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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 08:55:49 -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/2007/Nov/23/t1195833024m559x38anhmdcz3.htm/, Retrieved Sun, 28 Apr 2024 20:03:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6210, Retrieved Sun, 28 Apr 2024 20:03:36 +0000

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No (this computation is public)

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Estimated Impact

183

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

-       [(Partial) Autocorrelation Function] [] [2007-11-23 15:55:49] [2467046df5c61f7ccf2ce4e184abae94] [Current]

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Summary of compuational 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 compuational 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=6210&T=0

[TABLE]
[ROW][C]Summary of compuational 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=6210&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6210&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 compuational 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
0	1	7.6811	0
1	0.365548	2.8078	0.003376
2	0.124479	0.9561	0.17145
3	0.019764	0.1518	0.439928
4	-0.154303	-1.1852	0.87966
5	-0.100021	-0.7683	0.777307
6	-0.112304	-0.8626	0.804081
7	0.004034	0.031	0.487694
8	-0.063704	-0.4893	0.686785
9	0.012053	0.0926	0.463274
10	0.006582	0.0506	0.479924
11	-0.093766	-0.7202	0.762888
12	-0.014559	-0.1118	0.54433
13	-0.023335	-0.1792	0.570818
14	-0.014857	-0.1141	0.545234
15	0.054709	0.4202	0.337922
16	0.175549	1.3484	0.091339

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & 0.365548 & 2.8078 & 0.003376 \tabularnewline
2 & 0.124479 & 0.9561 & 0.17145 \tabularnewline
3 & 0.019764 & 0.1518 & 0.439928 \tabularnewline
4 & -0.154303 & -1.1852 & 0.87966 \tabularnewline
5 & -0.100021 & -0.7683 & 0.777307 \tabularnewline
6 & -0.112304 & -0.8626 & 0.804081 \tabularnewline
7 & 0.004034 & 0.031 & 0.487694 \tabularnewline
8 & -0.063704 & -0.4893 & 0.686785 \tabularnewline
9 & 0.012053 & 0.0926 & 0.463274 \tabularnewline
10 & 0.006582 & 0.0506 & 0.479924 \tabularnewline
11 & -0.093766 & -0.7202 & 0.762888 \tabularnewline
12 & -0.014559 & -0.1118 & 0.54433 \tabularnewline
13 & -0.023335 & -0.1792 & 0.570818 \tabularnewline
14 & -0.014857 & -0.1141 & 0.545234 \tabularnewline
15 & 0.054709 & 0.4202 & 0.337922 \tabularnewline
16 & 0.175549 & 1.3484 & 0.091339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6210&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]0[/C][C]1[/C][C]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.365548[/C][C]2.8078[/C][C]0.003376[/C][/ROW]
[ROW][C]2[/C][C]0.124479[/C][C]0.9561[/C][C]0.17145[/C][/ROW]
[ROW][C]3[/C][C]0.019764[/C][C]0.1518[/C][C]0.439928[/C][/ROW]
[ROW][C]4[/C][C]-0.154303[/C][C]-1.1852[/C][C]0.87966[/C][/ROW]
[ROW][C]5[/C][C]-0.100021[/C][C]-0.7683[/C][C]0.777307[/C][/ROW]
[ROW][C]6[/C][C]-0.112304[/C][C]-0.8626[/C][C]0.804081[/C][/ROW]
[ROW][C]7[/C][C]0.004034[/C][C]0.031[/C][C]0.487694[/C][/ROW]
[ROW][C]8[/C][C]-0.063704[/C][C]-0.4893[/C][C]0.686785[/C][/ROW]
[ROW][C]9[/C][C]0.012053[/C][C]0.0926[/C][C]0.463274[/C][/ROW]
[ROW][C]10[/C][C]0.006582[/C][C]0.0506[/C][C]0.479924[/C][/ROW]
[ROW][C]11[/C][C]-0.093766[/C][C]-0.7202[/C][C]0.762888[/C][/ROW]
[ROW][C]12[/C][C]-0.014559[/C][C]-0.1118[/C][C]0.54433[/C][/ROW]
[ROW][C]13[/C][C]-0.023335[/C][C]-0.1792[/C][C]0.570818[/C][/ROW]
[ROW][C]14[/C][C]-0.014857[/C][C]-0.1141[/C][C]0.545234[/C][/ROW]
[ROW][C]15[/C][C]0.054709[/C][C]0.4202[/C][C]0.337922[/C][/ROW]
[ROW][C]16[/C][C]0.175549[/C][C]1.3484[/C][C]0.091339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6210&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6210&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
0	1	7.6811	0
1	0.365548	2.8078	0.003376
2	0.124479	0.9561	0.17145
3	0.019764	0.1518	0.439928
4	-0.154303	-1.1852	0.87966
5	-0.100021	-0.7683	0.777307
6	-0.112304	-0.8626	0.804081
7	0.004034	0.031	0.487694
8	-0.063704	-0.4893	0.686785
9	0.012053	0.0926	0.463274
10	0.006582	0.0506	0.479924
11	-0.093766	-0.7202	0.762888
12	-0.014559	-0.1118	0.54433
13	-0.023335	-0.1792	0.570818
14	-0.014857	-0.1141	0.545234
15	0.054709	0.4202	0.337922
16	0.175549	1.3484	0.091339

