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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 03 Dec 2007 03:43:46 -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/Dec/03/t11966779474l1gpb2ct3p8ukr.htm/, Retrieved Sat, 04 May 2024 03:32:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2309, Retrieved Sat, 04 May 2024 03:32:14 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Q1 Estimation of ARMA processes

Estimated Impact

217

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

-       [(Partial) Autocorrelation Function] [Q1 Estimation of ...] [2007-12-03 10:43:46] [0cecb02636bfe8ebd97a7fef80b2b9e7] [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=2309&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=2309&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2309&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	6.9282	0
1	0.144005	0.9977	0.161714
2	0.05347	0.3705	0.356337
3	0.201314	1.3947	0.084757
4	0.009045	0.0627	0.475147
5	0.076541	0.5303	0.299177
6	0.144096	0.9983	0.161563
7	-0.163556	-1.1331	0.86861
8	0.005203	0.036	0.485696
9	0.185607	1.2859	0.10232
10	-0.158944	-1.1012	0.861848
11	-0.115718	-0.8017	0.786666
12	-0.178473	-1.2365	0.888855
13	-0.111832	-0.7748	0.778869
14	0.096786	0.6706	0.252859
15	-0.114129	-0.7907	0.783499
16	-0.127459	-0.8831	0.809197

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & 0.144005 & 0.9977 & 0.161714 \tabularnewline
2 & 0.05347 & 0.3705 & 0.356337 \tabularnewline
3 & 0.201314 & 1.3947 & 0.084757 \tabularnewline
4 & 0.009045 & 0.0627 & 0.475147 \tabularnewline
5 & 0.076541 & 0.5303 & 0.299177 \tabularnewline
6 & 0.144096 & 0.9983 & 0.161563 \tabularnewline
7 & -0.163556 & -1.1331 & 0.86861 \tabularnewline
8 & 0.005203 & 0.036 & 0.485696 \tabularnewline
9 & 0.185607 & 1.2859 & 0.10232 \tabularnewline
10 & -0.158944 & -1.1012 & 0.861848 \tabularnewline
11 & -0.115718 & -0.8017 & 0.786666 \tabularnewline
12 & -0.178473 & -1.2365 & 0.888855 \tabularnewline
13 & -0.111832 & -0.7748 & 0.778869 \tabularnewline
14 & 0.096786 & 0.6706 & 0.252859 \tabularnewline
15 & -0.114129 & -0.7907 & 0.783499 \tabularnewline
16 & -0.127459 & -0.8831 & 0.809197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2309&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]6.9282[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.144005[/C][C]0.9977[/C][C]0.161714[/C][/ROW]
[ROW][C]2[/C][C]0.05347[/C][C]0.3705[/C][C]0.356337[/C][/ROW]
[ROW][C]3[/C][C]0.201314[/C][C]1.3947[/C][C]0.084757[/C][/ROW]
[ROW][C]4[/C][C]0.009045[/C][C]0.0627[/C][C]0.475147[/C][/ROW]
[ROW][C]5[/C][C]0.076541[/C][C]0.5303[/C][C]0.299177[/C][/ROW]
[ROW][C]6[/C][C]0.144096[/C][C]0.9983[/C][C]0.161563[/C][/ROW]
[ROW][C]7[/C][C]-0.163556[/C][C]-1.1331[/C][C]0.86861[/C][/ROW]
[ROW][C]8[/C][C]0.005203[/C][C]0.036[/C][C]0.485696[/C][/ROW]
[ROW][C]9[/C][C]0.185607[/C][C]1.2859[/C][C]0.10232[/C][/ROW]
[ROW][C]10[/C][C]-0.158944[/C][C]-1.1012[/C][C]0.861848[/C][/ROW]
[ROW][C]11[/C][C]-0.115718[/C][C]-0.8017[/C][C]0.786666[/C][/ROW]
[ROW][C]12[/C][C]-0.178473[/C][C]-1.2365[/C][C]0.888855[/C][/ROW]
[ROW][C]13[/C][C]-0.111832[/C][C]-0.7748[/C][C]0.778869[/C][/ROW]
[ROW][C]14[/C][C]0.096786[/C][C]0.6706[/C][C]0.252859[/C][/ROW]
[ROW][C]15[/C][C]-0.114129[/C][C]-0.7907[/C][C]0.783499[/C][/ROW]
[ROW][C]16[/C][C]-0.127459[/C][C]-0.8831[/C][C]0.809197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2309&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2309&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	6.9282	0
1	0.144005	0.9977	0.161714
2	0.05347	0.3705	0.356337
3	0.201314	1.3947	0.084757
4	0.009045	0.0627	0.475147
5	0.076541	0.5303	0.299177
6	0.144096	0.9983	0.161563
7	-0.163556	-1.1331	0.86861
8	0.005203	0.036	0.485696
9	0.185607	1.2859	0.10232
10	-0.158944	-1.1012	0.861848
11	-0.115718	-0.8017	0.786666
12	-0.178473	-1.2365	0.888855
13	-0.111832	-0.7748	0.778869
14	0.096786	0.6706	0.252859
15	-0.114129	-0.7907	0.783499
16	-0.127459	-0.8831	0.809197

