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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

Tue, 08 Dec 2009 14:48:58 -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/2009/Dec/08/t1260308992c45al81qg0mgwh5.htm/, Retrieved Sun, 28 Apr 2024 08:45:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64871, Retrieved Sun, 28 Apr 2024 08:45:49 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

103

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]
- RMP   [ARIMA Backward Selection] [] [2009-11-27 14:53:14] [b98453cac15ba1066b407e146608df68]
F   PD    [ARIMA Backward Selection] [arima backward se...] [2009-12-03 14:09:26] [f7fc9270f813d017f9fa5b506fdc7682]
- RMP         [(Partial) Autocorrelation Function] [Verbetering works...] [2009-12-08 21:48:58] [3d2053c5f7c50d3c075d87ce0bd87294] [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	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=64871&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=64871&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64871&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	0.143105	1.0119	0.158228
2	0.259615	1.8358	0.036172
3	0.32812	2.3202	0.012227
4	0.198734	1.4053	0.083063
5	0.108201	0.7651	0.223905
6	0.164967	1.1665	0.124474
7	0.036957	0.2613	0.397457
8	0.151003	1.0678	0.14538
9	0.04736	0.3349	0.369556
10	-0.060647	-0.4288	0.33494
11	0.324759	2.2964	0.01294
12	-0.050971	-0.3604	0.360025
13	-0.017444	-0.1233	0.451164
14	0.18157	1.2839	0.102548
15	0.051761	0.366	0.357952
16	0.007482	0.0529	0.47901
17	0.067605	0.478	0.317352

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.143105 & 1.0119 & 0.158228 \tabularnewline
2 & 0.259615 & 1.8358 & 0.036172 \tabularnewline
3 & 0.32812 & 2.3202 & 0.012227 \tabularnewline
4 & 0.198734 & 1.4053 & 0.083063 \tabularnewline
5 & 0.108201 & 0.7651 & 0.223905 \tabularnewline
6 & 0.164967 & 1.1665 & 0.124474 \tabularnewline
7 & 0.036957 & 0.2613 & 0.397457 \tabularnewline
8 & 0.151003 & 1.0678 & 0.14538 \tabularnewline
9 & 0.04736 & 0.3349 & 0.369556 \tabularnewline
10 & -0.060647 & -0.4288 & 0.33494 \tabularnewline
11 & 0.324759 & 2.2964 & 0.01294 \tabularnewline
12 & -0.050971 & -0.3604 & 0.360025 \tabularnewline
13 & -0.017444 & -0.1233 & 0.451164 \tabularnewline
14 & 0.18157 & 1.2839 & 0.102548 \tabularnewline
15 & 0.051761 & 0.366 & 0.357952 \tabularnewline
16 & 0.007482 & 0.0529 & 0.47901 \tabularnewline
17 & 0.067605 & 0.478 & 0.317352 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64871&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]0.143105[/C][C]1.0119[/C][C]0.158228[/C][/ROW]
[ROW][C]2[/C][C]0.259615[/C][C]1.8358[/C][C]0.036172[/C][/ROW]
[ROW][C]3[/C][C]0.32812[/C][C]2.3202[/C][C]0.012227[/C][/ROW]
[ROW][C]4[/C][C]0.198734[/C][C]1.4053[/C][C]0.083063[/C][/ROW]
[ROW][C]5[/C][C]0.108201[/C][C]0.7651[/C][C]0.223905[/C][/ROW]
[ROW][C]6[/C][C]0.164967[/C][C]1.1665[/C][C]0.124474[/C][/ROW]
[ROW][C]7[/C][C]0.036957[/C][C]0.2613[/C][C]0.397457[/C][/ROW]
[ROW][C]8[/C][C]0.151003[/C][C]1.0678[/C][C]0.14538[/C][/ROW]
[ROW][C]9[/C][C]0.04736[/C][C]0.3349[/C][C]0.369556[/C][/ROW]
[ROW][C]10[/C][C]-0.060647[/C][C]-0.4288[/C][C]0.33494[/C][/ROW]
[ROW][C]11[/C][C]0.324759[/C][C]2.2964[/C][C]0.01294[/C][/ROW]
[ROW][C]12[/C][C]-0.050971[/C][C]-0.3604[/C][C]0.360025[/C][/ROW]
[ROW][C]13[/C][C]-0.017444[/C][C]-0.1233[/C][C]0.451164[/C][/ROW]
[ROW][C]14[/C][C]0.18157[/C][C]1.2839[/C][C]0.102548[/C][/ROW]
[ROW][C]15[/C][C]0.051761[/C][C]0.366[/C][C]0.357952[/C][/ROW]
[ROW][C]16[/C][C]0.007482[/C][C]0.0529[/C][C]0.47901[/C][/ROW]
[ROW][C]17[/C][C]0.067605[/C][C]0.478[/C][C]0.317352[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64871&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64871&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	0.143105	1.0119	0.158228
2	0.259615	1.8358	0.036172
3	0.32812	2.3202	0.012227
4	0.198734	1.4053	0.083063
5	0.108201	0.7651	0.223905
6	0.164967	1.1665	0.124474
7	0.036957	0.2613	0.397457
8	0.151003	1.0678	0.14538
9	0.04736	0.3349	0.369556
10	-0.060647	-0.4288	0.33494
11	0.324759	2.2964	0.01294
12	-0.050971	-0.3604	0.360025
13	-0.017444	-0.1233	0.451164
14	0.18157	1.2839	0.102548
15	0.051761	0.366	0.357952
16	0.007482	0.0529	0.47901
17	0.067605	0.478	0.317352

