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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 19:24:23 +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/t14138294848hr8rntu0jah9u1.htm/, Retrieved Sat, 11 May 2024 11:37:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=244215, Retrieved Sat, 11 May 2024 11:37:11 +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 18:24:23] [f2e79deb6e51141b138dd10990a8e48d] [Current]
- R P       [(Partial) Autocorrelation Function] [] [2014-12-13 15:27:28] [deebc1e457a5ecb4dd1aad0be1fbee4a] 

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Dataseries X:

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Histogram

Boxplots

5.06
5.05
5.05
5.04
5.06
5.07
5.09
5.08
5.09
5.09
5.09
5.1
5.12
5.14
5.14
5.14
5.13
5.15
5.16
5.17
5.17
5.18
5.21
5.19
5.22
5.24
5.21
5.24
5.28
5.3
5.32
5.32
5.29
5.3
5.32
5.31
5.35
5.36
5.33
5.35
5.35
5.35
5.37
5.39
5.4
5.39
5.4
5.4
5.4
5.38
5.32
5.36
5.35
5.39
5.4
5.41
5.36
5.38
5.41
5.35
5.4
5.41
5.42
5.41
5.41
5.42
5.4
5.42
5.41
5.34
5.46
5.45
5.47
5.48
5.43
5.5
5.51
5.51
5.52
5.55
5.55
5.48
5.61
5.59
5.68
5.71
5.68
5.7
5.76
5.78
5.77
5.85
5.82
5.84
5.89
5.84

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=244215&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=244215&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244215&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	-0.28128	-2.5626	0.006098
2	0.002593	0.0236	0.490603
3	-0.056417	-0.514	0.304315
4	-0.053958	-0.4916	0.312158
5	0.047625	0.4339	0.33275
6	-0.143212	-1.3047	0.097797
7	0.101247	0.9224	0.179495
8	0.09825	0.8951	0.18666
9	0.185225	1.6875	0.047633
10	-0.011505	-0.1048	0.458386
11	0.015933	0.1452	0.442469
12	-0.388424	-3.5387	0.000331
13	0.157812	1.4377	0.077134
14	0.04745	0.4323	0.333325
15	0.036591	0.3334	0.369851
16	-0.010873	-0.0991	0.460664
17	0.015092	0.1375	0.445487
18	0.279615	2.5474	0.006349
19	-0.262601	-2.3924	0.009498

