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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 08 Dec 2008 06:14:12 -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/2008/Dec/08/t1228742091k4kgyg3u6doisw0.htm/, Retrieved Thu, 16 May 2024 09:41:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30461, Retrieved Thu, 16 May 2024 09:41:37 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

ACF

Estimated Impact

192

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP   [Standard Deviation-Mean Plot] [q1] [2008-12-08 12:37:39] [3ffd109c9e040b1ae7e5dbe576d4698c]
F    D    [Standard Deviation-Mean Plot] [SMP] [2008-12-08 12:41:29] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RM        [Variance Reduction Matrix] [VRM] [2008-12-08 13:10:17] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RM            [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:14:12] [962e6c9020896982bc8283b8971710a9] [Current]
F                 [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:16:18] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-   P               [(Partial) Autocorrelation Function] [ACF met meer lags] [2008-12-15 14:07:02] [f77c9ab3b413812d7baee6b7ec69a15d] 
-   P               [(Partial) Autocorrelation Function] [ACF] [2008-12-16 11:53:49] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P               [(Partial) Autocorrelation Function] [ACF] [2008-12-18 16:25:12] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-   P                 [(Partial) Autocorrelation Function] [ACF] [2008-12-24 12:57:31] [b28ef2aea2cd58ceb5ad90223572c703] 
F                 [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:17:45] [3ffd109c9e040b1ae7e5dbe576d4698c] 
F RM                [Spectral Analysis] [spectraal] [2008-12-08 13:20:34] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P                 [Spectral Analysis] [Spectraal] [2008-12-18 16:27:12] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-                       [Spectral Analysis] [spectraal analyse] [2008-12-24 12:59:19] [b28ef2aea2cd58ceb5ad90223572c703] 
- R P                 [Spectral Analysis] [spectraal] [2008-12-18 18:22:50] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- RM                [Spectral Analysis] [spectraal] [2008-12-08 13:22:13] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P                 [Spectral Analysis] [spectraal] [2008-12-18 18:23:46] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-                       [Spectral Analysis] [spectraal analyse] [2008-12-24 13:02:50] [b28ef2aea2cd58ceb5ad90223572c703] 
-   P                   [Spectral Analysis] [spectraal] [2008-12-24 13:21:21] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- RM                [Spectral Analysis] [spectraal] [2008-12-08 13:23:27] [3ffd109c9e040b1ae7e5dbe576d4698c] 
F RM                  [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:40:41] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P                   [(Partial) Autocorrelation Function] [acf] [2008-12-18 18:26:49] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-   P                   [(Partial) Autocorrelation Function] [autocorrelatie en...] [2008-12-19 10:44:18] [3f66c6f083b1153972739491b89fa2dd] 
-                     [Spectral Analysis] [spectraal] [2008-12-08 13:42:55] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P                   [Spectral Analysis] [spectraal] [2008-12-18 18:28:37] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P                 [Spectral Analysis] [spectraal] [2008-12-18 18:25:11] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-   P                   [Spectral Analysis] [spectraal analyse] [2008-12-24 13:07:13] [b28ef2aea2cd58ceb5ad90223572c703] 
-   P               [(Partial) Autocorrelation Function] [ACF met meer lags] [2008-12-15 14:18:46] [f77c9ab3b413812d7baee6b7ec69a15d] 
- R P               [(Partial) Autocorrelation Function] [ACF] [2008-12-18 16:54:54] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-   P                 [(Partial) Autocorrelation Function] [ACF] [2008-12-24 13:04:28] [b28ef2aea2cd58ceb5ad90223572c703] 
- R P             [(Partial) Autocorrelation Function] [ACF] [2008-12-18 16:48:38] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-   P               [(Partial) Autocorrelation Function] [ACF] [2008-12-24 13:00:55] [b28ef2aea2cd58ceb5ad90223572c703] 

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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=30461&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=30461&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30461&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	0.31826	2.4652	0.008286
2	-0.12001	-0.9296	0.178153
3	-0.315932	-2.4472	0.008671
4	-0.278481	-2.1571	0.017506
5	-0.082666	-0.6403	0.262198
6	-0.003703	-0.0287	0.488608
7	-0.063709	-0.4935	0.311736
8	-0.280249	-2.1708	0.016957
9	-0.251417	-1.9475	0.028082
10	-0.085691	-0.6638	0.254694
11	0.295274	2.2872	0.012863
12	0.779642	6.0391	0
13	0.23974	1.857	0.034109
14	-0.098102	-0.7599	0.225146
15	-0.257709	-1.9962	0.025228
16	-0.215498	-1.6692	0.05014
17	-0.056931	-0.441	0.330403

