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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 03 May 2010 18:06:05 +0000

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/2010/May/03/t127291000888pja6nlk07t9n7.htm/, Retrieved Fri, 09 May 2025 16:16:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=75280, Retrieved Fri, 09 May 2025 16:16:13 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W21

Estimated Impact

292

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

-     [Histogram] [Datareeks-Inschri...] [2010-02-08 14:03:15] [c656187b38b4f6e6948d94f8dfe6ded2]
- RMP   [Harrell-Davis Quantiles] [Datareeks-Opdrach...] [2010-03-08 17:35:01] [1f3241a8f2363a866734862cbbf73252]
- RMPD    [Mean Plot] [Opgave 6 oefening...] [2010-04-26 21:57:04] [1f3241a8f2363a866734862cbbf73252]
- RMPD        [(Partial) Autocorrelation Function] [Opgave 6 BIS oefe...] [2010-05-03 18:06:05] [8c87877ca0a068b5d9f0f8fa9cf6c0e7] [Current]
-   P           [(Partial) Autocorrelation Function] [Opgave 6 BIS oefe...] [2010-05-03 18:08:48] [1f3241a8f2363a866734862cbbf73252] 
-   P           [(Partial) Autocorrelation Function] [Opgave 6 BIS oefe...] [2010-05-03 18:11:43] [1f3241a8f2363a866734862cbbf73252] 
-   P           [(Partial) Autocorrelation Function] [Opgave 6 BIS oefe...] [2010-05-03 18:13:08] [1f3241a8f2363a866734862cbbf73252] 

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Dataseries X:

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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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75280&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]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=75280&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75280&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.470068	5.1493	1e-06
2	0.263449	2.8859	0.002314
3	0.137393	1.5051	0.067467
4	-0.048318	-0.5293	0.298789
5	-0.149293	-1.6354	0.052291
6	-0.277304	-3.0377	0.001463
7	-0.193611	-2.1209	0.017994
8	-0.097985	-1.0734	0.14263
9	0.028697	0.3144	0.376897
10	0.093056	1.0194	0.155036
11	0.272221	2.982	0.001734
12	0.72629	7.9561	0
13	0.293246	3.2123	0.000845
14	0.136823	1.4988	0.068274
15	0.046742	0.512	0.304785
16	-0.110833	-1.2141	0.113543
17	-0.160419	-1.7573	0.040708
18	-0.293747	-3.2178	0.000831
19	-0.216268	-2.3691	0.009714
20	-0.110613	-1.2117	0.114002

