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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

Sat, 28 Nov 2009 11:26:28 -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/2009/Nov/28/t1259432848mfurxc5mhhz1xhr.htm/, Retrieved Fri, 03 May 2024 11:24:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61518, Retrieved Fri, 03 May 2024 11:24:31 +0000

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No (this computation is public)

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Estimated Impact

132

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

-       [(Partial) Autocorrelation Function] [Workshop 8] [2009-11-28 18:26:28] [aef022288383377281176d9807aba5bf] [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=61518&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=61518&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61518&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	0.906963	6.2836	0
2	0.795279	5.5099	1e-06
3	0.638986	4.427	2.7e-05
4	0.479131	3.3195	0.000864
5	0.312189	2.1629	0.01778
6	0.178496	1.2367	0.111115
7	0.030231	0.2094	0.417494
8	-0.095479	-0.6615	0.255728
9	-0.217713	-1.5084	0.069009
10	-0.317791	-2.2017	0.016262
11	-0.396318	-2.7458	0.004236
12	-0.438264	-3.0364	0.001931
13	-0.429282	-2.9742	0.002293
14	-0.398167	-2.7586	0.004095
15	-0.356765	-2.4717	0.008522
16	-0.31828	-2.2051	0.016135
17	-0.276012	-1.9123	0.03091

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.906963 & 6.2836 & 0 \tabularnewline
2 & 0.795279 & 5.5099 & 1e-06 \tabularnewline
3 & 0.638986 & 4.427 & 2.7e-05 \tabularnewline
4 & 0.479131 & 3.3195 & 0.000864 \tabularnewline
5 & 0.312189 & 2.1629 & 0.01778 \tabularnewline
6 & 0.178496 & 1.2367 & 0.111115 \tabularnewline
7 & 0.030231 & 0.2094 & 0.417494 \tabularnewline
8 & -0.095479 & -0.6615 & 0.255728 \tabularnewline
9 & -0.217713 & -1.5084 & 0.069009 \tabularnewline
10 & -0.317791 & -2.2017 & 0.016262 \tabularnewline
11 & -0.396318 & -2.7458 & 0.004236 \tabularnewline
12 & -0.438264 & -3.0364 & 0.001931 \tabularnewline
13 & -0.429282 & -2.9742 & 0.002293 \tabularnewline
14 & -0.398167 & -2.7586 & 0.004095 \tabularnewline
15 & -0.356765 & -2.4717 & 0.008522 \tabularnewline
16 & -0.31828 & -2.2051 & 0.016135 \tabularnewline
17 & -0.276012 & -1.9123 & 0.03091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61518&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]0.906963[/C][C]6.2836[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.795279[/C][C]5.5099[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.638986[/C][C]4.427[/C][C]2.7e-05[/C][/ROW]
[ROW][C]4[/C][C]0.479131[/C][C]3.3195[/C][C]0.000864[/C][/ROW]
[ROW][C]5[/C][C]0.312189[/C][C]2.1629[/C][C]0.01778[/C][/ROW]
[ROW][C]6[/C][C]0.178496[/C][C]1.2367[/C][C]0.111115[/C][/ROW]
[ROW][C]7[/C][C]0.030231[/C][C]0.2094[/C][C]0.417494[/C][/ROW]
[ROW][C]8[/C][C]-0.095479[/C][C]-0.6615[/C][C]0.255728[/C][/ROW]
[ROW][C]9[/C][C]-0.217713[/C][C]-1.5084[/C][C]0.069009[/C][/ROW]
[ROW][C]10[/C][C]-0.317791[/C][C]-2.2017[/C][C]0.016262[/C][/ROW]
[ROW][C]11[/C][C]-0.396318[/C][C]-2.7458[/C][C]0.004236[/C][/ROW]
[ROW][C]12[/C][C]-0.438264[/C][C]-3.0364[/C][C]0.001931[/C][/ROW]
[ROW][C]13[/C][C]-0.429282[/C][C]-2.9742[/C][C]0.002293[/C][/ROW]
[ROW][C]14[/C][C]-0.398167[/C][C]-2.7586[/C][C]0.004095[/C][/ROW]
[ROW][C]15[/C][C]-0.356765[/C][C]-2.4717[/C][C]0.008522[/C][/ROW]
[ROW][C]16[/C][C]-0.31828[/C][C]-2.2051[/C][C]0.016135[/C][/ROW]
[ROW][C]17[/C][C]-0.276012[/C][C]-1.9123[/C][C]0.03091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61518&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61518&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	0.906963	6.2836	0
2	0.795279	5.5099	1e-06
3	0.638986	4.427	2.7e-05
4	0.479131	3.3195	0.000864
5	0.312189	2.1629	0.01778
6	0.178496	1.2367	0.111115
7	0.030231	0.2094	0.417494
8	-0.095479	-0.6615	0.255728
9	-0.217713	-1.5084	0.069009
10	-0.317791	-2.2017	0.016262
11	-0.396318	-2.7458	0.004236
12	-0.438264	-3.0364	0.001931
13	-0.429282	-2.9742	0.002293
14	-0.398167	-2.7586	0.004095
15	-0.356765	-2.4717	0.008522
16	-0.31828	-2.2051	0.016135
17	-0.276012	-1.9123	0.03091

