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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 27 Nov 2007 03:35:58 -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/27/t1196159385nl6w2i29k4do5vg.htm/, Retrieved Sun, 05 May 2024 10:43:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6834, Retrieved Sun, 05 May 2024 10:43:55 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Q2, reeks 1

Estimated Impact

174

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

-       [(Partial) Autocorrelation Function] [Workshop 3, Q2] [2007-11-27 10:35:58] [416884147cddda4911f05e55b43ccb0c] [Current]

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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=6834&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=6834&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6834&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	8.3066	0
1	0.320654	2.6636	0.004808
2	0.437048	3.6304	0.00027
3	0.532435	4.4227	1.8e-05
4	0.24929	2.0708	0.021062
5	0.243518	2.0228	0.023485
6	0.187894	1.5608	0.061577
7	-0.072133	-0.5992	0.724492
8	-0.058594	-0.4867	0.685999
9	-0.045798	-0.3804	0.647601
10	-0.282547	-2.347	0.9891
11	-0.154983	-1.2874	0.898869
12	-0.266494	-2.2137	0.98492
13	-0.230892	-1.9179	0.97037
14	-0.098451	-0.8178	0.791855
15	-0.141919	-1.1789	0.87875
16	-0.183263	-1.5223	0.933748
17	0.055327	0.4596	0.323631
18	0.018793	0.1561	0.438204

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.3066 & 0 \tabularnewline
1 & 0.320654 & 2.6636 & 0.004808 \tabularnewline
2 & 0.437048 & 3.6304 & 0.00027 \tabularnewline
3 & 0.532435 & 4.4227 & 1.8e-05 \tabularnewline
4 & 0.24929 & 2.0708 & 0.021062 \tabularnewline
5 & 0.243518 & 2.0228 & 0.023485 \tabularnewline
6 & 0.187894 & 1.5608 & 0.061577 \tabularnewline
7 & -0.072133 & -0.5992 & 0.724492 \tabularnewline
8 & -0.058594 & -0.4867 & 0.685999 \tabularnewline
9 & -0.045798 & -0.3804 & 0.647601 \tabularnewline
10 & -0.282547 & -2.347 & 0.9891 \tabularnewline
11 & -0.154983 & -1.2874 & 0.898869 \tabularnewline
12 & -0.266494 & -2.2137 & 0.98492 \tabularnewline
13 & -0.230892 & -1.9179 & 0.97037 \tabularnewline
14 & -0.098451 & -0.8178 & 0.791855 \tabularnewline
15 & -0.141919 & -1.1789 & 0.87875 \tabularnewline
16 & -0.183263 & -1.5223 & 0.933748 \tabularnewline
17 & 0.055327 & 0.4596 & 0.323631 \tabularnewline
18 & 0.018793 & 0.1561 & 0.438204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6834&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]0.320654[/C][C]2.6636[/C][C]0.004808[/C][/ROW]
[ROW][C]2[/C][C]0.437048[/C][C]3.6304[/C][C]0.00027[/C][/ROW]
[ROW][C]3[/C][C]0.532435[/C][C]4.4227[/C][C]1.8e-05[/C][/ROW]
[ROW][C]4[/C][C]0.24929[/C][C]2.0708[/C][C]0.021062[/C][/ROW]
[ROW][C]5[/C][C]0.243518[/C][C]2.0228[/C][C]0.023485[/C][/ROW]
[ROW][C]6[/C][C]0.187894[/C][C]1.5608[/C][C]0.061577[/C][/ROW]
[ROW][C]7[/C][C]-0.072133[/C][C]-0.5992[/C][C]0.724492[/C][/ROW]
[ROW][C]8[/C][C]-0.058594[/C][C]-0.4867[/C][C]0.685999[/C][/ROW]
[ROW][C]9[/C][C]-0.045798[/C][C]-0.3804[/C][C]0.647601[/C][/ROW]
[ROW][C]10[/C][C]-0.282547[/C][C]-2.347[/C][C]0.9891[/C][/ROW]
[ROW][C]11[/C][C]-0.154983[/C][C]-1.2874[/C][C]0.898869[/C][/ROW]
[ROW][C]12[/C][C]-0.266494[/C][C]-2.2137[/C][C]0.98492[/C][/ROW]
[ROW][C]13[/C][C]-0.230892[/C][C]-1.9179[/C][C]0.97037[/C][/ROW]
[ROW][C]14[/C][C]-0.098451[/C][C]-0.8178[/C][C]0.791855[/C][/ROW]
[ROW][C]15[/C][C]-0.141919[/C][C]-1.1789[/C][C]0.87875[/C][/ROW]
[ROW][C]16[/C][C]-0.183263[/C][C]-1.5223[/C][C]0.933748[/C][/ROW]
[ROW][C]17[/C][C]0.055327[/C][C]0.4596[/C][C]0.323631[/C][/ROW]
[ROW][C]18[/C][C]0.018793[/C][C]0.1561[/C][C]0.438204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6834&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6834&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	0.320654	2.6636	0.004808
2	0.437048	3.6304	0.00027
3	0.532435	4.4227	1.8e-05
4	0.24929	2.0708	0.021062
5	0.243518	2.0228	0.023485
6	0.187894	1.5608	0.061577
7	-0.072133	-0.5992	0.724492
8	-0.058594	-0.4867	0.685999
9	-0.045798	-0.3804	0.647601
10	-0.282547	-2.347	0.9891
11	-0.154983	-1.2874	0.898869
12	-0.266494	-2.2137	0.98492
13	-0.230892	-1.9179	0.97037
14	-0.098451	-0.8178	0.791855
15	-0.141919	-1.1789	0.87875
16	-0.183263	-1.5223	0.933748
17	0.055327	0.4596	0.323631
18	0.018793	0.1561	0.438204