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.28128 & -2.5626 & 0.006098 \tabularnewline
2 & 0.002593 & 0.0236 & 0.490603 \tabularnewline
3 & -0.056417 & -0.514 & 0.304315 \tabularnewline
4 & -0.053958 & -0.4916 & 0.312158 \tabularnewline
5 & 0.047625 & 0.4339 & 0.33275 \tabularnewline
6 & -0.143212 & -1.3047 & 0.097797 \tabularnewline
7 & 0.101247 & 0.9224 & 0.179495 \tabularnewline
8 & 0.09825 & 0.8951 & 0.18666 \tabularnewline
9 & 0.185225 & 1.6875 & 0.047633 \tabularnewline
10 & -0.011505 & -0.1048 & 0.458386 \tabularnewline
11 & 0.015933 & 0.1452 & 0.442469 \tabularnewline
12 & -0.388424 & -3.5387 & 0.000331 \tabularnewline
13 & 0.157812 & 1.4377 & 0.077134 \tabularnewline
14 & 0.04745 & 0.4323 & 0.333325 \tabularnewline
15 & 0.036591 & 0.3334 & 0.369851 \tabularnewline
16 & -0.010873 & -0.0991 & 0.460664 \tabularnewline
17 & 0.015092 & 0.1375 & 0.445487 \tabularnewline
18 & 0.279615 & 2.5474 & 0.006349 \tabularnewline
19 & -0.262601 & -2.3924 & 0.009498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244215&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]-0.28128[/C][C]-2.5626[/C][C]0.006098[/C][/ROW]
[ROW][C]2[/C][C]0.002593[/C][C]0.0236[/C][C]0.490603[/C][/ROW]
[ROW][C]3[/C][C]-0.056417[/C][C]-0.514[/C][C]0.304315[/C][/ROW]
[ROW][C]4[/C][C]-0.053958[/C][C]-0.4916[/C][C]0.312158[/C][/ROW]
[ROW][C]5[/C][C]0.047625[/C][C]0.4339[/C][C]0.33275[/C][/ROW]
[ROW][C]6[/C][C]-0.143212[/C][C]-1.3047[/C][C]0.097797[/C][/ROW]
[ROW][C]7[/C][C]0.101247[/C][C]0.9224[/C][C]0.179495[/C][/ROW]
[ROW][C]8[/C][C]0.09825[/C][C]0.8951[/C][C]0.18666[/C][/ROW]
[ROW][C]9[/C][C]0.185225[/C][C]1.6875[/C][C]0.047633[/C][/ROW]
[ROW][C]10[/C][C]-0.011505[/C][C]-0.1048[/C][C]0.458386[/C][/ROW]
[ROW][C]11[/C][C]0.015933[/C][C]0.1452[/C][C]0.442469[/C][/ROW]
[ROW][C]12[/C][C]-0.388424[/C][C]-3.5387[/C][C]0.000331[/C][/ROW]
[ROW][C]13[/C][C]0.157812[/C][C]1.4377[/C][C]0.077134[/C][/ROW]
[ROW][C]14[/C][C]0.04745[/C][C]0.4323[/C][C]0.333325[/C][/ROW]
[ROW][C]15[/C][C]0.036591[/C][C]0.3334[/C][C]0.369851[/C][/ROW]
[ROW][C]16[/C][C]-0.010873[/C][C]-0.0991[/C][C]0.460664[/C][/ROW]
[ROW][C]17[/C][C]0.015092[/C][C]0.1375[/C][C]0.445487[/C][/ROW]
[ROW][C]18[/C][C]0.279615[/C][C]2.5474[/C][C]0.006349[/C][/ROW]
[ROW][C]19[/C][C]-0.262601[/C][C]-2.3924[/C][C]0.009498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244215&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244215&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	-0.28128	-2.5626	0.006098
2	0.002593	0.0236	0.490603
3	-0.056417	-0.514	0.304315
4	-0.053958	-0.4916	0.312158
5	0.047625	0.4339	0.33275
6	-0.143212	-1.3047	0.097797
7	0.101247	0.9224	0.179495
8	0.09825	0.8951	0.18666
9	0.185225	1.6875	0.047633
10	-0.011505	-0.1048	0.458386
11	0.015933	0.1452	0.442469
12	-0.388424	-3.5387	0.000331
13	0.157812	1.4377	0.077134
14	0.04745	0.4323	0.333325
15	0.036591	0.3334	0.369851
16	-0.010873	-0.0991	0.460664
17	0.015092	0.1375	0.445487
18	0.279615	2.5474	0.006349
19	-0.262601	-2.3924	0.009498

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.28128	-2.5626	0.006098
2	-0.0831	-0.7571	0.225575
3	-0.086385	-0.787	0.21676
4	-0.105283	-0.9592	0.17013
5	-0.006483	-0.0591	0.476522
6	-0.159066	-1.4492	0.07553
7	0.002748	0.025	0.490043
8	0.124317	1.1326	0.130326
9	0.278775	2.5398	0.006479
10	0.175694	1.6006	0.056627
11	0.170178	1.5504	0.062426
12	-0.379411	-3.4566	0.000432
13	-0.082441	-0.7511	0.227366
14	0.08002	0.729	0.23402
15	0.162109	1.4769	0.071746
16	-0.033701	-0.307	0.379793
17	-0.089258	-0.8132	0.209221
18	0.127639	1.1628	0.124113
19	-0.083804	-0.7635	0.223668