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.31826 & 2.4652 & 0.008286 \tabularnewline
2 & -0.12001 & -0.9296 & 0.178153 \tabularnewline
3 & -0.315932 & -2.4472 & 0.008671 \tabularnewline
4 & -0.278481 & -2.1571 & 0.017506 \tabularnewline
5 & -0.082666 & -0.6403 & 0.262198 \tabularnewline
6 & -0.003703 & -0.0287 & 0.488608 \tabularnewline
7 & -0.063709 & -0.4935 & 0.311736 \tabularnewline
8 & -0.280249 & -2.1708 & 0.016957 \tabularnewline
9 & -0.251417 & -1.9475 & 0.028082 \tabularnewline
10 & -0.085691 & -0.6638 & 0.254694 \tabularnewline
11 & 0.295274 & 2.2872 & 0.012863 \tabularnewline
12 & 0.779642 & 6.0391 & 0 \tabularnewline
13 & 0.23974 & 1.857 & 0.034109 \tabularnewline
14 & -0.098102 & -0.7599 & 0.225146 \tabularnewline
15 & -0.257709 & -1.9962 & 0.025228 \tabularnewline
16 & -0.215498 & -1.6692 & 0.05014 \tabularnewline
17 & -0.056931 & -0.441 & 0.330403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30461&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]0.31826[/C][C]2.4652[/C][C]0.008286[/C][/ROW]
[ROW][C]2[/C][C]-0.12001[/C][C]-0.9296[/C][C]0.178153[/C][/ROW]
[ROW][C]3[/C][C]-0.315932[/C][C]-2.4472[/C][C]0.008671[/C][/ROW]
[ROW][C]4[/C][C]-0.278481[/C][C]-2.1571[/C][C]0.017506[/C][/ROW]
[ROW][C]5[/C][C]-0.082666[/C][C]-0.6403[/C][C]0.262198[/C][/ROW]
[ROW][C]6[/C][C]-0.003703[/C][C]-0.0287[/C][C]0.488608[/C][/ROW]
[ROW][C]7[/C][C]-0.063709[/C][C]-0.4935[/C][C]0.311736[/C][/ROW]
[ROW][C]8[/C][C]-0.280249[/C][C]-2.1708[/C][C]0.016957[/C][/ROW]
[ROW][C]9[/C][C]-0.251417[/C][C]-1.9475[/C][C]0.028082[/C][/ROW]
[ROW][C]10[/C][C]-0.085691[/C][C]-0.6638[/C][C]0.254694[/C][/ROW]
[ROW][C]11[/C][C]0.295274[/C][C]2.2872[/C][C]0.012863[/C][/ROW]
[ROW][C]12[/C][C]0.779642[/C][C]6.0391[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.23974[/C][C]1.857[/C][C]0.034109[/C][/ROW]
[ROW][C]14[/C][C]-0.098102[/C][C]-0.7599[/C][C]0.225146[/C][/ROW]
[ROW][C]15[/C][C]-0.257709[/C][C]-1.9962[/C][C]0.025228[/C][/ROW]
[ROW][C]16[/C][C]-0.215498[/C][C]-1.6692[/C][C]0.05014[/C][/ROW]
[ROW][C]17[/C][C]-0.056931[/C][C]-0.441[/C][C]0.330403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30461&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30461&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	0.31826	2.4652	0.008286
2	-0.12001	-0.9296	0.178153
3	-0.315932	-2.4472	0.008671
4	-0.278481	-2.1571	0.017506
5	-0.082666	-0.6403	0.262198
6	-0.003703	-0.0287	0.488608
7	-0.063709	-0.4935	0.311736
8	-0.280249	-2.1708	0.016957
9	-0.251417	-1.9475	0.028082
10	-0.085691	-0.6638	0.254694
11	0.295274	2.2872	0.012863
12	0.779642	6.0391	0
13	0.23974	1.857	0.034109
14	-0.098102	-0.7599	0.225146
15	-0.257709	-1.9962	0.025228
16	-0.215498	-1.6692	0.05014
17	-0.056931	-0.441	0.330403

