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, 21 Dec 2010 13:17:58 +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/Dec/21/t1292937356udmevse37l96omu.htm/, Retrieved Fri, 17 May 2024 05:02:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113488, Retrieved Fri, 17 May 2024 05:02:40 +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

190

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

-     [(Partial) Autocorrelation Function] [s 0650692 paper] [2008-01-15 16:51:07] [d530bc48164a192180949b2df4f47d02]
-  MPD  [(Partial) Autocorrelation Function] [b-r0245787] [2010-12-21 13:15:12] [ebb35fb07def4d07c0eb7ec8d2fd3b0e]
-           [(Partial) Autocorrelation Function] [b-r0245095] [2010-12-21 13:17:58] [4bfaadb29d89ff24ebcdd4f425066435] [Current]
-   P         [(Partial) Autocorrelation Function] [b-r0245095] [2010-12-22 13:10:30] [ec8d68d52c1e9c5e97bb689b42436a8c] 

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

0.86
0.88
0.93
0.98
0.97
1.03
1.06
1.06
1.08
1.09
1.04
1.00
1.01
1.02
1.04
1.06
1.06
1.06
1.06
1.06
1.02
0.98
0.99
0.99
0.94
0.96
0.98
1.01
1.01
1.02
1.04
1.03
1.05
1.08
1.17
1.11
1.11
1.11
1.11
1.21
1.31
1.37
1.37
1.26
1.23
1.17
1.06
0.95
0.92
0.92
0.90
0.93
0.93
0.97
0.96
0.99
0.98
0.96
1.00
0.99
1.03

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113488&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113488&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113488&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.8102	0
1	0.896534	7.0022	0
2	0.732014	5.7172	0
3	0.545883	4.2635	3.6e-05
4	0.359032	2.8041	0.003379
5	0.18149	1.4175	0.080715
6	0.043092	0.3366	0.368802
7	-0.051126	-0.3993	0.654468
8	-0.12935	-1.0103	0.841818
9	-0.177214	-1.3841	0.914312
10	-0.20269	-1.5831	0.94071
11	-0.232438	-1.8154	0.962811
12	-0.281238	-2.1965	0.984068
13	-0.3248	-2.5368	0.993119
14	-0.348132	-2.719	0.995742
15	-0.363232	-2.8369	0.996913
16	-0.35426	-2.7669	0.996259

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.8102 & 0 \tabularnewline
1 & 0.896534 & 7.0022 & 0 \tabularnewline
2 & 0.732014 & 5.7172 & 0 \tabularnewline
3 & 0.545883 & 4.2635 & 3.6e-05 \tabularnewline
4 & 0.359032 & 2.8041 & 0.003379 \tabularnewline
5 & 0.18149 & 1.4175 & 0.080715 \tabularnewline
6 & 0.043092 & 0.3366 & 0.368802 \tabularnewline
7 & -0.051126 & -0.3993 & 0.654468 \tabularnewline
8 & -0.12935 & -1.0103 & 0.841818 \tabularnewline
9 & -0.177214 & -1.3841 & 0.914312 \tabularnewline
10 & -0.20269 & -1.5831 & 0.94071 \tabularnewline
11 & -0.232438 & -1.8154 & 0.962811 \tabularnewline
12 & -0.281238 & -2.1965 & 0.984068 \tabularnewline
13 & -0.3248 & -2.5368 & 0.993119 \tabularnewline
14 & -0.348132 & -2.719 & 0.995742 \tabularnewline
15 & -0.363232 & -2.8369 & 0.996913 \tabularnewline
16 & -0.35426 & -2.7669 & 0.996259 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113488&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]0[/C][C]1[/C][C]7.8102[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.896534[/C][C]7.0022[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.732014[/C][C]5.7172[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.545883[/C][C]4.2635[/C][C]3.6e-05[/C][/ROW]
[ROW][C]4[/C][C]0.359032[/C][C]2.8041[/C][C]0.003379[/C][/ROW]
[ROW][C]5[/C][C]0.18149[/C][C]1.4175[/C][C]0.080715[/C][/ROW]
[ROW][C]6[/C][C]0.043092[/C][C]0.3366[/C][C]0.368802[/C][/ROW]
[ROW][C]7[/C][C]-0.051126[/C][C]-0.3993[/C][C]0.654468[/C][/ROW]
[ROW][C]8[/C][C]-0.12935[/C][C]-1.0103[/C][C]0.841818[/C][/ROW]
[ROW][C]9[/C][C]-0.177214[/C][C]-1.3841[/C][C]0.914312[/C][/ROW]
[ROW][C]10[/C][C]-0.20269[/C][C]-1.5831[/C][C]0.94071[/C][/ROW]
[ROW][C]11[/C][C]-0.232438[/C][C]-1.8154[/C][C]0.962811[/C][/ROW]
[ROW][C]12[/C][C]-0.281238[/C][C]-2.1965[/C][C]0.984068[/C][/ROW]
[ROW][C]13[/C][C]-0.3248[/C][C]-2.5368[/C][C]0.993119[/C][/ROW]
[ROW][C]14[/C][C]-0.348132[/C][C]-2.719[/C][C]0.995742[/C][/ROW]
[ROW][C]15[/C][C]-0.363232[/C][C]-2.8369[/C][C]0.996913[/C][/ROW]
[ROW][C]16[/C][C]-0.35426[/C][C]-2.7669[/C][C]0.996259[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113488&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113488&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
0	1	7.8102	0
1	0.896534	7.0022	0
2	0.732014	5.7172	0
3	0.545883	4.2635	3.6e-05
4	0.359032	2.8041	0.003379
5	0.18149	1.4175	0.080715
6	0.043092	0.3366	0.368802
7	-0.051126	-0.3993	0.654468
8	-0.12935	-1.0103	0.841818
9	-0.177214	-1.3841	0.914312
10	-0.20269	-1.5831	0.94071
11	-0.232438	-1.8154	0.962811
12	-0.281238	-2.1965	0.984068
13	-0.3248	-2.5368	0.993119
14	-0.348132	-2.719	0.995742
15	-0.363232	-2.8369	0.996913
16	-0.35426	-2.7669	0.996259

