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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Nov 2007 09:00:00 -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/28/t1196265001b4n5olye0c922g7.htm/, Retrieved Wed, 01 May 2024 23:11:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7108, Retrieved Wed, 01 May 2024 23:11:03 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

199

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

-       [(Partial) Autocorrelation Function] [Workshop4 Q2] [2007-11-28 16:00:00] [17bc0c288da41f7bf1607b4a2b3ca793] [Current]

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Dataseries X:

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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=7108&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=7108&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7108&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	7.746	0
1	0.21709	1.6816	0.048925
2	-0.174023	-1.348	0.908633
3	-0.139129	-1.0777	0.857256
4	0.144479	1.1191	0.133772
5	0.075852	0.5875	0.279522
6	-0.247741	-1.919	0.970127
7	-0.068768	-0.5327	0.701886
8	0.015153	0.1174	0.453478
9	0.09724	0.7532	0.227133
10	0.020658	0.16	0.436704
11	0.014625	0.1133	0.455093
12	-0.012139	-0.094	0.537301
13	0.039911	0.3091	0.37914
14	0.107308	0.8312	0.204576
15	-0.08418	-0.6521	0.741571
16	-0.149307	-1.1565	0.873975

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.21709 & 1.6816 & 0.048925 \tabularnewline
2 & -0.174023 & -1.348 & 0.908633 \tabularnewline
3 & -0.139129 & -1.0777 & 0.857256 \tabularnewline
4 & 0.144479 & 1.1191 & 0.133772 \tabularnewline
5 & 0.075852 & 0.5875 & 0.279522 \tabularnewline
6 & -0.247741 & -1.919 & 0.970127 \tabularnewline
7 & -0.068768 & -0.5327 & 0.701886 \tabularnewline
8 & 0.015153 & 0.1174 & 0.453478 \tabularnewline
9 & 0.09724 & 0.7532 & 0.227133 \tabularnewline
10 & 0.020658 & 0.16 & 0.436704 \tabularnewline
11 & 0.014625 & 0.1133 & 0.455093 \tabularnewline
12 & -0.012139 & -0.094 & 0.537301 \tabularnewline
13 & 0.039911 & 0.3091 & 0.37914 \tabularnewline
14 & 0.107308 & 0.8312 & 0.204576 \tabularnewline
15 & -0.08418 & -0.6521 & 0.741571 \tabularnewline
16 & -0.149307 & -1.1565 & 0.873975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7108&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.21709[/C][C]1.6816[/C][C]0.048925[/C][/ROW]
[ROW][C]2[/C][C]-0.174023[/C][C]-1.348[/C][C]0.908633[/C][/ROW]
[ROW][C]3[/C][C]-0.139129[/C][C]-1.0777[/C][C]0.857256[/C][/ROW]
[ROW][C]4[/C][C]0.144479[/C][C]1.1191[/C][C]0.133772[/C][/ROW]
[ROW][C]5[/C][C]0.075852[/C][C]0.5875[/C][C]0.279522[/C][/ROW]
[ROW][C]6[/C][C]-0.247741[/C][C]-1.919[/C][C]0.970127[/C][/ROW]
[ROW][C]7[/C][C]-0.068768[/C][C]-0.5327[/C][C]0.701886[/C][/ROW]
[ROW][C]8[/C][C]0.015153[/C][C]0.1174[/C][C]0.453478[/C][/ROW]
[ROW][C]9[/C][C]0.09724[/C][C]0.7532[/C][C]0.227133[/C][/ROW]
[ROW][C]10[/C][C]0.020658[/C][C]0.16[/C][C]0.436704[/C][/ROW]
[ROW][C]11[/C][C]0.014625[/C][C]0.1133[/C][C]0.455093[/C][/ROW]
[ROW][C]12[/C][C]-0.012139[/C][C]-0.094[/C][C]0.537301[/C][/ROW]
[ROW][C]13[/C][C]0.039911[/C][C]0.3091[/C][C]0.37914[/C][/ROW]
[ROW][C]14[/C][C]0.107308[/C][C]0.8312[/C][C]0.204576[/C][/ROW]
[ROW][C]15[/C][C]-0.08418[/C][C]-0.6521[/C][C]0.741571[/C][/ROW]
[ROW][C]16[/C][C]-0.149307[/C][C]-1.1565[/C][C]0.873975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7108&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7108&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	7.746	0
1	0.21709	1.6816	0.048925
2	-0.174023	-1.348	0.908633
3	-0.139129	-1.0777	0.857256
4	0.144479	1.1191	0.133772
5	0.075852	0.5875	0.279522
6	-0.247741	-1.919	0.970127
7	-0.068768	-0.5327	0.701886
8	0.015153	0.1174	0.453478
9	0.09724	0.7532	0.227133
10	0.020658	0.16	0.436704
11	0.014625	0.1133	0.455093
12	-0.012139	-0.094	0.537301
13	0.039911	0.3091	0.37914
14	0.107308	0.8312	0.204576
15	-0.08418	-0.6521	0.741571
16	-0.149307	-1.1565	0.873975