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.31826	2.4652	0.008286
2	-0.246241	-1.9074	0.030631
3	-0.225018	-1.743	0.04323
4	-0.147111	-1.1395	0.129508
5	-0.035603	-0.2758	0.391831
6	-0.118515	-0.918	0.181143
7	-0.191707	-1.485	0.071396
8	-0.398082	-3.0835	0.001545
9	-0.316535	-2.4519	0.00857
10	-0.400049	-3.0988	0.001478
11	-0.173114	-1.3409	0.092498
12	0.536278	4.154	5.3e-05
13	-0.301362	-2.3343	0.011472
14	0.0314	0.2432	0.404331
15	0.044593	0.3454	0.365496
16	-0.057269	-0.4436	0.329463
17	0.03153	0.2442	0.403944

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.31826 & 2.4652 & 0.008286 \tabularnewline
2 & -0.246241 & -1.9074 & 0.030631 \tabularnewline
3 & -0.225018 & -1.743 & 0.04323 \tabularnewline
4 & -0.147111 & -1.1395 & 0.129508 \tabularnewline
5 & -0.035603 & -0.2758 & 0.391831 \tabularnewline
6 & -0.118515 & -0.918 & 0.181143 \tabularnewline
7 & -0.191707 & -1.485 & 0.071396 \tabularnewline
8 & -0.398082 & -3.0835 & 0.001545 \tabularnewline
9 & -0.316535 & -2.4519 & 0.00857 \tabularnewline
10 & -0.400049 & -3.0988 & 0.001478 \tabularnewline
11 & -0.173114 & -1.3409 & 0.092498 \tabularnewline
12 & 0.536278 & 4.154 & 5.3e-05 \tabularnewline
13 & -0.301362 & -2.3343 & 0.011472 \tabularnewline
14 & 0.0314 & 0.2432 & 0.404331 \tabularnewline
15 & 0.044593 & 0.3454 & 0.365496 \tabularnewline
16 & -0.057269 & -0.4436 & 0.329463 \tabularnewline
17 & 0.03153 & 0.2442 & 0.403944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30461&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]0.31826[/C][C]2.4652[/C][C]0.008286[/C][/ROW]
[ROW][C]2[/C][C]-0.246241[/C][C]-1.9074[/C][C]0.030631[/C][/ROW]
[ROW][C]3[/C][C]-0.225018[/C][C]-1.743[/C][C]0.04323[/C][/ROW]
[ROW][C]4[/C][C]-0.147111[/C][C]-1.1395[/C][C]0.129508[/C][/ROW]
[ROW][C]5[/C][C]-0.035603[/C][C]-0.2758[/C][C]0.391831[/C][/ROW]
[ROW][C]6[/C][C]-0.118515[/C][C]-0.918[/C][C]0.181143[/C][/ROW]
[ROW][C]7[/C][C]-0.191707[/C][C]-1.485[/C][C]0.071396[/C][/ROW]
[ROW][C]8[/C][C]-0.398082[/C][C]-3.0835[/C][C]0.001545[/C][/ROW]
[ROW][C]9[/C][C]-0.316535[/C][C]-2.4519[/C][C]0.00857[/C][/ROW]
[ROW][C]10[/C][C]-0.400049[/C][C]-3.0988[/C][C]0.001478[/C][/ROW]
[ROW][C]11[/C][C]-0.173114[/C][C]-1.3409[/C][C]0.092498[/C][/ROW]
[ROW][C]12[/C][C]0.536278[/C][C]4.154[/C][C]5.3e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.301362[/C][C]-2.3343[/C][C]0.011472[/C][/ROW]
[ROW][C]14[/C][C]0.0314[/C][C]0.2432[/C][C]0.404331[/C][/ROW]
[ROW][C]15[/C][C]0.044593[/C][C]0.3454[/C][C]0.365496[/C][/ROW]
[ROW][C]16[/C][C]-0.057269[/C][C]-0.4436[/C][C]0.329463[/C][/ROW]
[ROW][C]17[/C][C]0.03153[/C][C]0.2442[/C][C]0.403944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30461&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30461&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	0.31826	2.4652	0.008286
2	-0.246241	-1.9074	0.030631
3	-0.225018	-1.743	0.04323
4	-0.147111	-1.1395	0.129508
5	-0.035603	-0.2758	0.391831
6	-0.118515	-0.918	0.181143
7	-0.191707	-1.485	0.071396
8	-0.398082	-3.0835	0.001545
9	-0.316535	-2.4519	0.00857
10	-0.400049	-3.0988	0.001478
11	-0.173114	-1.3409	0.092498
12	0.536278	4.154	5.3e-05
13	-0.301362	-2.3343	0.011472
14	0.0314	0.2432	0.404331
15	0.044593	0.3454	0.365496
16	-0.057269	-0.4436	0.329463
17	0.03153	0.2442	0.403944

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 = 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 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code