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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

Tue, 20 May 2014 09:45:18 -0400

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/2014/May/20/t1400593620xmkygyy53eyagcu.htm/, Retrieved Wed, 15 May 2024 17:45:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234988, Retrieved Wed, 15 May 2024 17:45:35 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

142

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

-     [Standard Deviation Plot] [] [2014-04-28 15:57:15] [ccb4fa85fbb66dbee3adf4746bc114a3]
- RMPD    [(Partial) Autocorrelation Function] [] [2014-05-20 13:45:18] [c97636ecf0aef6cf672ffb6fe15d6b60] [Current]

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Dataseries X:

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Histogram

Boxplots

2.79
3.08
3.89
3.7
4.61
5.07
5.22
4.93
5.15
4.8
3.89
3.54
3.34
2.8
1.6
1.53
0.69
-0.11
-0.67
-0.2
-0.62
-0.58
-0.31
-0.25
-0.08
0.13
0.94
1.05
1.59
2.03
2.15
2.06
2.56
2.55
2.53
2.6
2.71
2.82
2.93
2.88
2.89
3.27
3.32
3.14
3.04
3.08
3.39
3.23
3.38
3.41
3.14
2.96
2.73
2.21
2.23
2.56
2.39
2.49
2.17
2.16
1.48
1.09
1.25
1.26
1.39
1.69
1.55
1.19
1.08
0.93
0.98
1.01

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234988&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234988&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234988&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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.329626	2.7775	0.003501
2	0.318217	2.6813	0.004556
3	0.365221	3.0774	0.001483
4	0.316219	2.6645	0.004768
5	-0.078599	-0.6623	0.254967
6	0.051246	0.4318	0.333596
7	0.179898	1.5159	0.066998
8	-0.129328	-1.0897	0.139756
9	-0.185022	-1.559	0.061718
10	-0.181324	-1.5279	0.065495
11	-0.157589	-1.3279	0.094237
12	-0.547344	-4.612	9e-06
13	-0.174555	-1.4708	0.072878
14	-0.200155	-1.6865	0.048041
15	-0.23394	-1.9712	0.026299
16	-0.221166	-1.8636	0.033258
17	0.00739	0.0623	0.475262
18	-0.115829	-0.976	0.166191