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.21709	1.6816	0.048925
1	-0.232089	-1.7978	0.961376
2	-0.046806	-0.3626	0.640894
3	0.169117	1.31	0.097599
4	-0.045958	-0.356	0.638452
5	-0.244991	-1.8977	0.968724
6	0.122096	0.9458	0.174033
7	-0.100637	-0.7795	0.780635
8	0.048563	0.3762	0.354059
9	0.071969	0.5575	0.28964
10	0.020581	0.1594	0.436937
11	-0.078387	-0.6072	0.72699
12	0.109274	0.8464	0.200337
13	0.051041	0.3954	0.346989
14	-0.147946	-1.146	0.871824
15	-0.036138	-0.2799	0.60975
16	0.053518	0.4145	0.339975

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.21709 & 1.6816 & 0.048925 \tabularnewline
1 & -0.232089 & -1.7978 & 0.961376 \tabularnewline
2 & -0.046806 & -0.3626 & 0.640894 \tabularnewline
3 & 0.169117 & 1.31 & 0.097599 \tabularnewline
4 & -0.045958 & -0.356 & 0.638452 \tabularnewline
5 & -0.244991 & -1.8977 & 0.968724 \tabularnewline
6 & 0.122096 & 0.9458 & 0.174033 \tabularnewline
7 & -0.100637 & -0.7795 & 0.780635 \tabularnewline
8 & 0.048563 & 0.3762 & 0.354059 \tabularnewline
9 & 0.071969 & 0.5575 & 0.28964 \tabularnewline
10 & 0.020581 & 0.1594 & 0.436937 \tabularnewline
11 & -0.078387 & -0.6072 & 0.72699 \tabularnewline
12 & 0.109274 & 0.8464 & 0.200337 \tabularnewline
13 & 0.051041 & 0.3954 & 0.346989 \tabularnewline
14 & -0.147946 & -1.146 & 0.871824 \tabularnewline
15 & -0.036138 & -0.2799 & 0.60975 \tabularnewline
16 & 0.053518 & 0.4145 & 0.339975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7108&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]0.21709[/C][C]1.6816[/C][C]0.048925[/C][/ROW]
[ROW][C]1[/C][C]-0.232089[/C][C]-1.7978[/C][C]0.961376[/C][/ROW]
[ROW][C]2[/C][C]-0.046806[/C][C]-0.3626[/C][C]0.640894[/C][/ROW]
[ROW][C]3[/C][C]0.169117[/C][C]1.31[/C][C]0.097599[/C][/ROW]
[ROW][C]4[/C][C]-0.045958[/C][C]-0.356[/C][C]0.638452[/C][/ROW]
[ROW][C]5[/C][C]-0.244991[/C][C]-1.8977[/C][C]0.968724[/C][/ROW]
[ROW][C]6[/C][C]0.122096[/C][C]0.9458[/C][C]0.174033[/C][/ROW]
[ROW][C]7[/C][C]-0.100637[/C][C]-0.7795[/C][C]0.780635[/C][/ROW]
[ROW][C]8[/C][C]0.048563[/C][C]0.3762[/C][C]0.354059[/C][/ROW]
[ROW][C]9[/C][C]0.071969[/C][C]0.5575[/C][C]0.28964[/C][/ROW]
[ROW][C]10[/C][C]0.020581[/C][C]0.1594[/C][C]0.436937[/C][/ROW]
[ROW][C]11[/C][C]-0.078387[/C][C]-0.6072[/C][C]0.72699[/C][/ROW]
[ROW][C]12[/C][C]0.109274[/C][C]0.8464[/C][C]0.200337[/C][/ROW]
[ROW][C]13[/C][C]0.051041[/C][C]0.3954[/C][C]0.346989[/C][/ROW]
[ROW][C]14[/C][C]-0.147946[/C][C]-1.146[/C][C]0.871824[/C][/ROW]
[ROW][C]15[/C][C]-0.036138[/C][C]-0.2799[/C][C]0.60975[/C][/ROW]
[ROW][C]16[/C][C]0.053518[/C][C]0.4145[/C][C]0.339975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7108&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7108&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	0.21709	1.6816	0.048925
1	-0.232089	-1.7978	0.961376
2	-0.046806	-0.3626	0.640894
3	0.169117	1.31	0.097599
4	-0.045958	-0.356	0.638452
5	-0.244991	-1.8977	0.968724
6	0.122096	0.9458	0.174033
7	-0.100637	-0.7795	0.780635
8	0.048563	0.3762	0.354059
9	0.071969	0.5575	0.28964
10	0.020581	0.1594	0.436937
11	-0.078387	-0.6072	0.72699
12	0.109274	0.8464	0.200337
13	0.051041	0.3954	0.346989
14	-0.147946	-1.146	0.871824
15	-0.036138	-0.2799	0.60975
16	0.053518	0.4145	0.339975

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 = 0 ; par5 = 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code