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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 04 Dec 2007 05:26:06 -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/Dec/04/t1196770552hthpyzb104b8anr.htm/, Retrieved Thu, 02 May 2024 06:49:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2370, Retrieved Thu, 02 May 2024 06:49:49 +0000

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No (this computation is public)

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Estimated Impact

223

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

-       [(Partial) Autocorrelation Function] [] [2007-12-04 12:26:06] [67794d83edd3193bd9ea9816803ddb96] [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=2370&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=2370&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2370&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	7.746	0
1	0.457558	3.5442	0.000385
2	0.208774	1.6172	0.055546
3	0.20702	1.6036	0.05703
4	0.20254	1.5689	0.060969
5	0.177193	1.3725	0.087503
6	0.044034	0.3411	0.367115
7	-0.127976	-0.9913	0.83724
8	-0.109005	-0.8444	0.799087
9	-0.105975	-0.8209	0.792517
10	-0.08336	-0.6457	0.739533
11	-0.185818	-1.4393	0.922375
12	-0.392687	-3.0417	0.998257
13	-0.19789	-1.5329	0.934716
14	-0.00309	-0.0239	0.509507
15	-0.009701	-0.0751	0.529823
16	-0.158713	-1.2294	0.888136

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.457558 & 3.5442 & 0.000385 \tabularnewline
2 & 0.208774 & 1.6172 & 0.055546 \tabularnewline
3 & 0.20702 & 1.6036 & 0.05703 \tabularnewline
4 & 0.20254 & 1.5689 & 0.060969 \tabularnewline
5 & 0.177193 & 1.3725 & 0.087503 \tabularnewline
6 & 0.044034 & 0.3411 & 0.367115 \tabularnewline
7 & -0.127976 & -0.9913 & 0.83724 \tabularnewline
8 & -0.109005 & -0.8444 & 0.799087 \tabularnewline
9 & -0.105975 & -0.8209 & 0.792517 \tabularnewline
10 & -0.08336 & -0.6457 & 0.739533 \tabularnewline
11 & -0.185818 & -1.4393 & 0.922375 \tabularnewline
12 & -0.392687 & -3.0417 & 0.998257 \tabularnewline
13 & -0.19789 & -1.5329 & 0.934716 \tabularnewline
14 & -0.00309 & -0.0239 & 0.509507 \tabularnewline
15 & -0.009701 & -0.0751 & 0.529823 \tabularnewline
16 & -0.158713 & -1.2294 & 0.888136 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2370&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.457558[/C][C]3.5442[/C][C]0.000385[/C][/ROW]
[ROW][C]2[/C][C]0.208774[/C][C]1.6172[/C][C]0.055546[/C][/ROW]
[ROW][C]3[/C][C]0.20702[/C][C]1.6036[/C][C]0.05703[/C][/ROW]
[ROW][C]4[/C][C]0.20254[/C][C]1.5689[/C][C]0.060969[/C][/ROW]
[ROW][C]5[/C][C]0.177193[/C][C]1.3725[/C][C]0.087503[/C][/ROW]
[ROW][C]6[/C][C]0.044034[/C][C]0.3411[/C][C]0.367115[/C][/ROW]
[ROW][C]7[/C][C]-0.127976[/C][C]-0.9913[/C][C]0.83724[/C][/ROW]
[ROW][C]8[/C][C]-0.109005[/C][C]-0.8444[/C][C]0.799087[/C][/ROW]
[ROW][C]9[/C][C]-0.105975[/C][C]-0.8209[/C][C]0.792517[/C][/ROW]
[ROW][C]10[/C][C]-0.08336[/C][C]-0.6457[/C][C]0.739533[/C][/ROW]
[ROW][C]11[/C][C]-0.185818[/C][C]-1.4393[/C][C]0.922375[/C][/ROW]
[ROW][C]12[/C][C]-0.392687[/C][C]-3.0417[/C][C]0.998257[/C][/ROW]
[ROW][C]13[/C][C]-0.19789[/C][C]-1.5329[/C][C]0.934716[/C][/ROW]
[ROW][C]14[/C][C]-0.00309[/C][C]-0.0239[/C][C]0.509507[/C][/ROW]
[ROW][C]15[/C][C]-0.009701[/C][C]-0.0751[/C][C]0.529823[/C][/ROW]
[ROW][C]16[/C][C]-0.158713[/C][C]-1.2294[/C][C]0.888136[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2370&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2370&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	7.746	0
1	0.457558	3.5442	0.000385
2	0.208774	1.6172	0.055546
3	0.20702	1.6036	0.05703
4	0.20254	1.5689	0.060969
5	0.177193	1.3725	0.087503
6	0.044034	0.3411	0.367115
7	-0.127976	-0.9913	0.83724
8	-0.109005	-0.8444	0.799087
9	-0.105975	-0.8209	0.792517
10	-0.08336	-0.6457	0.739533
11	-0.185818	-1.4393	0.922375
12	-0.392687	-3.0417	0.998257
13	-0.19789	-1.5329	0.934716
14	-0.00309	-0.0239	0.509507
15	-0.009701	-0.0751	0.529823
16	-0.158713	-1.2294	0.888136

