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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 16 Dec 2009 03:44:20 -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/2009/Dec/16/t1260960391ayrpnatvt5jwc1i.htm/, Retrieved Tue, 30 Apr 2024 08:31:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68232, Retrieved Tue, 30 Apr 2024 08:31:43 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W21

Estimated Impact

162

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

-       [(Partial) Autocorrelation Function] [KDGP2W21] [2009-12-16 10:44:20] [d00efe1a3b3f6588aa0a3288268f2e7e] [Current]
-   P     [(Partial) Autocorrelation Function] [KDGP2W21] [2010-01-26 19:04:20] [74be16979710d4c4e7c6647856088456] 

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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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68232&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]2 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=68232&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68232&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.404297	-3.4543	0.000461
2	0.029681	0.2536	0.400262
3	-0.043191	-0.369	0.356588
4	0.029167	0.2492	0.401951
5	0.045375	0.3877	0.34969
6	-0.095516	-0.8161	0.208552
7	0.00971	0.083	0.467053
8	0.052401	0.4477	0.327842
9	-0.098494	-0.8415	0.201399
10	0.052083	0.445	0.328819
11	-0.123162	-1.0523	0.148067
12	0.211897	1.8105	0.03717
13	-0.115834	-0.9897	0.162798
14	-0.015835	-0.1353	0.446375
15	-0.034328	-0.2933	0.385062
16	0.060864	0.52	0.302312
17	-0.006751	-0.0577	0.477081
18	-0.05679	-0.4852	0.31449

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.404297 & -3.4543 & 0.000461 \tabularnewline
2 & 0.029681 & 0.2536 & 0.400262 \tabularnewline
3 & -0.043191 & -0.369 & 0.356588 \tabularnewline
4 & 0.029167 & 0.2492 & 0.401951 \tabularnewline
5 & 0.045375 & 0.3877 & 0.34969 \tabularnewline
6 & -0.095516 & -0.8161 & 0.208552 \tabularnewline
7 & 0.00971 & 0.083 & 0.467053 \tabularnewline
8 & 0.052401 & 0.4477 & 0.327842 \tabularnewline
9 & -0.098494 & -0.8415 & 0.201399 \tabularnewline
10 & 0.052083 & 0.445 & 0.328819 \tabularnewline
11 & -0.123162 & -1.0523 & 0.148067 \tabularnewline
12 & 0.211897 & 1.8105 & 0.03717 \tabularnewline
13 & -0.115834 & -0.9897 & 0.162798 \tabularnewline
14 & -0.015835 & -0.1353 & 0.446375 \tabularnewline
15 & -0.034328 & -0.2933 & 0.385062 \tabularnewline
16 & 0.060864 & 0.52 & 0.302312 \tabularnewline
17 & -0.006751 & -0.0577 & 0.477081 \tabularnewline
18 & -0.05679 & -0.4852 & 0.31449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68232&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]-0.404297[/C][C]-3.4543[/C][C]0.000461[/C][/ROW]
[ROW][C]2[/C][C]0.029681[/C][C]0.2536[/C][C]0.400262[/C][/ROW]
[ROW][C]3[/C][C]-0.043191[/C][C]-0.369[/C][C]0.356588[/C][/ROW]
[ROW][C]4[/C][C]0.029167[/C][C]0.2492[/C][C]0.401951[/C][/ROW]
[ROW][C]5[/C][C]0.045375[/C][C]0.3877[/C][C]0.34969[/C][/ROW]
[ROW][C]6[/C][C]-0.095516[/C][C]-0.8161[/C][C]0.208552[/C][/ROW]
[ROW][C]7[/C][C]0.00971[/C][C]0.083[/C][C]0.467053[/C][/ROW]
[ROW][C]8[/C][C]0.052401[/C][C]0.4477[/C][C]0.327842[/C][/ROW]
[ROW][C]9[/C][C]-0.098494[/C][C]-0.8415[/C][C]0.201399[/C][/ROW]
[ROW][C]10[/C][C]0.052083[/C][C]0.445[/C][C]0.328819[/C][/ROW]
[ROW][C]11[/C][C]-0.123162[/C][C]-1.0523[/C][C]0.148067[/C][/ROW]
[ROW][C]12[/C][C]0.211897[/C][C]1.8105[/C][C]0.03717[/C][/ROW]
[ROW][C]13[/C][C]-0.115834[/C][C]-0.9897[/C][C]0.162798[/C][/ROW]
[ROW][C]14[/C][C]-0.015835[/C][C]-0.1353[/C][C]0.446375[/C][/ROW]
[ROW][C]15[/C][C]-0.034328[/C][C]-0.2933[/C][C]0.385062[/C][/ROW]
[ROW][C]16[/C][C]0.060864[/C][C]0.52[/C][C]0.302312[/C][/ROW]
[ROW][C]17[/C][C]-0.006751[/C][C]-0.0577[/C][C]0.477081[/C][/ROW]
[ROW][C]18[/C][C]-0.05679[/C][C]-0.4852[/C][C]0.31449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68232&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68232&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	-0.404297	-3.4543	0.000461
2	0.029681	0.2536	0.400262
3	-0.043191	-0.369	0.356588
4	0.029167	0.2492	0.401951
5	0.045375	0.3877	0.34969
6	-0.095516	-0.8161	0.208552
7	0.00971	0.083	0.467053
8	0.052401	0.4477	0.327842
9	-0.098494	-0.8415	0.201399
10	0.052083	0.445	0.328819
11	-0.123162	-1.0523	0.148067
12	0.211897	1.8105	0.03717
13	-0.115834	-0.9897	0.162798
14	-0.015835	-0.1353	0.446375
15	-0.034328	-0.2933	0.385062
16	0.060864	0.52	0.302312
17	-0.006751	-0.0577	0.477081
18	-0.05679	-0.4852	0.31449

