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

Tue, 15 Dec 2009 13:51:15 -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/15/t1260910336s1ym1hx49biuf45.htm/, Retrieved Wed, 08 May 2024 09:50:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68144, Retrieved Wed, 08 May 2024 09:50:35 +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

Estimated Impact

111

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

-     [(Partial) Autocorrelation Function] [] [2009-11-26 17:29:27] [69bbb86d5181c362d5647cae31af3dc7]
-    D    [(Partial) Autocorrelation Function] [] [2009-12-15 20:51:15] [8cd69d0f4298074aa572ca2f9b39b6ae] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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=68144&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=68144&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68144&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	0.939418	6.5085	0
2	0.866164	6.001	0
3	0.780214	5.4055	1e-06
4	0.681134	4.719	1e-05
5	0.572121	3.9638	0.000122
6	0.46101	3.194	0.00124
7	0.347018	2.4042	0.010058
8	0.235623	1.6324	0.054565
9	0.135437	0.9383	0.176384
10	0.048303	0.3347	0.369672
11	-0.025232	-0.1748	0.430982
12	-0.10007	-0.6933	0.245729
13	-0.153979	-1.0668	0.1457
14	-0.199665	-1.3833	0.086483
15	-0.244988	-1.6973	0.048055
16	-0.296525	-2.0544	0.022703
17	-0.348398	-2.4138	0.009826

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.939418 & 6.5085 & 0 \tabularnewline
2 & 0.866164 & 6.001 & 0 \tabularnewline
3 & 0.780214 & 5.4055 & 1e-06 \tabularnewline
4 & 0.681134 & 4.719 & 1e-05 \tabularnewline
5 & 0.572121 & 3.9638 & 0.000122 \tabularnewline
6 & 0.46101 & 3.194 & 0.00124 \tabularnewline
7 & 0.347018 & 2.4042 & 0.010058 \tabularnewline
8 & 0.235623 & 1.6324 & 0.054565 \tabularnewline
9 & 0.135437 & 0.9383 & 0.176384 \tabularnewline
10 & 0.048303 & 0.3347 & 0.369672 \tabularnewline
11 & -0.025232 & -0.1748 & 0.430982 \tabularnewline
12 & -0.10007 & -0.6933 & 0.245729 \tabularnewline
13 & -0.153979 & -1.0668 & 0.1457 \tabularnewline
14 & -0.199665 & -1.3833 & 0.086483 \tabularnewline
15 & -0.244988 & -1.6973 & 0.048055 \tabularnewline
16 & -0.296525 & -2.0544 & 0.022703 \tabularnewline
17 & -0.348398 & -2.4138 & 0.009826 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68144&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]0.939418[/C][C]6.5085[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.866164[/C][C]6.001[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.780214[/C][C]5.4055[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.681134[/C][C]4.719[/C][C]1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.572121[/C][C]3.9638[/C][C]0.000122[/C][/ROW]
[ROW][C]6[/C][C]0.46101[/C][C]3.194[/C][C]0.00124[/C][/ROW]
[ROW][C]7[/C][C]0.347018[/C][C]2.4042[/C][C]0.010058[/C][/ROW]
[ROW][C]8[/C][C]0.235623[/C][C]1.6324[/C][C]0.054565[/C][/ROW]
[ROW][C]9[/C][C]0.135437[/C][C]0.9383[/C][C]0.176384[/C][/ROW]
[ROW][C]10[/C][C]0.048303[/C][C]0.3347[/C][C]0.369672[/C][/ROW]
[ROW][C]11[/C][C]-0.025232[/C][C]-0.1748[/C][C]0.430982[/C][/ROW]
[ROW][C]12[/C][C]-0.10007[/C][C]-0.6933[/C][C]0.245729[/C][/ROW]
[ROW][C]13[/C][C]-0.153979[/C][C]-1.0668[/C][C]0.1457[/C][/ROW]
[ROW][C]14[/C][C]-0.199665[/C][C]-1.3833[/C][C]0.086483[/C][/ROW]
[ROW][C]15[/C][C]-0.244988[/C][C]-1.6973[/C][C]0.048055[/C][/ROW]
[ROW][C]16[/C][C]-0.296525[/C][C]-2.0544[/C][C]0.022703[/C][/ROW]
[ROW][C]17[/C][C]-0.348398[/C][C]-2.4138[/C][C]0.009826[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68144&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68144&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	0.939418	6.5085	0
2	0.866164	6.001	0
3	0.780214	5.4055	1e-06
4	0.681134	4.719	1e-05
5	0.572121	3.9638	0.000122
6	0.46101	3.194	0.00124
7	0.347018	2.4042	0.010058
8	0.235623	1.6324	0.054565
9	0.135437	0.9383	0.176384
10	0.048303	0.3347	0.369672
11	-0.025232	-0.1748	0.430982
12	-0.10007	-0.6933	0.245729
13	-0.153979	-1.0668	0.1457
14	-0.199665	-1.3833	0.086483
15	-0.244988	-1.6973	0.048055
16	-0.296525	-2.0544	0.022703
17	-0.348398	-2.4138	0.009826

