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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 06:39:21 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/27/t12593292050i1agoe3jblq28x.htm/, Retrieved Mon, 29 Apr 2024 20:41:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60749, Retrieved Mon, 29 Apr 2024 20:41:30 +0000

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No (this computation is public)

User-defined keywords

shwws8

Estimated Impact

145

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [] [2009-11-20 13:47:03] [5482608004c1d7bbf873930172393a2d]
- RMPD        [(Partial) Autocorrelation Function] [] [2009-11-27 13:39:21] [efdfe680cd785c4af09f858b30f777ec] [Current]
-   P           [(Partial) Autocorrelation Function] [workshop 8] [2009-11-28 12:43:04] [eaf42bcf5162b5692bb3c7f9d4636222] 

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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	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=60749&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=60749&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60749&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	0.131606	1.0109	0.158099
2	-0.145613	-1.1185	0.133948
3	-0.023035	-0.1769	0.430082
4	-0.117769	-0.9046	0.184677
5	0.0375	0.288	0.387163
6	0.437356	3.3594	0.000687
7	0.067918	0.5217	0.30192
8	-0.259815	-1.9957	0.025296
9	-0.099824	-0.7668	0.223141
10	-0.307159	-2.3593	0.010818
11	0.139164	1.0689	0.144726
12	0.469752	3.6082	0.000318
13	0.012471	0.0958	0.462005
14	-0.25858	-1.9862	0.025832
15	-0.004127	-0.0317	0.487408
16	-0.188971	-1.4515	0.075967
17	0.05392	0.4142	0.340126

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.131606 & 1.0109 & 0.158099 \tabularnewline
2 & -0.145613 & -1.1185 & 0.133948 \tabularnewline
3 & -0.023035 & -0.1769 & 0.430082 \tabularnewline
4 & -0.117769 & -0.9046 & 0.184677 \tabularnewline
5 & 0.0375 & 0.288 & 0.387163 \tabularnewline
6 & 0.437356 & 3.3594 & 0.000687 \tabularnewline
7 & 0.067918 & 0.5217 & 0.30192 \tabularnewline
8 & -0.259815 & -1.9957 & 0.025296 \tabularnewline
9 & -0.099824 & -0.7668 & 0.223141 \tabularnewline
10 & -0.307159 & -2.3593 & 0.010818 \tabularnewline
11 & 0.139164 & 1.0689 & 0.144726 \tabularnewline
12 & 0.469752 & 3.6082 & 0.000318 \tabularnewline
13 & 0.012471 & 0.0958 & 0.462005 \tabularnewline
14 & -0.25858 & -1.9862 & 0.025832 \tabularnewline
15 & -0.004127 & -0.0317 & 0.487408 \tabularnewline
16 & -0.188971 & -1.4515 & 0.075967 \tabularnewline
17 & 0.05392 & 0.4142 & 0.340126 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60749&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]0.131606[/C][C]1.0109[/C][C]0.158099[/C][/ROW]
[ROW][C]2[/C][C]-0.145613[/C][C]-1.1185[/C][C]0.133948[/C][/ROW]
[ROW][C]3[/C][C]-0.023035[/C][C]-0.1769[/C][C]0.430082[/C][/ROW]
[ROW][C]4[/C][C]-0.117769[/C][C]-0.9046[/C][C]0.184677[/C][/ROW]
[ROW][C]5[/C][C]0.0375[/C][C]0.288[/C][C]0.387163[/C][/ROW]
[ROW][C]6[/C][C]0.437356[/C][C]3.3594[/C][C]0.000687[/C][/ROW]
[ROW][C]7[/C][C]0.067918[/C][C]0.5217[/C][C]0.30192[/C][/ROW]
[ROW][C]8[/C][C]-0.259815[/C][C]-1.9957[/C][C]0.025296[/C][/ROW]
[ROW][C]9[/C][C]-0.099824[/C][C]-0.7668[/C][C]0.223141[/C][/ROW]
[ROW][C]10[/C][C]-0.307159[/C][C]-2.3593[/C][C]0.010818[/C][/ROW]
[ROW][C]11[/C][C]0.139164[/C][C]1.0689[/C][C]0.144726[/C][/ROW]
[ROW][C]12[/C][C]0.469752[/C][C]3.6082[/C][C]0.000318[/C][/ROW]
[ROW][C]13[/C][C]0.012471[/C][C]0.0958[/C][C]0.462005[/C][/ROW]
[ROW][C]14[/C][C]-0.25858[/C][C]-1.9862[/C][C]0.025832[/C][/ROW]
[ROW][C]15[/C][C]-0.004127[/C][C]-0.0317[/C][C]0.487408[/C][/ROW]
[ROW][C]16[/C][C]-0.188971[/C][C]-1.4515[/C][C]0.075967[/C][/ROW]
[ROW][C]17[/C][C]0.05392[/C][C]0.4142[/C][C]0.340126[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60749&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60749&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	0.131606	1.0109	0.158099
2	-0.145613	-1.1185	0.133948
3	-0.023035	-0.1769	0.430082
4	-0.117769	-0.9046	0.184677
5	0.0375	0.288	0.387163
6	0.437356	3.3594	0.000687
7	0.067918	0.5217	0.30192
8	-0.259815	-1.9957	0.025296
9	-0.099824	-0.7668	0.223141
10	-0.307159	-2.3593	0.010818
11	0.139164	1.0689	0.144726
12	0.469752	3.6082	0.000318
13	0.012471	0.0958	0.462005
14	-0.25858	-1.9862	0.025832
15	-0.004127	-0.0317	0.487408
16	-0.188971	-1.4515	0.075967
17	0.05392	0.4142	0.340126

