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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

Mon, 20 Oct 2014 19:21:17 +0100

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/Oct/20/t1413829296md00455mg5nbec1.htm/, Retrieved Sat, 11 May 2024 05:55:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=244211, Retrieved Sat, 11 May 2024 05:55:43 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-     [(Partial) Autocorrelation Function] [] [2014-10-20 18:15:32] [deebc1e457a5ecb4dd1aad0be1fbee4a]
- R PD    [(Partial) Autocorrelation Function] [] [2014-10-20 18:21:17] [f2e79deb6e51141b138dd10990a8e48d] [Current]

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Dataseries X:

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Histogram

Boxplots

1.38
1.96
1.36
1.24
1.35
1.23
1.09
1.08
1.33
1.35
1.38
1.5
1.47
2.09
1.52
1.29
1.52
1.27
1.35
1.29
1.41
1.39
1.45
1.53
1.45
2.11
1.53
1.38
1.54
1.35
1.29
1.33
1.47
1.47
1.54
1.59
1.5
2
1.51
1.4
1.62
1.44
1.29
1.28
1.4
1.39
1.46
1.49
1.45
2.05
1.59
1.42
1.73
1.39
1.23
1.37
1.51
1.47
1.5
1.54
1.54
2.15
1.62
1.4
1.65
1.49
1.45
1.45
1.51
1.48
1.56
1.57
1.57
2.28
1.7
1.56
1.8
1.56
1.51
1.46
1.51
1.55
1.57
1.64
1.58
2.16
1.77
1.54
1.64
1.53
1.49
1.43
1.52
1.56
1.59
1.64

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	'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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244211&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244211&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244211&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.451381	4.137	4.2e-05
2	0.215584	1.9759	0.025727
3	0.148404	1.3601	0.088711
4	0.108261	0.9922	0.161969
5	0.163906	1.5022	0.068395
6	0.156091	1.4306	0.078128
7	0.098162	0.8997	0.185433
8	0.064451	0.5907	0.278153
9	0.090713	0.8314	0.204052
10	0.048104	0.4409	0.330215
11	-0.050589	-0.4637	0.322047
12	-0.312145	-2.8609	0.002665
13	-0.175304	-1.6067	0.055937
14	-0.091799	-0.8413	0.201271
15	-0.003746	-0.0343	0.486347
16	0.099322	0.9103	0.182633
17	0.061978	0.568	0.285764
18	-0.091907	-0.8423	0.200994
19	-0.191867	-1.7585	0.041153

