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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 23 Dec 2008 10:02:17 -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/2008/Dec/23/t12300517827ua9c7d9soifxo9.htm/, Retrieved Sat, 18 May 2024 21:19:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36356, Retrieved Sat, 18 May 2024 21:19:09 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

137

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

-     [Variance Reduction Matrix] [] [2008-12-23 15:10:07] [74be16979710d4c4e7c6647856088456]
- RMP   [Spectral Analysis] [] [2008-12-23 16:32:35] [74be16979710d4c4e7c6647856088456]
-   P     [Spectral Analysis] [] [2008-12-23 16:40:41] [74be16979710d4c4e7c6647856088456]
- RMPD        [(Partial) Autocorrelation Function] [] [2008-12-23 17:02:17] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36356&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]2 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=36356&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36356&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.910391	7.8315	0
2	0.780211	6.7116	0
3	0.673363	5.7925	0
4	0.611032	5.2563	1e-06
5	0.579025	4.981	2e-06
6	0.540994	4.6538	7e-06
7	0.475794	4.0929	5.4e-05
8	0.400045	3.4413	0.000478
9	0.376503	3.2388	0.000899
10	0.400982	3.4494	0.000466
11	0.45619	3.9243	9.7e-05
12	0.479102	4.1214	4.9e-05
13	0.383895	3.3024	0.000739
14	0.261718	2.2514	0.013665
15	0.159268	1.3701	0.087403
16	0.102137	0.8786	0.191226
17	0.074522	0.6411	0.261731
18	0.041601	0.3579	0.36073

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.910391 & 7.8315 & 0 \tabularnewline
2 & 0.780211 & 6.7116 & 0 \tabularnewline
3 & 0.673363 & 5.7925 & 0 \tabularnewline
4 & 0.611032 & 5.2563 & 1e-06 \tabularnewline
5 & 0.579025 & 4.981 & 2e-06 \tabularnewline
6 & 0.540994 & 4.6538 & 7e-06 \tabularnewline
7 & 0.475794 & 4.0929 & 5.4e-05 \tabularnewline
8 & 0.400045 & 3.4413 & 0.000478 \tabularnewline
9 & 0.376503 & 3.2388 & 0.000899 \tabularnewline
10 & 0.400982 & 3.4494 & 0.000466 \tabularnewline
11 & 0.45619 & 3.9243 & 9.7e-05 \tabularnewline
12 & 0.479102 & 4.1214 & 4.9e-05 \tabularnewline
13 & 0.383895 & 3.3024 & 0.000739 \tabularnewline
14 & 0.261718 & 2.2514 & 0.013665 \tabularnewline
15 & 0.159268 & 1.3701 & 0.087403 \tabularnewline
16 & 0.102137 & 0.8786 & 0.191226 \tabularnewline
17 & 0.074522 & 0.6411 & 0.261731 \tabularnewline
18 & 0.041601 & 0.3579 & 0.36073 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36356&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]0.910391[/C][C]7.8315[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.780211[/C][C]6.7116[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.673363[/C][C]5.7925[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.611032[/C][C]5.2563[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.579025[/C][C]4.981[/C][C]2e-06[/C][/ROW]
[ROW][C]6[/C][C]0.540994[/C][C]4.6538[/C][C]7e-06[/C][/ROW]
[ROW][C]7[/C][C]0.475794[/C][C]4.0929[/C][C]5.4e-05[/C][/ROW]
[ROW][C]8[/C][C]0.400045[/C][C]3.4413[/C][C]0.000478[/C][/ROW]
[ROW][C]9[/C][C]0.376503[/C][C]3.2388[/C][C]0.000899[/C][/ROW]
[ROW][C]10[/C][C]0.400982[/C][C]3.4494[/C][C]0.000466[/C][/ROW]
[ROW][C]11[/C][C]0.45619[/C][C]3.9243[/C][C]9.7e-05[/C][/ROW]
[ROW][C]12[/C][C]0.479102[/C][C]4.1214[/C][C]4.9e-05[/C][/ROW]
[ROW][C]13[/C][C]0.383895[/C][C]3.3024[/C][C]0.000739[/C][/ROW]
[ROW][C]14[/C][C]0.261718[/C][C]2.2514[/C][C]0.013665[/C][/ROW]
[ROW][C]15[/C][C]0.159268[/C][C]1.3701[/C][C]0.087403[/C][/ROW]
[ROW][C]16[/C][C]0.102137[/C][C]0.8786[/C][C]0.191226[/C][/ROW]
[ROW][C]17[/C][C]0.074522[/C][C]0.6411[/C][C]0.261731[/C][/ROW]
[ROW][C]18[/C][C]0.041601[/C][C]0.3579[/C][C]0.36073[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36356&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36356&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	0.910391	7.8315	0
2	0.780211	6.7116	0
3	0.673363	5.7925	0
4	0.611032	5.2563	1e-06
5	0.579025	4.981	2e-06
6	0.540994	4.6538	7e-06
7	0.475794	4.0929	5.4e-05
8	0.400045	3.4413	0.000478
9	0.376503	3.2388	0.000899
10	0.400982	3.4494	0.000466
11	0.45619	3.9243	9.7e-05
12	0.479102	4.1214	4.9e-05
13	0.383895	3.3024	0.000739
14	0.261718	2.2514	0.013665
15	0.159268	1.3701	0.087403
16	0.102137	0.8786	0.191226
17	0.074522	0.6411	0.261731
18	0.041601	0.3579	0.36073

