Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 03 Dec 2009 06:04:30 -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/03/t1259845504i6rfmbgif8yy5qn.htm/, Retrieved Fri, 19 Apr 2024 16:27:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62708, Retrieved Fri, 19 Apr 2024 16:27:04 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

JSSHWWS9P5

Estimated Impact

115

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD    [(Partial) Autocorrelation Function] [Autocorrelation F...] [2009-12-03 13:04:30] [c8fd62404619100d8e91184019148412] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

11.1
10.9
10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.7
7.2
7.3
8.1

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=62708&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=62708&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62708&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	0.310831	2.1082	0.020247
2	-0.157599	-1.0689	0.145349
3	-0.564308	-3.8273	0.000195
4	-0.44761	-3.0358	0.00197
5	-0.151526	-1.0277	0.154733
6	0.283213	1.9208	0.030481
7	0.261803	1.7756	0.041205
8	0.251394	1.705	0.047466
9	0.102643	0.6962	0.244915
10	-0.051647	-0.3503	0.36386
11	-0.158185	-1.0729	0.144464
12	-0.25934	-1.7589	0.04262
13	-0.215675	-1.4628	0.075164
14	0.096483	0.6544	0.258064
15	0.163946	1.1119	0.135972
16	0.158063	1.072	0.144648
17	0.120814	0.8194	0.208392

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.310831 & 2.1082 & 0.020247 \tabularnewline
2 & -0.157599 & -1.0689 & 0.145349 \tabularnewline
3 & -0.564308 & -3.8273 & 0.000195 \tabularnewline
4 & -0.44761 & -3.0358 & 0.00197 \tabularnewline
5 & -0.151526 & -1.0277 & 0.154733 \tabularnewline
6 & 0.283213 & 1.9208 & 0.030481 \tabularnewline
7 & 0.261803 & 1.7756 & 0.041205 \tabularnewline
8 & 0.251394 & 1.705 & 0.047466 \tabularnewline
9 & 0.102643 & 0.6962 & 0.244915 \tabularnewline
10 & -0.051647 & -0.3503 & 0.36386 \tabularnewline
11 & -0.158185 & -1.0729 & 0.144464 \tabularnewline
12 & -0.25934 & -1.7589 & 0.04262 \tabularnewline
13 & -0.215675 & -1.4628 & 0.075164 \tabularnewline
14 & 0.096483 & 0.6544 & 0.258064 \tabularnewline
15 & 0.163946 & 1.1119 & 0.135972 \tabularnewline
16 & 0.158063 & 1.072 & 0.144648 \tabularnewline
17 & 0.120814 & 0.8194 & 0.208392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62708&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]0.310831[/C][C]2.1082[/C][C]0.020247[/C][/ROW]
[ROW][C]2[/C][C]-0.157599[/C][C]-1.0689[/C][C]0.145349[/C][/ROW]
[ROW][C]3[/C][C]-0.564308[/C][C]-3.8273[/C][C]0.000195[/C][/ROW]
[ROW][C]4[/C][C]-0.44761[/C][C]-3.0358[/C][C]0.00197[/C][/ROW]
[ROW][C]5[/C][C]-0.151526[/C][C]-1.0277[/C][C]0.154733[/C][/ROW]
[ROW][C]6[/C][C]0.283213[/C][C]1.9208[/C][C]0.030481[/C][/ROW]
[ROW][C]7[/C][C]0.261803[/C][C]1.7756[/C][C]0.041205[/C][/ROW]
[ROW][C]8[/C][C]0.251394[/C][C]1.705[/C][C]0.047466[/C][/ROW]
[ROW][C]9[/C][C]0.102643[/C][C]0.6962[/C][C]0.244915[/C][/ROW]
[ROW][C]10[/C][C]-0.051647[/C][C]-0.3503[/C][C]0.36386[/C][/ROW]
[ROW][C]11[/C][C]-0.158185[/C][C]-1.0729[/C][C]0.144464[/C][/ROW]
[ROW][C]12[/C][C]-0.25934[/C][C]-1.7589[/C][C]0.04262[/C][/ROW]
[ROW][C]13[/C][C]-0.215675[/C][C]-1.4628[/C][C]0.075164[/C][/ROW]
[ROW][C]14[/C][C]0.096483[/C][C]0.6544[/C][C]0.258064[/C][/ROW]
[ROW][C]15[/C][C]0.163946[/C][C]1.1119[/C][C]0.135972[/C][/ROW]
[ROW][C]16[/C][C]0.158063[/C][C]1.072[/C][C]0.144648[/C][/ROW]
[ROW][C]17[/C][C]0.120814[/C][C]0.8194[/C][C]0.208392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62708&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62708&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	0.310831	2.1082	0.020247
2	-0.157599	-1.0689	0.145349
3	-0.564308	-3.8273	0.000195
4	-0.44761	-3.0358	0.00197
5	-0.151526	-1.0277	0.154733
6	0.283213	1.9208	0.030481
7	0.261803	1.7756	0.041205
8	0.251394	1.705	0.047466
9	0.102643	0.6962	0.244915
10	-0.051647	-0.3503	0.36386
11	-0.158185	-1.0729	0.144464
12	-0.25934	-1.7589	0.04262
13	-0.215675	-1.4628	0.075164
14	0.096483	0.6544	0.258064
15	0.163946	1.1119	0.135972
16	0.158063	1.072	0.144648
17	0.120814	0.8194	0.208392

