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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 24 Dec 2008 08:30:25 -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/2008/Dec/24/t12301326729y8p2srdqnrkel4.htm/, Retrieved Sat, 25 May 2024 03:43:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36614, Retrieved Sat, 25 May 2024 03:43:03 +0000

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No (this computation is public)

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Estimated Impact

151

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

-       [(Partial) Autocorrelation Function] [] [2008-12-24 15:30:25] [d41d8cd98f00b204e9800998ecf8427e] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36614&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36614&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.056864	-0.3898	0.349208
2	0.108431	0.7434	0.230481
3	0.151307	1.0373	0.15245
4	0.120968	0.8293	0.205559
5	0.022829	0.1565	0.438153
6	0.05079	0.3482	0.364623
7	0.025625	0.1757	0.430653
8	0.092491	0.6341	0.264549
9	-0.031185	-0.2138	0.415817
10	-0.086338	-0.5919	0.278376
11	0.281755	1.9316	0.029724
12	-0.168471	-1.155	0.126969
13	-0.09393	-0.644	0.261368
14	0.037365	0.2562	0.399473
15	-0.064856	-0.4446	0.329314
16	-0.118855	-0.8148	0.209639
17	-0.028555	-0.1958	0.422821

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.056864 & -0.3898 & 0.349208 \tabularnewline
2 & 0.108431 & 0.7434 & 0.230481 \tabularnewline
3 & 0.151307 & 1.0373 & 0.15245 \tabularnewline
4 & 0.120968 & 0.8293 & 0.205559 \tabularnewline
5 & 0.022829 & 0.1565 & 0.438153 \tabularnewline
6 & 0.05079 & 0.3482 & 0.364623 \tabularnewline
7 & 0.025625 & 0.1757 & 0.430653 \tabularnewline
8 & 0.092491 & 0.6341 & 0.264549 \tabularnewline
9 & -0.031185 & -0.2138 & 0.415817 \tabularnewline
10 & -0.086338 & -0.5919 & 0.278376 \tabularnewline
11 & 0.281755 & 1.9316 & 0.029724 \tabularnewline
12 & -0.168471 & -1.155 & 0.126969 \tabularnewline
13 & -0.09393 & -0.644 & 0.261368 \tabularnewline
14 & 0.037365 & 0.2562 & 0.399473 \tabularnewline
15 & -0.064856 & -0.4446 & 0.329314 \tabularnewline
16 & -0.118855 & -0.8148 & 0.209639 \tabularnewline
17 & -0.028555 & -0.1958 & 0.422821 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36614&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]-0.056864[/C][C]-0.3898[/C][C]0.349208[/C][/ROW]
[ROW][C]2[/C][C]0.108431[/C][C]0.7434[/C][C]0.230481[/C][/ROW]
[ROW][C]3[/C][C]0.151307[/C][C]1.0373[/C][C]0.15245[/C][/ROW]
[ROW][C]4[/C][C]0.120968[/C][C]0.8293[/C][C]0.205559[/C][/ROW]
[ROW][C]5[/C][C]0.022829[/C][C]0.1565[/C][C]0.438153[/C][/ROW]
[ROW][C]6[/C][C]0.05079[/C][C]0.3482[/C][C]0.364623[/C][/ROW]
[ROW][C]7[/C][C]0.025625[/C][C]0.1757[/C][C]0.430653[/C][/ROW]
[ROW][C]8[/C][C]0.092491[/C][C]0.6341[/C][C]0.264549[/C][/ROW]
[ROW][C]9[/C][C]-0.031185[/C][C]-0.2138[/C][C]0.415817[/C][/ROW]
[ROW][C]10[/C][C]-0.086338[/C][C]-0.5919[/C][C]0.278376[/C][/ROW]
[ROW][C]11[/C][C]0.281755[/C][C]1.9316[/C][C]0.029724[/C][/ROW]
[ROW][C]12[/C][C]-0.168471[/C][C]-1.155[/C][C]0.126969[/C][/ROW]
[ROW][C]13[/C][C]-0.09393[/C][C]-0.644[/C][C]0.261368[/C][/ROW]
[ROW][C]14[/C][C]0.037365[/C][C]0.2562[/C][C]0.399473[/C][/ROW]
[ROW][C]15[/C][C]-0.064856[/C][C]-0.4446[/C][C]0.329314[/C][/ROW]
[ROW][C]16[/C][C]-0.118855[/C][C]-0.8148[/C][C]0.209639[/C][/ROW]
[ROW][C]17[/C][C]-0.028555[/C][C]-0.1958[/C][C]0.422821[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36614&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	-0.056864	-0.3898	0.349208
2	0.108431	0.7434	0.230481
3	0.151307	1.0373	0.15245
4	0.120968	0.8293	0.205559
5	0.022829	0.1565	0.438153
6	0.05079	0.3482	0.364623
7	0.025625	0.1757	0.430653
8	0.092491	0.6341	0.264549
9	-0.031185	-0.2138	0.415817
10	-0.086338	-0.5919	0.278376
11	0.281755	1.9316	0.029724
12	-0.168471	-1.155	0.126969
13	-0.09393	-0.644	0.261368
14	0.037365	0.2562	0.399473
15	-0.064856	-0.4446	0.329314
16	-0.118855	-0.8148	0.209639
17	-0.028555	-0.1958	0.422821