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.144005	0.9977	0.161714
1	0.033426	0.2316	0.408923
2	0.193277	1.3391	0.093428
3	-0.0487	-0.3374	0.631359
4	0.074741	0.5178	0.303482
5	0.091326	0.6327	0.264958
6	-0.204731	-1.4184	0.918736
7	0.031142	0.2158	0.415046
8	0.164037	1.1365	0.130698
9	-0.170365	-1.1803	0.878157
10	-0.118721	-0.8225	0.792576
11	-0.206857	-1.4331	0.920851
12	0.061914	0.429	0.334938
13	0.12414	0.8601	0.197014
14	-0.140758	-0.9752	0.832825
15	0.020772	0.1439	0.443085
16	0.128786	0.8923	0.188354

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.144005 & 0.9977 & 0.161714 \tabularnewline
1 & 0.033426 & 0.2316 & 0.408923 \tabularnewline
2 & 0.193277 & 1.3391 & 0.093428 \tabularnewline
3 & -0.0487 & -0.3374 & 0.631359 \tabularnewline
4 & 0.074741 & 0.5178 & 0.303482 \tabularnewline
5 & 0.091326 & 0.6327 & 0.264958 \tabularnewline
6 & -0.204731 & -1.4184 & 0.918736 \tabularnewline
7 & 0.031142 & 0.2158 & 0.415046 \tabularnewline
8 & 0.164037 & 1.1365 & 0.130698 \tabularnewline
9 & -0.170365 & -1.1803 & 0.878157 \tabularnewline
10 & -0.118721 & -0.8225 & 0.792576 \tabularnewline
11 & -0.206857 & -1.4331 & 0.920851 \tabularnewline
12 & 0.061914 & 0.429 & 0.334938 \tabularnewline
13 & 0.12414 & 0.8601 & 0.197014 \tabularnewline
14 & -0.140758 & -0.9752 & 0.832825 \tabularnewline
15 & 0.020772 & 0.1439 & 0.443085 \tabularnewline
16 & 0.128786 & 0.8923 & 0.188354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2309&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]0.144005[/C][C]0.9977[/C][C]0.161714[/C][/ROW]
[ROW][C]1[/C][C]0.033426[/C][C]0.2316[/C][C]0.408923[/C][/ROW]
[ROW][C]2[/C][C]0.193277[/C][C]1.3391[/C][C]0.093428[/C][/ROW]
[ROW][C]3[/C][C]-0.0487[/C][C]-0.3374[/C][C]0.631359[/C][/ROW]
[ROW][C]4[/C][C]0.074741[/C][C]0.5178[/C][C]0.303482[/C][/ROW]
[ROW][C]5[/C][C]0.091326[/C][C]0.6327[/C][C]0.264958[/C][/ROW]
[ROW][C]6[/C][C]-0.204731[/C][C]-1.4184[/C][C]0.918736[/C][/ROW]
[ROW][C]7[/C][C]0.031142[/C][C]0.2158[/C][C]0.415046[/C][/ROW]
[ROW][C]8[/C][C]0.164037[/C][C]1.1365[/C][C]0.130698[/C][/ROW]
[ROW][C]9[/C][C]-0.170365[/C][C]-1.1803[/C][C]0.878157[/C][/ROW]
[ROW][C]10[/C][C]-0.118721[/C][C]-0.8225[/C][C]0.792576[/C][/ROW]
[ROW][C]11[/C][C]-0.206857[/C][C]-1.4331[/C][C]0.920851[/C][/ROW]
[ROW][C]12[/C][C]0.061914[/C][C]0.429[/C][C]0.334938[/C][/ROW]
[ROW][C]13[/C][C]0.12414[/C][C]0.8601[/C][C]0.197014[/C][/ROW]
[ROW][C]14[/C][C]-0.140758[/C][C]-0.9752[/C][C]0.832825[/C][/ROW]
[ROW][C]15[/C][C]0.020772[/C][C]0.1439[/C][C]0.443085[/C][/ROW]
[ROW][C]16[/C][C]0.128786[/C][C]0.8923[/C][C]0.188354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2309&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2309&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	0.144005	0.9977	0.161714
1	0.033426	0.2316	0.408923
2	0.193277	1.3391	0.093428
3	-0.0487	-0.3374	0.631359
4	0.074741	0.5178	0.303482
5	0.091326	0.6327	0.264958
6	-0.204731	-1.4184	0.918736
7	0.031142	0.2158	0.415046
8	0.164037	1.1365	0.130698
9	-0.170365	-1.1803	0.878157
10	-0.118721	-0.8225	0.792576
11	-0.206857	-1.4331	0.920851
12	0.061914	0.429	0.334938
13	0.12414	0.8601	0.197014
14	-0.140758	-0.9752	0.832825
15	0.020772	0.1439	0.443085
16	0.128786	0.8923	0.188354

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 ;

Parameters (R input):

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

Tables (Output of Computation)

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Input Parameters & R Code