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.906963	6.2836	0
2	-0.153887	-1.0662	0.145842
3	-0.310188	-2.149	0.018351
4	-0.086485	-0.5992	0.275934
5	-0.100513	-0.6964	0.244777
6	0.084591	0.5861	0.280289
7	-0.22377	-1.5503	0.063816
8	-0.076117	-0.5274	0.300189
9	-0.095026	-0.6584	0.256727
10	-0.05614	-0.3889	0.349517
11	0.002017	0.014	0.494454
12	-0.007044	-0.0488	0.480641
13	0.185308	1.2839	0.102679
14	-0.061558	-0.4265	0.335831
15	-0.109846	-0.761	0.225178
16	-0.118656	-0.8221	0.207551
17	-0.007852	-0.0544	0.478422

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.906963 & 6.2836 & 0 \tabularnewline
2 & -0.153887 & -1.0662 & 0.145842 \tabularnewline
3 & -0.310188 & -2.149 & 0.018351 \tabularnewline
4 & -0.086485 & -0.5992 & 0.275934 \tabularnewline
5 & -0.100513 & -0.6964 & 0.244777 \tabularnewline
6 & 0.084591 & 0.5861 & 0.280289 \tabularnewline
7 & -0.22377 & -1.5503 & 0.063816 \tabularnewline
8 & -0.076117 & -0.5274 & 0.300189 \tabularnewline
9 & -0.095026 & -0.6584 & 0.256727 \tabularnewline
10 & -0.05614 & -0.3889 & 0.349517 \tabularnewline
11 & 0.002017 & 0.014 & 0.494454 \tabularnewline
12 & -0.007044 & -0.0488 & 0.480641 \tabularnewline
13 & 0.185308 & 1.2839 & 0.102679 \tabularnewline
14 & -0.061558 & -0.4265 & 0.335831 \tabularnewline
15 & -0.109846 & -0.761 & 0.225178 \tabularnewline
16 & -0.118656 & -0.8221 & 0.207551 \tabularnewline
17 & -0.007852 & -0.0544 & 0.478422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61518&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]0.906963[/C][C]6.2836[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.153887[/C][C]-1.0662[/C][C]0.145842[/C][/ROW]
[ROW][C]3[/C][C]-0.310188[/C][C]-2.149[/C][C]0.018351[/C][/ROW]
[ROW][C]4[/C][C]-0.086485[/C][C]-0.5992[/C][C]0.275934[/C][/ROW]
[ROW][C]5[/C][C]-0.100513[/C][C]-0.6964[/C][C]0.244777[/C][/ROW]
[ROW][C]6[/C][C]0.084591[/C][C]0.5861[/C][C]0.280289[/C][/ROW]
[ROW][C]7[/C][C]-0.22377[/C][C]-1.5503[/C][C]0.063816[/C][/ROW]
[ROW][C]8[/C][C]-0.076117[/C][C]-0.5274[/C][C]0.300189[/C][/ROW]
[ROW][C]9[/C][C]-0.095026[/C][C]-0.6584[/C][C]0.256727[/C][/ROW]
[ROW][C]10[/C][C]-0.05614[/C][C]-0.3889[/C][C]0.349517[/C][/ROW]
[ROW][C]11[/C][C]0.002017[/C][C]0.014[/C][C]0.494454[/C][/ROW]
[ROW][C]12[/C][C]-0.007044[/C][C]-0.0488[/C][C]0.480641[/C][/ROW]
[ROW][C]13[/C][C]0.185308[/C][C]1.2839[/C][C]0.102679[/C][/ROW]
[ROW][C]14[/C][C]-0.061558[/C][C]-0.4265[/C][C]0.335831[/C][/ROW]
[ROW][C]15[/C][C]-0.109846[/C][C]-0.761[/C][C]0.225178[/C][/ROW]
[ROW][C]16[/C][C]-0.118656[/C][C]-0.8221[/C][C]0.207551[/C][/ROW]
[ROW][C]17[/C][C]-0.007852[/C][C]-0.0544[/C][C]0.478422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61518&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61518&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	0.906963	6.2836	0
2	-0.153887	-1.0662	0.145842
3	-0.310188	-2.149	0.018351
4	-0.086485	-0.5992	0.275934
5	-0.100513	-0.6964	0.244777
6	0.084591	0.5861	0.280289
7	-0.22377	-1.5503	0.063816
8	-0.076117	-0.5274	0.300189
9	-0.095026	-0.6584	0.256727
10	-0.05614	-0.3889	0.349517
11	0.002017	0.014	0.494454
12	-0.007044	-0.0488	0.480641
13	0.185308	1.2839	0.102679
14	-0.061558	-0.4265	0.335831
15	-0.109846	-0.761	0.225178
16	-0.118656	-0.8221	0.207551
17	-0.007852	-0.0544	0.478422

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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