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.457558	3.5442	0.000385
1	-0.000741	-0.0057	0.502279
2	0.141356	1.0949	0.138959
3	0.073194	0.567	0.286429
4	0.055902	0.433	0.333279
5	-0.103755	-0.8037	0.787623
6	-0.189522	-1.468	0.926341
7	-0.022428	-0.1737	0.568668
8	-0.06774	-0.5247	0.699142
9	0.029535	0.2288	0.409909
10	-0.129754	-1.0051	0.840549
11	-0.280057	-2.1693	0.982984
12	0.143603	1.1123	0.135213
13	0.126874	0.9828	0.164835
14	0.045702	0.354	0.362288
15	-0.172239	-1.3342	0.906403
16	0.279258	2.1631	0.017263

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.457558 & 3.5442 & 0.000385 \tabularnewline
1 & -0.000741 & -0.0057 & 0.502279 \tabularnewline
2 & 0.141356 & 1.0949 & 0.138959 \tabularnewline
3 & 0.073194 & 0.567 & 0.286429 \tabularnewline
4 & 0.055902 & 0.433 & 0.333279 \tabularnewline
5 & -0.103755 & -0.8037 & 0.787623 \tabularnewline
6 & -0.189522 & -1.468 & 0.926341 \tabularnewline
7 & -0.022428 & -0.1737 & 0.568668 \tabularnewline
8 & -0.06774 & -0.5247 & 0.699142 \tabularnewline
9 & 0.029535 & 0.2288 & 0.409909 \tabularnewline
10 & -0.129754 & -1.0051 & 0.840549 \tabularnewline
11 & -0.280057 & -2.1693 & 0.982984 \tabularnewline
12 & 0.143603 & 1.1123 & 0.135213 \tabularnewline
13 & 0.126874 & 0.9828 & 0.164835 \tabularnewline
14 & 0.045702 & 0.354 & 0.362288 \tabularnewline
15 & -0.172239 & -1.3342 & 0.906403 \tabularnewline
16 & 0.279258 & 2.1631 & 0.017263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2370&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]0.457558[/C][C]3.5442[/C][C]0.000385[/C][/ROW]
[ROW][C]1[/C][C]-0.000741[/C][C]-0.0057[/C][C]0.502279[/C][/ROW]
[ROW][C]2[/C][C]0.141356[/C][C]1.0949[/C][C]0.138959[/C][/ROW]
[ROW][C]3[/C][C]0.073194[/C][C]0.567[/C][C]0.286429[/C][/ROW]
[ROW][C]4[/C][C]0.055902[/C][C]0.433[/C][C]0.333279[/C][/ROW]
[ROW][C]5[/C][C]-0.103755[/C][C]-0.8037[/C][C]0.787623[/C][/ROW]
[ROW][C]6[/C][C]-0.189522[/C][C]-1.468[/C][C]0.926341[/C][/ROW]
[ROW][C]7[/C][C]-0.022428[/C][C]-0.1737[/C][C]0.568668[/C][/ROW]
[ROW][C]8[/C][C]-0.06774[/C][C]-0.5247[/C][C]0.699142[/C][/ROW]
[ROW][C]9[/C][C]0.029535[/C][C]0.2288[/C][C]0.409909[/C][/ROW]
[ROW][C]10[/C][C]-0.129754[/C][C]-1.0051[/C][C]0.840549[/C][/ROW]
[ROW][C]11[/C][C]-0.280057[/C][C]-2.1693[/C][C]0.982984[/C][/ROW]
[ROW][C]12[/C][C]0.143603[/C][C]1.1123[/C][C]0.135213[/C][/ROW]
[ROW][C]13[/C][C]0.126874[/C][C]0.9828[/C][C]0.164835[/C][/ROW]
[ROW][C]14[/C][C]0.045702[/C][C]0.354[/C][C]0.362288[/C][/ROW]
[ROW][C]15[/C][C]-0.172239[/C][C]-1.3342[/C][C]0.906403[/C][/ROW]
[ROW][C]16[/C][C]0.279258[/C][C]2.1631[/C][C]0.017263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2370&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2370&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	0.457558	3.5442	0.000385
1	-0.000741	-0.0057	0.502279
2	0.141356	1.0949	0.138959
3	0.073194	0.567	0.286429
4	0.055902	0.433	0.333279
5	-0.103755	-0.8037	0.787623
6	-0.189522	-1.468	0.926341
7	-0.022428	-0.1737	0.568668
8	-0.06774	-0.5247	0.699142
9	0.029535	0.2288	0.409909
10	-0.129754	-1.0051	0.840549
11	-0.280057	-2.1693	0.982984
12	0.143603	1.1123	0.135213
13	0.126874	0.9828	0.164835
14	0.045702	0.354	0.362288
15	-0.172239	-1.3342	0.906403
16	0.279258	2.1631	0.017263

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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Input Parameters & R Code