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

Mon, 10 Dec 2007 09:08:41 -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/Dec/10/t11973020844p9opyg11gwyvi3.htm/, Retrieved Tue, 07 May 2024 00:15:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2995, Retrieved Tue, 07 May 2024 00:15:21 +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

superbenzine

Estimated Impact

228

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

-       [(Partial) Autocorrelation Function] [Paper XIII acf pacf] [2007-12-10 16:08:41] [fd802f308f037a9692de8c23f8b60e49] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of compuational 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 compuational 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=2995&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]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=2995&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2995&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.6811	0
1	0.176852	1.3584	0.08975
2	-0.156777	-1.2042	0.883345
3	-0.081949	-0.6295	0.734262
4	-0.106847	-0.8207	0.792442
5	0.083429	0.6408	0.262057
6	-0.058518	-0.4495	0.672635
7	-0.16866	-1.2955	0.899903
8	-0.201122	-1.5448	0.936135
9	-0.132206	-1.0155	0.842991
10	0.040464	0.3108	0.37852
11	0.304832	2.3415	0.011303
12	0.079965	0.6142	0.270716
13	-0.101222	-0.7775	0.780016
14	0.095146	0.7308	0.233887
15	-0.029426	-0.226	0.58902
16	0.069462	0.5335	0.29783

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & 0.176852 & 1.3584 & 0.08975 \tabularnewline
2 & -0.156777 & -1.2042 & 0.883345 \tabularnewline
3 & -0.081949 & -0.6295 & 0.734262 \tabularnewline
4 & -0.106847 & -0.8207 & 0.792442 \tabularnewline
5 & 0.083429 & 0.6408 & 0.262057 \tabularnewline
6 & -0.058518 & -0.4495 & 0.672635 \tabularnewline
7 & -0.16866 & -1.2955 & 0.899903 \tabularnewline
8 & -0.201122 & -1.5448 & 0.936135 \tabularnewline
9 & -0.132206 & -1.0155 & 0.842991 \tabularnewline
10 & 0.040464 & 0.3108 & 0.37852 \tabularnewline
11 & 0.304832 & 2.3415 & 0.011303 \tabularnewline
12 & 0.079965 & 0.6142 & 0.270716 \tabularnewline
13 & -0.101222 & -0.7775 & 0.780016 \tabularnewline
14 & 0.095146 & 0.7308 & 0.233887 \tabularnewline
15 & -0.029426 & -0.226 & 0.58902 \tabularnewline
16 & 0.069462 & 0.5335 & 0.29783 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2995&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]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.176852[/C][C]1.3584[/C][C]0.08975[/C][/ROW]
[ROW][C]2[/C][C]-0.156777[/C][C]-1.2042[/C][C]0.883345[/C][/ROW]
[ROW][C]3[/C][C]-0.081949[/C][C]-0.6295[/C][C]0.734262[/C][/ROW]
[ROW][C]4[/C][C]-0.106847[/C][C]-0.8207[/C][C]0.792442[/C][/ROW]
[ROW][C]5[/C][C]0.083429[/C][C]0.6408[/C][C]0.262057[/C][/ROW]
[ROW][C]6[/C][C]-0.058518[/C][C]-0.4495[/C][C]0.672635[/C][/ROW]
[ROW][C]7[/C][C]-0.16866[/C][C]-1.2955[/C][C]0.899903[/C][/ROW]
[ROW][C]8[/C][C]-0.201122[/C][C]-1.5448[/C][C]0.936135[/C][/ROW]
[ROW][C]9[/C][C]-0.132206[/C][C]-1.0155[/C][C]0.842991[/C][/ROW]
[ROW][C]10[/C][C]0.040464[/C][C]0.3108[/C][C]0.37852[/C][/ROW]
[ROW][C]11[/C][C]0.304832[/C][C]2.3415[/C][C]0.011303[/C][/ROW]
[ROW][C]12[/C][C]0.079965[/C][C]0.6142[/C][C]0.270716[/C][/ROW]
[ROW][C]13[/C][C]-0.101222[/C][C]-0.7775[/C][C]0.780016[/C][/ROW]
[ROW][C]14[/C][C]0.095146[/C][C]0.7308[/C][C]0.233887[/C][/ROW]
[ROW][C]15[/C][C]-0.029426[/C][C]-0.226[/C][C]0.58902[/C][/ROW]
[ROW][C]16[/C][C]0.069462[/C][C]0.5335[/C][C]0.29783[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2995&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2995&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	7.6811	0
1	0.176852	1.3584	0.08975
2	-0.156777	-1.2042	0.883345
3	-0.081949	-0.6295	0.734262
4	-0.106847	-0.8207	0.792442
5	0.083429	0.6408	0.262057
6	-0.058518	-0.4495	0.672635
7	-0.16866	-1.2955	0.899903
8	-0.201122	-1.5448	0.936135
9	-0.132206	-1.0155	0.842991
10	0.040464	0.3108	0.37852
11	0.304832	2.3415	0.011303
12	0.079965	0.6142	0.270716
13	-0.101222	-0.7775	0.780016
14	0.095146	0.7308	0.233887
15	-0.029426	-0.226	0.58902
16	0.069462	0.5335	0.29783

