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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

Fri, 17 Oct 2014 11:37:25 +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/17/t1413542280x8vzet45603sdik.htm/, Retrieved Fri, 10 May 2024 12:27:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243213, Retrieved Fri, 10 May 2024 12:27:09 +0000

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Original text written by user:

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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] [] [2014-10-17 10:37:25] [56e8cb9ede54fa5ca6b1344bd59af70d] [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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243213&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243213&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243213&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.393421	-3.8346	0.000113
2	-0.185935	-1.8123	0.036552
3	0.283916	2.7673	0.003398
4	-0.139211	-1.3569	0.089021
5	0.00885	0.0863	0.465719
6	-0.142209	-1.3861	0.084483
7	0.006734	0.0656	0.473904
8	-0.130182	-1.2689	0.103796
9	0.263258	2.5659	0.005927
10	-0.143458	-1.3983	0.082646
11	-0.364141	-3.5492	0.000301
12	0.850907	8.2936	0
13	-0.325844	-3.1759	0.001007
14	-0.174817	-1.7039	0.045834
15	0.26719	2.6042	0.005343
16	-0.136045	-1.326	0.094009
17	0.025261	0.2462	0.403025
18	-0.107444	-1.0472	0.148823
19	-0.021409	-0.2087	0.417578

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.393421 & -3.8346 & 0.000113 \tabularnewline
2 & -0.185935 & -1.8123 & 0.036552 \tabularnewline
3 & 0.283916 & 2.7673 & 0.003398 \tabularnewline
4 & -0.139211 & -1.3569 & 0.089021 \tabularnewline
5 & 0.00885 & 0.0863 & 0.465719 \tabularnewline
6 & -0.142209 & -1.3861 & 0.084483 \tabularnewline
7 & 0.006734 & 0.0656 & 0.473904 \tabularnewline
8 & -0.130182 & -1.2689 & 0.103796 \tabularnewline
9 & 0.263258 & 2.5659 & 0.005927 \tabularnewline
10 & -0.143458 & -1.3983 & 0.082646 \tabularnewline
11 & -0.364141 & -3.5492 & 0.000301 \tabularnewline
12 & 0.850907 & 8.2936 & 0 \tabularnewline
13 & -0.325844 & -3.1759 & 0.001007 \tabularnewline
14 & -0.174817 & -1.7039 & 0.045834 \tabularnewline
15 & 0.26719 & 2.6042 & 0.005343 \tabularnewline
16 & -0.136045 & -1.326 & 0.094009 \tabularnewline
17 & 0.025261 & 0.2462 & 0.403025 \tabularnewline
18 & -0.107444 & -1.0472 & 0.148823 \tabularnewline
19 & -0.021409 & -0.2087 & 0.417578 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243213&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]-0.393421[/C][C]-3.8346[/C][C]0.000113[/C][/ROW]
[ROW][C]2[/C][C]-0.185935[/C][C]-1.8123[/C][C]0.036552[/C][/ROW]
[ROW][C]3[/C][C]0.283916[/C][C]2.7673[/C][C]0.003398[/C][/ROW]
[ROW][C]4[/C][C]-0.139211[/C][C]-1.3569[/C][C]0.089021[/C][/ROW]
[ROW][C]5[/C][C]0.00885[/C][C]0.0863[/C][C]0.465719[/C][/ROW]
[ROW][C]6[/C][C]-0.142209[/C][C]-1.3861[/C][C]0.084483[/C][/ROW]
[ROW][C]7[/C][C]0.006734[/C][C]0.0656[/C][C]0.473904[/C][/ROW]
[ROW][C]8[/C][C]-0.130182[/C][C]-1.2689[/C][C]0.103796[/C][/ROW]
[ROW][C]9[/C][C]0.263258[/C][C]2.5659[/C][C]0.005927[/C][/ROW]
[ROW][C]10[/C][C]-0.143458[/C][C]-1.3983[/C][C]0.082646[/C][/ROW]
[ROW][C]11[/C][C]-0.364141[/C][C]-3.5492[/C][C]0.000301[/C][/ROW]
[ROW][C]12[/C][C]0.850907[/C][C]8.2936[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.325844[/C][C]-3.1759[/C][C]0.001007[/C][/ROW]
[ROW][C]14[/C][C]-0.174817[/C][C]-1.7039[/C][C]0.045834[/C][/ROW]
[ROW][C]15[/C][C]0.26719[/C][C]2.6042[/C][C]0.005343[/C][/ROW]
[ROW][C]16[/C][C]-0.136045[/C][C]-1.326[/C][C]0.094009[/C][/ROW]
[ROW][C]17[/C][C]0.025261[/C][C]0.2462[/C][C]0.403025[/C][/ROW]
[ROW][C]18[/C][C]-0.107444[/C][C]-1.0472[/C][C]0.148823[/C][/ROW]
[ROW][C]19[/C][C]-0.021409[/C][C]-0.2087[/C][C]0.417578[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243213&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243213&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	-0.393421	-3.8346	0.000113
2	-0.185935	-1.8123	0.036552
3	0.283916	2.7673	0.003398
4	-0.139211	-1.3569	0.089021
5	0.00885	0.0863	0.465719
6	-0.142209	-1.3861	0.084483
7	0.006734	0.0656	0.473904
8	-0.130182	-1.2689	0.103796
9	0.263258	2.5659	0.005927
10	-0.143458	-1.3983	0.082646
11	-0.364141	-3.5492	0.000301
12	0.850907	8.2936	0
13	-0.325844	-3.1759	0.001007
14	-0.174817	-1.7039	0.045834
15	0.26719	2.6042	0.005343
16	-0.136045	-1.326	0.094009
17	0.025261	0.2462	0.403025
18	-0.107444	-1.0472	0.148823
19	-0.021409	-0.2087	0.417578

