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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 03 Dec 2010 17:12:55 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/03/t1291396256a1u94ci0f8bnyk3.htm/, Retrieved Tue, 07 May 2024 08:53:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104928, Retrieved Tue, 07 May 2024 08:53:36 +0000

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Estimated Impact

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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   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-   PD    [(Partial) Autocorrelation Function] [ws9] [2010-12-03 17:10:35] [c7506ced21a6c0dca45d37c8a93c80e0]
-             [(Partial) Autocorrelation Function] [ws9] [2010-12-03 17:12:55] [0cadca125c925bcc9e6efbdd1941e458] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104928&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104928&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104928&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.078036	0.6529	0.257981
2	-0.213502	-1.7863	0.039192
3	0.048007	0.4017	0.344582
4	0.036222	0.3031	0.381372
5	-0.111835	-0.9357	0.176328
6	-0.01834	-0.1534	0.439245
7	0.024546	0.2054	0.41894
8	-0.106293	-0.8893	0.18844
9	0.014	0.1171	0.453545
10	-0.099215	-0.8301	0.204656
11	0.039066	0.3268	0.372379
12	0.103609	0.8669	0.194491
13	0.053838	0.4504	0.326893
14	-0.0632	-0.5288	0.29932
15	0.146023	1.2217	0.112956
16	0.16675	1.3951	0.083694
17	-0.152639	-1.2771	0.102899
18	-0.132904	-1.112	0.134981

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.078036 & 0.6529 & 0.257981 \tabularnewline
2 & -0.213502 & -1.7863 & 0.039192 \tabularnewline
3 & 0.048007 & 0.4017 & 0.344582 \tabularnewline
4 & 0.036222 & 0.3031 & 0.381372 \tabularnewline
5 & -0.111835 & -0.9357 & 0.176328 \tabularnewline
6 & -0.01834 & -0.1534 & 0.439245 \tabularnewline
7 & 0.024546 & 0.2054 & 0.41894 \tabularnewline
8 & -0.106293 & -0.8893 & 0.18844 \tabularnewline
9 & 0.014 & 0.1171 & 0.453545 \tabularnewline
10 & -0.099215 & -0.8301 & 0.204656 \tabularnewline
11 & 0.039066 & 0.3268 & 0.372379 \tabularnewline
12 & 0.103609 & 0.8669 & 0.194491 \tabularnewline
13 & 0.053838 & 0.4504 & 0.326893 \tabularnewline
14 & -0.0632 & -0.5288 & 0.29932 \tabularnewline
15 & 0.146023 & 1.2217 & 0.112956 \tabularnewline
16 & 0.16675 & 1.3951 & 0.083694 \tabularnewline
17 & -0.152639 & -1.2771 & 0.102899 \tabularnewline
18 & -0.132904 & -1.112 & 0.134981 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104928&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]0.078036[/C][C]0.6529[/C][C]0.257981[/C][/ROW]
[ROW][C]2[/C][C]-0.213502[/C][C]-1.7863[/C][C]0.039192[/C][/ROW]
[ROW][C]3[/C][C]0.048007[/C][C]0.4017[/C][C]0.344582[/C][/ROW]
[ROW][C]4[/C][C]0.036222[/C][C]0.3031[/C][C]0.381372[/C][/ROW]
[ROW][C]5[/C][C]-0.111835[/C][C]-0.9357[/C][C]0.176328[/C][/ROW]
[ROW][C]6[/C][C]-0.01834[/C][C]-0.1534[/C][C]0.439245[/C][/ROW]
[ROW][C]7[/C][C]0.024546[/C][C]0.2054[/C][C]0.41894[/C][/ROW]
[ROW][C]8[/C][C]-0.106293[/C][C]-0.8893[/C][C]0.18844[/C][/ROW]
[ROW][C]9[/C][C]0.014[/C][C]0.1171[/C][C]0.453545[/C][/ROW]
[ROW][C]10[/C][C]-0.099215[/C][C]-0.8301[/C][C]0.204656[/C][/ROW]
[ROW][C]11[/C][C]0.039066[/C][C]0.3268[/C][C]0.372379[/C][/ROW]
[ROW][C]12[/C][C]0.103609[/C][C]0.8669[/C][C]0.194491[/C][/ROW]
[ROW][C]13[/C][C]0.053838[/C][C]0.4504[/C][C]0.326893[/C][/ROW]
[ROW][C]14[/C][C]-0.0632[/C][C]-0.5288[/C][C]0.29932[/C][/ROW]
[ROW][C]15[/C][C]0.146023[/C][C]1.2217[/C][C]0.112956[/C][/ROW]
[ROW][C]16[/C][C]0.16675[/C][C]1.3951[/C][C]0.083694[/C][/ROW]
[ROW][C]17[/C][C]-0.152639[/C][C]-1.2771[/C][C]0.102899[/C][/ROW]
[ROW][C]18[/C][C]-0.132904[/C][C]-1.112[/C][C]0.134981[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104928&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104928&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	0.078036	0.6529	0.257981
2	-0.213502	-1.7863	0.039192
3	0.048007	0.4017	0.344582
4	0.036222	0.3031	0.381372
5	-0.111835	-0.9357	0.176328
6	-0.01834	-0.1534	0.439245
7	0.024546	0.2054	0.41894
8	-0.106293	-0.8893	0.18844
9	0.014	0.1171	0.453545
10	-0.099215	-0.8301	0.204656
11	0.039066	0.3268	0.372379
12	0.103609	0.8669	0.194491
13	0.053838	0.4504	0.326893
14	-0.0632	-0.5288	0.29932
15	0.146023	1.2217	0.112956
16	0.16675	1.3951	0.083694
17	-0.152639	-1.2771	0.102899
18	-0.132904	-1.112	0.134981

