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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 18 Dec 2010 13:06:04 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/18/t129267747677tct09sg3kbnte.htm/, Retrieved Tue, 30 Apr 2024 07:40:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111938, Retrieved Tue, 30 Apr 2024 07:40:03 +0000

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Estimated Impact

159

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

-     [Spectral Analysis] [Spectraalanalyse ...] [2008-12-11 17:29:14] [12d343c4448a5f9e527bb31caeac580b]
- RMPD  [(Partial) Autocorrelation Function] [Paper PACF d=2] [2009-12-27 10:30:59] [83058a88a37d754675a5cd22dab372fc]
-   PD      [(Partial) Autocorrelation Function] [paper lambda 2] [2010-12-18 13:06:04] [912a7c71b856221ca57f8714938acfc7] [Current]

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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=111938&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=111938&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111938&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	-0.199449	-1.7502	0.042037
2	-0.587922	-5.159	1e-06
3	0.049536	0.4347	0.332506
4	0.543317	4.7676	4e-06
5	0.021616	0.1897	0.42503
6	-0.573055	-5.0285	2e-06
7	0.014845	0.1303	0.448349
8	0.54224	4.7581	4e-06
9	-0.067839	-0.5953	0.2767
10	-0.441185	-3.8714	0.000113
11	0.028867	0.2533	0.400354
12	0.43741	3.8383	0.000126
13	-0.079844	-0.7006	0.242823
14	-0.357269	-3.135	0.001216
15	0.012611	0.1107	0.456088
16	0.420198	3.6872	0.00021
17	-0.094308	-0.8275	0.205241
18	-0.338602	-2.9712	0.001978

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.199449 & -1.7502 & 0.042037 \tabularnewline
2 & -0.587922 & -5.159 & 1e-06 \tabularnewline
3 & 0.049536 & 0.4347 & 0.332506 \tabularnewline
4 & 0.543317 & 4.7676 & 4e-06 \tabularnewline
5 & 0.021616 & 0.1897 & 0.42503 \tabularnewline
6 & -0.573055 & -5.0285 & 2e-06 \tabularnewline
7 & 0.014845 & 0.1303 & 0.448349 \tabularnewline
8 & 0.54224 & 4.7581 & 4e-06 \tabularnewline
9 & -0.067839 & -0.5953 & 0.2767 \tabularnewline
10 & -0.441185 & -3.8714 & 0.000113 \tabularnewline
11 & 0.028867 & 0.2533 & 0.400354 \tabularnewline
12 & 0.43741 & 3.8383 & 0.000126 \tabularnewline
13 & -0.079844 & -0.7006 & 0.242823 \tabularnewline
14 & -0.357269 & -3.135 & 0.001216 \tabularnewline
15 & 0.012611 & 0.1107 & 0.456088 \tabularnewline
16 & 0.420198 & 3.6872 & 0.00021 \tabularnewline
17 & -0.094308 & -0.8275 & 0.205241 \tabularnewline
18 & -0.338602 & -2.9712 & 0.001978 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111938&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]-0.199449[/C][C]-1.7502[/C][C]0.042037[/C][/ROW]
[ROW][C]2[/C][C]-0.587922[/C][C]-5.159[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.049536[/C][C]0.4347[/C][C]0.332506[/C][/ROW]
[ROW][C]4[/C][C]0.543317[/C][C]4.7676[/C][C]4e-06[/C][/ROW]
[ROW][C]5[/C][C]0.021616[/C][C]0.1897[/C][C]0.42503[/C][/ROW]
[ROW][C]6[/C][C]-0.573055[/C][C]-5.0285[/C][C]2e-06[/C][/ROW]
[ROW][C]7[/C][C]0.014845[/C][C]0.1303[/C][C]0.448349[/C][/ROW]
[ROW][C]8[/C][C]0.54224[/C][C]4.7581[/C][C]4e-06[/C][/ROW]
[ROW][C]9[/C][C]-0.067839[/C][C]-0.5953[/C][C]0.2767[/C][/ROW]
[ROW][C]10[/C][C]-0.441185[/C][C]-3.8714[/C][C]0.000113[/C][/ROW]
[ROW][C]11[/C][C]0.028867[/C][C]0.2533[/C][C]0.400354[/C][/ROW]
[ROW][C]12[/C][C]0.43741[/C][C]3.8383[/C][C]0.000126[/C][/ROW]
[ROW][C]13[/C][C]-0.079844[/C][C]-0.7006[/C][C]0.242823[/C][/ROW]
[ROW][C]14[/C][C]-0.357269[/C][C]-3.135[/C][C]0.001216[/C][/ROW]
[ROW][C]15[/C][C]0.012611[/C][C]0.1107[/C][C]0.456088[/C][/ROW]
[ROW][C]16[/C][C]0.420198[/C][C]3.6872[/C][C]0.00021[/C][/ROW]
[ROW][C]17[/C][C]-0.094308[/C][C]-0.8275[/C][C]0.205241[/C][/ROW]
[ROW][C]18[/C][C]-0.338602[/C][C]-2.9712[/C][C]0.001978[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111938&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111938&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	-0.199449	-1.7502	0.042037
2	-0.587922	-5.159	1e-06
3	0.049536	0.4347	0.332506
4	0.543317	4.7676	4e-06
5	0.021616	0.1897	0.42503
6	-0.573055	-5.0285	2e-06
7	0.014845	0.1303	0.448349
8	0.54224	4.7581	4e-06
9	-0.067839	-0.5953	0.2767
10	-0.441185	-3.8714	0.000113
11	0.028867	0.2533	0.400354
12	0.43741	3.8383	0.000126
13	-0.079844	-0.7006	0.242823
14	-0.357269	-3.135	0.001216
15	0.012611	0.1107	0.456088
16	0.420198	3.6872	0.00021
17	-0.094308	-0.8275	0.205241
18	-0.338602	-2.9712	0.001978