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.451381 & 4.137 & 4.2e-05 \tabularnewline
2 & 0.215584 & 1.9759 & 0.025727 \tabularnewline
3 & 0.148404 & 1.3601 & 0.088711 \tabularnewline
4 & 0.108261 & 0.9922 & 0.161969 \tabularnewline
5 & 0.163906 & 1.5022 & 0.068395 \tabularnewline
6 & 0.156091 & 1.4306 & 0.078128 \tabularnewline
7 & 0.098162 & 0.8997 & 0.185433 \tabularnewline
8 & 0.064451 & 0.5907 & 0.278153 \tabularnewline
9 & 0.090713 & 0.8314 & 0.204052 \tabularnewline
10 & 0.048104 & 0.4409 & 0.330215 \tabularnewline
11 & -0.050589 & -0.4637 & 0.322047 \tabularnewline
12 & -0.312145 & -2.8609 & 0.002665 \tabularnewline
13 & -0.175304 & -1.6067 & 0.055937 \tabularnewline
14 & -0.091799 & -0.8413 & 0.201271 \tabularnewline
15 & -0.003746 & -0.0343 & 0.486347 \tabularnewline
16 & 0.099322 & 0.9103 & 0.182633 \tabularnewline
17 & 0.061978 & 0.568 & 0.285764 \tabularnewline
18 & -0.091907 & -0.8423 & 0.200994 \tabularnewline
19 & -0.191867 & -1.7585 & 0.041153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244211&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]0.451381[/C][C]4.137[/C][C]4.2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.215584[/C][C]1.9759[/C][C]0.025727[/C][/ROW]
[ROW][C]3[/C][C]0.148404[/C][C]1.3601[/C][C]0.088711[/C][/ROW]
[ROW][C]4[/C][C]0.108261[/C][C]0.9922[/C][C]0.161969[/C][/ROW]
[ROW][C]5[/C][C]0.163906[/C][C]1.5022[/C][C]0.068395[/C][/ROW]
[ROW][C]6[/C][C]0.156091[/C][C]1.4306[/C][C]0.078128[/C][/ROW]
[ROW][C]7[/C][C]0.098162[/C][C]0.8997[/C][C]0.185433[/C][/ROW]
[ROW][C]8[/C][C]0.064451[/C][C]0.5907[/C][C]0.278153[/C][/ROW]
[ROW][C]9[/C][C]0.090713[/C][C]0.8314[/C][C]0.204052[/C][/ROW]
[ROW][C]10[/C][C]0.048104[/C][C]0.4409[/C][C]0.330215[/C][/ROW]
[ROW][C]11[/C][C]-0.050589[/C][C]-0.4637[/C][C]0.322047[/C][/ROW]
[ROW][C]12[/C][C]-0.312145[/C][C]-2.8609[/C][C]0.002665[/C][/ROW]
[ROW][C]13[/C][C]-0.175304[/C][C]-1.6067[/C][C]0.055937[/C][/ROW]
[ROW][C]14[/C][C]-0.091799[/C][C]-0.8413[/C][C]0.201271[/C][/ROW]
[ROW][C]15[/C][C]-0.003746[/C][C]-0.0343[/C][C]0.486347[/C][/ROW]
[ROW][C]16[/C][C]0.099322[/C][C]0.9103[/C][C]0.182633[/C][/ROW]
[ROW][C]17[/C][C]0.061978[/C][C]0.568[/C][C]0.285764[/C][/ROW]
[ROW][C]18[/C][C]-0.091907[/C][C]-0.8423[/C][C]0.200994[/C][/ROW]
[ROW][C]19[/C][C]-0.191867[/C][C]-1.7585[/C][C]0.041153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244211&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244211&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	0.451381	4.137	4.2e-05
2	0.215584	1.9759	0.025727
3	0.148404	1.3601	0.088711
4	0.108261	0.9922	0.161969
5	0.163906	1.5022	0.068395
6	0.156091	1.4306	0.078128
7	0.098162	0.8997	0.185433
8	0.064451	0.5907	0.278153
9	0.090713	0.8314	0.204052
10	0.048104	0.4409	0.330215
11	-0.050589	-0.4637	0.322047
12	-0.312145	-2.8609	0.002665
13	-0.175304	-1.6067	0.055937
14	-0.091799	-0.8413	0.201271
15	-0.003746	-0.0343	0.486347
16	0.099322	0.9103	0.182633
17	0.061978	0.568	0.285764
18	-0.091907	-0.8423	0.200994
19	-0.191867	-1.7585	0.041153

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.451381	4.137	4.2e-05
2	0.014868	0.1363	0.445967
3	0.057569	0.5276	0.299574
4	0.023599	0.2163	0.414643
5	0.122012	1.1183	0.133323
6	0.038526	0.3531	0.36245
7	-0.010143	-0.093	0.463077
8	-0.000955	-0.0088	0.496519
9	0.059491	0.5452	0.293514
10	-0.039695	-0.3638	0.358456
11	-0.112455	-1.0307	0.152827
12	-0.350964	-3.2166	0.000921
13	0.110678	1.0144	0.156657
14	-0.012036	-0.1103	0.456212
15	0.095708	0.8772	0.191445
16	0.126836	1.1625	0.124168
17	0.083543	0.7657	0.223006
18	-0.142911	-1.3098	0.096917
19	-0.166949	-1.5301	0.064873