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.329626 & 2.7775 & 0.003501 \tabularnewline
2 & 0.318217 & 2.6813 & 0.004556 \tabularnewline
3 & 0.365221 & 3.0774 & 0.001483 \tabularnewline
4 & 0.316219 & 2.6645 & 0.004768 \tabularnewline
5 & -0.078599 & -0.6623 & 0.254967 \tabularnewline
6 & 0.051246 & 0.4318 & 0.333596 \tabularnewline
7 & 0.179898 & 1.5159 & 0.066998 \tabularnewline
8 & -0.129328 & -1.0897 & 0.139756 \tabularnewline
9 & -0.185022 & -1.559 & 0.061718 \tabularnewline
10 & -0.181324 & -1.5279 & 0.065495 \tabularnewline
11 & -0.157589 & -1.3279 & 0.094237 \tabularnewline
12 & -0.547344 & -4.612 & 9e-06 \tabularnewline
13 & -0.174555 & -1.4708 & 0.072878 \tabularnewline
14 & -0.200155 & -1.6865 & 0.048041 \tabularnewline
15 & -0.23394 & -1.9712 & 0.026299 \tabularnewline
16 & -0.221166 & -1.8636 & 0.033258 \tabularnewline
17 & 0.00739 & 0.0623 & 0.475262 \tabularnewline
18 & -0.115829 & -0.976 & 0.166191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234988&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]0.329626[/C][C]2.7775[/C][C]0.003501[/C][/ROW]
[ROW][C]2[/C][C]0.318217[/C][C]2.6813[/C][C]0.004556[/C][/ROW]
[ROW][C]3[/C][C]0.365221[/C][C]3.0774[/C][C]0.001483[/C][/ROW]
[ROW][C]4[/C][C]0.316219[/C][C]2.6645[/C][C]0.004768[/C][/ROW]
[ROW][C]5[/C][C]-0.078599[/C][C]-0.6623[/C][C]0.254967[/C][/ROW]
[ROW][C]6[/C][C]0.051246[/C][C]0.4318[/C][C]0.333596[/C][/ROW]
[ROW][C]7[/C][C]0.179898[/C][C]1.5159[/C][C]0.066998[/C][/ROW]
[ROW][C]8[/C][C]-0.129328[/C][C]-1.0897[/C][C]0.139756[/C][/ROW]
[ROW][C]9[/C][C]-0.185022[/C][C]-1.559[/C][C]0.061718[/C][/ROW]
[ROW][C]10[/C][C]-0.181324[/C][C]-1.5279[/C][C]0.065495[/C][/ROW]
[ROW][C]11[/C][C]-0.157589[/C][C]-1.3279[/C][C]0.094237[/C][/ROW]
[ROW][C]12[/C][C]-0.547344[/C][C]-4.612[/C][C]9e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.174555[/C][C]-1.4708[/C][C]0.072878[/C][/ROW]
[ROW][C]14[/C][C]-0.200155[/C][C]-1.6865[/C][C]0.048041[/C][/ROW]
[ROW][C]15[/C][C]-0.23394[/C][C]-1.9712[/C][C]0.026299[/C][/ROW]
[ROW][C]16[/C][C]-0.221166[/C][C]-1.8636[/C][C]0.033258[/C][/ROW]
[ROW][C]17[/C][C]0.00739[/C][C]0.0623[/C][C]0.475262[/C][/ROW]
[ROW][C]18[/C][C]-0.115829[/C][C]-0.976[/C][C]0.166191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234988&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234988&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	0.329626	2.7775	0.003501
2	0.318217	2.6813	0.004556
3	0.365221	3.0774	0.001483
4	0.316219	2.6645	0.004768
5	-0.078599	-0.6623	0.254967
6	0.051246	0.4318	0.333596
7	0.179898	1.5159	0.066998
8	-0.129328	-1.0897	0.139756
9	-0.185022	-1.559	0.061718
10	-0.181324	-1.5279	0.065495
11	-0.157589	-1.3279	0.094237
12	-0.547344	-4.612	9e-06
13	-0.174555	-1.4708	0.072878
14	-0.200155	-1.6865	0.048041
15	-0.23394	-1.9712	0.026299
16	-0.221166	-1.8636	0.033258
17	0.00739	0.0623	0.475262
18	-0.115829	-0.976	0.166191

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.329626	2.7775	0.003501
2	0.235109	1.9811	0.025729
3	0.246404	2.0762	0.020747
4	0.137843	1.1615	0.124667
5	-0.385431	-3.2477	0.000889
6	-0.065984	-0.556	0.289983
7	0.239679	2.0196	0.023602
8	-0.154951	-1.3056	0.097946
9	-0.15982	-1.3467	0.091185
10	-0.300208	-2.5296	0.00682
11	-0.02006	-0.169	0.433126
12	-0.281687	-2.3735	0.010164
13	0.241628	2.036	0.022741
14	0.039097	0.3294	0.371398
15	-0.035118	-0.2959	0.384082
16	0.006112	0.0515	0.479537
17	-0.051549	-0.4344	0.332672
18	-0.03641	-0.3068	0.379949