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.176852	1.3584	0.08975
1	-0.194125	-1.4911	0.929369
2	-0.015564	-0.1195	0.547376
3	-0.125489	-0.9639	0.830486
4	0.121778	0.9354	0.176699
5	-0.157376	-1.2088	0.884224
6	-0.105264	-0.8085	0.788988
7	-0.216715	-1.6646	0.949355
8	-0.100748	-0.7739	0.778949
9	-0.051065	-0.3922	0.651852
10	0.27259	2.0938	0.020292
11	-0.086252	-0.6625	0.744889
12	-0.013723	-0.1054	0.541796
13	0.105612	0.8112	0.21025
14	-0.110469	-0.8485	0.800214
15	0.035829	0.2752	0.392059
16	0.019608	0.1506	0.440397

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.176852 & 1.3584 & 0.08975 \tabularnewline
1 & -0.194125 & -1.4911 & 0.929369 \tabularnewline
2 & -0.015564 & -0.1195 & 0.547376 \tabularnewline
3 & -0.125489 & -0.9639 & 0.830486 \tabularnewline
4 & 0.121778 & 0.9354 & 0.176699 \tabularnewline
5 & -0.157376 & -1.2088 & 0.884224 \tabularnewline
6 & -0.105264 & -0.8085 & 0.788988 \tabularnewline
7 & -0.216715 & -1.6646 & 0.949355 \tabularnewline
8 & -0.100748 & -0.7739 & 0.778949 \tabularnewline
9 & -0.051065 & -0.3922 & 0.651852 \tabularnewline
10 & 0.27259 & 2.0938 & 0.020292 \tabularnewline
11 & -0.086252 & -0.6625 & 0.744889 \tabularnewline
12 & -0.013723 & -0.1054 & 0.541796 \tabularnewline
13 & 0.105612 & 0.8112 & 0.21025 \tabularnewline
14 & -0.110469 & -0.8485 & 0.800214 \tabularnewline
15 & 0.035829 & 0.2752 & 0.392059 \tabularnewline
16 & 0.019608 & 0.1506 & 0.440397 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2995&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]0.176852[/C][C]1.3584[/C][C]0.08975[/C][/ROW]
[ROW][C]1[/C][C]-0.194125[/C][C]-1.4911[/C][C]0.929369[/C][/ROW]
[ROW][C]2[/C][C]-0.015564[/C][C]-0.1195[/C][C]0.547376[/C][/ROW]
[ROW][C]3[/C][C]-0.125489[/C][C]-0.9639[/C][C]0.830486[/C][/ROW]
[ROW][C]4[/C][C]0.121778[/C][C]0.9354[/C][C]0.176699[/C][/ROW]
[ROW][C]5[/C][C]-0.157376[/C][C]-1.2088[/C][C]0.884224[/C][/ROW]
[ROW][C]6[/C][C]-0.105264[/C][C]-0.8085[/C][C]0.788988[/C][/ROW]
[ROW][C]7[/C][C]-0.216715[/C][C]-1.6646[/C][C]0.949355[/C][/ROW]
[ROW][C]8[/C][C]-0.100748[/C][C]-0.7739[/C][C]0.778949[/C][/ROW]
[ROW][C]9[/C][C]-0.051065[/C][C]-0.3922[/C][C]0.651852[/C][/ROW]
[ROW][C]10[/C][C]0.27259[/C][C]2.0938[/C][C]0.020292[/C][/ROW]
[ROW][C]11[/C][C]-0.086252[/C][C]-0.6625[/C][C]0.744889[/C][/ROW]
[ROW][C]12[/C][C]-0.013723[/C][C]-0.1054[/C][C]0.541796[/C][/ROW]
[ROW][C]13[/C][C]0.105612[/C][C]0.8112[/C][C]0.21025[/C][/ROW]
[ROW][C]14[/C][C]-0.110469[/C][C]-0.8485[/C][C]0.800214[/C][/ROW]
[ROW][C]15[/C][C]0.035829[/C][C]0.2752[/C][C]0.392059[/C][/ROW]
[ROW][C]16[/C][C]0.019608[/C][C]0.1506[/C][C]0.440397[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2995&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2995&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	0.176852	1.3584	0.08975
1	-0.194125	-1.4911	0.929369
2	-0.015564	-0.1195	0.547376
3	-0.125489	-0.9639	0.830486
4	0.121778	0.9354	0.176699
5	-0.157376	-1.2088	0.884224
6	-0.105264	-0.8085	0.788988
7	-0.216715	-1.6646	0.949355
8	-0.100748	-0.7739	0.778949
9	-0.051065	-0.3922	0.651852
10	0.27259	2.0938	0.020292
11	-0.086252	-0.6625	0.744889
12	-0.013723	-0.1054	0.541796
13	0.105612	0.8112	0.21025
14	-0.110469	-0.8485	0.800214
15	0.035829	0.2752	0.392059
16	0.019608	0.1506	0.440397

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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