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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 24 May 2013 09:48:24 -0400

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/2013/May/24/t136940356053q3kn2ei52mb5j.htm/, Retrieved Wed, 01 May 2024 00:24:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210419, Retrieved Wed, 01 May 2024 00:24:03 +0000

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IsPrivate?

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User-defined keywords

Estimated Impact

123

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

-     [Harrell-Davis Quantiles] [Percentiles gem c...] [2013-02-26 15:25:06] [24d90246389fe4497d617beae262e001]
- RMP     [(Partial) Autocorrelation Function] [autocorrelation g...] [2013-05-24 13:48:24] [47b39896cec6a073b4964677b3e89d38] [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	3 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210419&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210419&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210419&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	3 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.213677	1.8005	0.038016
2	-0.057547	-0.4849	0.314619
3	-0.236733	-1.9947	0.024955
4	-0.369792	-3.1159	0.001323
5	-0.022751	-0.1917	0.424262
6	-0.014721	-0.124	0.450817
7	-0.033303	-0.2806	0.389912
8	-0.272922	-2.2997	0.012205
9	-0.225716	-1.9019	0.030619
10	-0.023087	-0.1945	0.423157
11	0.219934	1.8532	0.034005
12	0.672621	5.6676	0
13	0.270403	2.2785	0.012855
14	-0.0514	-0.4331	0.333126
15	-0.233607	-1.9684	0.026463
16	-0.273188	-2.3019	0.012138
17	-0.030272	-0.2551	0.399699
18	-0.014859	-0.1252	0.450358

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.213677 & 1.8005 & 0.038016 \tabularnewline
2 & -0.057547 & -0.4849 & 0.314619 \tabularnewline
3 & -0.236733 & -1.9947 & 0.024955 \tabularnewline
4 & -0.369792 & -3.1159 & 0.001323 \tabularnewline
5 & -0.022751 & -0.1917 & 0.424262 \tabularnewline
6 & -0.014721 & -0.124 & 0.450817 \tabularnewline
7 & -0.033303 & -0.2806 & 0.389912 \tabularnewline
8 & -0.272922 & -2.2997 & 0.012205 \tabularnewline
9 & -0.225716 & -1.9019 & 0.030619 \tabularnewline
10 & -0.023087 & -0.1945 & 0.423157 \tabularnewline
11 & 0.219934 & 1.8532 & 0.034005 \tabularnewline
12 & 0.672621 & 5.6676 & 0 \tabularnewline
13 & 0.270403 & 2.2785 & 0.012855 \tabularnewline
14 & -0.0514 & -0.4331 & 0.333126 \tabularnewline
15 & -0.233607 & -1.9684 & 0.026463 \tabularnewline
16 & -0.273188 & -2.3019 & 0.012138 \tabularnewline
17 & -0.030272 & -0.2551 & 0.399699 \tabularnewline
18 & -0.014859 & -0.1252 & 0.450358 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210419&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]0.213677[/C][C]1.8005[/C][C]0.038016[/C][/ROW]
[ROW][C]2[/C][C]-0.057547[/C][C]-0.4849[/C][C]0.314619[/C][/ROW]
[ROW][C]3[/C][C]-0.236733[/C][C]-1.9947[/C][C]0.024955[/C][/ROW]
[ROW][C]4[/C][C]-0.369792[/C][C]-3.1159[/C][C]0.001323[/C][/ROW]
[ROW][C]5[/C][C]-0.022751[/C][C]-0.1917[/C][C]0.424262[/C][/ROW]
[ROW][C]6[/C][C]-0.014721[/C][C]-0.124[/C][C]0.450817[/C][/ROW]
[ROW][C]7[/C][C]-0.033303[/C][C]-0.2806[/C][C]0.389912[/C][/ROW]
[ROW][C]8[/C][C]-0.272922[/C][C]-2.2997[/C][C]0.012205[/C][/ROW]
[ROW][C]9[/C][C]-0.225716[/C][C]-1.9019[/C][C]0.030619[/C][/ROW]
[ROW][C]10[/C][C]-0.023087[/C][C]-0.1945[/C][C]0.423157[/C][/ROW]
[ROW][C]11[/C][C]0.219934[/C][C]1.8532[/C][C]0.034005[/C][/ROW]
[ROW][C]12[/C][C]0.672621[/C][C]5.6676[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.270403[/C][C]2.2785[/C][C]0.012855[/C][/ROW]
[ROW][C]14[/C][C]-0.0514[/C][C]-0.4331[/C][C]0.333126[/C][/ROW]
[ROW][C]15[/C][C]-0.233607[/C][C]-1.9684[/C][C]0.026463[/C][/ROW]
[ROW][C]16[/C][C]-0.273188[/C][C]-2.3019[/C][C]0.012138[/C][/ROW]
[ROW][C]17[/C][C]-0.030272[/C][C]-0.2551[/C][C]0.399699[/C][/ROW]
[ROW][C]18[/C][C]-0.014859[/C][C]-0.1252[/C][C]0.450358[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210419&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210419&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	0.213677	1.8005	0.038016
2	-0.057547	-0.4849	0.314619
3	-0.236733	-1.9947	0.024955
4	-0.369792	-3.1159	0.001323
5	-0.022751	-0.1917	0.424262
6	-0.014721	-0.124	0.450817
7	-0.033303	-0.2806	0.389912
8	-0.272922	-2.2997	0.012205
9	-0.225716	-1.9019	0.030619
10	-0.023087	-0.1945	0.423157
11	0.219934	1.8532	0.034005
12	0.672621	5.6676	0
13	0.270403	2.2785	0.012855
14	-0.0514	-0.4331	0.333126
15	-0.233607	-1.9684	0.026463
16	-0.273188	-2.3019	0.012138
17	-0.030272	-0.2551	0.399699
18	-0.014859	-0.1252	0.450358

