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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 26 Nov 2007 13:31:54 -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/2007/Nov/26/t1196108526x9z4ub16zrroppg.htm/, Retrieved Thu, 02 May 2024 15:51:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6686, Retrieved Thu, 02 May 2024 15:51:46 +0000

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Estimated Impact

166

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-       [(Partial) Autocorrelation Function] [] [2007-11-26 20:31:54] [a5d60d21ad00400c5f1209c78aa5829c] [Current]

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Summary of compuational 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 compuational 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=6686&T=0

[TABLE]
[ROW][C]Summary of compuational 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=6686&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6686&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 compuational 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
0	1	9.6437	0
1	0.929101	8.9599	0
2	0.868171	8.3723	0
3	0.804134	7.7548	0
4	0.734799	7.0861	0
5	0.679231	6.5503	0
6	0.638285	6.1554	0
7	0.59518	5.7397	0
8	0.551988	5.3232	0
9	0.520312	5.0177	1e-06
10	0.493552	4.7596	4e-06
11	0.466605	4.4998	1e-05
12	0.449213	4.3321	1.9e-05
13	0.439439	4.2378	2.7e-05
14	0.422441	4.0739	4.9e-05
15	0.388413	3.7457	0.000156
16	0.362639	3.4972	0.000361
17	0.329865	3.1811	0.000997
18	0.300395	2.8969	0.002349

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.6437 & 0 \tabularnewline
1 & 0.929101 & 8.9599 & 0 \tabularnewline
2 & 0.868171 & 8.3723 & 0 \tabularnewline
3 & 0.804134 & 7.7548 & 0 \tabularnewline
4 & 0.734799 & 7.0861 & 0 \tabularnewline
5 & 0.679231 & 6.5503 & 0 \tabularnewline
6 & 0.638285 & 6.1554 & 0 \tabularnewline
7 & 0.59518 & 5.7397 & 0 \tabularnewline
8 & 0.551988 & 5.3232 & 0 \tabularnewline
9 & 0.520312 & 5.0177 & 1e-06 \tabularnewline
10 & 0.493552 & 4.7596 & 4e-06 \tabularnewline
11 & 0.466605 & 4.4998 & 1e-05 \tabularnewline
12 & 0.449213 & 4.3321 & 1.9e-05 \tabularnewline
13 & 0.439439 & 4.2378 & 2.7e-05 \tabularnewline
14 & 0.422441 & 4.0739 & 4.9e-05 \tabularnewline
15 & 0.388413 & 3.7457 & 0.000156 \tabularnewline
16 & 0.362639 & 3.4972 & 0.000361 \tabularnewline
17 & 0.329865 & 3.1811 & 0.000997 \tabularnewline
18 & 0.300395 & 2.8969 & 0.002349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6686&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]0[/C][C]1[/C][C]9.6437[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.929101[/C][C]8.9599[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.868171[/C][C]8.3723[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.804134[/C][C]7.7548[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.734799[/C][C]7.0861[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.679231[/C][C]6.5503[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.638285[/C][C]6.1554[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.59518[/C][C]5.7397[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.551988[/C][C]5.3232[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.520312[/C][C]5.0177[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.493552[/C][C]4.7596[/C][C]4e-06[/C][/ROW]
[ROW][C]11[/C][C]0.466605[/C][C]4.4998[/C][C]1e-05[/C][/ROW]
[ROW][C]12[/C][C]0.449213[/C][C]4.3321[/C][C]1.9e-05[/C][/ROW]
[ROW][C]13[/C][C]0.439439[/C][C]4.2378[/C][C]2.7e-05[/C][/ROW]
[ROW][C]14[/C][C]0.422441[/C][C]4.0739[/C][C]4.9e-05[/C][/ROW]
[ROW][C]15[/C][C]0.388413[/C][C]3.7457[/C][C]0.000156[/C][/ROW]
[ROW][C]16[/C][C]0.362639[/C][C]3.4972[/C][C]0.000361[/C][/ROW]
[ROW][C]17[/C][C]0.329865[/C][C]3.1811[/C][C]0.000997[/C][/ROW]
[ROW][C]18[/C][C]0.300395[/C][C]2.8969[/C][C]0.002349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6686&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6686&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
0	1	9.6437	0
1	0.929101	8.9599	0
2	0.868171	8.3723	0
3	0.804134	7.7548	0
4	0.734799	7.0861	0
5	0.679231	6.5503	0
6	0.638285	6.1554	0
7	0.59518	5.7397	0
8	0.551988	5.3232	0
9	0.520312	5.0177	1e-06
10	0.493552	4.7596	4e-06
11	0.466605	4.4998	1e-05
12	0.449213	4.3321	1.9e-05
13	0.439439	4.2378	2.7e-05
14	0.422441	4.0739	4.9e-05
15	0.388413	3.7457	0.000156
16	0.362639	3.4972	0.000361
17	0.329865	3.1811	0.000997
18	0.300395	2.8969	0.002349