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.939418	6.5085	0
2	-0.139099	-0.9637	0.170012
3	-0.13876	-0.9614	0.170595
4	-0.145869	-1.0106	0.158635
5	-0.124366	-0.8616	0.196587
6	-0.064016	-0.4435	0.329693
7	-0.084492	-0.5854	0.280517
8	-0.049031	-0.3397	0.367785
9	0.015184	0.1052	0.45833
10	0.020034	0.1388	0.445096
11	0.014896	0.1032	0.459116
12	-0.135882	-0.9414	0.175602
13	0.067885	0.4703	0.320128
14	-0.045739	-0.3169	0.376351
15	-0.111424	-0.772	0.221959
16	-0.17166	-1.1893	0.120086
17	-0.116362	-0.8062	0.212058

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.939418 & 6.5085 & 0 \tabularnewline
2 & -0.139099 & -0.9637 & 0.170012 \tabularnewline
3 & -0.13876 & -0.9614 & 0.170595 \tabularnewline
4 & -0.145869 & -1.0106 & 0.158635 \tabularnewline
5 & -0.124366 & -0.8616 & 0.196587 \tabularnewline
6 & -0.064016 & -0.4435 & 0.329693 \tabularnewline
7 & -0.084492 & -0.5854 & 0.280517 \tabularnewline
8 & -0.049031 & -0.3397 & 0.367785 \tabularnewline
9 & 0.015184 & 0.1052 & 0.45833 \tabularnewline
10 & 0.020034 & 0.1388 & 0.445096 \tabularnewline
11 & 0.014896 & 0.1032 & 0.459116 \tabularnewline
12 & -0.135882 & -0.9414 & 0.175602 \tabularnewline
13 & 0.067885 & 0.4703 & 0.320128 \tabularnewline
14 & -0.045739 & -0.3169 & 0.376351 \tabularnewline
15 & -0.111424 & -0.772 & 0.221959 \tabularnewline
16 & -0.17166 & -1.1893 & 0.120086 \tabularnewline
17 & -0.116362 & -0.8062 & 0.212058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68144&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]0.939418[/C][C]6.5085[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.139099[/C][C]-0.9637[/C][C]0.170012[/C][/ROW]
[ROW][C]3[/C][C]-0.13876[/C][C]-0.9614[/C][C]0.170595[/C][/ROW]
[ROW][C]4[/C][C]-0.145869[/C][C]-1.0106[/C][C]0.158635[/C][/ROW]
[ROW][C]5[/C][C]-0.124366[/C][C]-0.8616[/C][C]0.196587[/C][/ROW]
[ROW][C]6[/C][C]-0.064016[/C][C]-0.4435[/C][C]0.329693[/C][/ROW]
[ROW][C]7[/C][C]-0.084492[/C][C]-0.5854[/C][C]0.280517[/C][/ROW]
[ROW][C]8[/C][C]-0.049031[/C][C]-0.3397[/C][C]0.367785[/C][/ROW]
[ROW][C]9[/C][C]0.015184[/C][C]0.1052[/C][C]0.45833[/C][/ROW]
[ROW][C]10[/C][C]0.020034[/C][C]0.1388[/C][C]0.445096[/C][/ROW]
[ROW][C]11[/C][C]0.014896[/C][C]0.1032[/C][C]0.459116[/C][/ROW]
[ROW][C]12[/C][C]-0.135882[/C][C]-0.9414[/C][C]0.175602[/C][/ROW]
[ROW][C]13[/C][C]0.067885[/C][C]0.4703[/C][C]0.320128[/C][/ROW]
[ROW][C]14[/C][C]-0.045739[/C][C]-0.3169[/C][C]0.376351[/C][/ROW]
[ROW][C]15[/C][C]-0.111424[/C][C]-0.772[/C][C]0.221959[/C][/ROW]
[ROW][C]16[/C][C]-0.17166[/C][C]-1.1893[/C][C]0.120086[/C][/ROW]
[ROW][C]17[/C][C]-0.116362[/C][C]-0.8062[/C][C]0.212058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68144&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68144&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	0.939418	6.5085	0
2	-0.139099	-0.9637	0.170012
3	-0.13876	-0.9614	0.170595
4	-0.145869	-1.0106	0.158635
5	-0.124366	-0.8616	0.196587
6	-0.064016	-0.4435	0.329693
7	-0.084492	-0.5854	0.280517
8	-0.049031	-0.3397	0.367785
9	0.015184	0.1052	0.45833
10	0.020034	0.1388	0.445096
11	0.014896	0.1032	0.459116
12	-0.135882	-0.9414	0.175602
13	0.067885	0.4703	0.320128
14	-0.045739	-0.3169	0.376351
15	-0.111424	-0.772	0.221959
16	-0.17166	-1.1893	0.120086
17	-0.116362	-0.8062	0.212058

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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