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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 05:58:36 -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/25/t1195995011pio6uzu8pp8wl4n.htm/, Retrieved Sat, 04 May 2024 08:25:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6432, Retrieved Sat, 04 May 2024 08:25:47 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

219

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

-       [(Partial) Autocorrelation Function] [Autocorrelation f...] [2007-11-25 12:58:36] [9fe578921d87f9af8e79a90d6142ba02] [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=6432&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=6432&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6432&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	6.9282	0
1	-0.053565	-0.3711	0.643907
2	0.034438	0.2386	0.406219
3	-0.077723	-0.5385	0.703632
4	-0.04424	-0.3065	0.619727
5	-0.033953	-0.2352	0.592485
6	-0.210897	-1.4611	0.924753
7	0.046419	0.3216	0.374577
8	0.008519	0.059	0.47659
9	0.183065	1.2683	0.105402
10	-0.044692	-0.3096	0.620911
11	0.048359	0.335	0.369528
12	-0.350178	-2.4261	0.990465
13	0.019562	0.1355	0.446379
14	-0.021714	-0.1504	0.559477
15	-0.004499	-0.0312	0.512367
16	0.026286	0.1821	0.42813

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & -0.053565 & -0.3711 & 0.643907 \tabularnewline
2 & 0.034438 & 0.2386 & 0.406219 \tabularnewline
3 & -0.077723 & -0.5385 & 0.703632 \tabularnewline
4 & -0.04424 & -0.3065 & 0.619727 \tabularnewline
5 & -0.033953 & -0.2352 & 0.592485 \tabularnewline
6 & -0.210897 & -1.4611 & 0.924753 \tabularnewline
7 & 0.046419 & 0.3216 & 0.374577 \tabularnewline
8 & 0.008519 & 0.059 & 0.47659 \tabularnewline
9 & 0.183065 & 1.2683 & 0.105402 \tabularnewline
10 & -0.044692 & -0.3096 & 0.620911 \tabularnewline
11 & 0.048359 & 0.335 & 0.369528 \tabularnewline
12 & -0.350178 & -2.4261 & 0.990465 \tabularnewline
13 & 0.019562 & 0.1355 & 0.446379 \tabularnewline
14 & -0.021714 & -0.1504 & 0.559477 \tabularnewline
15 & -0.004499 & -0.0312 & 0.512367 \tabularnewline
16 & 0.026286 & 0.1821 & 0.42813 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6432&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]6.9282[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.053565[/C][C]-0.3711[/C][C]0.643907[/C][/ROW]
[ROW][C]2[/C][C]0.034438[/C][C]0.2386[/C][C]0.406219[/C][/ROW]
[ROW][C]3[/C][C]-0.077723[/C][C]-0.5385[/C][C]0.703632[/C][/ROW]
[ROW][C]4[/C][C]-0.04424[/C][C]-0.3065[/C][C]0.619727[/C][/ROW]
[ROW][C]5[/C][C]-0.033953[/C][C]-0.2352[/C][C]0.592485[/C][/ROW]
[ROW][C]6[/C][C]-0.210897[/C][C]-1.4611[/C][C]0.924753[/C][/ROW]
[ROW][C]7[/C][C]0.046419[/C][C]0.3216[/C][C]0.374577[/C][/ROW]
[ROW][C]8[/C][C]0.008519[/C][C]0.059[/C][C]0.47659[/C][/ROW]
[ROW][C]9[/C][C]0.183065[/C][C]1.2683[/C][C]0.105402[/C][/ROW]
[ROW][C]10[/C][C]-0.044692[/C][C]-0.3096[/C][C]0.620911[/C][/ROW]
[ROW][C]11[/C][C]0.048359[/C][C]0.335[/C][C]0.369528[/C][/ROW]
[ROW][C]12[/C][C]-0.350178[/C][C]-2.4261[/C][C]0.990465[/C][/ROW]
[ROW][C]13[/C][C]0.019562[/C][C]0.1355[/C][C]0.446379[/C][/ROW]
[ROW][C]14[/C][C]-0.021714[/C][C]-0.1504[/C][C]0.559477[/C][/ROW]
[ROW][C]15[/C][C]-0.004499[/C][C]-0.0312[/C][C]0.512367[/C][/ROW]
[ROW][C]16[/C][C]0.026286[/C][C]0.1821[/C][C]0.42813[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6432&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6432&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	6.9282	0
1	-0.053565	-0.3711	0.643907
2	0.034438	0.2386	0.406219
3	-0.077723	-0.5385	0.703632
4	-0.04424	-0.3065	0.619727
5	-0.033953	-0.2352	0.592485
6	-0.210897	-1.4611	0.924753
7	0.046419	0.3216	0.374577
8	0.008519	0.059	0.47659
9	0.183065	1.2683	0.105402
10	-0.044692	-0.3096	0.620911
11	0.048359	0.335	0.369528
12	-0.350178	-2.4261	0.990465
13	0.019562	0.1355	0.446379
14	-0.021714	-0.1504	0.559477
15	-0.004499	-0.0312	0.512367
16	0.026286	0.1821	0.42813