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.470068 & 5.1493 & 1e-06 \tabularnewline
2 & 0.263449 & 2.8859 & 0.002314 \tabularnewline
3 & 0.137393 & 1.5051 & 0.067467 \tabularnewline
4 & -0.048318 & -0.5293 & 0.298789 \tabularnewline
5 & -0.149293 & -1.6354 & 0.052291 \tabularnewline
6 & -0.277304 & -3.0377 & 0.001463 \tabularnewline
7 & -0.193611 & -2.1209 & 0.017994 \tabularnewline
8 & -0.097985 & -1.0734 & 0.14263 \tabularnewline
9 & 0.028697 & 0.3144 & 0.376897 \tabularnewline
10 & 0.093056 & 1.0194 & 0.155036 \tabularnewline
11 & 0.272221 & 2.982 & 0.001734 \tabularnewline
12 & 0.72629 & 7.9561 & 0 \tabularnewline
13 & 0.293246 & 3.2123 & 0.000845 \tabularnewline
14 & 0.136823 & 1.4988 & 0.068274 \tabularnewline
15 & 0.046742 & 0.512 & 0.304785 \tabularnewline
16 & -0.110833 & -1.2141 & 0.113543 \tabularnewline
17 & -0.160419 & -1.7573 & 0.040708 \tabularnewline
18 & -0.293747 & -3.2178 & 0.000831 \tabularnewline
19 & -0.216268 & -2.3691 & 0.009714 \tabularnewline
20 & -0.110613 & -1.2117 & 0.114002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75280&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]0.470068[/C][C]5.1493[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.263449[/C][C]2.8859[/C][C]0.002314[/C][/ROW]
[ROW][C]3[/C][C]0.137393[/C][C]1.5051[/C][C]0.067467[/C][/ROW]
[ROW][C]4[/C][C]-0.048318[/C][C]-0.5293[/C][C]0.298789[/C][/ROW]
[ROW][C]5[/C][C]-0.149293[/C][C]-1.6354[/C][C]0.052291[/C][/ROW]
[ROW][C]6[/C][C]-0.277304[/C][C]-3.0377[/C][C]0.001463[/C][/ROW]
[ROW][C]7[/C][C]-0.193611[/C][C]-2.1209[/C][C]0.017994[/C][/ROW]
[ROW][C]8[/C][C]-0.097985[/C][C]-1.0734[/C][C]0.14263[/C][/ROW]
[ROW][C]9[/C][C]0.028697[/C][C]0.3144[/C][C]0.376897[/C][/ROW]
[ROW][C]10[/C][C]0.093056[/C][C]1.0194[/C][C]0.155036[/C][/ROW]
[ROW][C]11[/C][C]0.272221[/C][C]2.982[/C][C]0.001734[/C][/ROW]
[ROW][C]12[/C][C]0.72629[/C][C]7.9561[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.293246[/C][C]3.2123[/C][C]0.000845[/C][/ROW]
[ROW][C]14[/C][C]0.136823[/C][C]1.4988[/C][C]0.068274[/C][/ROW]
[ROW][C]15[/C][C]0.046742[/C][C]0.512[/C][C]0.304785[/C][/ROW]
[ROW][C]16[/C][C]-0.110833[/C][C]-1.2141[/C][C]0.113543[/C][/ROW]
[ROW][C]17[/C][C]-0.160419[/C][C]-1.7573[/C][C]0.040708[/C][/ROW]
[ROW][C]18[/C][C]-0.293747[/C][C]-3.2178[/C][C]0.000831[/C][/ROW]
[ROW][C]19[/C][C]-0.216268[/C][C]-2.3691[/C][C]0.009714[/C][/ROW]
[ROW][C]20[/C][C]-0.110613[/C][C]-1.2117[/C][C]0.114002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75280&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75280&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	0.470068	5.1493	1e-06
2	0.263449	2.8859	0.002314
3	0.137393	1.5051	0.067467
4	-0.048318	-0.5293	0.298789
5	-0.149293	-1.6354	0.052291
6	-0.277304	-3.0377	0.001463
7	-0.193611	-2.1209	0.017994
8	-0.097985	-1.0734	0.14263
9	0.028697	0.3144	0.376897
10	0.093056	1.0194	0.155036
11	0.272221	2.982	0.001734
12	0.72629	7.9561	0
13	0.293246	3.2123	0.000845
14	0.136823	1.4988	0.068274
15	0.046742	0.512	0.304785
16	-0.110833	-1.2141	0.113543
17	-0.160419	-1.7573	0.040708
18	-0.293747	-3.2178	0.000831
19	-0.216268	-2.3691	0.009714
20	-0.110613	-1.2117	0.114002

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.470068	5.1493	1e-06
2	0.054535	0.5974	0.275681
3	-0.006859	-0.0751	0.470116
4	-0.156277	-1.7119	0.044747
5	-0.105641	-1.1572	0.124737
6	-0.188293	-2.0627	0.020652
7	0.054636	0.5985	0.275316
8	0.055219	0.6049	0.273196
9	0.120016	1.3147	0.095557
10	0.013281	0.1455	0.442285
11	0.214316	2.3477	0.010263
12	0.673896	7.3822	0
13	-0.565816	-6.1982	0
14	-0.140631	-1.5405	0.063031
15	0.055179	0.6045	0.27334
16	0.033731	0.3695	0.356202
17	0.024152	0.2646	0.395895
18	-0.041503	-0.4546	0.325095
19	0.012037	0.1319	0.447658
20	-0.004244	-0.0465	0.481497