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.131606	1.0109	0.158099
2	-0.165805	-1.2736	0.103904
3	0.022107	0.1698	0.432871
4	-0.148344	-1.1394	0.12956
5	0.083545	0.6417	0.261769
6	0.403621	3.1003	0.001481
7	-0.047102	-0.3618	0.359398
8	-0.203034	-1.5595	0.062109
9	-0.046218	-0.355	0.361924
10	-0.331553	-2.5467	0.006752
11	0.296179	2.275	0.013278
12	0.262822	2.0188	0.024032
13	-0.103755	-0.797	0.214337
14	-0.116366	-0.8938	0.187524
15	0.091748	0.7047	0.241875
16	-0.063423	-0.4872	0.313974
17	0.029127	0.2237	0.411871

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.131606 & 1.0109 & 0.158099 \tabularnewline
2 & -0.165805 & -1.2736 & 0.103904 \tabularnewline
3 & 0.022107 & 0.1698 & 0.432871 \tabularnewline
4 & -0.148344 & -1.1394 & 0.12956 \tabularnewline
5 & 0.083545 & 0.6417 & 0.261769 \tabularnewline
6 & 0.403621 & 3.1003 & 0.001481 \tabularnewline
7 & -0.047102 & -0.3618 & 0.359398 \tabularnewline
8 & -0.203034 & -1.5595 & 0.062109 \tabularnewline
9 & -0.046218 & -0.355 & 0.361924 \tabularnewline
10 & -0.331553 & -2.5467 & 0.006752 \tabularnewline
11 & 0.296179 & 2.275 & 0.013278 \tabularnewline
12 & 0.262822 & 2.0188 & 0.024032 \tabularnewline
13 & -0.103755 & -0.797 & 0.214337 \tabularnewline
14 & -0.116366 & -0.8938 & 0.187524 \tabularnewline
15 & 0.091748 & 0.7047 & 0.241875 \tabularnewline
16 & -0.063423 & -0.4872 & 0.313974 \tabularnewline
17 & 0.029127 & 0.2237 & 0.411871 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60749&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]0.131606[/C][C]1.0109[/C][C]0.158099[/C][/ROW]
[ROW][C]2[/C][C]-0.165805[/C][C]-1.2736[/C][C]0.103904[/C][/ROW]
[ROW][C]3[/C][C]0.022107[/C][C]0.1698[/C][C]0.432871[/C][/ROW]
[ROW][C]4[/C][C]-0.148344[/C][C]-1.1394[/C][C]0.12956[/C][/ROW]
[ROW][C]5[/C][C]0.083545[/C][C]0.6417[/C][C]0.261769[/C][/ROW]
[ROW][C]6[/C][C]0.403621[/C][C]3.1003[/C][C]0.001481[/C][/ROW]
[ROW][C]7[/C][C]-0.047102[/C][C]-0.3618[/C][C]0.359398[/C][/ROW]
[ROW][C]8[/C][C]-0.203034[/C][C]-1.5595[/C][C]0.062109[/C][/ROW]
[ROW][C]9[/C][C]-0.046218[/C][C]-0.355[/C][C]0.361924[/C][/ROW]
[ROW][C]10[/C][C]-0.331553[/C][C]-2.5467[/C][C]0.006752[/C][/ROW]
[ROW][C]11[/C][C]0.296179[/C][C]2.275[/C][C]0.013278[/C][/ROW]
[ROW][C]12[/C][C]0.262822[/C][C]2.0188[/C][C]0.024032[/C][/ROW]
[ROW][C]13[/C][C]-0.103755[/C][C]-0.797[/C][C]0.214337[/C][/ROW]
[ROW][C]14[/C][C]-0.116366[/C][C]-0.8938[/C][C]0.187524[/C][/ROW]
[ROW][C]15[/C][C]0.091748[/C][C]0.7047[/C][C]0.241875[/C][/ROW]
[ROW][C]16[/C][C]-0.063423[/C][C]-0.4872[/C][C]0.313974[/C][/ROW]
[ROW][C]17[/C][C]0.029127[/C][C]0.2237[/C][C]0.411871[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60749&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60749&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	0.131606	1.0109	0.158099
2	-0.165805	-1.2736	0.103904
3	0.022107	0.1698	0.432871
4	-0.148344	-1.1394	0.12956
5	0.083545	0.6417	0.261769
6	0.403621	3.1003	0.001481
7	-0.047102	-0.3618	0.359398
8	-0.203034	-1.5595	0.062109
9	-0.046218	-0.355	0.361924
10	-0.331553	-2.5467	0.006752
11	0.296179	2.275	0.013278
12	0.262822	2.0188	0.024032
13	-0.103755	-0.797	0.214337
14	-0.116366	-0.8938	0.187524
15	0.091748	0.7047	0.241875
16	-0.063423	-0.4872	0.313974
17	0.029127	0.2237	0.411871

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code