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.056864	-0.3898	0.349208
2	0.105538	0.7235	0.236468
3	0.165192	1.1325	0.131585
4	0.13386	0.9177	0.18173
5	0.00801	0.0549	0.478221
6	0.000757	0.0052	0.49794
7	-0.014987	-0.1027	0.459302
8	0.071255	0.4885	0.313733
9	-0.032705	-0.2242	0.411782
10	-0.12535	-0.8594	0.197253
11	0.261503	1.7928	0.039723
12	-0.135284	-0.9275	0.179213
13	-0.151025	-1.0354	0.152896
14	0.00191	0.0131	0.494803
15	-0.064394	-0.4415	0.330452
16	-0.07876	-0.54	0.29589
17	-0.006102	-0.0418	0.483403

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.056864 & -0.3898 & 0.349208 \tabularnewline
2 & 0.105538 & 0.7235 & 0.236468 \tabularnewline
3 & 0.165192 & 1.1325 & 0.131585 \tabularnewline
4 & 0.13386 & 0.9177 & 0.18173 \tabularnewline
5 & 0.00801 & 0.0549 & 0.478221 \tabularnewline
6 & 0.000757 & 0.0052 & 0.49794 \tabularnewline
7 & -0.014987 & -0.1027 & 0.459302 \tabularnewline
8 & 0.071255 & 0.4885 & 0.313733 \tabularnewline
9 & -0.032705 & -0.2242 & 0.411782 \tabularnewline
10 & -0.12535 & -0.8594 & 0.197253 \tabularnewline
11 & 0.261503 & 1.7928 & 0.039723 \tabularnewline
12 & -0.135284 & -0.9275 & 0.179213 \tabularnewline
13 & -0.151025 & -1.0354 & 0.152896 \tabularnewline
14 & 0.00191 & 0.0131 & 0.494803 \tabularnewline
15 & -0.064394 & -0.4415 & 0.330452 \tabularnewline
16 & -0.07876 & -0.54 & 0.29589 \tabularnewline
17 & -0.006102 & -0.0418 & 0.483403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36614&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]-0.056864[/C][C]-0.3898[/C][C]0.349208[/C][/ROW]
[ROW][C]2[/C][C]0.105538[/C][C]0.7235[/C][C]0.236468[/C][/ROW]
[ROW][C]3[/C][C]0.165192[/C][C]1.1325[/C][C]0.131585[/C][/ROW]
[ROW][C]4[/C][C]0.13386[/C][C]0.9177[/C][C]0.18173[/C][/ROW]
[ROW][C]5[/C][C]0.00801[/C][C]0.0549[/C][C]0.478221[/C][/ROW]
[ROW][C]6[/C][C]0.000757[/C][C]0.0052[/C][C]0.49794[/C][/ROW]
[ROW][C]7[/C][C]-0.014987[/C][C]-0.1027[/C][C]0.459302[/C][/ROW]
[ROW][C]8[/C][C]0.071255[/C][C]0.4885[/C][C]0.313733[/C][/ROW]
[ROW][C]9[/C][C]-0.032705[/C][C]-0.2242[/C][C]0.411782[/C][/ROW]
[ROW][C]10[/C][C]-0.12535[/C][C]-0.8594[/C][C]0.197253[/C][/ROW]
[ROW][C]11[/C][C]0.261503[/C][C]1.7928[/C][C]0.039723[/C][/ROW]
[ROW][C]12[/C][C]-0.135284[/C][C]-0.9275[/C][C]0.179213[/C][/ROW]
[ROW][C]13[/C][C]-0.151025[/C][C]-1.0354[/C][C]0.152896[/C][/ROW]
[ROW][C]14[/C][C]0.00191[/C][C]0.0131[/C][C]0.494803[/C][/ROW]
[ROW][C]15[/C][C]-0.064394[/C][C]-0.4415[/C][C]0.330452[/C][/ROW]
[ROW][C]16[/C][C]-0.07876[/C][C]-0.54[/C][C]0.29589[/C][/ROW]
[ROW][C]17[/C][C]-0.006102[/C][C]-0.0418[/C][C]0.483403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36614&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36614&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	-0.056864	-0.3898	0.349208
2	0.105538	0.7235	0.236468
3	0.165192	1.1325	0.131585
4	0.13386	0.9177	0.18173
5	0.00801	0.0549	0.478221
6	0.000757	0.0052	0.49794
7	-0.014987	-0.1027	0.459302
8	0.071255	0.4885	0.313733
9	-0.032705	-0.2242	0.411782
10	-0.12535	-0.8594	0.197253
11	0.261503	1.7928	0.039723
12	-0.135284	-0.9275	0.179213
13	-0.151025	-1.0354	0.152896
14	0.00191	0.0131	0.494803
15	-0.064394	-0.4415	0.330452
16	-0.07876	-0.54	0.29589
17	-0.006102	-0.0418	0.483403

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 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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Dataset

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Input Parameters & R Code