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.329626 & 2.7775 & 0.003501 \tabularnewline
2 & 0.235109 & 1.9811 & 0.025729 \tabularnewline
3 & 0.246404 & 2.0762 & 0.020747 \tabularnewline
4 & 0.137843 & 1.1615 & 0.124667 \tabularnewline
5 & -0.385431 & -3.2477 & 0.000889 \tabularnewline
6 & -0.065984 & -0.556 & 0.289983 \tabularnewline
7 & 0.239679 & 2.0196 & 0.023602 \tabularnewline
8 & -0.154951 & -1.3056 & 0.097946 \tabularnewline
9 & -0.15982 & -1.3467 & 0.091185 \tabularnewline
10 & -0.300208 & -2.5296 & 0.00682 \tabularnewline
11 & -0.02006 & -0.169 & 0.433126 \tabularnewline
12 & -0.281687 & -2.3735 & 0.010164 \tabularnewline
13 & 0.241628 & 2.036 & 0.022741 \tabularnewline
14 & 0.039097 & 0.3294 & 0.371398 \tabularnewline
15 & -0.035118 & -0.2959 & 0.384082 \tabularnewline
16 & 0.006112 & 0.0515 & 0.479537 \tabularnewline
17 & -0.051549 & -0.4344 & 0.332672 \tabularnewline
18 & -0.03641 & -0.3068 & 0.379949 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234988&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]0.329626[/C][C]2.7775[/C][C]0.003501[/C][/ROW]
[ROW][C]2[/C][C]0.235109[/C][C]1.9811[/C][C]0.025729[/C][/ROW]
[ROW][C]3[/C][C]0.246404[/C][C]2.0762[/C][C]0.020747[/C][/ROW]
[ROW][C]4[/C][C]0.137843[/C][C]1.1615[/C][C]0.124667[/C][/ROW]
[ROW][C]5[/C][C]-0.385431[/C][C]-3.2477[/C][C]0.000889[/C][/ROW]
[ROW][C]6[/C][C]-0.065984[/C][C]-0.556[/C][C]0.289983[/C][/ROW]
[ROW][C]7[/C][C]0.239679[/C][C]2.0196[/C][C]0.023602[/C][/ROW]
[ROW][C]8[/C][C]-0.154951[/C][C]-1.3056[/C][C]0.097946[/C][/ROW]
[ROW][C]9[/C][C]-0.15982[/C][C]-1.3467[/C][C]0.091185[/C][/ROW]
[ROW][C]10[/C][C]-0.300208[/C][C]-2.5296[/C][C]0.00682[/C][/ROW]
[ROW][C]11[/C][C]-0.02006[/C][C]-0.169[/C][C]0.433126[/C][/ROW]
[ROW][C]12[/C][C]-0.281687[/C][C]-2.3735[/C][C]0.010164[/C][/ROW]
[ROW][C]13[/C][C]0.241628[/C][C]2.036[/C][C]0.022741[/C][/ROW]
[ROW][C]14[/C][C]0.039097[/C][C]0.3294[/C][C]0.371398[/C][/ROW]
[ROW][C]15[/C][C]-0.035118[/C][C]-0.2959[/C][C]0.384082[/C][/ROW]
[ROW][C]16[/C][C]0.006112[/C][C]0.0515[/C][C]0.479537[/C][/ROW]
[ROW][C]17[/C][C]-0.051549[/C][C]-0.4344[/C][C]0.332672[/C][/ROW]
[ROW][C]18[/C][C]-0.03641[/C][C]-0.3068[/C][C]0.379949[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234988&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234988&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	0.329626	2.7775	0.003501
2	0.235109	1.9811	0.025729
3	0.246404	2.0762	0.020747
4	0.137843	1.1615	0.124667
5	-0.385431	-3.2477	0.000889
6	-0.065984	-0.556	0.289983
7	0.239679	2.0196	0.023602
8	-0.154951	-1.3056	0.097946
9	-0.15982	-1.3467	0.091185
10	-0.300208	-2.5296	0.00682
11	-0.02006	-0.169	0.433126
12	-0.281687	-2.3735	0.010164
13	0.241628	2.036	0.022741
14	0.039097	0.3294	0.371398
15	-0.035118	-0.2959	0.384082
16	0.006112	0.0515	0.479537
17	-0.051549	-0.4344	0.332672
18	-0.03641	-0.3068	0.379949

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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