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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 08 Dec 2008 11:36:48 -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/t12287614469feohwvi4zndk1l.htm/, Retrieved Thu, 16 May 2024 05:40:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30667, Retrieved Thu, 16 May 2024 05:40:45 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

206

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

-     [Univariate Data Series] [Run sequence plot...] [2008-12-02 22:19:27] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMPD  [Standard Deviation-Mean Plot] [SD mean plot] [2008-12-06 11:49:39] [ed2ba3b6182103c15c0ab511ae4e6284]
F RM      [Variance Reduction Matrix] [variance reduction] [2008-12-06 12:44:59] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMPD      [(Partial) Autocorrelation Function] [ACF] [2008-12-08 18:32:31] [077ffec662d24c06be4c491541a44245]
-   P         [(Partial) Autocorrelation Function] [ACF] [2008-12-08 18:34:40] [077ffec662d24c06be4c491541a44245]
-   P             [(Partial) Autocorrelation Function] [ACF] [2008-12-08 18:36:48] [3817f5e632a8bfeb1be7b5e8c86bd450] [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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30667&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30667&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30667&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.217924	-1.5098	0.068822
2	-0.116045	-0.804	0.212685
3	0.212954	1.4754	0.073319
4	0.022109	0.1532	0.439452
5	0.007053	0.0489	0.480615
6	0.229298	1.5886	0.059356
7	-0.141504	-0.9804	0.165909
8	-0.019727	-0.1367	0.44593
9	0.098123	0.6798	0.249944
10	-0.045576	-0.3158	0.376778
11	-0.116483	-0.807	0.211819
12	0.023423	0.1623	0.435884
13	-0.033639	-0.2331	0.408355
14	-0.052875	-0.3663	0.357864
15	0.042195	0.2923	0.385645
16	-0.179825	-1.2459	0.109431
17	0.024921	0.1727	0.431824

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.217924 & -1.5098 & 0.068822 \tabularnewline
2 & -0.116045 & -0.804 & 0.212685 \tabularnewline
3 & 0.212954 & 1.4754 & 0.073319 \tabularnewline
4 & 0.022109 & 0.1532 & 0.439452 \tabularnewline
5 & 0.007053 & 0.0489 & 0.480615 \tabularnewline
6 & 0.229298 & 1.5886 & 0.059356 \tabularnewline
7 & -0.141504 & -0.9804 & 0.165909 \tabularnewline
8 & -0.019727 & -0.1367 & 0.44593 \tabularnewline
9 & 0.098123 & 0.6798 & 0.249944 \tabularnewline
10 & -0.045576 & -0.3158 & 0.376778 \tabularnewline
11 & -0.116483 & -0.807 & 0.211819 \tabularnewline
12 & 0.023423 & 0.1623 & 0.435884 \tabularnewline
13 & -0.033639 & -0.2331 & 0.408355 \tabularnewline
14 & -0.052875 & -0.3663 & 0.357864 \tabularnewline
15 & 0.042195 & 0.2923 & 0.385645 \tabularnewline
16 & -0.179825 & -1.2459 & 0.109431 \tabularnewline
17 & 0.024921 & 0.1727 & 0.431824 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30667&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]-0.217924[/C][C]-1.5098[/C][C]0.068822[/C][/ROW]
[ROW][C]2[/C][C]-0.116045[/C][C]-0.804[/C][C]0.212685[/C][/ROW]
[ROW][C]3[/C][C]0.212954[/C][C]1.4754[/C][C]0.073319[/C][/ROW]
[ROW][C]4[/C][C]0.022109[/C][C]0.1532[/C][C]0.439452[/C][/ROW]
[ROW][C]5[/C][C]0.007053[/C][C]0.0489[/C][C]0.480615[/C][/ROW]
[ROW][C]6[/C][C]0.229298[/C][C]1.5886[/C][C]0.059356[/C][/ROW]
[ROW][C]7[/C][C]-0.141504[/C][C]-0.9804[/C][C]0.165909[/C][/ROW]
[ROW][C]8[/C][C]-0.019727[/C][C]-0.1367[/C][C]0.44593[/C][/ROW]
[ROW][C]9[/C][C]0.098123[/C][C]0.6798[/C][C]0.249944[/C][/ROW]
[ROW][C]10[/C][C]-0.045576[/C][C]-0.3158[/C][C]0.376778[/C][/ROW]
[ROW][C]11[/C][C]-0.116483[/C][C]-0.807[/C][C]0.211819[/C][/ROW]
[ROW][C]12[/C][C]0.023423[/C][C]0.1623[/C][C]0.435884[/C][/ROW]
[ROW][C]13[/C][C]-0.033639[/C][C]-0.2331[/C][C]0.408355[/C][/ROW]
[ROW][C]14[/C][C]-0.052875[/C][C]-0.3663[/C][C]0.357864[/C][/ROW]
[ROW][C]15[/C][C]0.042195[/C][C]0.2923[/C][C]0.385645[/C][/ROW]
[ROW][C]16[/C][C]-0.179825[/C][C]-1.2459[/C][C]0.109431[/C][/ROW]
[ROW][C]17[/C][C]0.024921[/C][C]0.1727[/C][C]0.431824[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30667&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30667&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	-0.217924	-1.5098	0.068822
2	-0.116045	-0.804	0.212685
3	0.212954	1.4754	0.073319
4	0.022109	0.1532	0.439452
5	0.007053	0.0489	0.480615
6	0.229298	1.5886	0.059356
7	-0.141504	-0.9804	0.165909
8	-0.019727	-0.1367	0.44593
9	0.098123	0.6798	0.249944
10	-0.045576	-0.3158	0.376778
11	-0.116483	-0.807	0.211819
12	0.023423	0.1623	0.435884
13	-0.033639	-0.2331	0.408355
14	-0.052875	-0.3663	0.357864
15	0.042195	0.2923	0.385645
16	-0.179825	-1.2459	0.109431
17	0.024921	0.1727	0.431824

