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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Nov 2007 06:26:46 -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/22/t11957375246niiiqd8hullk4h.htm/, Retrieved Thu, 02 May 2024 19:36:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5983, Retrieved Thu, 02 May 2024 19:36:43 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

W10Q2G7

Estimated Impact

173

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2007-11-22 13:26:46] [65108f21b143a71c6470aac06bd65b08] [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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5983&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5983&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5983&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.4853	0
1	-0.102261	-0.8677	0.805784
2	-0.091381	-0.7754	0.779676
3	-0.060962	-0.5173	0.696728
4	-0.077001	-0.6534	0.742203
5	-0.020646	-0.1752	0.569287
6	-0.050697	-0.4302	0.665824
7	0.124894	1.0598	0.146398
8	-0.177453	-1.5057	0.931746
9	0.139043	1.1798	0.120978
10	-0.043133	-0.366	0.642279
11	-0.050961	-0.4324	0.666635
12	-0.097633	-0.8284	0.794922
13	-0.157612	-1.3374	0.907347
14	0.04344	0.3686	0.356754
15	-0.01482	-0.1258	0.54986
16	0.241852	2.0522	0.021894
17	-0.10112	-0.858	0.80314

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & -0.102261 & -0.8677 & 0.805784 \tabularnewline
2 & -0.091381 & -0.7754 & 0.779676 \tabularnewline
3 & -0.060962 & -0.5173 & 0.696728 \tabularnewline
4 & -0.077001 & -0.6534 & 0.742203 \tabularnewline
5 & -0.020646 & -0.1752 & 0.569287 \tabularnewline
6 & -0.050697 & -0.4302 & 0.665824 \tabularnewline
7 & 0.124894 & 1.0598 & 0.146398 \tabularnewline
8 & -0.177453 & -1.5057 & 0.931746 \tabularnewline
9 & 0.139043 & 1.1798 & 0.120978 \tabularnewline
10 & -0.043133 & -0.366 & 0.642279 \tabularnewline
11 & -0.050961 & -0.4324 & 0.666635 \tabularnewline
12 & -0.097633 & -0.8284 & 0.794922 \tabularnewline
13 & -0.157612 & -1.3374 & 0.907347 \tabularnewline
14 & 0.04344 & 0.3686 & 0.356754 \tabularnewline
15 & -0.01482 & -0.1258 & 0.54986 \tabularnewline
16 & 0.241852 & 2.0522 & 0.021894 \tabularnewline
17 & -0.10112 & -0.858 & 0.80314 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5983&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]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.102261[/C][C]-0.8677[/C][C]0.805784[/C][/ROW]
[ROW][C]2[/C][C]-0.091381[/C][C]-0.7754[/C][C]0.779676[/C][/ROW]
[ROW][C]3[/C][C]-0.060962[/C][C]-0.5173[/C][C]0.696728[/C][/ROW]
[ROW][C]4[/C][C]-0.077001[/C][C]-0.6534[/C][C]0.742203[/C][/ROW]
[ROW][C]5[/C][C]-0.020646[/C][C]-0.1752[/C][C]0.569287[/C][/ROW]
[ROW][C]6[/C][C]-0.050697[/C][C]-0.4302[/C][C]0.665824[/C][/ROW]
[ROW][C]7[/C][C]0.124894[/C][C]1.0598[/C][C]0.146398[/C][/ROW]
[ROW][C]8[/C][C]-0.177453[/C][C]-1.5057[/C][C]0.931746[/C][/ROW]
[ROW][C]9[/C][C]0.139043[/C][C]1.1798[/C][C]0.120978[/C][/ROW]
[ROW][C]10[/C][C]-0.043133[/C][C]-0.366[/C][C]0.642279[/C][/ROW]
[ROW][C]11[/C][C]-0.050961[/C][C]-0.4324[/C][C]0.666635[/C][/ROW]
[ROW][C]12[/C][C]-0.097633[/C][C]-0.8284[/C][C]0.794922[/C][/ROW]
[ROW][C]13[/C][C]-0.157612[/C][C]-1.3374[/C][C]0.907347[/C][/ROW]
[ROW][C]14[/C][C]0.04344[/C][C]0.3686[/C][C]0.356754[/C][/ROW]
[ROW][C]15[/C][C]-0.01482[/C][C]-0.1258[/C][C]0.54986[/C][/ROW]
[ROW][C]16[/C][C]0.241852[/C][C]2.0522[/C][C]0.021894[/C][/ROW]
[ROW][C]17[/C][C]-0.10112[/C][C]-0.858[/C][C]0.80314[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5983&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5983&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	8.4853	0
1	-0.102261	-0.8677	0.805784
2	-0.091381	-0.7754	0.779676
3	-0.060962	-0.5173	0.696728
4	-0.077001	-0.6534	0.742203
5	-0.020646	-0.1752	0.569287
6	-0.050697	-0.4302	0.665824
7	0.124894	1.0598	0.146398
8	-0.177453	-1.5057	0.931746
9	0.139043	1.1798	0.120978
10	-0.043133	-0.366	0.642279
11	-0.050961	-0.4324	0.666635
12	-0.097633	-0.8284	0.794922
13	-0.157612	-1.3374	0.907347
14	0.04344	0.3686	0.356754
15	-0.01482	-0.1258	0.54986
16	0.241852	2.0522	0.021894
17	-0.10112	-0.858	0.80314