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.365548	2.8078	0.003376
1	-0.010557	-0.0811	0.532176
2	-0.025812	-0.1983	0.578242
3	-0.175622	-1.349	0.908751
4	0.018598	0.1429	0.443447
5	-0.072339	-0.5556	0.709723
6	0.089736	0.6893	0.246677
7	-0.133987	-1.0292	0.846201
8	0.080057	0.6149	0.270484
9	-0.058755	-0.4513	0.673288
10	-0.073552	-0.565	0.712881
11	0.014661	0.1126	0.45536
12	0.004742	0.0364	0.485533
13	-0.026788	-0.2058	0.581159
14	0.068378	0.5252	0.300698
15	0.147666	1.1342	0.130641
16	-0.172527	-1.3252	0.904894

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.365548 & 2.8078 & 0.003376 \tabularnewline
1 & -0.010557 & -0.0811 & 0.532176 \tabularnewline
2 & -0.025812 & -0.1983 & 0.578242 \tabularnewline
3 & -0.175622 & -1.349 & 0.908751 \tabularnewline
4 & 0.018598 & 0.1429 & 0.443447 \tabularnewline
5 & -0.072339 & -0.5556 & 0.709723 \tabularnewline
6 & 0.089736 & 0.6893 & 0.246677 \tabularnewline
7 & -0.133987 & -1.0292 & 0.846201 \tabularnewline
8 & 0.080057 & 0.6149 & 0.270484 \tabularnewline
9 & -0.058755 & -0.4513 & 0.673288 \tabularnewline
10 & -0.073552 & -0.565 & 0.712881 \tabularnewline
11 & 0.014661 & 0.1126 & 0.45536 \tabularnewline
12 & 0.004742 & 0.0364 & 0.485533 \tabularnewline
13 & -0.026788 & -0.2058 & 0.581159 \tabularnewline
14 & 0.068378 & 0.5252 & 0.300698 \tabularnewline
15 & 0.147666 & 1.1342 & 0.130641 \tabularnewline
16 & -0.172527 & -1.3252 & 0.904894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6210&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]0[/C][C]0.365548[/C][C]2.8078[/C][C]0.003376[/C][/ROW]
[ROW][C]1[/C][C]-0.010557[/C][C]-0.0811[/C][C]0.532176[/C][/ROW]
[ROW][C]2[/C][C]-0.025812[/C][C]-0.1983[/C][C]0.578242[/C][/ROW]
[ROW][C]3[/C][C]-0.175622[/C][C]-1.349[/C][C]0.908751[/C][/ROW]
[ROW][C]4[/C][C]0.018598[/C][C]0.1429[/C][C]0.443447[/C][/ROW]
[ROW][C]5[/C][C]-0.072339[/C][C]-0.5556[/C][C]0.709723[/C][/ROW]
[ROW][C]6[/C][C]0.089736[/C][C]0.6893[/C][C]0.246677[/C][/ROW]
[ROW][C]7[/C][C]-0.133987[/C][C]-1.0292[/C][C]0.846201[/C][/ROW]
[ROW][C]8[/C][C]0.080057[/C][C]0.6149[/C][C]0.270484[/C][/ROW]
[ROW][C]9[/C][C]-0.058755[/C][C]-0.4513[/C][C]0.673288[/C][/ROW]
[ROW][C]10[/C][C]-0.073552[/C][C]-0.565[/C][C]0.712881[/C][/ROW]
[ROW][C]11[/C][C]0.014661[/C][C]0.1126[/C][C]0.45536[/C][/ROW]
[ROW][C]12[/C][C]0.004742[/C][C]0.0364[/C][C]0.485533[/C][/ROW]
[ROW][C]13[/C][C]-0.026788[/C][C]-0.2058[/C][C]0.581159[/C][/ROW]
[ROW][C]14[/C][C]0.068378[/C][C]0.5252[/C][C]0.300698[/C][/ROW]
[ROW][C]15[/C][C]0.147666[/C][C]1.1342[/C][C]0.130641[/C][/ROW]
[ROW][C]16[/C][C]-0.172527[/C][C]-1.3252[/C][C]0.904894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6210&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6210&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
0	0.365548	2.8078	0.003376
1	-0.010557	-0.0811	0.532176
2	-0.025812	-0.1983	0.578242
3	-0.175622	-1.349	0.908751
4	0.018598	0.1429	0.443447
5	-0.072339	-0.5556	0.709723
6	0.089736	0.6893	0.246677
7	-0.133987	-1.0292	0.846201
8	0.080057	0.6149	0.270484
9	-0.058755	-0.4513	0.673288
10	-0.073552	-0.565	0.712881
11	0.014661	0.1126	0.45536
12	0.004742	0.0364	0.485533
13	-0.026788	-0.2058	0.581159
14	0.068378	0.5252	0.300698
15	0.147666	1.1342	0.130641
16	-0.172527	-1.3252	0.904894

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 = 0 ; par5 = 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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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