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.143105	1.0119	0.158228
2	0.244136	1.7263	0.045234
3	0.287797	2.035	0.023583
4	0.106306	0.7517	0.227879
5	-0.05339	-0.3775	0.35369
6	0.007462	0.0528	0.479065
7	-0.080526	-0.5694	0.285816
8	0.097674	0.6907	0.246486
9	-0.002333	-0.0165	0.493451
10	-0.135771	-0.96	0.170827
11	0.330226	2.3351	0.011798
12	-0.108181	-0.765	0.223947
13	-0.099663	-0.7047	0.242126
14	0.09924	0.7017	0.243049
15	0.014773	0.1045	0.458612
16	0.014293	0.1011	0.459952
17	-0.065149	-0.4607	0.323514

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.143105 & 1.0119 & 0.158228 \tabularnewline
2 & 0.244136 & 1.7263 & 0.045234 \tabularnewline
3 & 0.287797 & 2.035 & 0.023583 \tabularnewline
4 & 0.106306 & 0.7517 & 0.227879 \tabularnewline
5 & -0.05339 & -0.3775 & 0.35369 \tabularnewline
6 & 0.007462 & 0.0528 & 0.479065 \tabularnewline
7 & -0.080526 & -0.5694 & 0.285816 \tabularnewline
8 & 0.097674 & 0.6907 & 0.246486 \tabularnewline
9 & -0.002333 & -0.0165 & 0.493451 \tabularnewline
10 & -0.135771 & -0.96 & 0.170827 \tabularnewline
11 & 0.330226 & 2.3351 & 0.011798 \tabularnewline
12 & -0.108181 & -0.765 & 0.223947 \tabularnewline
13 & -0.099663 & -0.7047 & 0.242126 \tabularnewline
14 & 0.09924 & 0.7017 & 0.243049 \tabularnewline
15 & 0.014773 & 0.1045 & 0.458612 \tabularnewline
16 & 0.014293 & 0.1011 & 0.459952 \tabularnewline
17 & -0.065149 & -0.4607 & 0.323514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64871&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]0.143105[/C][C]1.0119[/C][C]0.158228[/C][/ROW]
[ROW][C]2[/C][C]0.244136[/C][C]1.7263[/C][C]0.045234[/C][/ROW]
[ROW][C]3[/C][C]0.287797[/C][C]2.035[/C][C]0.023583[/C][/ROW]
[ROW][C]4[/C][C]0.106306[/C][C]0.7517[/C][C]0.227879[/C][/ROW]
[ROW][C]5[/C][C]-0.05339[/C][C]-0.3775[/C][C]0.35369[/C][/ROW]
[ROW][C]6[/C][C]0.007462[/C][C]0.0528[/C][C]0.479065[/C][/ROW]
[ROW][C]7[/C][C]-0.080526[/C][C]-0.5694[/C][C]0.285816[/C][/ROW]
[ROW][C]8[/C][C]0.097674[/C][C]0.6907[/C][C]0.246486[/C][/ROW]
[ROW][C]9[/C][C]-0.002333[/C][C]-0.0165[/C][C]0.493451[/C][/ROW]
[ROW][C]10[/C][C]-0.135771[/C][C]-0.96[/C][C]0.170827[/C][/ROW]
[ROW][C]11[/C][C]0.330226[/C][C]2.3351[/C][C]0.011798[/C][/ROW]
[ROW][C]12[/C][C]-0.108181[/C][C]-0.765[/C][C]0.223947[/C][/ROW]
[ROW][C]13[/C][C]-0.099663[/C][C]-0.7047[/C][C]0.242126[/C][/ROW]
[ROW][C]14[/C][C]0.09924[/C][C]0.7017[/C][C]0.243049[/C][/ROW]
[ROW][C]15[/C][C]0.014773[/C][C]0.1045[/C][C]0.458612[/C][/ROW]
[ROW][C]16[/C][C]0.014293[/C][C]0.1011[/C][C]0.459952[/C][/ROW]
[ROW][C]17[/C][C]-0.065149[/C][C]-0.4607[/C][C]0.323514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64871&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64871&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	0.143105	1.0119	0.158228
2	0.244136	1.7263	0.045234
3	0.287797	2.035	0.023583
4	0.106306	0.7517	0.227879
5	-0.05339	-0.3775	0.35369
6	0.007462	0.0528	0.479065
7	-0.080526	-0.5694	0.285816
8	0.097674	0.6907	0.246486
9	-0.002333	-0.0165	0.493451
10	-0.135771	-0.96	0.170827
11	0.330226	2.3351	0.011798
12	-0.108181	-0.765	0.223947
13	-0.099663	-0.7047	0.242126
14	0.09924	0.7017	0.243049
15	0.014773	0.1045	0.458612
16	0.014293	0.1011	0.459952
17	-0.065149	-0.4607	0.323514

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code