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.910391	7.8315	0
2	-0.283906	-2.4422	0.008492
3	0.126271	1.0862	0.140452
4	0.139017	1.1959	0.117783
5	0.06181	0.5317	0.298261
6	-0.073836	-0.6352	0.26364
7	-0.107784	-0.9272	0.178421
8	-0.01049	-0.0902	0.464172
9	0.283508	2.4388	0.008567
10	0.101264	0.8711	0.193258
11	0.154537	1.3294	0.093904
12	-0.132742	-1.1419	0.12859
13	-0.598544	-5.1489	1e-06
14	0.103325	0.8888	0.188487
15	-0.080224	-0.6901	0.24614
16	0.029349	0.2525	0.400689
17	0.122006	1.0495	0.148673
18	-0.072599	-0.6245	0.267102

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.910391 & 7.8315 & 0 \tabularnewline
2 & -0.283906 & -2.4422 & 0.008492 \tabularnewline
3 & 0.126271 & 1.0862 & 0.140452 \tabularnewline
4 & 0.139017 & 1.1959 & 0.117783 \tabularnewline
5 & 0.06181 & 0.5317 & 0.298261 \tabularnewline
6 & -0.073836 & -0.6352 & 0.26364 \tabularnewline
7 & -0.107784 & -0.9272 & 0.178421 \tabularnewline
8 & -0.01049 & -0.0902 & 0.464172 \tabularnewline
9 & 0.283508 & 2.4388 & 0.008567 \tabularnewline
10 & 0.101264 & 0.8711 & 0.193258 \tabularnewline
11 & 0.154537 & 1.3294 & 0.093904 \tabularnewline
12 & -0.132742 & -1.1419 & 0.12859 \tabularnewline
13 & -0.598544 & -5.1489 & 1e-06 \tabularnewline
14 & 0.103325 & 0.8888 & 0.188487 \tabularnewline
15 & -0.080224 & -0.6901 & 0.24614 \tabularnewline
16 & 0.029349 & 0.2525 & 0.400689 \tabularnewline
17 & 0.122006 & 1.0495 & 0.148673 \tabularnewline
18 & -0.072599 & -0.6245 & 0.267102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36356&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]0.910391[/C][C]7.8315[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.283906[/C][C]-2.4422[/C][C]0.008492[/C][/ROW]
[ROW][C]3[/C][C]0.126271[/C][C]1.0862[/C][C]0.140452[/C][/ROW]
[ROW][C]4[/C][C]0.139017[/C][C]1.1959[/C][C]0.117783[/C][/ROW]
[ROW][C]5[/C][C]0.06181[/C][C]0.5317[/C][C]0.298261[/C][/ROW]
[ROW][C]6[/C][C]-0.073836[/C][C]-0.6352[/C][C]0.26364[/C][/ROW]
[ROW][C]7[/C][C]-0.107784[/C][C]-0.9272[/C][C]0.178421[/C][/ROW]
[ROW][C]8[/C][C]-0.01049[/C][C]-0.0902[/C][C]0.464172[/C][/ROW]
[ROW][C]9[/C][C]0.283508[/C][C]2.4388[/C][C]0.008567[/C][/ROW]
[ROW][C]10[/C][C]0.101264[/C][C]0.8711[/C][C]0.193258[/C][/ROW]
[ROW][C]11[/C][C]0.154537[/C][C]1.3294[/C][C]0.093904[/C][/ROW]
[ROW][C]12[/C][C]-0.132742[/C][C]-1.1419[/C][C]0.12859[/C][/ROW]
[ROW][C]13[/C][C]-0.598544[/C][C]-5.1489[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]0.103325[/C][C]0.8888[/C][C]0.188487[/C][/ROW]
[ROW][C]15[/C][C]-0.080224[/C][C]-0.6901[/C][C]0.24614[/C][/ROW]
[ROW][C]16[/C][C]0.029349[/C][C]0.2525[/C][C]0.400689[/C][/ROW]
[ROW][C]17[/C][C]0.122006[/C][C]1.0495[/C][C]0.148673[/C][/ROW]
[ROW][C]18[/C][C]-0.072599[/C][C]-0.6245[/C][C]0.267102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36356&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36356&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	0.910391	7.8315	0
2	-0.283906	-2.4422	0.008492
3	0.126271	1.0862	0.140452
4	0.139017	1.1959	0.117783
5	0.06181	0.5317	0.298261
6	-0.073836	-0.6352	0.26364
7	-0.107784	-0.9272	0.178421
8	-0.01049	-0.0902	0.464172
9	0.283508	2.4388	0.008567
10	0.101264	0.8711	0.193258
11	0.154537	1.3294	0.093904
12	-0.132742	-1.1419	0.12859
13	-0.598544	-5.1489	1e-06
14	0.103325	0.8888	0.188487
15	-0.080224	-0.6901	0.24614
16	0.029349	0.2525	0.400689
17	0.122006	1.0495	0.148673
18	-0.072599	-0.6245	0.267102

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 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')

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