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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 05 Dec 2007 13:40:27 -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/05/t1196886461n4yokvyn04g4d6n.htm/, Retrieved Thu, 02 May 2024 23:10:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2514, Retrieved Thu, 02 May 2024 23:10:19 +0000

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Estimated Impact

217

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-       [(Partial) Autocorrelation Function] [ws 7] [2007-12-05 20:40:27] [d41d8cd98f00b204e9800998ecf8427e] [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	4 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 & 4 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=2514&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]4 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=2514&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2514&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	4 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	8.1854	0
1	-0.407721	-3.3373	0.999308
2	-0.170895	-1.3988	0.916763
3	0.100731	0.8245	0.206285
4	0.020279	0.166	0.434332
5	0.031473	0.2576	0.398746
6	-0.016085	-0.1317	0.552177
7	0.035058	0.287	0.387512
8	-0.144392	-1.1819	0.879288
9	0.08692	0.7115	0.239632
10	-0.03167	-0.2592	0.601873
11	0.098775	0.8085	0.210829
12	-0.188395	-1.5421	0.936118
13	-0.041572	-0.3403	0.632646
14	0.175851	1.4394	0.077346
15	-0.033528	-0.2744	0.607704
16	0.010038	0.0822	0.467382
17	-0.127741	-1.0456	0.850249
18	0.093636	0.7664	0.223051

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.1854 & 0 \tabularnewline
1 & -0.407721 & -3.3373 & 0.999308 \tabularnewline
2 & -0.170895 & -1.3988 & 0.916763 \tabularnewline
3 & 0.100731 & 0.8245 & 0.206285 \tabularnewline
4 & 0.020279 & 0.166 & 0.434332 \tabularnewline
5 & 0.031473 & 0.2576 & 0.398746 \tabularnewline
6 & -0.016085 & -0.1317 & 0.552177 \tabularnewline
7 & 0.035058 & 0.287 & 0.387512 \tabularnewline
8 & -0.144392 & -1.1819 & 0.879288 \tabularnewline
9 & 0.08692 & 0.7115 & 0.239632 \tabularnewline
10 & -0.03167 & -0.2592 & 0.601873 \tabularnewline
11 & 0.098775 & 0.8085 & 0.210829 \tabularnewline
12 & -0.188395 & -1.5421 & 0.936118 \tabularnewline
13 & -0.041572 & -0.3403 & 0.632646 \tabularnewline
14 & 0.175851 & 1.4394 & 0.077346 \tabularnewline
15 & -0.033528 & -0.2744 & 0.607704 \tabularnewline
16 & 0.010038 & 0.0822 & 0.467382 \tabularnewline
17 & -0.127741 & -1.0456 & 0.850249 \tabularnewline
18 & 0.093636 & 0.7664 & 0.223051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2514&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]8.1854[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.407721[/C][C]-3.3373[/C][C]0.999308[/C][/ROW]
[ROW][C]2[/C][C]-0.170895[/C][C]-1.3988[/C][C]0.916763[/C][/ROW]
[ROW][C]3[/C][C]0.100731[/C][C]0.8245[/C][C]0.206285[/C][/ROW]
[ROW][C]4[/C][C]0.020279[/C][C]0.166[/C][C]0.434332[/C][/ROW]
[ROW][C]5[/C][C]0.031473[/C][C]0.2576[/C][C]0.398746[/C][/ROW]
[ROW][C]6[/C][C]-0.016085[/C][C]-0.1317[/C][C]0.552177[/C][/ROW]
[ROW][C]7[/C][C]0.035058[/C][C]0.287[/C][C]0.387512[/C][/ROW]
[ROW][C]8[/C][C]-0.144392[/C][C]-1.1819[/C][C]0.879288[/C][/ROW]
[ROW][C]9[/C][C]0.08692[/C][C]0.7115[/C][C]0.239632[/C][/ROW]
[ROW][C]10[/C][C]-0.03167[/C][C]-0.2592[/C][C]0.601873[/C][/ROW]
[ROW][C]11[/C][C]0.098775[/C][C]0.8085[/C][C]0.210829[/C][/ROW]
[ROW][C]12[/C][C]-0.188395[/C][C]-1.5421[/C][C]0.936118[/C][/ROW]
[ROW][C]13[/C][C]-0.041572[/C][C]-0.3403[/C][C]0.632646[/C][/ROW]
[ROW][C]14[/C][C]0.175851[/C][C]1.4394[/C][C]0.077346[/C][/ROW]
[ROW][C]15[/C][C]-0.033528[/C][C]-0.2744[/C][C]0.607704[/C][/ROW]
[ROW][C]16[/C][C]0.010038[/C][C]0.0822[/C][C]0.467382[/C][/ROW]
[ROW][C]17[/C][C]-0.127741[/C][C]-1.0456[/C][C]0.850249[/C][/ROW]
[ROW][C]18[/C][C]0.093636[/C][C]0.7664[/C][C]0.223051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2514&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2514&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	8.1854	0
1	-0.407721	-3.3373	0.999308
2	-0.170895	-1.3988	0.916763
3	0.100731	0.8245	0.206285
4	0.020279	0.166	0.434332
5	0.031473	0.2576	0.398746
6	-0.016085	-0.1317	0.552177
7	0.035058	0.287	0.387512
8	-0.144392	-1.1819	0.879288
9	0.08692	0.7115	0.239632
10	-0.03167	-0.2592	0.601873
11	0.098775	0.8085	0.210829
12	-0.188395	-1.5421	0.936118
13	-0.041572	-0.3403	0.632646
14	0.175851	1.4394	0.077346
15	-0.033528	-0.2744	0.607704
16	0.010038	0.0822	0.467382
17	-0.127741	-1.0456	0.850249
18	0.093636	0.7664	0.223051