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.053565	-0.3711	0.643907
1	0.031659	0.2193	0.413657
2	-0.074529	-0.5164	0.69601
3	-0.053541	-0.3709	0.643843
4	-0.034678	-0.2403	0.594423
5	-0.220429	-1.5272	0.93336
6	0.016477	0.1142	0.454796
7	0.014917	0.1033	0.45906
8	0.152357	1.0556	0.148227
9	-0.045014	-0.3119	0.621755
10	0.027279	0.189	0.425448
11	-0.395821	-2.7423	0.995726
12	0.009003	0.0624	0.475262
13	0.002511	0.0174	0.493097
14	0.055729	0.3861	0.350563
15	-0.037782	-0.2618	0.602688
16	-0.01125	-0.0779	0.530901

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.053565 & -0.3711 & 0.643907 \tabularnewline
1 & 0.031659 & 0.2193 & 0.413657 \tabularnewline
2 & -0.074529 & -0.5164 & 0.69601 \tabularnewline
3 & -0.053541 & -0.3709 & 0.643843 \tabularnewline
4 & -0.034678 & -0.2403 & 0.594423 \tabularnewline
5 & -0.220429 & -1.5272 & 0.93336 \tabularnewline
6 & 0.016477 & 0.1142 & 0.454796 \tabularnewline
7 & 0.014917 & 0.1033 & 0.45906 \tabularnewline
8 & 0.152357 & 1.0556 & 0.148227 \tabularnewline
9 & -0.045014 & -0.3119 & 0.621755 \tabularnewline
10 & 0.027279 & 0.189 & 0.425448 \tabularnewline
11 & -0.395821 & -2.7423 & 0.995726 \tabularnewline
12 & 0.009003 & 0.0624 & 0.475262 \tabularnewline
13 & 0.002511 & 0.0174 & 0.493097 \tabularnewline
14 & 0.055729 & 0.3861 & 0.350563 \tabularnewline
15 & -0.037782 & -0.2618 & 0.602688 \tabularnewline
16 & -0.01125 & -0.0779 & 0.530901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6432&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]-0.053565[/C][C]-0.3711[/C][C]0.643907[/C][/ROW]
[ROW][C]1[/C][C]0.031659[/C][C]0.2193[/C][C]0.413657[/C][/ROW]
[ROW][C]2[/C][C]-0.074529[/C][C]-0.5164[/C][C]0.69601[/C][/ROW]
[ROW][C]3[/C][C]-0.053541[/C][C]-0.3709[/C][C]0.643843[/C][/ROW]
[ROW][C]4[/C][C]-0.034678[/C][C]-0.2403[/C][C]0.594423[/C][/ROW]
[ROW][C]5[/C][C]-0.220429[/C][C]-1.5272[/C][C]0.93336[/C][/ROW]
[ROW][C]6[/C][C]0.016477[/C][C]0.1142[/C][C]0.454796[/C][/ROW]
[ROW][C]7[/C][C]0.014917[/C][C]0.1033[/C][C]0.45906[/C][/ROW]
[ROW][C]8[/C][C]0.152357[/C][C]1.0556[/C][C]0.148227[/C][/ROW]
[ROW][C]9[/C][C]-0.045014[/C][C]-0.3119[/C][C]0.621755[/C][/ROW]
[ROW][C]10[/C][C]0.027279[/C][C]0.189[/C][C]0.425448[/C][/ROW]
[ROW][C]11[/C][C]-0.395821[/C][C]-2.7423[/C][C]0.995726[/C][/ROW]
[ROW][C]12[/C][C]0.009003[/C][C]0.0624[/C][C]0.475262[/C][/ROW]
[ROW][C]13[/C][C]0.002511[/C][C]0.0174[/C][C]0.493097[/C][/ROW]
[ROW][C]14[/C][C]0.055729[/C][C]0.3861[/C][C]0.350563[/C][/ROW]
[ROW][C]15[/C][C]-0.037782[/C][C]-0.2618[/C][C]0.602688[/C][/ROW]
[ROW][C]16[/C][C]-0.01125[/C][C]-0.0779[/C][C]0.530901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6432&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6432&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	-0.053565	-0.3711	0.643907
1	0.031659	0.2193	0.413657
2	-0.074529	-0.5164	0.69601
3	-0.053541	-0.3709	0.643843
4	-0.034678	-0.2403	0.594423
5	-0.220429	-1.5272	0.93336
6	0.016477	0.1142	0.454796
7	0.014917	0.1033	0.45906
8	0.152357	1.0556	0.148227
9	-0.045014	-0.3119	0.621755
10	0.027279	0.189	0.425448
11	-0.395821	-2.7423	0.995726
12	0.009003	0.0624	0.475262
13	0.002511	0.0174	0.493097
14	0.055729	0.3861	0.350563
15	-0.037782	-0.2618	0.602688
16	-0.01125	-0.0779	0.530901

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 ;

Parameters (R input):

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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code