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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 11 Dec 2007 12:32:13 -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/11/t1197400647vk10fuqd6xs6kpw.htm/, Retrieved Mon, 29 Apr 2024 04:47:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3162, Retrieved Mon, 29 Apr 2024 04:47:12 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

211

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

-       [(Partial) Autocorrelation Function] [Inducing stationa...] [2007-12-11 19:32:13] [578856645eee7b4b8f74dcf589866e9b] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3162&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]2 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=3162&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3162&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.4261	0
1	0.312739	2.6352	0.005159
2	-0.136067	-1.1465	0.872285
3	-0.162708	-1.371	0.912654
4	0.079968	0.6738	0.251307
5	0.018447	0.1554	0.43846
6	-0.191041	-1.6097	0.944054
7	-0.056051	-0.4723	0.680916
8	0.071481	0.6023	0.274445
9	0.115351	0.972	0.167184
10	0.082566	0.6957	0.244439
11	0.021606	0.1821	0.428031
12	-0.030352	-0.2557	0.600558
13	-0.031849	-0.2684	0.605403
14	-0.030578	-0.2577	0.601292
15	-0.134263	-1.1313	0.869137
16	-0.185344	-1.5617	0.938602
17	0.078031	0.6575	0.256494

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4261 & 0 \tabularnewline
1 & 0.312739 & 2.6352 & 0.005159 \tabularnewline
2 & -0.136067 & -1.1465 & 0.872285 \tabularnewline
3 & -0.162708 & -1.371 & 0.912654 \tabularnewline
4 & 0.079968 & 0.6738 & 0.251307 \tabularnewline
5 & 0.018447 & 0.1554 & 0.43846 \tabularnewline
6 & -0.191041 & -1.6097 & 0.944054 \tabularnewline
7 & -0.056051 & -0.4723 & 0.680916 \tabularnewline
8 & 0.071481 & 0.6023 & 0.274445 \tabularnewline
9 & 0.115351 & 0.972 & 0.167184 \tabularnewline
10 & 0.082566 & 0.6957 & 0.244439 \tabularnewline
11 & 0.021606 & 0.1821 & 0.428031 \tabularnewline
12 & -0.030352 & -0.2557 & 0.600558 \tabularnewline
13 & -0.031849 & -0.2684 & 0.605403 \tabularnewline
14 & -0.030578 & -0.2577 & 0.601292 \tabularnewline
15 & -0.134263 & -1.1313 & 0.869137 \tabularnewline
16 & -0.185344 & -1.5617 & 0.938602 \tabularnewline
17 & 0.078031 & 0.6575 & 0.256494 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3162&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]8.4261[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.312739[/C][C]2.6352[/C][C]0.005159[/C][/ROW]
[ROW][C]2[/C][C]-0.136067[/C][C]-1.1465[/C][C]0.872285[/C][/ROW]
[ROW][C]3[/C][C]-0.162708[/C][C]-1.371[/C][C]0.912654[/C][/ROW]
[ROW][C]4[/C][C]0.079968[/C][C]0.6738[/C][C]0.251307[/C][/ROW]
[ROW][C]5[/C][C]0.018447[/C][C]0.1554[/C][C]0.43846[/C][/ROW]
[ROW][C]6[/C][C]-0.191041[/C][C]-1.6097[/C][C]0.944054[/C][/ROW]
[ROW][C]7[/C][C]-0.056051[/C][C]-0.4723[/C][C]0.680916[/C][/ROW]
[ROW][C]8[/C][C]0.071481[/C][C]0.6023[/C][C]0.274445[/C][/ROW]
[ROW][C]9[/C][C]0.115351[/C][C]0.972[/C][C]0.167184[/C][/ROW]
[ROW][C]10[/C][C]0.082566[/C][C]0.6957[/C][C]0.244439[/C][/ROW]
[ROW][C]11[/C][C]0.021606[/C][C]0.1821[/C][C]0.428031[/C][/ROW]
[ROW][C]12[/C][C]-0.030352[/C][C]-0.2557[/C][C]0.600558[/C][/ROW]
[ROW][C]13[/C][C]-0.031849[/C][C]-0.2684[/C][C]0.605403[/C][/ROW]
[ROW][C]14[/C][C]-0.030578[/C][C]-0.2577[/C][C]0.601292[/C][/ROW]
[ROW][C]15[/C][C]-0.134263[/C][C]-1.1313[/C][C]0.869137[/C][/ROW]
[ROW][C]16[/C][C]-0.185344[/C][C]-1.5617[/C][C]0.938602[/C][/ROW]
[ROW][C]17[/C][C]0.078031[/C][C]0.6575[/C][C]0.256494[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3162&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3162&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	8.4261	0
1	0.312739	2.6352	0.005159
2	-0.136067	-1.1465	0.872285
3	-0.162708	-1.371	0.912654
4	0.079968	0.6738	0.251307
5	0.018447	0.1554	0.43846
6	-0.191041	-1.6097	0.944054
7	-0.056051	-0.4723	0.680916
8	0.071481	0.6023	0.274445
9	0.115351	0.972	0.167184
10	0.082566	0.6957	0.244439
11	0.021606	0.1821	0.428031
12	-0.030352	-0.2557	0.600558
13	-0.031849	-0.2684	0.605403
14	-0.030578	-0.2577	0.601292
15	-0.134263	-1.1313	0.869137
16	-0.185344	-1.5617	0.938602
17	0.078031	0.6575	0.256494

