 \tabularnewline
9 & -0.028809 & -0.2137 & 0.415804 \tabularnewline
10 & -0.242793 & -1.8006 & 0.038625 \tabularnewline
11 & -0.12828 & -0.9514 & 0.172794 \tabularnewline
12 & 0.062062 & 0.4603 & 0.32357 \tabularnewline
13 & -0.212876 & -1.5787 & 0.060067 \tabularnewline
14 & -0.344768 & -2.5569 & 0.006676 \tabularnewline
15 & -0.260041 & -1.9285 & 0.029479 \tabularnewline
16 & -0.2122 & -1.5737 & 0.060644 \tabularnewline
17 & -0.232678 & -1.7256 & 0.045018 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106990&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]0.530773[/C][C]3.9363[/C][C]0.000117[/C][/ROW]
[ROW][C]2[/C][C]0.361681[/C][C]2.6823[/C][C]0.004818[/C][/ROW]
[ROW][C]3[/C][C]0.492013[/C][C]3.6489[/C][C]0.000293[/C][/ROW]
[ROW][C]4[/C][C]0.428335[/C][C]3.1766[/C][C]0.001222[/C][/ROW]
[ROW][C]5[/C][C]0.293715[/C][C]2.1782[/C][C]0.016846[/C][/ROW]
[ROW][C]6[/C][C]0.253013[/C][C]1.8764[/C][C]0.032955[/C][/ROW]
[ROW][C]7[/C][C]0.093812[/C][C]0.6957[/C][C]0.244765[/C][/ROW]
[ROW][C]8[/C][C]0.13625[/C][C]1.0105[/C][C]0.158351[/C][/ROW]
[ROW][C]9[/C][C]-0.028809[/C][C]-0.2137[/C][C]0.415804[/C][/ROW]
[ROW][C]10[/C][C]-0.242793[/C][C]-1.8006[/C][C]0.038625[/C][/ROW]
[ROW][C]11[/C][C]-0.12828[/C][C]-0.9514[/C][C]0.172794[/C][/ROW]
[ROW][C]12[/C][C]0.062062[/C][C]0.4603[/C][C]0.32357[/C][/ROW]
[ROW][C]13[/C][C]-0.212876[/C][C]-1.5787[/C][C]0.060067[/C][/ROW]
[ROW][C]14[/C][C]-0.344768[/C][C]-2.5569[/C][C]0.006676[/C][/ROW]
[ROW][C]15[/C][C]-0.260041[/C][C]-1.9285[/C][C]0.029479[/C][/ROW]
[ROW][C]16[/C][C]-0.2122[/C][C]-1.5737[/C][C]0.060644[/C][/ROW]
[ROW][C]17[/C][C]-0.232678[/C][C]-1.7256[/C][C]0.045018[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106990&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106990&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	0.530773	3.9363	0.000117
2	0.361681	2.6823	0.004818
3	0.492013	3.6489	0.000293
4	0.428335	3.1766	0.001222
5	0.293715	2.1782	0.016846
6	0.253013	1.8764	0.032955
7	0.093812	0.6957	0.244765
8	0.13625	1.0105	0.158351
9	-0.028809	-0.2137	0.415804
10	-0.242793	-1.8006	0.038625
11	-0.12828	-0.9514	0.172794
12	0.062062	0.4603	0.32357
13	-0.212876	-1.5787	0.060067
14	-0.344768	-2.5569	0.006676
15	-0.260041	-1.9285	0.029479
16	-0.2122	-1.5737	0.060644
17	-0.232678	-1.7256	0.045018

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.530773	3.9363	0.000117
2	0.111322	0.8256	0.206303
3	0.369797	2.7425	0.004107
4	0.070316	0.5215	0.302065
5	-0.017739	-0.1316	0.447907
6	-0.047223	-0.3502	0.363757
7	-0.260674	-1.9332	0.029182
8	0.093562	0.6939	0.245341
9	-0.308448	-2.2875	0.013018
10	-0.237351	-1.7602	0.041964
11	0.079839	0.5921	0.278104
12	0.364054	2.6999	0.004599
13	-0.120541	-0.894	0.18762
14	-0.227984	-1.6908	0.04827
15	-0.12773	-0.9473	0.173822
16	-0.00073	-0.0054	0.497849
17	0.055475	0.4114	0.341185