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.310831	2.1082	0.020247
2	-0.281402	-1.9086	0.031285
3	-0.497769	-3.376	0.000752
4	-0.256132	-1.7372	0.044525
5	-0.24005	-1.6281	0.055168
6	-0.032566	-0.2209	0.413083
7	-0.285813	-1.9385	0.029358
8	-0.019595	-0.1329	0.447427
9	0.145401	0.9862	0.164607
10	0.079644	0.5402	0.295843
11	0.142236	0.9647	0.169872
12	-0.070458	-0.4779	0.317504
13	-0.03473	-0.2355	0.407415
14	0.179109	1.2148	0.115325
15	-0.178339	-1.2096	0.116315
16	-0.185965	-1.2613	0.106785
17	0.022924	0.1555	0.438563

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.310831 & 2.1082 & 0.020247 \tabularnewline
2 & -0.281402 & -1.9086 & 0.031285 \tabularnewline
3 & -0.497769 & -3.376 & 0.000752 \tabularnewline
4 & -0.256132 & -1.7372 & 0.044525 \tabularnewline
5 & -0.24005 & -1.6281 & 0.055168 \tabularnewline
6 & -0.032566 & -0.2209 & 0.413083 \tabularnewline
7 & -0.285813 & -1.9385 & 0.029358 \tabularnewline
8 & -0.019595 & -0.1329 & 0.447427 \tabularnewline
9 & 0.145401 & 0.9862 & 0.164607 \tabularnewline
10 & 0.079644 & 0.5402 & 0.295843 \tabularnewline
11 & 0.142236 & 0.9647 & 0.169872 \tabularnewline
12 & -0.070458 & -0.4779 & 0.317504 \tabularnewline
13 & -0.03473 & -0.2355 & 0.407415 \tabularnewline
14 & 0.179109 & 1.2148 & 0.115325 \tabularnewline
15 & -0.178339 & -1.2096 & 0.116315 \tabularnewline
16 & -0.185965 & -1.2613 & 0.106785 \tabularnewline
17 & 0.022924 & 0.1555 & 0.438563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62708&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]0.310831[/C][C]2.1082[/C][C]0.020247[/C][/ROW]
[ROW][C]2[/C][C]-0.281402[/C][C]-1.9086[/C][C]0.031285[/C][/ROW]
[ROW][C]3[/C][C]-0.497769[/C][C]-3.376[/C][C]0.000752[/C][/ROW]
[ROW][C]4[/C][C]-0.256132[/C][C]-1.7372[/C][C]0.044525[/C][/ROW]
[ROW][C]5[/C][C]-0.24005[/C][C]-1.6281[/C][C]0.055168[/C][/ROW]
[ROW][C]6[/C][C]-0.032566[/C][C]-0.2209[/C][C]0.413083[/C][/ROW]
[ROW][C]7[/C][C]-0.285813[/C][C]-1.9385[/C][C]0.029358[/C][/ROW]
[ROW][C]8[/C][C]-0.019595[/C][C]-0.1329[/C][C]0.447427[/C][/ROW]
[ROW][C]9[/C][C]0.145401[/C][C]0.9862[/C][C]0.164607[/C][/ROW]
[ROW][C]10[/C][C]0.079644[/C][C]0.5402[/C][C]0.295843[/C][/ROW]
[ROW][C]11[/C][C]0.142236[/C][C]0.9647[/C][C]0.169872[/C][/ROW]
[ROW][C]12[/C][C]-0.070458[/C][C]-0.4779[/C][C]0.317504[/C][/ROW]
[ROW][C]13[/C][C]-0.03473[/C][C]-0.2355[/C][C]0.407415[/C][/ROW]
[ROW][C]14[/C][C]0.179109[/C][C]1.2148[/C][C]0.115325[/C][/ROW]
[ROW][C]15[/C][C]-0.178339[/C][C]-1.2096[/C][C]0.116315[/C][/ROW]
[ROW][C]16[/C][C]-0.185965[/C][C]-1.2613[/C][C]0.106785[/C][/ROW]
[ROW][C]17[/C][C]0.022924[/C][C]0.1555[/C][C]0.438563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62708&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62708&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	0.310831	2.1082	0.020247
2	-0.281402	-1.9086	0.031285
3	-0.497769	-3.376	0.000752
4	-0.256132	-1.7372	0.044525
5	-0.24005	-1.6281	0.055168
6	-0.032566	-0.2209	0.413083
7	-0.285813	-1.9385	0.029358
8	-0.019595	-0.1329	0.447427
9	0.145401	0.9862	0.164607
10	0.079644	0.5402	0.295843
11	0.142236	0.9647	0.169872
12	-0.070458	-0.4779	0.317504
13	-0.03473	-0.2355	0.407415
14	0.179109	1.2148	0.115325
15	-0.178339	-1.2096	0.116315
16	-0.185965	-1.2613	0.106785
17	0.022924	0.1555	0.438563

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; 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