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.217924	-1.5098	0.068822
2	-0.17169	-1.1895	0.120047
3	0.157835	1.0935	0.139813
4	0.099692	0.6907	0.246545
5	0.089999	0.6235	0.267944
6	0.256505	1.7771	0.040943
7	-0.047847	-0.3315	0.370858
8	-0.047135	-0.3266	0.37271
9	-0.043618	-0.3022	0.381906
10	-0.058297	-0.4039	0.344042
11	-0.156817	-1.0865	0.141351
12	-0.111798	-0.7746	0.221199
13	-0.035737	-0.2476	0.402753
14	-0.028095	-0.1946	0.423244
15	0.061641	0.4271	0.335623
16	-0.123658	-0.8567	0.197926
17	0.044844	0.3107	0.37869

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.217924 & -1.5098 & 0.068822 \tabularnewline
2 & -0.17169 & -1.1895 & 0.120047 \tabularnewline
3 & 0.157835 & 1.0935 & 0.139813 \tabularnewline
4 & 0.099692 & 0.6907 & 0.246545 \tabularnewline
5 & 0.089999 & 0.6235 & 0.267944 \tabularnewline
6 & 0.256505 & 1.7771 & 0.040943 \tabularnewline
7 & -0.047847 & -0.3315 & 0.370858 \tabularnewline
8 & -0.047135 & -0.3266 & 0.37271 \tabularnewline
9 & -0.043618 & -0.3022 & 0.381906 \tabularnewline
10 & -0.058297 & -0.4039 & 0.344042 \tabularnewline
11 & -0.156817 & -1.0865 & 0.141351 \tabularnewline
12 & -0.111798 & -0.7746 & 0.221199 \tabularnewline
13 & -0.035737 & -0.2476 & 0.402753 \tabularnewline
14 & -0.028095 & -0.1946 & 0.423244 \tabularnewline
15 & 0.061641 & 0.4271 & 0.335623 \tabularnewline
16 & -0.123658 & -0.8567 & 0.197926 \tabularnewline
17 & 0.044844 & 0.3107 & 0.37869 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30667&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]-0.217924[/C][C]-1.5098[/C][C]0.068822[/C][/ROW]
[ROW][C]2[/C][C]-0.17169[/C][C]-1.1895[/C][C]0.120047[/C][/ROW]
[ROW][C]3[/C][C]0.157835[/C][C]1.0935[/C][C]0.139813[/C][/ROW]
[ROW][C]4[/C][C]0.099692[/C][C]0.6907[/C][C]0.246545[/C][/ROW]
[ROW][C]5[/C][C]0.089999[/C][C]0.6235[/C][C]0.267944[/C][/ROW]
[ROW][C]6[/C][C]0.256505[/C][C]1.7771[/C][C]0.040943[/C][/ROW]
[ROW][C]7[/C][C]-0.047847[/C][C]-0.3315[/C][C]0.370858[/C][/ROW]
[ROW][C]8[/C][C]-0.047135[/C][C]-0.3266[/C][C]0.37271[/C][/ROW]
[ROW][C]9[/C][C]-0.043618[/C][C]-0.3022[/C][C]0.381906[/C][/ROW]
[ROW][C]10[/C][C]-0.058297[/C][C]-0.4039[/C][C]0.344042[/C][/ROW]
[ROW][C]11[/C][C]-0.156817[/C][C]-1.0865[/C][C]0.141351[/C][/ROW]
[ROW][C]12[/C][C]-0.111798[/C][C]-0.7746[/C][C]0.221199[/C][/ROW]
[ROW][C]13[/C][C]-0.035737[/C][C]-0.2476[/C][C]0.402753[/C][/ROW]
[ROW][C]14[/C][C]-0.028095[/C][C]-0.1946[/C][C]0.423244[/C][/ROW]
[ROW][C]15[/C][C]0.061641[/C][C]0.4271[/C][C]0.335623[/C][/ROW]
[ROW][C]16[/C][C]-0.123658[/C][C]-0.8567[/C][C]0.197926[/C][/ROW]
[ROW][C]17[/C][C]0.044844[/C][C]0.3107[/C][C]0.37869[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30667&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30667&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	-0.217924	-1.5098	0.068822
2	-0.17169	-1.1895	0.120047
3	0.157835	1.0935	0.139813
4	0.099692	0.6907	0.246545
5	0.089999	0.6235	0.267944
6	0.256505	1.7771	0.040943
7	-0.047847	-0.3315	0.370858
8	-0.047135	-0.3266	0.37271
9	-0.043618	-0.3022	0.381906
10	-0.058297	-0.4039	0.344042
11	-0.156817	-1.0865	0.141351
12	-0.111798	-0.7746	0.221199
13	-0.035737	-0.2476	0.402753
14	-0.028095	-0.1946	0.423244
15	0.061641	0.4271	0.335623
16	-0.123658	-0.8567	0.197926
17	0.044844	0.3107	0.37869

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.6 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.6 ; 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 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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Input Parameters & R Code