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.929101	8.9599	0
1	0.036137	0.3485	0.36413
2	-0.050597	-0.4879	0.686629
3	-0.077036	-0.7429	0.770295
4	0.056599	0.5458	0.293247
5	0.089327	0.8614	0.195607
6	-0.029983	-0.2891	0.613444
7	-0.043946	-0.4238	0.663656
8	0.056823	0.548	0.292508
9	0.048547	0.4682	0.320378
10	-0.009309	-0.0898	0.535669
11	0.037021	0.357	0.360943
12	0.061572	0.5938	0.27705
13	-0.031775	-0.3064	0.620018
14	-0.148555	-1.4326	0.92234
15	0.030068	0.29	0.386245
16	-0.016385	-0.158	0.562605
17	0.015447	0.149	0.440954
18	-0.032988	-0.3181	0.624449

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.929101 & 8.9599 & 0 \tabularnewline
1 & 0.036137 & 0.3485 & 0.36413 \tabularnewline
2 & -0.050597 & -0.4879 & 0.686629 \tabularnewline
3 & -0.077036 & -0.7429 & 0.770295 \tabularnewline
4 & 0.056599 & 0.5458 & 0.293247 \tabularnewline
5 & 0.089327 & 0.8614 & 0.195607 \tabularnewline
6 & -0.029983 & -0.2891 & 0.613444 \tabularnewline
7 & -0.043946 & -0.4238 & 0.663656 \tabularnewline
8 & 0.056823 & 0.548 & 0.292508 \tabularnewline
9 & 0.048547 & 0.4682 & 0.320378 \tabularnewline
10 & -0.009309 & -0.0898 & 0.535669 \tabularnewline
11 & 0.037021 & 0.357 & 0.360943 \tabularnewline
12 & 0.061572 & 0.5938 & 0.27705 \tabularnewline
13 & -0.031775 & -0.3064 & 0.620018 \tabularnewline
14 & -0.148555 & -1.4326 & 0.92234 \tabularnewline
15 & 0.030068 & 0.29 & 0.386245 \tabularnewline
16 & -0.016385 & -0.158 & 0.562605 \tabularnewline
17 & 0.015447 & 0.149 & 0.440954 \tabularnewline
18 & -0.032988 & -0.3181 & 0.624449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6686&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]0[/C][C]0.929101[/C][C]8.9599[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.036137[/C][C]0.3485[/C][C]0.36413[/C][/ROW]
[ROW][C]2[/C][C]-0.050597[/C][C]-0.4879[/C][C]0.686629[/C][/ROW]
[ROW][C]3[/C][C]-0.077036[/C][C]-0.7429[/C][C]0.770295[/C][/ROW]
[ROW][C]4[/C][C]0.056599[/C][C]0.5458[/C][C]0.293247[/C][/ROW]
[ROW][C]5[/C][C]0.089327[/C][C]0.8614[/C][C]0.195607[/C][/ROW]
[ROW][C]6[/C][C]-0.029983[/C][C]-0.2891[/C][C]0.613444[/C][/ROW]
[ROW][C]7[/C][C]-0.043946[/C][C]-0.4238[/C][C]0.663656[/C][/ROW]
[ROW][C]8[/C][C]0.056823[/C][C]0.548[/C][C]0.292508[/C][/ROW]
[ROW][C]9[/C][C]0.048547[/C][C]0.4682[/C][C]0.320378[/C][/ROW]
[ROW][C]10[/C][C]-0.009309[/C][C]-0.0898[/C][C]0.535669[/C][/ROW]
[ROW][C]11[/C][C]0.037021[/C][C]0.357[/C][C]0.360943[/C][/ROW]
[ROW][C]12[/C][C]0.061572[/C][C]0.5938[/C][C]0.27705[/C][/ROW]
[ROW][C]13[/C][C]-0.031775[/C][C]-0.3064[/C][C]0.620018[/C][/ROW]
[ROW][C]14[/C][C]-0.148555[/C][C]-1.4326[/C][C]0.92234[/C][/ROW]
[ROW][C]15[/C][C]0.030068[/C][C]0.29[/C][C]0.386245[/C][/ROW]
[ROW][C]16[/C][C]-0.016385[/C][C]-0.158[/C][C]0.562605[/C][/ROW]
[ROW][C]17[/C][C]0.015447[/C][C]0.149[/C][C]0.440954[/C][/ROW]
[ROW][C]18[/C][C]-0.032988[/C][C]-0.3181[/C][C]0.624449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6686&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6686&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
0	0.929101	8.9599	0
1	0.036137	0.3485	0.36413
2	-0.050597	-0.4879	0.686629
3	-0.077036	-0.7429	0.770295
4	0.056599	0.5458	0.293247
5	0.089327	0.8614	0.195607
6	-0.029983	-0.2891	0.613444
7	-0.043946	-0.4238	0.663656
8	0.056823	0.548	0.292508
9	0.048547	0.4682	0.320378
10	-0.009309	-0.0898	0.535669
11	0.037021	0.357	0.360943
12	0.061572	0.5938	0.27705
13	-0.031775	-0.3064	0.620018
14	-0.148555	-1.4326	0.92234
15	0.030068	0.29	0.386245
16	-0.016385	-0.158	0.562605
17	0.015447	0.149	0.440954
18	-0.032988	-0.3181	0.624449

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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