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.312739	2.6352	0.005159
1	-0.259226	-2.1843	0.983877
2	-0.033335	-0.2809	0.610192
3	0.142246	1.1986	0.117337
4	-0.125733	-1.0594	0.853505
5	-0.16544	-1.394	0.916171
6	0.128148	1.0798	0.141944
7	-0.03398	-0.2863	0.612268
8	0.050945	0.4293	0.334513
9	0.122159	1.0293	0.153409
10	-0.036026	-0.3036	0.618824
11	-0.051862	-0.437	0.66828
12	0.043115	0.3633	0.358732
13	-0.055821	-0.4704	0.680229
14	-0.150072	-1.2645	0.894913
15	-0.066986	-0.5644	0.71288
16	0.185569	1.5636	0.061175
17	-0.135379	-1.1407	0.871092

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.312739 & 2.6352 & 0.005159 \tabularnewline
1 & -0.259226 & -2.1843 & 0.983877 \tabularnewline
2 & -0.033335 & -0.2809 & 0.610192 \tabularnewline
3 & 0.142246 & 1.1986 & 0.117337 \tabularnewline
4 & -0.125733 & -1.0594 & 0.853505 \tabularnewline
5 & -0.16544 & -1.394 & 0.916171 \tabularnewline
6 & 0.128148 & 1.0798 & 0.141944 \tabularnewline
7 & -0.03398 & -0.2863 & 0.612268 \tabularnewline
8 & 0.050945 & 0.4293 & 0.334513 \tabularnewline
9 & 0.122159 & 1.0293 & 0.153409 \tabularnewline
10 & -0.036026 & -0.3036 & 0.618824 \tabularnewline
11 & -0.051862 & -0.437 & 0.66828 \tabularnewline
12 & 0.043115 & 0.3633 & 0.358732 \tabularnewline
13 & -0.055821 & -0.4704 & 0.680229 \tabularnewline
14 & -0.150072 & -1.2645 & 0.894913 \tabularnewline
15 & -0.066986 & -0.5644 & 0.71288 \tabularnewline
16 & 0.185569 & 1.5636 & 0.061175 \tabularnewline
17 & -0.135379 & -1.1407 & 0.871092 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3162&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]0.312739[/C][C]2.6352[/C][C]0.005159[/C][/ROW]
[ROW][C]1[/C][C]-0.259226[/C][C]-2.1843[/C][C]0.983877[/C][/ROW]
[ROW][C]2[/C][C]-0.033335[/C][C]-0.2809[/C][C]0.610192[/C][/ROW]
[ROW][C]3[/C][C]0.142246[/C][C]1.1986[/C][C]0.117337[/C][/ROW]
[ROW][C]4[/C][C]-0.125733[/C][C]-1.0594[/C][C]0.853505[/C][/ROW]
[ROW][C]5[/C][C]-0.16544[/C][C]-1.394[/C][C]0.916171[/C][/ROW]
[ROW][C]6[/C][C]0.128148[/C][C]1.0798[/C][C]0.141944[/C][/ROW]
[ROW][C]7[/C][C]-0.03398[/C][C]-0.2863[/C][C]0.612268[/C][/ROW]
[ROW][C]8[/C][C]0.050945[/C][C]0.4293[/C][C]0.334513[/C][/ROW]
[ROW][C]9[/C][C]0.122159[/C][C]1.0293[/C][C]0.153409[/C][/ROW]
[ROW][C]10[/C][C]-0.036026[/C][C]-0.3036[/C][C]0.618824[/C][/ROW]
[ROW][C]11[/C][C]-0.051862[/C][C]-0.437[/C][C]0.66828[/C][/ROW]
[ROW][C]12[/C][C]0.043115[/C][C]0.3633[/C][C]0.358732[/C][/ROW]
[ROW][C]13[/C][C]-0.055821[/C][C]-0.4704[/C][C]0.680229[/C][/ROW]
[ROW][C]14[/C][C]-0.150072[/C][C]-1.2645[/C][C]0.894913[/C][/ROW]
[ROW][C]15[/C][C]-0.066986[/C][C]-0.5644[/C][C]0.71288[/C][/ROW]
[ROW][C]16[/C][C]0.185569[/C][C]1.5636[/C][C]0.061175[/C][/ROW]
[ROW][C]17[/C][C]-0.135379[/C][C]-1.1407[/C][C]0.871092[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3162&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3162&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	0.312739	2.6352	0.005159
1	-0.259226	-2.1843	0.983877
2	-0.033335	-0.2809	0.610192
3	0.142246	1.1986	0.117337
4	-0.125733	-1.0594	0.853505
5	-0.16544	-1.394	0.916171
6	0.128148	1.0798	0.141944
7	-0.03398	-0.2863	0.612268
8	0.050945	0.4293	0.334513
9	0.122159	1.0293	0.153409
10	-0.036026	-0.3036	0.618824
11	-0.051862	-0.437	0.66828
12	0.043115	0.3633	0.358732
13	-0.055821	-0.4704	0.680229
14	-0.150072	-1.2645	0.894913
15	-0.066986	-0.5644	0.71288
16	0.185569	1.5636	0.061175
17	-0.135379	-1.1407	0.871092

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1.6 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1.6 ; 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')

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