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.404297	-3.4543	0.000461
2	-0.159915	-1.3663	0.088017
3	-0.115225	-0.9845	0.164065
4	-0.039932	-0.3412	0.366975
5	0.04728	0.404	0.343712
6	-0.065806	-0.5623	0.287834
7	-0.06452	-0.5513	0.291568
8	0.025936	0.2216	0.412624
9	-0.093109	-0.7955	0.214444
10	-0.030299	-0.2589	0.398229
11	-0.145393	-1.2422	0.109062
12	0.110053	0.9403	0.175084
13	0.004245	0.0363	0.485582
14	-0.045388	-0.3878	0.349649
15	-0.088459	-0.7558	0.226102
16	-0.004197	-0.0359	0.485746
17	-0.015067	-0.1287	0.44896
18	-0.058411	-0.4991	0.309618

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.404297 & -3.4543 & 0.000461 \tabularnewline
2 & -0.159915 & -1.3663 & 0.088017 \tabularnewline
3 & -0.115225 & -0.9845 & 0.164065 \tabularnewline
4 & -0.039932 & -0.3412 & 0.366975 \tabularnewline
5 & 0.04728 & 0.404 & 0.343712 \tabularnewline
6 & -0.065806 & -0.5623 & 0.287834 \tabularnewline
7 & -0.06452 & -0.5513 & 0.291568 \tabularnewline
8 & 0.025936 & 0.2216 & 0.412624 \tabularnewline
9 & -0.093109 & -0.7955 & 0.214444 \tabularnewline
10 & -0.030299 & -0.2589 & 0.398229 \tabularnewline
11 & -0.145393 & -1.2422 & 0.109062 \tabularnewline
12 & 0.110053 & 0.9403 & 0.175084 \tabularnewline
13 & 0.004245 & 0.0363 & 0.485582 \tabularnewline
14 & -0.045388 & -0.3878 & 0.349649 \tabularnewline
15 & -0.088459 & -0.7558 & 0.226102 \tabularnewline
16 & -0.004197 & -0.0359 & 0.485746 \tabularnewline
17 & -0.015067 & -0.1287 & 0.44896 \tabularnewline
18 & -0.058411 & -0.4991 & 0.309618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68232&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]-0.404297[/C][C]-3.4543[/C][C]0.000461[/C][/ROW]
[ROW][C]2[/C][C]-0.159915[/C][C]-1.3663[/C][C]0.088017[/C][/ROW]
[ROW][C]3[/C][C]-0.115225[/C][C]-0.9845[/C][C]0.164065[/C][/ROW]
[ROW][C]4[/C][C]-0.039932[/C][C]-0.3412[/C][C]0.366975[/C][/ROW]
[ROW][C]5[/C][C]0.04728[/C][C]0.404[/C][C]0.343712[/C][/ROW]
[ROW][C]6[/C][C]-0.065806[/C][C]-0.5623[/C][C]0.287834[/C][/ROW]
[ROW][C]7[/C][C]-0.06452[/C][C]-0.5513[/C][C]0.291568[/C][/ROW]
[ROW][C]8[/C][C]0.025936[/C][C]0.2216[/C][C]0.412624[/C][/ROW]
[ROW][C]9[/C][C]-0.093109[/C][C]-0.7955[/C][C]0.214444[/C][/ROW]
[ROW][C]10[/C][C]-0.030299[/C][C]-0.2589[/C][C]0.398229[/C][/ROW]
[ROW][C]11[/C][C]-0.145393[/C][C]-1.2422[/C][C]0.109062[/C][/ROW]
[ROW][C]12[/C][C]0.110053[/C][C]0.9403[/C][C]0.175084[/C][/ROW]
[ROW][C]13[/C][C]0.004245[/C][C]0.0363[/C][C]0.485582[/C][/ROW]
[ROW][C]14[/C][C]-0.045388[/C][C]-0.3878[/C][C]0.349649[/C][/ROW]
[ROW][C]15[/C][C]-0.088459[/C][C]-0.7558[/C][C]0.226102[/C][/ROW]
[ROW][C]16[/C][C]-0.004197[/C][C]-0.0359[/C][C]0.485746[/C][/ROW]
[ROW][C]17[/C][C]-0.015067[/C][C]-0.1287[/C][C]0.44896[/C][/ROW]
[ROW][C]18[/C][C]-0.058411[/C][C]-0.4991[/C][C]0.309618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68232&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68232&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	-0.404297	-3.4543	0.000461
2	-0.159915	-1.3663	0.088017
3	-0.115225	-0.9845	0.164065
4	-0.039932	-0.3412	0.366975
5	0.04728	0.404	0.343712
6	-0.065806	-0.5623	0.287834
7	-0.06452	-0.5513	0.291568
8	0.025936	0.2216	0.412624
9	-0.093109	-0.7955	0.214444
10	-0.030299	-0.2589	0.398229
11	-0.145393	-1.2422	0.109062
12	0.110053	0.9403	0.175084
13	0.004245	0.0363	0.485582
14	-0.045388	-0.3878	0.349649
15	-0.088459	-0.7558	0.226102
16	-0.004197	-0.0359	0.485746
17	-0.015067	-0.1287	0.44896
18	-0.058411	-0.4991	0.309618

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 ; 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 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code