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.199449	-1.7502	0.042037
2	-0.653706	-5.7362	0
3	-0.499665	-4.3845	1.8e-05
4	-0.012221	-0.1072	0.45744
5	0.295065	2.5892	0.005749
6	-0.027641	-0.2426	0.404499
7	-0.126147	-1.1069	0.135885
8	0.057509	0.5046	0.307626
9	-0.023577	-0.2069	0.418323
10	-0.00021	-0.0018	0.499267
11	0.00852	0.0748	0.4703
12	0.062423	0.5478	0.29272
13	-0.082338	-0.7225	0.236083
14	0.001978	0.0174	0.493099
15	-0.116067	-1.0185	0.155819
16	0.08605	0.7551	0.22625
17	0.010106	0.0887	0.464784
18	0.038948	0.3418	0.366729

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.199449 & -1.7502 & 0.042037 \tabularnewline
2 & -0.653706 & -5.7362 & 0 \tabularnewline
3 & -0.499665 & -4.3845 & 1.8e-05 \tabularnewline
4 & -0.012221 & -0.1072 & 0.45744 \tabularnewline
5 & 0.295065 & 2.5892 & 0.005749 \tabularnewline
6 & -0.027641 & -0.2426 & 0.404499 \tabularnewline
7 & -0.126147 & -1.1069 & 0.135885 \tabularnewline
8 & 0.057509 & 0.5046 & 0.307626 \tabularnewline
9 & -0.023577 & -0.2069 & 0.418323 \tabularnewline
10 & -0.00021 & -0.0018 & 0.499267 \tabularnewline
11 & 0.00852 & 0.0748 & 0.4703 \tabularnewline
12 & 0.062423 & 0.5478 & 0.29272 \tabularnewline
13 & -0.082338 & -0.7225 & 0.236083 \tabularnewline
14 & 0.001978 & 0.0174 & 0.493099 \tabularnewline
15 & -0.116067 & -1.0185 & 0.155819 \tabularnewline
16 & 0.08605 & 0.7551 & 0.22625 \tabularnewline
17 & 0.010106 & 0.0887 & 0.464784 \tabularnewline
18 & 0.038948 & 0.3418 & 0.366729 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111938&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]-0.199449[/C][C]-1.7502[/C][C]0.042037[/C][/ROW]
[ROW][C]2[/C][C]-0.653706[/C][C]-5.7362[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.499665[/C][C]-4.3845[/C][C]1.8e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.012221[/C][C]-0.1072[/C][C]0.45744[/C][/ROW]
[ROW][C]5[/C][C]0.295065[/C][C]2.5892[/C][C]0.005749[/C][/ROW]
[ROW][C]6[/C][C]-0.027641[/C][C]-0.2426[/C][C]0.404499[/C][/ROW]
[ROW][C]7[/C][C]-0.126147[/C][C]-1.1069[/C][C]0.135885[/C][/ROW]
[ROW][C]8[/C][C]0.057509[/C][C]0.5046[/C][C]0.307626[/C][/ROW]
[ROW][C]9[/C][C]-0.023577[/C][C]-0.2069[/C][C]0.418323[/C][/ROW]
[ROW][C]10[/C][C]-0.00021[/C][C]-0.0018[/C][C]0.499267[/C][/ROW]
[ROW][C]11[/C][C]0.00852[/C][C]0.0748[/C][C]0.4703[/C][/ROW]
[ROW][C]12[/C][C]0.062423[/C][C]0.5478[/C][C]0.29272[/C][/ROW]
[ROW][C]13[/C][C]-0.082338[/C][C]-0.7225[/C][C]0.236083[/C][/ROW]
[ROW][C]14[/C][C]0.001978[/C][C]0.0174[/C][C]0.493099[/C][/ROW]
[ROW][C]15[/C][C]-0.116067[/C][C]-1.0185[/C][C]0.155819[/C][/ROW]
[ROW][C]16[/C][C]0.08605[/C][C]0.7551[/C][C]0.22625[/C][/ROW]
[ROW][C]17[/C][C]0.010106[/C][C]0.0887[/C][C]0.464784[/C][/ROW]
[ROW][C]18[/C][C]0.038948[/C][C]0.3418[/C][C]0.366729[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111938&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111938&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	-0.199449	-1.7502	0.042037
2	-0.653706	-5.7362	0
3	-0.499665	-4.3845	1.8e-05
4	-0.012221	-0.1072	0.45744
5	0.295065	2.5892	0.005749
6	-0.027641	-0.2426	0.404499
7	-0.126147	-1.1069	0.135885
8	0.057509	0.5046	0.307626
9	-0.023577	-0.2069	0.418323
10	-0.00021	-0.0018	0.499267
11	0.00852	0.0748	0.4703
12	0.062423	0.5478	0.29272
13	-0.082338	-0.7225	0.236083
14	0.001978	0.0174	0.493099
15	-0.116067	-1.0185	0.155819
16	0.08605	0.7551	0.22625
17	0.010106	0.0887	0.464784
18	0.038948	0.3418	0.366729

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -1.0 ; par3 = 2 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.98 ;

Parameters (R input):

par1 = Default ; par2 = -1.0 ; par3 = 2 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.98 ; par8 = ;

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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