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.407721	-3.3373	0.999308
1	-0.40435	-3.3097	0.999247
2	-0.232252	-1.9011	0.969202
3	-0.150201	-1.2294	0.888398
4	-0.01564	-0.128	0.550741
5	0.029831	0.2442	0.403919
6	0.120116	0.9832	0.164526
7	-0.089927	-0.7361	0.767875
8	-0.043842	-0.3589	0.639587
9	-0.148418	-1.2149	0.885657
10	0.043224	0.3538	0.362298
11	-0.18851	-1.543	0.936232
12	-0.267791	-2.192	0.984069
13	-0.147006	-1.2033	0.883452
14	-0.069422	-0.5682	0.714114
15	0.052757	0.4318	0.333623
16	-0.07339	-0.6007	0.724975
17	-0.02282	-0.1868	0.573804
18	-0.12251	-1.0028	0.840214

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.407721 & -3.3373 & 0.999308 \tabularnewline
1 & -0.40435 & -3.3097 & 0.999247 \tabularnewline
2 & -0.232252 & -1.9011 & 0.969202 \tabularnewline
3 & -0.150201 & -1.2294 & 0.888398 \tabularnewline
4 & -0.01564 & -0.128 & 0.550741 \tabularnewline
5 & 0.029831 & 0.2442 & 0.403919 \tabularnewline
6 & 0.120116 & 0.9832 & 0.164526 \tabularnewline
7 & -0.089927 & -0.7361 & 0.767875 \tabularnewline
8 & -0.043842 & -0.3589 & 0.639587 \tabularnewline
9 & -0.148418 & -1.2149 & 0.885657 \tabularnewline
10 & 0.043224 & 0.3538 & 0.362298 \tabularnewline
11 & -0.18851 & -1.543 & 0.936232 \tabularnewline
12 & -0.267791 & -2.192 & 0.984069 \tabularnewline
13 & -0.147006 & -1.2033 & 0.883452 \tabularnewline
14 & -0.069422 & -0.5682 & 0.714114 \tabularnewline
15 & 0.052757 & 0.4318 & 0.333623 \tabularnewline
16 & -0.07339 & -0.6007 & 0.724975 \tabularnewline
17 & -0.02282 & -0.1868 & 0.573804 \tabularnewline
18 & -0.12251 & -1.0028 & 0.840214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2514&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]-0.407721[/C][C]-3.3373[/C][C]0.999308[/C][/ROW]
[ROW][C]1[/C][C]-0.40435[/C][C]-3.3097[/C][C]0.999247[/C][/ROW]
[ROW][C]2[/C][C]-0.232252[/C][C]-1.9011[/C][C]0.969202[/C][/ROW]
[ROW][C]3[/C][C]-0.150201[/C][C]-1.2294[/C][C]0.888398[/C][/ROW]
[ROW][C]4[/C][C]-0.01564[/C][C]-0.128[/C][C]0.550741[/C][/ROW]
[ROW][C]5[/C][C]0.029831[/C][C]0.2442[/C][C]0.403919[/C][/ROW]
[ROW][C]6[/C][C]0.120116[/C][C]0.9832[/C][C]0.164526[/C][/ROW]
[ROW][C]7[/C][C]-0.089927[/C][C]-0.7361[/C][C]0.767875[/C][/ROW]
[ROW][C]8[/C][C]-0.043842[/C][C]-0.3589[/C][C]0.639587[/C][/ROW]
[ROW][C]9[/C][C]-0.148418[/C][C]-1.2149[/C][C]0.885657[/C][/ROW]
[ROW][C]10[/C][C]0.043224[/C][C]0.3538[/C][C]0.362298[/C][/ROW]
[ROW][C]11[/C][C]-0.18851[/C][C]-1.543[/C][C]0.936232[/C][/ROW]
[ROW][C]12[/C][C]-0.267791[/C][C]-2.192[/C][C]0.984069[/C][/ROW]
[ROW][C]13[/C][C]-0.147006[/C][C]-1.2033[/C][C]0.883452[/C][/ROW]
[ROW][C]14[/C][C]-0.069422[/C][C]-0.5682[/C][C]0.714114[/C][/ROW]
[ROW][C]15[/C][C]0.052757[/C][C]0.4318[/C][C]0.333623[/C][/ROW]
[ROW][C]16[/C][C]-0.07339[/C][C]-0.6007[/C][C]0.724975[/C][/ROW]
[ROW][C]17[/C][C]-0.02282[/C][C]-0.1868[/C][C]0.573804[/C][/ROW]
[ROW][C]18[/C][C]-0.12251[/C][C]-1.0028[/C][C]0.840214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2514&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2514&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	-0.407721	-3.3373	0.999308
1	-0.40435	-3.3097	0.999247
2	-0.232252	-1.9011	0.969202
3	-0.150201	-1.2294	0.888398
4	-0.01564	-0.128	0.550741
5	0.029831	0.2442	0.403919
6	0.120116	0.9832	0.164526
7	-0.089927	-0.7361	0.767875
8	-0.043842	-0.3589	0.639587
9	-0.148418	-1.2149	0.885657
10	0.043224	0.3538	0.362298
11	-0.18851	-1.543	0.936232
12	-0.267791	-2.192	0.984069
13	-0.147006	-1.2033	0.883452
14	-0.069422	-0.5682	0.714114
15	0.052757	0.4318	0.333623
16	-0.07339	-0.6007	0.724975
17	-0.02282	-0.1868	0.573804
18	-0.12251	-1.0028	0.840214

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

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