Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 11:02:01 -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/2007/Nov/25/t1196013207x1hh8ywn9tskdgc.htm/, Retrieved Sat, 04 May 2024 11:16:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6511, Retrieved Sat, 04 May 2024 11:16:43 +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

214

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

-       [(Partial) Autocorrelation Function] [ikhol] [2007-11-25 18:02:01] [fa77851485501f69e030fcd6dbd2de67] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

15
3
2
-2
1
1
-1
-6
-13
-25
-26
-9
1
3
6
2
5
5
0
-5
-4
-2
-1
-8
-16
-19
-28
-11
-4
-9
-12
-10
-2
-13
0
0
4
7
5
2
-2
6
-3
1
0
-7
-6
-4
-4
-2
2
-5
-15
-16
-18
-13
-23
-10
-10
-6
-3
-4
-7
-7
-7
-3
0
-5
-3
3
2
-7
-1
0
-3
4
2
3
0
-10
-10

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6511&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6511&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6511&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.3066	0
1	0.739136	6.1397	0
2	0.496544	4.1246	5.1e-05
3	0.283905	2.3583	0.010599
4	0.151278	1.2566	0.106566
5	0.081056	0.6733	0.251502
6	0.053218	0.4421	0.329914
7	0.003709	0.0308	0.487757
8	-0.166979	-1.387	0.915052
9	-0.257093	-2.1356	0.981867
10	-0.391362	-3.2509	0.99911
11	-0.467961	-3.8872	0.999885
12	-0.5191	-4.312	0.999974
13	-0.424868	-3.5292	0.999627
14	-0.314384	-2.6115	0.994474
15	-0.266527	-2.2139	0.98493
16	-0.176874	-1.4692	0.926842
17	-0.191215	-1.5883	0.94161
18	-0.17391	-1.4446	0.923453

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.3066 & 0 \tabularnewline
1 & 0.739136 & 6.1397 & 0 \tabularnewline
2 & 0.496544 & 4.1246 & 5.1e-05 \tabularnewline
3 & 0.283905 & 2.3583 & 0.010599 \tabularnewline
4 & 0.151278 & 1.2566 & 0.106566 \tabularnewline
5 & 0.081056 & 0.6733 & 0.251502 \tabularnewline
6 & 0.053218 & 0.4421 & 0.329914 \tabularnewline
7 & 0.003709 & 0.0308 & 0.487757 \tabularnewline
8 & -0.166979 & -1.387 & 0.915052 \tabularnewline
9 & -0.257093 & -2.1356 & 0.981867 \tabularnewline
10 & -0.391362 & -3.2509 & 0.99911 \tabularnewline
11 & -0.467961 & -3.8872 & 0.999885 \tabularnewline
12 & -0.5191 & -4.312 & 0.999974 \tabularnewline
13 & -0.424868 & -3.5292 & 0.999627 \tabularnewline
14 & -0.314384 & -2.6115 & 0.994474 \tabularnewline
15 & -0.266527 & -2.2139 & 0.98493 \tabularnewline
16 & -0.176874 & -1.4692 & 0.926842 \tabularnewline
17 & -0.191215 & -1.5883 & 0.94161 \tabularnewline
18 & -0.17391 & -1.4446 & 0.923453 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6511&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]8.3066[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.739136[/C][C]6.1397[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.496544[/C][C]4.1246[/C][C]5.1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.283905[/C][C]2.3583[/C][C]0.010599[/C][/ROW]
[ROW][C]4[/C][C]0.151278[/C][C]1.2566[/C][C]0.106566[/C][/ROW]
[ROW][C]5[/C][C]0.081056[/C][C]0.6733[/C][C]0.251502[/C][/ROW]
[ROW][C]6[/C][C]0.053218[/C][C]0.4421[/C][C]0.329914[/C][/ROW]
[ROW][C]7[/C][C]0.003709[/C][C]0.0308[/C][C]0.487757[/C][/ROW]
[ROW][C]8[/C][C]-0.166979[/C][C]-1.387[/C][C]0.915052[/C][/ROW]
[ROW][C]9[/C][C]-0.257093[/C][C]-2.1356[/C][C]0.981867[/C][/ROW]
[ROW][C]10[/C][C]-0.391362[/C][C]-3.2509[/C][C]0.99911[/C][/ROW]
[ROW][C]11[/C][C]-0.467961[/C][C]-3.8872[/C][C]0.999885[/C][/ROW]
[ROW][C]12[/C][C]-0.5191[/C][C]-4.312[/C][C]0.999974[/C][/ROW]
[ROW][C]13[/C][C]-0.424868[/C][C]-3.5292[/C][C]0.999627[/C][/ROW]
[ROW][C]14[/C][C]-0.314384[/C][C]-2.6115[/C][C]0.994474[/C][/ROW]
[ROW][C]15[/C][C]-0.266527[/C][C]-2.2139[/C][C]0.98493[/C][/ROW]
[ROW][C]16[/C][C]-0.176874[/C][C]-1.4692[/C][C]0.926842[/C][/ROW]
[ROW][C]17[/C][C]-0.191215[/C][C]-1.5883[/C][C]0.94161[/C][/ROW]
[ROW][C]18[/C][C]-0.17391[/C][C]-1.4446[/C][C]0.923453[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6511&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6511&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	8.3066	0
1	0.739136	6.1397	0
2	0.496544	4.1246	5.1e-05
3	0.283905	2.3583	0.010599
4	0.151278	1.2566	0.106566
5	0.081056	0.6733	0.251502
6	0.053218	0.4421	0.329914
7	0.003709	0.0308	0.487757
8	-0.166979	-1.387	0.915052
9	-0.257093	-2.1356	0.981867
10	-0.391362	-3.2509	0.99911
11	-0.467961	-3.8872	0.999885
12	-0.5191	-4.312	0.999974
13	-0.424868	-3.5292	0.999627
14	-0.314384	-2.6115	0.994474
15	-0.266527	-2.2139	0.98493
16	-0.176874	-1.4692	0.926842
17	-0.191215	-1.5883	0.94161
18	-0.17391	-1.4446	0.923453