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.470068 & 5.1493 & 1e-06 \tabularnewline
2 & 0.054535 & 0.5974 & 0.275681 \tabularnewline
3 & -0.006859 & -0.0751 & 0.470116 \tabularnewline
4 & -0.156277 & -1.7119 & 0.044747 \tabularnewline
5 & -0.105641 & -1.1572 & 0.124737 \tabularnewline
6 & -0.188293 & -2.0627 & 0.020652 \tabularnewline
7 & 0.054636 & 0.5985 & 0.275316 \tabularnewline
8 & 0.055219 & 0.6049 & 0.273196 \tabularnewline
9 & 0.120016 & 1.3147 & 0.095557 \tabularnewline
10 & 0.013281 & 0.1455 & 0.442285 \tabularnewline
11 & 0.214316 & 2.3477 & 0.010263 \tabularnewline
12 & 0.673896 & 7.3822 & 0 \tabularnewline
13 & -0.565816 & -6.1982 & 0 \tabularnewline
14 & -0.140631 & -1.5405 & 0.063031 \tabularnewline
15 & 0.055179 & 0.6045 & 0.27334 \tabularnewline
16 & 0.033731 & 0.3695 & 0.356202 \tabularnewline
17 & 0.024152 & 0.2646 & 0.395895 \tabularnewline
18 & -0.041503 & -0.4546 & 0.325095 \tabularnewline
19 & 0.012037 & 0.1319 & 0.447658 \tabularnewline
20 & -0.004244 & -0.0465 & 0.481497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75280&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]0.470068[/C][C]5.1493[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.054535[/C][C]0.5974[/C][C]0.275681[/C][/ROW]
[ROW][C]3[/C][C]-0.006859[/C][C]-0.0751[/C][C]0.470116[/C][/ROW]
[ROW][C]4[/C][C]-0.156277[/C][C]-1.7119[/C][C]0.044747[/C][/ROW]
[ROW][C]5[/C][C]-0.105641[/C][C]-1.1572[/C][C]0.124737[/C][/ROW]
[ROW][C]6[/C][C]-0.188293[/C][C]-2.0627[/C][C]0.020652[/C][/ROW]
[ROW][C]7[/C][C]0.054636[/C][C]0.5985[/C][C]0.275316[/C][/ROW]
[ROW][C]8[/C][C]0.055219[/C][C]0.6049[/C][C]0.273196[/C][/ROW]
[ROW][C]9[/C][C]0.120016[/C][C]1.3147[/C][C]0.095557[/C][/ROW]
[ROW][C]10[/C][C]0.013281[/C][C]0.1455[/C][C]0.442285[/C][/ROW]
[ROW][C]11[/C][C]0.214316[/C][C]2.3477[/C][C]0.010263[/C][/ROW]
[ROW][C]12[/C][C]0.673896[/C][C]7.3822[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.565816[/C][C]-6.1982[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.140631[/C][C]-1.5405[/C][C]0.063031[/C][/ROW]
[ROW][C]15[/C][C]0.055179[/C][C]0.6045[/C][C]0.27334[/C][/ROW]
[ROW][C]16[/C][C]0.033731[/C][C]0.3695[/C][C]0.356202[/C][/ROW]
[ROW][C]17[/C][C]0.024152[/C][C]0.2646[/C][C]0.395895[/C][/ROW]
[ROW][C]18[/C][C]-0.041503[/C][C]-0.4546[/C][C]0.325095[/C][/ROW]
[ROW][C]19[/C][C]0.012037[/C][C]0.1319[/C][C]0.447658[/C][/ROW]
[ROW][C]20[/C][C]-0.004244[/C][C]-0.0465[/C][C]0.481497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75280&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75280&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	0.470068	5.1493	1e-06
2	0.054535	0.5974	0.275681
3	-0.006859	-0.0751	0.470116
4	-0.156277	-1.7119	0.044747
5	-0.105641	-1.1572	0.124737
6	-0.188293	-2.0627	0.020652
7	0.054636	0.5985	0.275316
8	0.055219	0.6049	0.273196
9	0.120016	1.3147	0.095557
10	0.013281	0.1455	0.442285
11	0.214316	2.3477	0.010263
12	0.673896	7.3822	0
13	-0.565816	-6.1982	0
14	-0.140631	-1.5405	0.063031
15	0.055179	0.6045	0.27334
16	0.033731	0.3695	0.356202
17	0.024152	0.2646	0.395895
18	-0.041503	-0.4546	0.325095
19	0.012037	0.1319	0.447658
20	-0.004244	-0.0465	0.481497

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code