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.896534	7.0022	0
1	-0.365691	-2.8561	0.997073
2	-0.132552	-1.0353	0.847683
3	-0.09074	-0.7087	0.759397
4	-0.090591	-0.7075	0.759037
5	0.057124	0.4462	0.328533
6	0.022341	0.1745	0.431029
7	-0.139837	-1.0922	0.860472
8	0.036302	0.2835	0.388866
9	-0.037851	-0.2956	0.615739
10	-0.154286	-1.205	0.883573
11	-0.152052	-1.1876	0.880196
12	-0.017028	-0.133	0.552681
13	0.015846	0.1238	0.450956
14	-0.063469	-0.4957	0.689058
15	0.02235	0.1746	0.431002
16	-0.021291	-0.1663	0.56576

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.896534 & 7.0022 & 0 \tabularnewline
1 & -0.365691 & -2.8561 & 0.997073 \tabularnewline
2 & -0.132552 & -1.0353 & 0.847683 \tabularnewline
3 & -0.09074 & -0.7087 & 0.759397 \tabularnewline
4 & -0.090591 & -0.7075 & 0.759037 \tabularnewline
5 & 0.057124 & 0.4462 & 0.328533 \tabularnewline
6 & 0.022341 & 0.1745 & 0.431029 \tabularnewline
7 & -0.139837 & -1.0922 & 0.860472 \tabularnewline
8 & 0.036302 & 0.2835 & 0.388866 \tabularnewline
9 & -0.037851 & -0.2956 & 0.615739 \tabularnewline
10 & -0.154286 & -1.205 & 0.883573 \tabularnewline
11 & -0.152052 & -1.1876 & 0.880196 \tabularnewline
12 & -0.017028 & -0.133 & 0.552681 \tabularnewline
13 & 0.015846 & 0.1238 & 0.450956 \tabularnewline
14 & -0.063469 & -0.4957 & 0.689058 \tabularnewline
15 & 0.02235 & 0.1746 & 0.431002 \tabularnewline
16 & -0.021291 & -0.1663 & 0.56576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113488&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]0[/C][C]0.896534[/C][C]7.0022[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.365691[/C][C]-2.8561[/C][C]0.997073[/C][/ROW]
[ROW][C]2[/C][C]-0.132552[/C][C]-1.0353[/C][C]0.847683[/C][/ROW]
[ROW][C]3[/C][C]-0.09074[/C][C]-0.7087[/C][C]0.759397[/C][/ROW]
[ROW][C]4[/C][C]-0.090591[/C][C]-0.7075[/C][C]0.759037[/C][/ROW]
[ROW][C]5[/C][C]0.057124[/C][C]0.4462[/C][C]0.328533[/C][/ROW]
[ROW][C]6[/C][C]0.022341[/C][C]0.1745[/C][C]0.431029[/C][/ROW]
[ROW][C]7[/C][C]-0.139837[/C][C]-1.0922[/C][C]0.860472[/C][/ROW]
[ROW][C]8[/C][C]0.036302[/C][C]0.2835[/C][C]0.388866[/C][/ROW]
[ROW][C]9[/C][C]-0.037851[/C][C]-0.2956[/C][C]0.615739[/C][/ROW]
[ROW][C]10[/C][C]-0.154286[/C][C]-1.205[/C][C]0.883573[/C][/ROW]
[ROW][C]11[/C][C]-0.152052[/C][C]-1.1876[/C][C]0.880196[/C][/ROW]
[ROW][C]12[/C][C]-0.017028[/C][C]-0.133[/C][C]0.552681[/C][/ROW]
[ROW][C]13[/C][C]0.015846[/C][C]0.1238[/C][C]0.450956[/C][/ROW]
[ROW][C]14[/C][C]-0.063469[/C][C]-0.4957[/C][C]0.689058[/C][/ROW]
[ROW][C]15[/C][C]0.02235[/C][C]0.1746[/C][C]0.431002[/C][/ROW]
[ROW][C]16[/C][C]-0.021291[/C][C]-0.1663[/C][C]0.56576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113488&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113488&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
0	0.896534	7.0022	0
1	-0.365691	-2.8561	0.997073
2	-0.132552	-1.0353	0.847683
3	-0.09074	-0.7087	0.759397
4	-0.090591	-0.7075	0.759037
5	0.057124	0.4462	0.328533
6	0.022341	0.1745	0.431029
7	-0.139837	-1.0922	0.860472
8	0.036302	0.2835	0.388866
9	-0.037851	-0.2956	0.615739
10	-0.154286	-1.205	0.883573
11	-0.152052	-1.1876	0.880196
12	-0.017028	-0.133	0.552681
13	0.015846	0.1238	0.450956
14	-0.063469	-0.4957	0.689058
15	0.02235	0.1746	0.431002
16	-0.021291	-0.1663	0.56576

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = ; par8 = ;

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 1:par1) {
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(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-1,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(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