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.393421	-3.8346	0.000113
2	-0.403109	-3.929	8.1e-05
3	0.032047	0.3124	0.377727
4	-0.06393	-0.6231	0.267351
5	0.035369	0.3447	0.365528
6	-0.273567	-2.6664	0.004506
7	-0.223922	-2.1825	0.015768
8	-0.507216	-4.9437	2e-06
9	0.021459	0.2092	0.417385
10	-0.215618	-2.1016	0.019118
11	-0.749693	-7.3071	0
12	0.258209	2.5167	0.006761
13	-0.024386	-0.2377	0.406318
14	0.033316	0.3247	0.373054
15	-0.102793	-1.0019	0.159467
16	-0.111344	-1.0852	0.140279
17	-0.084768	-0.8262	0.205375
18	0.065296	0.6364	0.263016
19	-0.039637	-0.3863	0.350056

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.393421 & -3.8346 & 0.000113 \tabularnewline
2 & -0.403109 & -3.929 & 8.1e-05 \tabularnewline
3 & 0.032047 & 0.3124 & 0.377727 \tabularnewline
4 & -0.06393 & -0.6231 & 0.267351 \tabularnewline
5 & 0.035369 & 0.3447 & 0.365528 \tabularnewline
6 & -0.273567 & -2.6664 & 0.004506 \tabularnewline
7 & -0.223922 & -2.1825 & 0.015768 \tabularnewline
8 & -0.507216 & -4.9437 & 2e-06 \tabularnewline
9 & 0.021459 & 0.2092 & 0.417385 \tabularnewline
10 & -0.215618 & -2.1016 & 0.019118 \tabularnewline
11 & -0.749693 & -7.3071 & 0 \tabularnewline
12 & 0.258209 & 2.5167 & 0.006761 \tabularnewline
13 & -0.024386 & -0.2377 & 0.406318 \tabularnewline
14 & 0.033316 & 0.3247 & 0.373054 \tabularnewline
15 & -0.102793 & -1.0019 & 0.159467 \tabularnewline
16 & -0.111344 & -1.0852 & 0.140279 \tabularnewline
17 & -0.084768 & -0.8262 & 0.205375 \tabularnewline
18 & 0.065296 & 0.6364 & 0.263016 \tabularnewline
19 & -0.039637 & -0.3863 & 0.350056 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243213&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]-0.393421[/C][C]-3.8346[/C][C]0.000113[/C][/ROW]
[ROW][C]2[/C][C]-0.403109[/C][C]-3.929[/C][C]8.1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.032047[/C][C]0.3124[/C][C]0.377727[/C][/ROW]
[ROW][C]4[/C][C]-0.06393[/C][C]-0.6231[/C][C]0.267351[/C][/ROW]
[ROW][C]5[/C][C]0.035369[/C][C]0.3447[/C][C]0.365528[/C][/ROW]
[ROW][C]6[/C][C]-0.273567[/C][C]-2.6664[/C][C]0.004506[/C][/ROW]
[ROW][C]7[/C][C]-0.223922[/C][C]-2.1825[/C][C]0.015768[/C][/ROW]
[ROW][C]8[/C][C]-0.507216[/C][C]-4.9437[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]0.021459[/C][C]0.2092[/C][C]0.417385[/C][/ROW]
[ROW][C]10[/C][C]-0.215618[/C][C]-2.1016[/C][C]0.019118[/C][/ROW]
[ROW][C]11[/C][C]-0.749693[/C][C]-7.3071[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.258209[/C][C]2.5167[/C][C]0.006761[/C][/ROW]
[ROW][C]13[/C][C]-0.024386[/C][C]-0.2377[/C][C]0.406318[/C][/ROW]
[ROW][C]14[/C][C]0.033316[/C][C]0.3247[/C][C]0.373054[/C][/ROW]
[ROW][C]15[/C][C]-0.102793[/C][C]-1.0019[/C][C]0.159467[/C][/ROW]
[ROW][C]16[/C][C]-0.111344[/C][C]-1.0852[/C][C]0.140279[/C][/ROW]
[ROW][C]17[/C][C]-0.084768[/C][C]-0.8262[/C][C]0.205375[/C][/ROW]
[ROW][C]18[/C][C]0.065296[/C][C]0.6364[/C][C]0.263016[/C][/ROW]
[ROW][C]19[/C][C]-0.039637[/C][C]-0.3863[/C][C]0.350056[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243213&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243213&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	-0.393421	-3.8346	0.000113
2	-0.403109	-3.929	8.1e-05
3	0.032047	0.3124	0.377727
4	-0.06393	-0.6231	0.267351
5	0.035369	0.3447	0.365528
6	-0.273567	-2.6664	0.004506
7	-0.223922	-2.1825	0.015768
8	-0.507216	-4.9437	2e-06
9	0.021459	0.2092	0.417385
10	-0.215618	-2.1016	0.019118
11	-0.749693	-7.3071	0
12	0.258209	2.5167	0.006761
13	-0.024386	-0.2377	0.406318
14	0.033316	0.3247	0.373054
15	-0.102793	-1.0019	0.159467
16	-0.111344	-1.0852	0.140279
17	-0.084768	-0.8262	0.205375
18	0.065296	0.6364	0.263016
19	-0.039637	-0.3863	0.350056

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):

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