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.078036	0.6529	0.257981
2	-0.220937	-1.8485	0.034377
3	0.090533	0.7575	0.22566
4	-0.027077	-0.2265	0.410719
5	-0.088234	-0.7382	0.231424
6	0.002824	0.0236	0.490609
7	-0.021257	-0.1778	0.429677
8	-0.104879	-0.8775	0.191614
9	0.044909	0.3757	0.354126
10	-0.177391	-1.4842	0.071128
11	0.104001	0.8701	0.193601
12	0.029554	0.2473	0.402714
13	0.061394	0.5137	0.304555
14	-0.047937	-0.4011	0.344795
15	0.173944	1.4553	0.075025
16	0.098729	0.826	0.205798
17	-0.091451	-0.7651	0.223382
18	-0.09483	-0.7934	0.215111

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.078036 & 0.6529 & 0.257981 \tabularnewline
2 & -0.220937 & -1.8485 & 0.034377 \tabularnewline
3 & 0.090533 & 0.7575 & 0.22566 \tabularnewline
4 & -0.027077 & -0.2265 & 0.410719 \tabularnewline
5 & -0.088234 & -0.7382 & 0.231424 \tabularnewline
6 & 0.002824 & 0.0236 & 0.490609 \tabularnewline
7 & -0.021257 & -0.1778 & 0.429677 \tabularnewline
8 & -0.104879 & -0.8775 & 0.191614 \tabularnewline
9 & 0.044909 & 0.3757 & 0.354126 \tabularnewline
10 & -0.177391 & -1.4842 & 0.071128 \tabularnewline
11 & 0.104001 & 0.8701 & 0.193601 \tabularnewline
12 & 0.029554 & 0.2473 & 0.402714 \tabularnewline
13 & 0.061394 & 0.5137 & 0.304555 \tabularnewline
14 & -0.047937 & -0.4011 & 0.344795 \tabularnewline
15 & 0.173944 & 1.4553 & 0.075025 \tabularnewline
16 & 0.098729 & 0.826 & 0.205798 \tabularnewline
17 & -0.091451 & -0.7651 & 0.223382 \tabularnewline
18 & -0.09483 & -0.7934 & 0.215111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104928&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]0.078036[/C][C]0.6529[/C][C]0.257981[/C][/ROW]
[ROW][C]2[/C][C]-0.220937[/C][C]-1.8485[/C][C]0.034377[/C][/ROW]
[ROW][C]3[/C][C]0.090533[/C][C]0.7575[/C][C]0.22566[/C][/ROW]
[ROW][C]4[/C][C]-0.027077[/C][C]-0.2265[/C][C]0.410719[/C][/ROW]
[ROW][C]5[/C][C]-0.088234[/C][C]-0.7382[/C][C]0.231424[/C][/ROW]
[ROW][C]6[/C][C]0.002824[/C][C]0.0236[/C][C]0.490609[/C][/ROW]
[ROW][C]7[/C][C]-0.021257[/C][C]-0.1778[/C][C]0.429677[/C][/ROW]
[ROW][C]8[/C][C]-0.104879[/C][C]-0.8775[/C][C]0.191614[/C][/ROW]
[ROW][C]9[/C][C]0.044909[/C][C]0.3757[/C][C]0.354126[/C][/ROW]
[ROW][C]10[/C][C]-0.177391[/C][C]-1.4842[/C][C]0.071128[/C][/ROW]
[ROW][C]11[/C][C]0.104001[/C][C]0.8701[/C][C]0.193601[/C][/ROW]
[ROW][C]12[/C][C]0.029554[/C][C]0.2473[/C][C]0.402714[/C][/ROW]
[ROW][C]13[/C][C]0.061394[/C][C]0.5137[/C][C]0.304555[/C][/ROW]
[ROW][C]14[/C][C]-0.047937[/C][C]-0.4011[/C][C]0.344795[/C][/ROW]
[ROW][C]15[/C][C]0.173944[/C][C]1.4553[/C][C]0.075025[/C][/ROW]
[ROW][C]16[/C][C]0.098729[/C][C]0.826[/C][C]0.205798[/C][/ROW]
[ROW][C]17[/C][C]-0.091451[/C][C]-0.7651[/C][C]0.223382[/C][/ROW]
[ROW][C]18[/C][C]-0.09483[/C][C]-0.7934[/C][C]0.215111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104928&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104928&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	0.078036	0.6529	0.257981
2	-0.220937	-1.8485	0.034377
3	0.090533	0.7575	0.22566
4	-0.027077	-0.2265	0.410719
5	-0.088234	-0.7382	0.231424
6	0.002824	0.0236	0.490609
7	-0.021257	-0.1778	0.429677
8	-0.104879	-0.8775	0.191614
9	0.044909	0.3757	0.354126
10	-0.177391	-1.4842	0.071128
11	0.104001	0.8701	0.193601
12	0.029554	0.2473	0.402714
13	0.061394	0.5137	0.304555
14	-0.047937	-0.4011	0.344795
15	0.173944	1.4553	0.075025
16	0.098729	0.826	0.205798
17	-0.091451	-0.7651	0.223382
18	-0.09483	-0.7934	0.215111

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 2 ; par4 = 1 ;

Parameters (R input):

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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code