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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 13:24:45 -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/2009/Nov/26/t1259267147kkgrhnmdgdgv556.htm/, Retrieved Mon, 29 Apr 2024 00:00:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60370, Retrieved Mon, 29 Apr 2024 00:00:01 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

119

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:19:56] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [] [2009-11-26 20:24:45] [0744dbfa8cdb263e2e292d0a5ee9dc89] [Current]
- R  D            [(Partial) Autocorrelation Function] [] [2009-11-27 19:49:29] [859f65298c93b90426725427c75f8582] 

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Dataseries X:

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Boxplots

8,7
8,2
8,3
8,5
8,6
8,5
8,2
8,1
7,9
8,6
8,7
8,7
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8
8,2
8,1
8,1
8
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,4
6,1
6,5
7,7
7,9
7,5
6,9
6,6
6,9
7,7
8
8
7,7
7,3
7,4
8,1
8,3
8,2

Summary of computational 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 computational 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=60370&T=0

[TABLE]
[ROW][C]Summary of computational 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=60370&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60370&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 computational 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
1	0.883501	6.1211	0
2	0.676599	4.6876	1.2e-05
3	0.492185	3.41	0.000663
4	0.38868	2.6929	0.004864
5	0.374226	2.5927	0.006292
6	0.384355	2.6629	0.005256
7	0.352451	2.4418	0.009174
8	0.242157	1.6777	0.049952
9	0.084501	0.5854	0.280498
10	-0.049076	-0.34	0.367666
11	-0.140993	-0.9768	0.166777
12	-0.188861	-1.3085	0.098473
13	-0.208911	-1.4474	0.077146
14	-0.224744	-1.5571	0.063011
15	-0.260811	-1.807	0.03852
16	-0.302554	-2.0962	0.020682
17	-0.317326	-2.1985	0.016383

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.883501 & 6.1211 & 0 \tabularnewline
2 & 0.676599 & 4.6876 & 1.2e-05 \tabularnewline
3 & 0.492185 & 3.41 & 0.000663 \tabularnewline
4 & 0.38868 & 2.6929 & 0.004864 \tabularnewline
5 & 0.374226 & 2.5927 & 0.006292 \tabularnewline
6 & 0.384355 & 2.6629 & 0.005256 \tabularnewline
7 & 0.352451 & 2.4418 & 0.009174 \tabularnewline
8 & 0.242157 & 1.6777 & 0.049952 \tabularnewline
9 & 0.084501 & 0.5854 & 0.280498 \tabularnewline
10 & -0.049076 & -0.34 & 0.367666 \tabularnewline
11 & -0.140993 & -0.9768 & 0.166777 \tabularnewline
12 & -0.188861 & -1.3085 & 0.098473 \tabularnewline
13 & -0.208911 & -1.4474 & 0.077146 \tabularnewline
14 & -0.224744 & -1.5571 & 0.063011 \tabularnewline
15 & -0.260811 & -1.807 & 0.03852 \tabularnewline
16 & -0.302554 & -2.0962 & 0.020682 \tabularnewline
17 & -0.317326 & -2.1985 & 0.016383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60370&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]1[/C][C]0.883501[/C][C]6.1211[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.676599[/C][C]4.6876[/C][C]1.2e-05[/C][/ROW]
[ROW][C]3[/C][C]0.492185[/C][C]3.41[/C][C]0.000663[/C][/ROW]
[ROW][C]4[/C][C]0.38868[/C][C]2.6929[/C][C]0.004864[/C][/ROW]
[ROW][C]5[/C][C]0.374226[/C][C]2.5927[/C][C]0.006292[/C][/ROW]
[ROW][C]6[/C][C]0.384355[/C][C]2.6629[/C][C]0.005256[/C][/ROW]
[ROW][C]7[/C][C]0.352451[/C][C]2.4418[/C][C]0.009174[/C][/ROW]
[ROW][C]8[/C][C]0.242157[/C][C]1.6777[/C][C]0.049952[/C][/ROW]
[ROW][C]9[/C][C]0.084501[/C][C]0.5854[/C][C]0.280498[/C][/ROW]
[ROW][C]10[/C][C]-0.049076[/C][C]-0.34[/C][C]0.367666[/C][/ROW]
[ROW][C]11[/C][C]-0.140993[/C][C]-0.9768[/C][C]0.166777[/C][/ROW]
[ROW][C]12[/C][C]-0.188861[/C][C]-1.3085[/C][C]0.098473[/C][/ROW]
[ROW][C]13[/C][C]-0.208911[/C][C]-1.4474[/C][C]0.077146[/C][/ROW]
[ROW][C]14[/C][C]-0.224744[/C][C]-1.5571[/C][C]0.063011[/C][/ROW]
[ROW][C]15[/C][C]-0.260811[/C][C]-1.807[/C][C]0.03852[/C][/ROW]
[ROW][C]16[/C][C]-0.302554[/C][C]-2.0962[/C][C]0.020682[/C][/ROW]
[ROW][C]17[/C][C]-0.317326[/C][C]-2.1985[/C][C]0.016383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60370&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60370&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
1	0.883501	6.1211	0
2	0.676599	4.6876	1.2e-05
3	0.492185	3.41	0.000663
4	0.38868	2.6929	0.004864
5	0.374226	2.5927	0.006292
6	0.384355	2.6629	0.005256
7	0.352451	2.4418	0.009174
8	0.242157	1.6777	0.049952
9	0.084501	0.5854	0.280498
10	-0.049076	-0.34	0.367666
11	-0.140993	-0.9768	0.166777
12	-0.188861	-1.3085	0.098473
13	-0.208911	-1.4474	0.077146
14	-0.224744	-1.5571	0.063011
15	-0.260811	-1.807	0.03852
16	-0.302554	-2.0962	0.020682
17	-0.317326	-2.1985	0.016383