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.320654	2.6636	0.004808
1	0.372532	3.0945	0.001423
2	0.42068	3.4944	0.000417
3	-0.05521	-0.4586	0.676021
4	-0.161413	-1.3408	0.907808
5	-0.161093	-1.3381	0.907378
6	-0.322743	-2.6809	0.995412
7	-0.212753	-1.7673	0.959196
8	0.086773	0.7208	0.236736
9	-0.00769	-0.0639	0.525374
10	0.131282	1.0905	0.13964
11	-0.049933	-0.4148	0.660202
12	0.069089	0.5739	0.283952
13	0.160395	1.3323	0.093566
14	0.118465	0.984	0.164265
15	-0.160646	-1.3344	0.906775
16	-0.004132	-0.0343	0.51364
17	0.027679	0.2299	0.409418
18	-0.15744	-1.3078	0.902359

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.320654 & 2.6636 & 0.004808 \tabularnewline
1 & 0.372532 & 3.0945 & 0.001423 \tabularnewline
2 & 0.42068 & 3.4944 & 0.000417 \tabularnewline
3 & -0.05521 & -0.4586 & 0.676021 \tabularnewline
4 & -0.161413 & -1.3408 & 0.907808 \tabularnewline
5 & -0.161093 & -1.3381 & 0.907378 \tabularnewline
6 & -0.322743 & -2.6809 & 0.995412 \tabularnewline
7 & -0.212753 & -1.7673 & 0.959196 \tabularnewline
8 & 0.086773 & 0.7208 & 0.236736 \tabularnewline
9 & -0.00769 & -0.0639 & 0.525374 \tabularnewline
10 & 0.131282 & 1.0905 & 0.13964 \tabularnewline
11 & -0.049933 & -0.4148 & 0.660202 \tabularnewline
12 & 0.069089 & 0.5739 & 0.283952 \tabularnewline
13 & 0.160395 & 1.3323 & 0.093566 \tabularnewline
14 & 0.118465 & 0.984 & 0.164265 \tabularnewline
15 & -0.160646 & -1.3344 & 0.906775 \tabularnewline
16 & -0.004132 & -0.0343 & 0.51364 \tabularnewline
17 & 0.027679 & 0.2299 & 0.409418 \tabularnewline
18 & -0.15744 & -1.3078 & 0.902359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6834&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]0.320654[/C][C]2.6636[/C][C]0.004808[/C][/ROW]
[ROW][C]1[/C][C]0.372532[/C][C]3.0945[/C][C]0.001423[/C][/ROW]
[ROW][C]2[/C][C]0.42068[/C][C]3.4944[/C][C]0.000417[/C][/ROW]
[ROW][C]3[/C][C]-0.05521[/C][C]-0.4586[/C][C]0.676021[/C][/ROW]
[ROW][C]4[/C][C]-0.161413[/C][C]-1.3408[/C][C]0.907808[/C][/ROW]
[ROW][C]5[/C][C]-0.161093[/C][C]-1.3381[/C][C]0.907378[/C][/ROW]
[ROW][C]6[/C][C]-0.322743[/C][C]-2.6809[/C][C]0.995412[/C][/ROW]
[ROW][C]7[/C][C]-0.212753[/C][C]-1.7673[/C][C]0.959196[/C][/ROW]
[ROW][C]8[/C][C]0.086773[/C][C]0.7208[/C][C]0.236736[/C][/ROW]
[ROW][C]9[/C][C]-0.00769[/C][C]-0.0639[/C][C]0.525374[/C][/ROW]
[ROW][C]10[/C][C]0.131282[/C][C]1.0905[/C][C]0.13964[/C][/ROW]
[ROW][C]11[/C][C]-0.049933[/C][C]-0.4148[/C][C]0.660202[/C][/ROW]
[ROW][C]12[/C][C]0.069089[/C][C]0.5739[/C][C]0.283952[/C][/ROW]
[ROW][C]13[/C][C]0.160395[/C][C]1.3323[/C][C]0.093566[/C][/ROW]
[ROW][C]14[/C][C]0.118465[/C][C]0.984[/C][C]0.164265[/C][/ROW]
[ROW][C]15[/C][C]-0.160646[/C][C]-1.3344[/C][C]0.906775[/C][/ROW]
[ROW][C]16[/C][C]-0.004132[/C][C]-0.0343[/C][C]0.51364[/C][/ROW]
[ROW][C]17[/C][C]0.027679[/C][C]0.2299[/C][C]0.409418[/C][/ROW]
[ROW][C]18[/C][C]-0.15744[/C][C]-1.3078[/C][C]0.902359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6834&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6834&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	0.320654	2.6636	0.004808
1	0.372532	3.0945	0.001423
2	0.42068	3.4944	0.000417
3	-0.05521	-0.4586	0.676021
4	-0.161413	-1.3408	0.907808
5	-0.161093	-1.3381	0.907378
6	-0.322743	-2.6809	0.995412
7	-0.212753	-1.7673	0.959196
8	0.086773	0.7208	0.236736
9	-0.00769	-0.0639	0.525374
10	0.131282	1.0905	0.13964
11	-0.049933	-0.4148	0.660202
12	0.069089	0.5739	0.283952
13	0.160395	1.3323	0.093566
14	0.118465	0.984	0.164265
15	-0.160646	-1.3344	0.906775
16	-0.004132	-0.0343	0.51364
17	0.027679	0.2299	0.409418
18	-0.15744	-1.3078	0.902359

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')

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