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.102261	-0.8677	0.805784
1	-0.102914	-0.8733	0.807287
2	-0.083542	-0.7089	0.759655
3	-0.106158	-0.9008	0.814645
4	-0.060251	-0.5112	0.69463
5	-0.090258	-0.7659	0.77687
6	0.086886	0.7373	0.231681
7	-0.191383	-1.6239	0.94562
8	0.111969	0.9501	0.172623
9	-0.066439	-0.5637	0.712662
10	-0.045408	-0.3853	0.649424
11	-0.148938	-1.2638	0.894807
12	-0.20195	-1.7136	0.954548
13	-0.090459	-0.7676	0.777374
14	-0.071975	-0.6107	0.728349
15	0.120431	1.0219	0.155127
16	-0.09194	-0.7801	0.781065
17	-0.170313	-1.4452	0.923624

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.102261 & -0.8677 & 0.805784 \tabularnewline
1 & -0.102914 & -0.8733 & 0.807287 \tabularnewline
2 & -0.083542 & -0.7089 & 0.759655 \tabularnewline
3 & -0.106158 & -0.9008 & 0.814645 \tabularnewline
4 & -0.060251 & -0.5112 & 0.69463 \tabularnewline
5 & -0.090258 & -0.7659 & 0.77687 \tabularnewline
6 & 0.086886 & 0.7373 & 0.231681 \tabularnewline
7 & -0.191383 & -1.6239 & 0.94562 \tabularnewline
8 & 0.111969 & 0.9501 & 0.172623 \tabularnewline
9 & -0.066439 & -0.5637 & 0.712662 \tabularnewline
10 & -0.045408 & -0.3853 & 0.649424 \tabularnewline
11 & -0.148938 & -1.2638 & 0.894807 \tabularnewline
12 & -0.20195 & -1.7136 & 0.954548 \tabularnewline
13 & -0.090459 & -0.7676 & 0.777374 \tabularnewline
14 & -0.071975 & -0.6107 & 0.728349 \tabularnewline
15 & 0.120431 & 1.0219 & 0.155127 \tabularnewline
16 & -0.09194 & -0.7801 & 0.781065 \tabularnewline
17 & -0.170313 & -1.4452 & 0.923624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5983&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]-0.102261[/C][C]-0.8677[/C][C]0.805784[/C][/ROW]
[ROW][C]1[/C][C]-0.102914[/C][C]-0.8733[/C][C]0.807287[/C][/ROW]
[ROW][C]2[/C][C]-0.083542[/C][C]-0.7089[/C][C]0.759655[/C][/ROW]
[ROW][C]3[/C][C]-0.106158[/C][C]-0.9008[/C][C]0.814645[/C][/ROW]
[ROW][C]4[/C][C]-0.060251[/C][C]-0.5112[/C][C]0.69463[/C][/ROW]
[ROW][C]5[/C][C]-0.090258[/C][C]-0.7659[/C][C]0.77687[/C][/ROW]
[ROW][C]6[/C][C]0.086886[/C][C]0.7373[/C][C]0.231681[/C][/ROW]
[ROW][C]7[/C][C]-0.191383[/C][C]-1.6239[/C][C]0.94562[/C][/ROW]
[ROW][C]8[/C][C]0.111969[/C][C]0.9501[/C][C]0.172623[/C][/ROW]
[ROW][C]9[/C][C]-0.066439[/C][C]-0.5637[/C][C]0.712662[/C][/ROW]
[ROW][C]10[/C][C]-0.045408[/C][C]-0.3853[/C][C]0.649424[/C][/ROW]
[ROW][C]11[/C][C]-0.148938[/C][C]-1.2638[/C][C]0.894807[/C][/ROW]
[ROW][C]12[/C][C]-0.20195[/C][C]-1.7136[/C][C]0.954548[/C][/ROW]
[ROW][C]13[/C][C]-0.090459[/C][C]-0.7676[/C][C]0.777374[/C][/ROW]
[ROW][C]14[/C][C]-0.071975[/C][C]-0.6107[/C][C]0.728349[/C][/ROW]
[ROW][C]15[/C][C]0.120431[/C][C]1.0219[/C][C]0.155127[/C][/ROW]
[ROW][C]16[/C][C]-0.09194[/C][C]-0.7801[/C][C]0.781065[/C][/ROW]
[ROW][C]17[/C][C]-0.170313[/C][C]-1.4452[/C][C]0.923624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5983&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5983&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	-0.102261	-0.8677	0.805784
1	-0.102914	-0.8733	0.807287
2	-0.083542	-0.7089	0.759655
3	-0.106158	-0.9008	0.814645
4	-0.060251	-0.5112	0.69463
5	-0.090258	-0.7659	0.77687
6	0.086886	0.7373	0.231681
7	-0.191383	-1.6239	0.94562
8	0.111969	0.9501	0.172623
9	-0.066439	-0.5637	0.712662
10	-0.045408	-0.3853	0.649424
11	-0.148938	-1.2638	0.894807
12	-0.20195	-1.7136	0.954548
13	-0.090459	-0.7676	0.777374
14	-0.071975	-0.6107	0.728349
15	0.120431	1.0219	0.155127
16	-0.09194	-0.7801	0.781065
17	-0.170313	-1.4452	0.923624

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 ;

Parameters (R input):

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