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.213677	1.8005	0.038016
2	-0.108143	-0.9112	0.18263
3	-0.212047	-1.7867	0.039124
4	-0.307725	-2.5929	0.005774
5	0.087807	0.7399	0.230908
6	-0.128845	-1.0857	0.14065
7	-0.169854	-1.4312	0.078378
8	-0.456002	-3.8423	0.000131
9	-0.265236	-2.2349	0.014285
10	-0.275073	-2.3178	0.011673
11	-0.148133	-1.2482	0.10803
12	0.382048	3.2192	0.00097
13	0.069983	0.5897	0.278636
14	-0.042395	-0.3572	0.360992
15	-0.054591	-0.46	0.323465
16	0.113462	0.956	0.171146
17	0.045077	0.3798	0.352606
18	-0.032771	-0.2761	0.391624

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.213677 & 1.8005 & 0.038016 \tabularnewline
2 & -0.108143 & -0.9112 & 0.18263 \tabularnewline
3 & -0.212047 & -1.7867 & 0.039124 \tabularnewline
4 & -0.307725 & -2.5929 & 0.005774 \tabularnewline
5 & 0.087807 & 0.7399 & 0.230908 \tabularnewline
6 & -0.128845 & -1.0857 & 0.14065 \tabularnewline
7 & -0.169854 & -1.4312 & 0.078378 \tabularnewline
8 & -0.456002 & -3.8423 & 0.000131 \tabularnewline
9 & -0.265236 & -2.2349 & 0.014285 \tabularnewline
10 & -0.275073 & -2.3178 & 0.011673 \tabularnewline
11 & -0.148133 & -1.2482 & 0.10803 \tabularnewline
12 & 0.382048 & 3.2192 & 0.00097 \tabularnewline
13 & 0.069983 & 0.5897 & 0.278636 \tabularnewline
14 & -0.042395 & -0.3572 & 0.360992 \tabularnewline
15 & -0.054591 & -0.46 & 0.323465 \tabularnewline
16 & 0.113462 & 0.956 & 0.171146 \tabularnewline
17 & 0.045077 & 0.3798 & 0.352606 \tabularnewline
18 & -0.032771 & -0.2761 & 0.391624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210419&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]0.213677[/C][C]1.8005[/C][C]0.038016[/C][/ROW]
[ROW][C]2[/C][C]-0.108143[/C][C]-0.9112[/C][C]0.18263[/C][/ROW]
[ROW][C]3[/C][C]-0.212047[/C][C]-1.7867[/C][C]0.039124[/C][/ROW]
[ROW][C]4[/C][C]-0.307725[/C][C]-2.5929[/C][C]0.005774[/C][/ROW]
[ROW][C]5[/C][C]0.087807[/C][C]0.7399[/C][C]0.230908[/C][/ROW]
[ROW][C]6[/C][C]-0.128845[/C][C]-1.0857[/C][C]0.14065[/C][/ROW]
[ROW][C]7[/C][C]-0.169854[/C][C]-1.4312[/C][C]0.078378[/C][/ROW]
[ROW][C]8[/C][C]-0.456002[/C][C]-3.8423[/C][C]0.000131[/C][/ROW]
[ROW][C]9[/C][C]-0.265236[/C][C]-2.2349[/C][C]0.014285[/C][/ROW]
[ROW][C]10[/C][C]-0.275073[/C][C]-2.3178[/C][C]0.011673[/C][/ROW]
[ROW][C]11[/C][C]-0.148133[/C][C]-1.2482[/C][C]0.10803[/C][/ROW]
[ROW][C]12[/C][C]0.382048[/C][C]3.2192[/C][C]0.00097[/C][/ROW]
[ROW][C]13[/C][C]0.069983[/C][C]0.5897[/C][C]0.278636[/C][/ROW]
[ROW][C]14[/C][C]-0.042395[/C][C]-0.3572[/C][C]0.360992[/C][/ROW]
[ROW][C]15[/C][C]-0.054591[/C][C]-0.46[/C][C]0.323465[/C][/ROW]
[ROW][C]16[/C][C]0.113462[/C][C]0.956[/C][C]0.171146[/C][/ROW]
[ROW][C]17[/C][C]0.045077[/C][C]0.3798[/C][C]0.352606[/C][/ROW]
[ROW][C]18[/C][C]-0.032771[/C][C]-0.2761[/C][C]0.391624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210419&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210419&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	0.213677	1.8005	0.038016
2	-0.108143	-0.9112	0.18263
3	-0.212047	-1.7867	0.039124
4	-0.307725	-2.5929	0.005774
5	0.087807	0.7399	0.230908
6	-0.128845	-1.0857	0.14065
7	-0.169854	-1.4312	0.078378
8	-0.456002	-3.8423	0.000131
9	-0.265236	-2.2349	0.014285
10	-0.275073	-2.3178	0.011673
11	-0.148133	-1.2482	0.10803
12	0.382048	3.2192	0.00097
13	0.069983	0.5897	0.278636
14	-0.042395	-0.3572	0.360992
15	-0.054591	-0.46	0.323465
16	0.113462	0.956	0.171146
17	0.045077	0.3798	0.352606
18	-0.032771	-0.2761	0.391624

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code