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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 21 Dec 2008 12:08:42 -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/21/t1229886548re6xm3xi6emi6b9.htm/, Retrieved Fri, 17 May 2024 03:04:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35766, Retrieved Fri, 17 May 2024 03:04:10 +0000

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User-defined keywords

Estimated Impact

141

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

F       [(Partial) Autocorrelation Function] [] [2008-12-21 19:08:42] [d41d8cd98f00b204e9800998ecf8427e] [Current]

Feedback Forum

2009-01-08 13:05:10 [Aurélie Van Impe] [reply] 
Dat klopt inderdaad maar je legt niet uit hoe je dat kan zien. Je gaat er vanuit dat de lezer weet naar waar hij moet kijken. Je had nog kunnen zeggen dat de streepjes nu zo goed als allemaal binnen het betrouwbaarheidsinterval liggen. En dat het wel degelijk over een trend op lange termijn gaat.

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Dataseries X:

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1.8
1.7
1.4
1.2
1
1.7
2.4
2
2.1
2
1.8
2.7
2.3
1.9
2
2.3
2.8
2.4
2.3
2.7
2.7
2.9
3
2.2
2.3
2.8
2.8
2.8
2.2
2.6
2.8
2.5
2.4
2.3
1.9
1.7
2
2.1
1.7
1.8
1.8
1.8
1.3
1.3
1.3
1.2
1.4
2.2
2.9
3.1
3.5
3.6
4.4
4.1
5.1
5.8
5.9
5.4
5.5
4.8
3.2

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35766&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35766&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35766&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.130126	1.008	0.158762
2	-0.067332	-0.5216	0.301952
3	0.101419	0.7856	0.2176
4	0.018788	0.1455	0.442389
5	-0.004698	-0.0364	0.485545
6	-0.067293	-0.5212	0.302057
7	-0.031609	-0.2448	0.403708
8	-0.075481	-0.5847	0.280481
9	-0.124905	-0.9675	0.168587
10	0.007635	0.0591	0.476517
11	0.077625	0.6013	0.274958
12	-0.358929	-2.7803	0.003623
13	-0.223224	-1.7291	0.044468
14	0.016607	0.1286	0.449038
15	0.061759	0.4784	0.317058
16	-0.025244	-0.1955	0.422817
17	-0.129037	-0.9995	0.160779

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.130126 & 1.008 & 0.158762 \tabularnewline
2 & -0.067332 & -0.5216 & 0.301952 \tabularnewline
3 & 0.101419 & 0.7856 & 0.2176 \tabularnewline
4 & 0.018788 & 0.1455 & 0.442389 \tabularnewline
5 & -0.004698 & -0.0364 & 0.485545 \tabularnewline
6 & -0.067293 & -0.5212 & 0.302057 \tabularnewline
7 & -0.031609 & -0.2448 & 0.403708 \tabularnewline
8 & -0.075481 & -0.5847 & 0.280481 \tabularnewline
9 & -0.124905 & -0.9675 & 0.168587 \tabularnewline
10 & 0.007635 & 0.0591 & 0.476517 \tabularnewline
11 & 0.077625 & 0.6013 & 0.274958 \tabularnewline
12 & -0.358929 & -2.7803 & 0.003623 \tabularnewline
13 & -0.223224 & -1.7291 & 0.044468 \tabularnewline
14 & 0.016607 & 0.1286 & 0.449038 \tabularnewline
15 & 0.061759 & 0.4784 & 0.317058 \tabularnewline
16 & -0.025244 & -0.1955 & 0.422817 \tabularnewline
17 & -0.129037 & -0.9995 & 0.160779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35766&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]0.130126[/C][C]1.008[/C][C]0.158762[/C][/ROW]
[ROW][C]2[/C][C]-0.067332[/C][C]-0.5216[/C][C]0.301952[/C][/ROW]
[ROW][C]3[/C][C]0.101419[/C][C]0.7856[/C][C]0.2176[/C][/ROW]
[ROW][C]4[/C][C]0.018788[/C][C]0.1455[/C][C]0.442389[/C][/ROW]
[ROW][C]5[/C][C]-0.004698[/C][C]-0.0364[/C][C]0.485545[/C][/ROW]
[ROW][C]6[/C][C]-0.067293[/C][C]-0.5212[/C][C]0.302057[/C][/ROW]
[ROW][C]7[/C][C]-0.031609[/C][C]-0.2448[/C][C]0.403708[/C][/ROW]
[ROW][C]8[/C][C]-0.075481[/C][C]-0.5847[/C][C]0.280481[/C][/ROW]
[ROW][C]9[/C][C]-0.124905[/C][C]-0.9675[/C][C]0.168587[/C][/ROW]
[ROW][C]10[/C][C]0.007635[/C][C]0.0591[/C][C]0.476517[/C][/ROW]
[ROW][C]11[/C][C]0.077625[/C][C]0.6013[/C][C]0.274958[/C][/ROW]
[ROW][C]12[/C][C]-0.358929[/C][C]-2.7803[/C][C]0.003623[/C][/ROW]
[ROW][C]13[/C][C]-0.223224[/C][C]-1.7291[/C][C]0.044468[/C][/ROW]
[ROW][C]14[/C][C]0.016607[/C][C]0.1286[/C][C]0.449038[/C][/ROW]
[ROW][C]15[/C][C]0.061759[/C][C]0.4784[/C][C]0.317058[/C][/ROW]
[ROW][C]16[/C][C]-0.025244[/C][C]-0.1955[/C][C]0.422817[/C][/ROW]
[ROW][C]17[/C][C]-0.129037[/C][C]-0.9995[/C][C]0.160779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35766&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35766&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	0.130126	1.008	0.158762
2	-0.067332	-0.5216	0.301952
3	0.101419	0.7856	0.2176
4	0.018788	0.1455	0.442389
5	-0.004698	-0.0364	0.485545
6	-0.067293	-0.5212	0.302057
7	-0.031609	-0.2448	0.403708
8	-0.075481	-0.5847	0.280481
9	-0.124905	-0.9675	0.168587
10	0.007635	0.0591	0.476517
11	0.077625	0.6013	0.274958
12	-0.358929	-2.7803	0.003623
13	-0.223224	-1.7291	0.044468
14	0.016607	0.1286	0.449038
15	0.061759	0.4784	0.317058
16	-0.025244	-0.1955	0.422817
17	-0.129037	-0.9995	0.160779