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.530773 & 3.9363 & 0.000117 \tabularnewline
2 & 0.111322 & 0.8256 & 0.206303 \tabularnewline
3 & 0.369797 & 2.7425 & 0.004107 \tabularnewline
4 & 0.070316 & 0.5215 & 0.302065 \tabularnewline
5 & -0.017739 & -0.1316 & 0.447907 \tabularnewline
6 & -0.047223 & -0.3502 & 0.363757 \tabularnewline
7 & -0.260674 & -1.9332 & 0.029182 \tabularnewline
8 & 0.093562 & 0.6939 & 0.245341 \tabularnewline
9 & -0.308448 & -2.2875 & 0.013018 \tabularnewline
10 & -0.237351 & -1.7602 & 0.041964 \tabularnewline
11 & 0.079839 & 0.5921 & 0.278104 \tabularnewline
12 & 0.364054 & 2.6999 & 0.004599 \tabularnewline
13 & -0.120541 & -0.894 & 0.18762 \tabularnewline
14 & -0.227984 & -1.6908 & 0.04827 \tabularnewline
15 & -0.12773 & -0.9473 & 0.173822 \tabularnewline
16 & -0.00073 & -0.0054 & 0.497849 \tabularnewline
17 & 0.055475 & 0.4114 & 0.341185 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106990&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]0.530773[/C][C]3.9363[/C][C]0.000117[/C][/ROW]
[ROW][C]2[/C][C]0.111322[/C][C]0.8256[/C][C]0.206303[/C][/ROW]
[ROW][C]3[/C][C]0.369797[/C][C]2.7425[/C][C]0.004107[/C][/ROW]
[ROW][C]4[/C][C]0.070316[/C][C]0.5215[/C][C]0.302065[/C][/ROW]
[ROW][C]5[/C][C]-0.017739[/C][C]-0.1316[/C][C]0.447907[/C][/ROW]
[ROW][C]6[/C][C]-0.047223[/C][C]-0.3502[/C][C]0.363757[/C][/ROW]
[ROW][C]7[/C][C]-0.260674[/C][C]-1.9332[/C][C]0.029182[/C][/ROW]
[ROW][C]8[/C][C]0.093562[/C][C]0.6939[/C][C]0.245341[/C][/ROW]
[ROW][C]9[/C][C]-0.308448[/C][C]-2.2875[/C][C]0.013018[/C][/ROW]
[ROW][C]10[/C][C]-0.237351[/C][C]-1.7602[/C][C]0.041964[/C][/ROW]
[ROW][C]11[/C][C]0.079839[/C][C]0.5921[/C][C]0.278104[/C][/ROW]
[ROW][C]12[/C][C]0.364054[/C][C]2.6999[/C][C]0.004599[/C][/ROW]
[ROW][C]13[/C][C]-0.120541[/C][C]-0.894[/C][C]0.18762[/C][/ROW]
[ROW][C]14[/C][C]-0.227984[/C][C]-1.6908[/C][C]0.04827[/C][/ROW]
[ROW][C]15[/C][C]-0.12773[/C][C]-0.9473[/C][C]0.173822[/C][/ROW]
[ROW][C]16[/C][C]-0.00073[/C][C]-0.0054[/C][C]0.497849[/C][/ROW]
[ROW][C]17[/C][C]0.055475[/C][C]0.4114[/C][C]0.341185[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106990&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106990&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	0.530773	3.9363	0.000117
2	0.111322	0.8256	0.206303
3	0.369797	2.7425	0.004107
4	0.070316	0.5215	0.302065
5	-0.017739	-0.1316	0.447907
6	-0.047223	-0.3502	0.363757
7	-0.260674	-1.9332	0.029182
8	0.093562	0.6939	0.245341
9	-0.308448	-2.2875	0.013018
10	-0.237351	-1.7602	0.041964
11	0.079839	0.5921	0.278104
12	0.364054	2.6999	0.004599
13	-0.120541	-0.894	0.18762
14	-0.227984	-1.6908	0.04827
15	-0.12773	-0.9473	0.173822
16	-0.00073	-0.0054	0.497849
17	0.055475	0.4114	0.341185

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code