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.883501	6.1211	0
2	-0.473849	-3.2829	0.00096
3	0.175131	1.2133	0.115468
4	0.164376	1.1388	0.130213
5	0.16231	1.1245	0.133193
6	-0.09755	-0.6758	0.251191
7	-0.134063	-0.9288	0.178817
8	-0.209384	-1.4507	0.07669
9	-0.072688	-0.5036	0.308424
10	0.028399	0.1968	0.422425
11	-0.175507	-1.216	0.114975
12	-0.05433	-0.3764	0.354134
13	-0.011823	-0.0819	0.467527
14	0.032107	0.2224	0.412457
15	-0.091818	-0.6361	0.263855
16	0.047666	0.3302	0.371328
17	0.079546	0.5511	0.292057

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.883501 & 6.1211 & 0 \tabularnewline
2 & -0.473849 & -3.2829 & 0.00096 \tabularnewline
3 & 0.175131 & 1.2133 & 0.115468 \tabularnewline
4 & 0.164376 & 1.1388 & 0.130213 \tabularnewline
5 & 0.16231 & 1.1245 & 0.133193 \tabularnewline
6 & -0.09755 & -0.6758 & 0.251191 \tabularnewline
7 & -0.134063 & -0.9288 & 0.178817 \tabularnewline
8 & -0.209384 & -1.4507 & 0.07669 \tabularnewline
9 & -0.072688 & -0.5036 & 0.308424 \tabularnewline
10 & 0.028399 & 0.1968 & 0.422425 \tabularnewline
11 & -0.175507 & -1.216 & 0.114975 \tabularnewline
12 & -0.05433 & -0.3764 & 0.354134 \tabularnewline
13 & -0.011823 & -0.0819 & 0.467527 \tabularnewline
14 & 0.032107 & 0.2224 & 0.412457 \tabularnewline
15 & -0.091818 & -0.6361 & 0.263855 \tabularnewline
16 & 0.047666 & 0.3302 & 0.371328 \tabularnewline
17 & 0.079546 & 0.5511 & 0.292057 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60370&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]1[/C][C]0.883501[/C][C]6.1211[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.473849[/C][C]-3.2829[/C][C]0.00096[/C][/ROW]
[ROW][C]3[/C][C]0.175131[/C][C]1.2133[/C][C]0.115468[/C][/ROW]
[ROW][C]4[/C][C]0.164376[/C][C]1.1388[/C][C]0.130213[/C][/ROW]
[ROW][C]5[/C][C]0.16231[/C][C]1.1245[/C][C]0.133193[/C][/ROW]
[ROW][C]6[/C][C]-0.09755[/C][C]-0.6758[/C][C]0.251191[/C][/ROW]
[ROW][C]7[/C][C]-0.134063[/C][C]-0.9288[/C][C]0.178817[/C][/ROW]
[ROW][C]8[/C][C]-0.209384[/C][C]-1.4507[/C][C]0.07669[/C][/ROW]
[ROW][C]9[/C][C]-0.072688[/C][C]-0.5036[/C][C]0.308424[/C][/ROW]
[ROW][C]10[/C][C]0.028399[/C][C]0.1968[/C][C]0.422425[/C][/ROW]
[ROW][C]11[/C][C]-0.175507[/C][C]-1.216[/C][C]0.114975[/C][/ROW]
[ROW][C]12[/C][C]-0.05433[/C][C]-0.3764[/C][C]0.354134[/C][/ROW]
[ROW][C]13[/C][C]-0.011823[/C][C]-0.0819[/C][C]0.467527[/C][/ROW]
[ROW][C]14[/C][C]0.032107[/C][C]0.2224[/C][C]0.412457[/C][/ROW]
[ROW][C]15[/C][C]-0.091818[/C][C]-0.6361[/C][C]0.263855[/C][/ROW]
[ROW][C]16[/C][C]0.047666[/C][C]0.3302[/C][C]0.371328[/C][/ROW]
[ROW][C]17[/C][C]0.079546[/C][C]0.5511[/C][C]0.292057[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60370&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60370&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
1	0.883501	6.1211	0
2	-0.473849	-3.2829	0.00096
3	0.175131	1.2133	0.115468
4	0.164376	1.1388	0.130213
5	0.16231	1.1245	0.133193
6	-0.09755	-0.6758	0.251191
7	-0.134063	-0.9288	0.178817
8	-0.209384	-1.4507	0.07669
9	-0.072688	-0.5036	0.308424
10	0.028399	0.1968	0.422425
11	-0.175507	-1.216	0.114975
12	-0.05433	-0.3764	0.354134
13	-0.011823	-0.0819	0.467527
14	0.032107	0.2224	0.412457
15	-0.091818	-0.6361	0.263855
16	0.047666	0.3302	0.371328
17	0.079546	0.5511	0.292057

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 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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 2:(par1+1)) {
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(abs(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,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(abs(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