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.739136	6.1397	0
1	-0.10972	-0.9114	0.817372
2	-0.094326	-0.7835	0.782002
3	0.016053	0.1333	0.447153
4	0.019755	0.1641	0.435068
5	0.017228	0.1431	0.443312
6	-0.083195	-0.6911	0.754079
7	-0.318091	-2.6423	0.994909
8	0.029773	0.2473	0.4027
9	-0.249913	-2.0759	0.979186
10	-0.124189	-1.0316	0.847068
11	-0.173691	-1.4428	0.923197
12	0.130889	1.0872	0.140355
13	0.00105	0.0087	0.496533
14	-0.133283	-1.1071	0.863959
15	0.052256	0.4341	0.332796
16	-0.164611	-1.3674	0.912025
17	-0.04806	-0.3992	0.654517
18	-0.03484	-0.2894	0.613428

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.739136 & 6.1397 & 0 \tabularnewline
1 & -0.10972 & -0.9114 & 0.817372 \tabularnewline
2 & -0.094326 & -0.7835 & 0.782002 \tabularnewline
3 & 0.016053 & 0.1333 & 0.447153 \tabularnewline
4 & 0.019755 & 0.1641 & 0.435068 \tabularnewline
5 & 0.017228 & 0.1431 & 0.443312 \tabularnewline
6 & -0.083195 & -0.6911 & 0.754079 \tabularnewline
7 & -0.318091 & -2.6423 & 0.994909 \tabularnewline
8 & 0.029773 & 0.2473 & 0.4027 \tabularnewline
9 & -0.249913 & -2.0759 & 0.979186 \tabularnewline
10 & -0.124189 & -1.0316 & 0.847068 \tabularnewline
11 & -0.173691 & -1.4428 & 0.923197 \tabularnewline
12 & 0.130889 & 1.0872 & 0.140355 \tabularnewline
13 & 0.00105 & 0.0087 & 0.496533 \tabularnewline
14 & -0.133283 & -1.1071 & 0.863959 \tabularnewline
15 & 0.052256 & 0.4341 & 0.332796 \tabularnewline
16 & -0.164611 & -1.3674 & 0.912025 \tabularnewline
17 & -0.04806 & -0.3992 & 0.654517 \tabularnewline
18 & -0.03484 & -0.2894 & 0.613428 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6511&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]0.739136[/C][C]6.1397[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.10972[/C][C]-0.9114[/C][C]0.817372[/C][/ROW]
[ROW][C]2[/C][C]-0.094326[/C][C]-0.7835[/C][C]0.782002[/C][/ROW]
[ROW][C]3[/C][C]0.016053[/C][C]0.1333[/C][C]0.447153[/C][/ROW]
[ROW][C]4[/C][C]0.019755[/C][C]0.1641[/C][C]0.435068[/C][/ROW]
[ROW][C]5[/C][C]0.017228[/C][C]0.1431[/C][C]0.443312[/C][/ROW]
[ROW][C]6[/C][C]-0.083195[/C][C]-0.6911[/C][C]0.754079[/C][/ROW]
[ROW][C]7[/C][C]-0.318091[/C][C]-2.6423[/C][C]0.994909[/C][/ROW]
[ROW][C]8[/C][C]0.029773[/C][C]0.2473[/C][C]0.4027[/C][/ROW]
[ROW][C]9[/C][C]-0.249913[/C][C]-2.0759[/C][C]0.979186[/C][/ROW]
[ROW][C]10[/C][C]-0.124189[/C][C]-1.0316[/C][C]0.847068[/C][/ROW]
[ROW][C]11[/C][C]-0.173691[/C][C]-1.4428[/C][C]0.923197[/C][/ROW]
[ROW][C]12[/C][C]0.130889[/C][C]1.0872[/C][C]0.140355[/C][/ROW]
[ROW][C]13[/C][C]0.00105[/C][C]0.0087[/C][C]0.496533[/C][/ROW]
[ROW][C]14[/C][C]-0.133283[/C][C]-1.1071[/C][C]0.863959[/C][/ROW]
[ROW][C]15[/C][C]0.052256[/C][C]0.4341[/C][C]0.332796[/C][/ROW]
[ROW][C]16[/C][C]-0.164611[/C][C]-1.3674[/C][C]0.912025[/C][/ROW]
[ROW][C]17[/C][C]-0.04806[/C][C]-0.3992[/C][C]0.654517[/C][/ROW]
[ROW][C]18[/C][C]-0.03484[/C][C]-0.2894[/C][C]0.613428[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6511&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6511&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	0.739136	6.1397	0
1	-0.10972	-0.9114	0.817372
2	-0.094326	-0.7835	0.782002
3	0.016053	0.1333	0.447153
4	0.019755	0.1641	0.435068
5	0.017228	0.1431	0.443312
6	-0.083195	-0.6911	0.754079
7	-0.318091	-2.6423	0.994909
8	0.029773	0.2473	0.4027
9	-0.249913	-2.0759	0.979186
10	-0.124189	-1.0316	0.847068
11	-0.173691	-1.4428	0.923197
12	0.130889	1.0872	0.140355
13	0.00105	0.0087	0.496533
14	-0.133283	-1.1071	0.863959
15	0.052256	0.4341	0.332796
16	-0.164611	-1.3674	0.912025
17	-0.04806	-0.3992	0.654517
18	-0.03484	-0.2894	0.613428

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 ;

Parameters (R input):

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