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.451381 & 4.137 & 4.2e-05 \tabularnewline
2 & 0.014868 & 0.1363 & 0.445967 \tabularnewline
3 & 0.057569 & 0.5276 & 0.299574 \tabularnewline
4 & 0.023599 & 0.2163 & 0.414643 \tabularnewline
5 & 0.122012 & 1.1183 & 0.133323 \tabularnewline
6 & 0.038526 & 0.3531 & 0.36245 \tabularnewline
7 & -0.010143 & -0.093 & 0.463077 \tabularnewline
8 & -0.000955 & -0.0088 & 0.496519 \tabularnewline
9 & 0.059491 & 0.5452 & 0.293514 \tabularnewline
10 & -0.039695 & -0.3638 & 0.358456 \tabularnewline
11 & -0.112455 & -1.0307 & 0.152827 \tabularnewline
12 & -0.350964 & -3.2166 & 0.000921 \tabularnewline
13 & 0.110678 & 1.0144 & 0.156657 \tabularnewline
14 & -0.012036 & -0.1103 & 0.456212 \tabularnewline
15 & 0.095708 & 0.8772 & 0.191445 \tabularnewline
16 & 0.126836 & 1.1625 & 0.124168 \tabularnewline
17 & 0.083543 & 0.7657 & 0.223006 \tabularnewline
18 & -0.142911 & -1.3098 & 0.096917 \tabularnewline
19 & -0.166949 & -1.5301 & 0.064873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244211&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]0.451381[/C][C]4.137[/C][C]4.2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.014868[/C][C]0.1363[/C][C]0.445967[/C][/ROW]
[ROW][C]3[/C][C]0.057569[/C][C]0.5276[/C][C]0.299574[/C][/ROW]
[ROW][C]4[/C][C]0.023599[/C][C]0.2163[/C][C]0.414643[/C][/ROW]
[ROW][C]5[/C][C]0.122012[/C][C]1.1183[/C][C]0.133323[/C][/ROW]
[ROW][C]6[/C][C]0.038526[/C][C]0.3531[/C][C]0.36245[/C][/ROW]
[ROW][C]7[/C][C]-0.010143[/C][C]-0.093[/C][C]0.463077[/C][/ROW]
[ROW][C]8[/C][C]-0.000955[/C][C]-0.0088[/C][C]0.496519[/C][/ROW]
[ROW][C]9[/C][C]0.059491[/C][C]0.5452[/C][C]0.293514[/C][/ROW]
[ROW][C]10[/C][C]-0.039695[/C][C]-0.3638[/C][C]0.358456[/C][/ROW]
[ROW][C]11[/C][C]-0.112455[/C][C]-1.0307[/C][C]0.152827[/C][/ROW]
[ROW][C]12[/C][C]-0.350964[/C][C]-3.2166[/C][C]0.000921[/C][/ROW]
[ROW][C]13[/C][C]0.110678[/C][C]1.0144[/C][C]0.156657[/C][/ROW]
[ROW][C]14[/C][C]-0.012036[/C][C]-0.1103[/C][C]0.456212[/C][/ROW]
[ROW][C]15[/C][C]0.095708[/C][C]0.8772[/C][C]0.191445[/C][/ROW]
[ROW][C]16[/C][C]0.126836[/C][C]1.1625[/C][C]0.124168[/C][/ROW]
[ROW][C]17[/C][C]0.083543[/C][C]0.7657[/C][C]0.223006[/C][/ROW]
[ROW][C]18[/C][C]-0.142911[/C][C]-1.3098[/C][C]0.096917[/C][/ROW]
[ROW][C]19[/C][C]-0.166949[/C][C]-1.5301[/C][C]0.064873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244211&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244211&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	0.451381	4.137	4.2e-05
2	0.014868	0.1363	0.445967
3	0.057569	0.5276	0.299574
4	0.023599	0.2163	0.414643
5	0.122012	1.1183	0.133323
6	0.038526	0.3531	0.36245
7	-0.010143	-0.093	0.463077
8	-0.000955	-0.0088	0.496519
9	0.059491	0.5452	0.293514
10	-0.039695	-0.3638	0.358456
11	-0.112455	-1.0307	0.152827
12	-0.350964	-3.2166	0.000921
13	0.110678	1.0144	0.156657
14	-0.012036	-0.1103	0.456212
15	0.095708	0.8772	0.191445
16	0.126836	1.1625	0.124168
17	0.083543	0.7657	0.223006
18	-0.142911	-1.3098	0.096917
19	-0.166949	-1.5301	0.064873

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 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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 <- '0'
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