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.28128 & -2.5626 & 0.006098 \tabularnewline
2 & -0.0831 & -0.7571 & 0.225575 \tabularnewline
3 & -0.086385 & -0.787 & 0.21676 \tabularnewline
4 & -0.105283 & -0.9592 & 0.17013 \tabularnewline
5 & -0.006483 & -0.0591 & 0.476522 \tabularnewline
6 & -0.159066 & -1.4492 & 0.07553 \tabularnewline
7 & 0.002748 & 0.025 & 0.490043 \tabularnewline
8 & 0.124317 & 1.1326 & 0.130326 \tabularnewline
9 & 0.278775 & 2.5398 & 0.006479 \tabularnewline
10 & 0.175694 & 1.6006 & 0.056627 \tabularnewline
11 & 0.170178 & 1.5504 & 0.062426 \tabularnewline
12 & -0.379411 & -3.4566 & 0.000432 \tabularnewline
13 & -0.082441 & -0.7511 & 0.227366 \tabularnewline
14 & 0.08002 & 0.729 & 0.23402 \tabularnewline
15 & 0.162109 & 1.4769 & 0.071746 \tabularnewline
16 & -0.033701 & -0.307 & 0.379793 \tabularnewline
17 & -0.089258 & -0.8132 & 0.209221 \tabularnewline
18 & 0.127639 & 1.1628 & 0.124113 \tabularnewline
19 & -0.083804 & -0.7635 & 0.223668 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244215&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]-0.28128[/C][C]-2.5626[/C][C]0.006098[/C][/ROW]
[ROW][C]2[/C][C]-0.0831[/C][C]-0.7571[/C][C]0.225575[/C][/ROW]
[ROW][C]3[/C][C]-0.086385[/C][C]-0.787[/C][C]0.21676[/C][/ROW]
[ROW][C]4[/C][C]-0.105283[/C][C]-0.9592[/C][C]0.17013[/C][/ROW]
[ROW][C]5[/C][C]-0.006483[/C][C]-0.0591[/C][C]0.476522[/C][/ROW]
[ROW][C]6[/C][C]-0.159066[/C][C]-1.4492[/C][C]0.07553[/C][/ROW]
[ROW][C]7[/C][C]0.002748[/C][C]0.025[/C][C]0.490043[/C][/ROW]
[ROW][C]8[/C][C]0.124317[/C][C]1.1326[/C][C]0.130326[/C][/ROW]
[ROW][C]9[/C][C]0.278775[/C][C]2.5398[/C][C]0.006479[/C][/ROW]
[ROW][C]10[/C][C]0.175694[/C][C]1.6006[/C][C]0.056627[/C][/ROW]
[ROW][C]11[/C][C]0.170178[/C][C]1.5504[/C][C]0.062426[/C][/ROW]
[ROW][C]12[/C][C]-0.379411[/C][C]-3.4566[/C][C]0.000432[/C][/ROW]
[ROW][C]13[/C][C]-0.082441[/C][C]-0.7511[/C][C]0.227366[/C][/ROW]
[ROW][C]14[/C][C]0.08002[/C][C]0.729[/C][C]0.23402[/C][/ROW]
[ROW][C]15[/C][C]0.162109[/C][C]1.4769[/C][C]0.071746[/C][/ROW]
[ROW][C]16[/C][C]-0.033701[/C][C]-0.307[/C][C]0.379793[/C][/ROW]
[ROW][C]17[/C][C]-0.089258[/C][C]-0.8132[/C][C]0.209221[/C][/ROW]
[ROW][C]18[/C][C]0.127639[/C][C]1.1628[/C][C]0.124113[/C][/ROW]
[ROW][C]19[/C][C]-0.083804[/C][C]-0.7635[/C][C]0.223668[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244215&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244215&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	-0.28128	-2.5626	0.006098
2	-0.0831	-0.7571	0.225575
3	-0.086385	-0.787	0.21676
4	-0.105283	-0.9592	0.17013
5	-0.006483	-0.0591	0.476522
6	-0.159066	-1.4492	0.07553
7	0.002748	0.025	0.490043
8	0.124317	1.1326	0.130326
9	0.278775	2.5398	0.006479
10	0.175694	1.6006	0.056627
11	0.170178	1.5504	0.062426
12	-0.379411	-3.4566	0.000432
13	-0.082441	-0.7511	0.227366
14	0.08002	0.729	0.23402
15	0.162109	1.4769	0.071746
16	-0.033701	-0.307	0.379793
17	-0.089258	-0.8132	0.209221
18	0.127639	1.1628	0.124113
19	-0.083804	-0.7635	0.223668

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

Parameters (R input):

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