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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 26 Nov 2007 16:29:57 -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/2007/Nov/27/t11961192239iezbqwz7yuu0uw.htm/, Retrieved Sun, 05 May 2024 09:51:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6742, Retrieved Sun, 05 May 2024 09:51:29 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

205

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

-       [(Partial) Autocorrelation Function] [Inducing Stationa...] [2007-11-26 23:29:57] [640491d00f3c9cca22cbf779aa38ac16] [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=6742&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=6742&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6742&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	8.9443	0
1	0.94054	8.4124	0
2	0.896701	8.0203	0
3	0.854548	7.6433	0
4	0.804248	7.1934	0
5	0.759897	6.7967	0
6	0.719574	6.4361	0
7	0.68729	6.1473	0
8	0.634394	5.6742	0
9	0.58059	5.193	1e-06
10	0.530705	4.7468	4e-06
11	0.479764	4.2911	2.5e-05
12	0.43977	3.9334	8.9e-05
13	0.400572	3.5828	0.000291
14	0.359234	3.2131	0.000947
15	0.330852	2.9592	0.002028
16	0.294469	2.6338	0.005066
17	0.252523	2.2586	0.013314
18	0.22383	2.002	0.024337

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.9443 & 0 \tabularnewline
1 & 0.94054 & 8.4124 & 0 \tabularnewline
2 & 0.896701 & 8.0203 & 0 \tabularnewline
3 & 0.854548 & 7.6433 & 0 \tabularnewline
4 & 0.804248 & 7.1934 & 0 \tabularnewline
5 & 0.759897 & 6.7967 & 0 \tabularnewline
6 & 0.719574 & 6.4361 & 0 \tabularnewline
7 & 0.68729 & 6.1473 & 0 \tabularnewline
8 & 0.634394 & 5.6742 & 0 \tabularnewline
9 & 0.58059 & 5.193 & 1e-06 \tabularnewline
10 & 0.530705 & 4.7468 & 4e-06 \tabularnewline
11 & 0.479764 & 4.2911 & 2.5e-05 \tabularnewline
12 & 0.43977 & 3.9334 & 8.9e-05 \tabularnewline
13 & 0.400572 & 3.5828 & 0.000291 \tabularnewline
14 & 0.359234 & 3.2131 & 0.000947 \tabularnewline
15 & 0.330852 & 2.9592 & 0.002028 \tabularnewline
16 & 0.294469 & 2.6338 & 0.005066 \tabularnewline
17 & 0.252523 & 2.2586 & 0.013314 \tabularnewline
18 & 0.22383 & 2.002 & 0.024337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6742&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]8.9443[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.94054[/C][C]8.4124[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.896701[/C][C]8.0203[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.854548[/C][C]7.6433[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.804248[/C][C]7.1934[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.759897[/C][C]6.7967[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.719574[/C][C]6.4361[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.68729[/C][C]6.1473[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.634394[/C][C]5.6742[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.58059[/C][C]5.193[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.530705[/C][C]4.7468[/C][C]4e-06[/C][/ROW]
[ROW][C]11[/C][C]0.479764[/C][C]4.2911[/C][C]2.5e-05[/C][/ROW]
[ROW][C]12[/C][C]0.43977[/C][C]3.9334[/C][C]8.9e-05[/C][/ROW]
[ROW][C]13[/C][C]0.400572[/C][C]3.5828[/C][C]0.000291[/C][/ROW]
[ROW][C]14[/C][C]0.359234[/C][C]3.2131[/C][C]0.000947[/C][/ROW]
[ROW][C]15[/C][C]0.330852[/C][C]2.9592[/C][C]0.002028[/C][/ROW]
[ROW][C]16[/C][C]0.294469[/C][C]2.6338[/C][C]0.005066[/C][/ROW]
[ROW][C]17[/C][C]0.252523[/C][C]2.2586[/C][C]0.013314[/C][/ROW]
[ROW][C]18[/C][C]0.22383[/C][C]2.002[/C][C]0.024337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6742&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6742&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	8.9443	0
1	0.94054	8.4124	0
2	0.896701	8.0203	0
3	0.854548	7.6433	0
4	0.804248	7.1934	0
5	0.759897	6.7967	0
6	0.719574	6.4361	0
7	0.68729	6.1473	0
8	0.634394	5.6742	0
9	0.58059	5.193	1e-06
10	0.530705	4.7468	4e-06
11	0.479764	4.2911	2.5e-05
12	0.43977	3.9334	8.9e-05
13	0.400572	3.5828	0.000291
14	0.359234	3.2131	0.000947
15	0.330852	2.9592	0.002028
16	0.294469	2.6338	0.005066
17	0.252523	2.2586	0.013314
18	0.22383	2.002	0.024337