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.130126	1.008	0.158762
2	-0.085716	-0.664	0.254632
3	0.125108	0.9691	0.168198
4	-0.020685	-0.1602	0.436622
5	0.015025	0.1164	0.453867
6	-0.084607	-0.6554	0.257369
7	-0.008499	-0.0658	0.473865
8	-0.088071	-0.6822	0.24887
9	-0.091963	-0.7123	0.239507
10	0.030551	0.2366	0.406868
11	0.075168	0.5823	0.28129
12	-0.38259	-2.9635	0.002178
13	-0.12512	-0.9692	0.168174
14	-0.029621	-0.2294	0.409652
15	0.11739	0.9093	0.183416
16	-0.04457	-0.3452	0.365562
17	-0.142768	-1.1059	0.136598

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.130126 & 1.008 & 0.158762 \tabularnewline
2 & -0.085716 & -0.664 & 0.254632 \tabularnewline
3 & 0.125108 & 0.9691 & 0.168198 \tabularnewline
4 & -0.020685 & -0.1602 & 0.436622 \tabularnewline
5 & 0.015025 & 0.1164 & 0.453867 \tabularnewline
6 & -0.084607 & -0.6554 & 0.257369 \tabularnewline
7 & -0.008499 & -0.0658 & 0.473865 \tabularnewline
8 & -0.088071 & -0.6822 & 0.24887 \tabularnewline
9 & -0.091963 & -0.7123 & 0.239507 \tabularnewline
10 & 0.030551 & 0.2366 & 0.406868 \tabularnewline
11 & 0.075168 & 0.5823 & 0.28129 \tabularnewline
12 & -0.38259 & -2.9635 & 0.002178 \tabularnewline
13 & -0.12512 & -0.9692 & 0.168174 \tabularnewline
14 & -0.029621 & -0.2294 & 0.409652 \tabularnewline
15 & 0.11739 & 0.9093 & 0.183416 \tabularnewline
16 & -0.04457 & -0.3452 & 0.365562 \tabularnewline
17 & -0.142768 & -1.1059 & 0.136598 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35766&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]0.130126[/C][C]1.008[/C][C]0.158762[/C][/ROW]
[ROW][C]2[/C][C]-0.085716[/C][C]-0.664[/C][C]0.254632[/C][/ROW]
[ROW][C]3[/C][C]0.125108[/C][C]0.9691[/C][C]0.168198[/C][/ROW]
[ROW][C]4[/C][C]-0.020685[/C][C]-0.1602[/C][C]0.436622[/C][/ROW]
[ROW][C]5[/C][C]0.015025[/C][C]0.1164[/C][C]0.453867[/C][/ROW]
[ROW][C]6[/C][C]-0.084607[/C][C]-0.6554[/C][C]0.257369[/C][/ROW]
[ROW][C]7[/C][C]-0.008499[/C][C]-0.0658[/C][C]0.473865[/C][/ROW]
[ROW][C]8[/C][C]-0.088071[/C][C]-0.6822[/C][C]0.24887[/C][/ROW]
[ROW][C]9[/C][C]-0.091963[/C][C]-0.7123[/C][C]0.239507[/C][/ROW]
[ROW][C]10[/C][C]0.030551[/C][C]0.2366[/C][C]0.406868[/C][/ROW]
[ROW][C]11[/C][C]0.075168[/C][C]0.5823[/C][C]0.28129[/C][/ROW]
[ROW][C]12[/C][C]-0.38259[/C][C]-2.9635[/C][C]0.002178[/C][/ROW]
[ROW][C]13[/C][C]-0.12512[/C][C]-0.9692[/C][C]0.168174[/C][/ROW]
[ROW][C]14[/C][C]-0.029621[/C][C]-0.2294[/C][C]0.409652[/C][/ROW]
[ROW][C]15[/C][C]0.11739[/C][C]0.9093[/C][C]0.183416[/C][/ROW]
[ROW][C]16[/C][C]-0.04457[/C][C]-0.3452[/C][C]0.365562[/C][/ROW]
[ROW][C]17[/C][C]-0.142768[/C][C]-1.1059[/C][C]0.136598[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35766&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35766&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	0.130126	1.008	0.158762
2	-0.085716	-0.664	0.254632
3	0.125108	0.9691	0.168198
4	-0.020685	-0.1602	0.436622
5	0.015025	0.1164	0.453867
6	-0.084607	-0.6554	0.257369
7	-0.008499	-0.0658	0.473865
8	-0.088071	-0.6822	0.24887
9	-0.091963	-0.7123	0.239507
10	0.030551	0.2366	0.406868
11	0.075168	0.5823	0.28129
12	-0.38259	-2.9635	0.002178
13	-0.12512	-0.9692	0.168174
14	-0.029621	-0.2294	0.409652
15	0.11739	0.9093	0.183416
16	-0.04457	-0.3452	0.365562
17	-0.142768	-1.1059	0.136598

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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