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.94054	8.4124	0
1	0.104733	0.9368	0.175851
2	0.008672	0.0776	0.469186
3	-0.088142	-0.7884	0.783594
4	0.007551	0.0675	0.473162
5	0.018635	0.1667	0.434024
6	0.063351	0.5666	0.286275
7	-0.186742	-1.6703	0.950613
8	-0.086156	-0.7706	0.778395
9	-0.017527	-0.1568	0.562089
10	-0.002563	-0.0229	0.509115
11	0.063617	0.569	0.285473
12	-0.014616	-0.1307	0.551843
13	-0.071404	-0.6387	0.737566
14	0.097187	0.8693	0.193652
15	-0.042143	-0.3769	0.64639
16	-0.083106	-0.7433	0.770267
17	0.064063	0.573	0.284127
18	0.006558	0.0587	0.476685

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.94054 & 8.4124 & 0 \tabularnewline
1 & 0.104733 & 0.9368 & 0.175851 \tabularnewline
2 & 0.008672 & 0.0776 & 0.469186 \tabularnewline
3 & -0.088142 & -0.7884 & 0.783594 \tabularnewline
4 & 0.007551 & 0.0675 & 0.473162 \tabularnewline
5 & 0.018635 & 0.1667 & 0.434024 \tabularnewline
6 & 0.063351 & 0.5666 & 0.286275 \tabularnewline
7 & -0.186742 & -1.6703 & 0.950613 \tabularnewline
8 & -0.086156 & -0.7706 & 0.778395 \tabularnewline
9 & -0.017527 & -0.1568 & 0.562089 \tabularnewline
10 & -0.002563 & -0.0229 & 0.509115 \tabularnewline
11 & 0.063617 & 0.569 & 0.285473 \tabularnewline
12 & -0.014616 & -0.1307 & 0.551843 \tabularnewline
13 & -0.071404 & -0.6387 & 0.737566 \tabularnewline
14 & 0.097187 & 0.8693 & 0.193652 \tabularnewline
15 & -0.042143 & -0.3769 & 0.64639 \tabularnewline
16 & -0.083106 & -0.7433 & 0.770267 \tabularnewline
17 & 0.064063 & 0.573 & 0.284127 \tabularnewline
18 & 0.006558 & 0.0587 & 0.476685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6742&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]0.94054[/C][C]8.4124[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.104733[/C][C]0.9368[/C][C]0.175851[/C][/ROW]
[ROW][C]2[/C][C]0.008672[/C][C]0.0776[/C][C]0.469186[/C][/ROW]
[ROW][C]3[/C][C]-0.088142[/C][C]-0.7884[/C][C]0.783594[/C][/ROW]
[ROW][C]4[/C][C]0.007551[/C][C]0.0675[/C][C]0.473162[/C][/ROW]
[ROW][C]5[/C][C]0.018635[/C][C]0.1667[/C][C]0.434024[/C][/ROW]
[ROW][C]6[/C][C]0.063351[/C][C]0.5666[/C][C]0.286275[/C][/ROW]
[ROW][C]7[/C][C]-0.186742[/C][C]-1.6703[/C][C]0.950613[/C][/ROW]
[ROW][C]8[/C][C]-0.086156[/C][C]-0.7706[/C][C]0.778395[/C][/ROW]
[ROW][C]9[/C][C]-0.017527[/C][C]-0.1568[/C][C]0.562089[/C][/ROW]
[ROW][C]10[/C][C]-0.002563[/C][C]-0.0229[/C][C]0.509115[/C][/ROW]
[ROW][C]11[/C][C]0.063617[/C][C]0.569[/C][C]0.285473[/C][/ROW]
[ROW][C]12[/C][C]-0.014616[/C][C]-0.1307[/C][C]0.551843[/C][/ROW]
[ROW][C]13[/C][C]-0.071404[/C][C]-0.6387[/C][C]0.737566[/C][/ROW]
[ROW][C]14[/C][C]0.097187[/C][C]0.8693[/C][C]0.193652[/C][/ROW]
[ROW][C]15[/C][C]-0.042143[/C][C]-0.3769[/C][C]0.64639[/C][/ROW]
[ROW][C]16[/C][C]-0.083106[/C][C]-0.7433[/C][C]0.770267[/C][/ROW]
[ROW][C]17[/C][C]0.064063[/C][C]0.573[/C][C]0.284127[/C][/ROW]
[ROW][C]18[/C][C]0.006558[/C][C]0.0587[/C][C]0.476685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6742&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6742&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	0.94054	8.4124	0
1	0.104733	0.9368	0.175851
2	0.008672	0.0776	0.469186
3	-0.088142	-0.7884	0.783594
4	0.007551	0.0675	0.473162
5	0.018635	0.1667	0.434024
6	0.063351	0.5666	0.286275
7	-0.186742	-1.6703	0.950613
8	-0.086156	-0.7706	0.778395
9	-0.017527	-0.1568	0.562089
10	-0.002563	-0.0229	0.509115
11	0.063617	0.569	0.285473
12	-0.014616	-0.1307	0.551843
13	-0.071404	-0.6387	0.737566
14	0.097187	0.8693	0.193652
15	-0.042143	-0.3769	0.64639
16	-0.083106	-0.7433	0.770267
17	0.064063	0.573	0.284127
18	0.006558	0.0587	0.476685

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 2.0 ; 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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