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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Oct 2015 17:12:34 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/23/t14456167850vru81c6887ae51.htm/, Retrieved Tue, 14 May 2024 18:45:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282922, Retrieved Tue, 14 May 2024 18:45:05 +0000

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

-       [(Partial) Autocorrelation Function] [Opgave 7 eigen wa...] [2015-10-23 16:12:34] [bcb0da8ff6be95621a49a67fe6a7b572] [Current]

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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	'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282922&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282922&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282922&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	'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.801025	7.3415	0
2	0.72039	6.6025	0
3	0.731018	6.6999	0
4	0.663451	6.0806	0
5	0.643322	5.8961	0
6	0.650918	5.9658	0
7	0.551896	5.0582	1e-06
8	0.498454	4.5684	8e-06
9	0.477985	4.3808	1.7e-05
10	0.382978	3.5101	0.000362
11	0.405182	3.7136	0.000183
12	0.448073	4.1067	4.6e-05
13	0.311779	2.8575	0.002691
14	0.248215	2.2749	0.012729
15	0.21245	1.9471	0.02743
16	0.148721	1.3631	0.088254
17	0.159551	1.4623	0.073694
18	0.133719	1.2256	0.111895
19	0.066149	0.6063	0.272987

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.801025 & 7.3415 & 0 \tabularnewline
2 & 0.72039 & 6.6025 & 0 \tabularnewline
3 & 0.731018 & 6.6999 & 0 \tabularnewline
4 & 0.663451 & 6.0806 & 0 \tabularnewline
5 & 0.643322 & 5.8961 & 0 \tabularnewline
6 & 0.650918 & 5.9658 & 0 \tabularnewline
7 & 0.551896 & 5.0582 & 1e-06 \tabularnewline
8 & 0.498454 & 4.5684 & 8e-06 \tabularnewline
9 & 0.477985 & 4.3808 & 1.7e-05 \tabularnewline
10 & 0.382978 & 3.5101 & 0.000362 \tabularnewline
11 & 0.405182 & 3.7136 & 0.000183 \tabularnewline
12 & 0.448073 & 4.1067 & 4.6e-05 \tabularnewline
13 & 0.311779 & 2.8575 & 0.002691 \tabularnewline
14 & 0.248215 & 2.2749 & 0.012729 \tabularnewline
15 & 0.21245 & 1.9471 & 0.02743 \tabularnewline
16 & 0.148721 & 1.3631 & 0.088254 \tabularnewline
17 & 0.159551 & 1.4623 & 0.073694 \tabularnewline
18 & 0.133719 & 1.2256 & 0.111895 \tabularnewline
19 & 0.066149 & 0.6063 & 0.272987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282922&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]0.801025[/C][C]7.3415[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.72039[/C][C]6.6025[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.731018[/C][C]6.6999[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.663451[/C][C]6.0806[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.643322[/C][C]5.8961[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.650918[/C][C]5.9658[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.551896[/C][C]5.0582[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.498454[/C][C]4.5684[/C][C]8e-06[/C][/ROW]
[ROW][C]9[/C][C]0.477985[/C][C]4.3808[/C][C]1.7e-05[/C][/ROW]
[ROW][C]10[/C][C]0.382978[/C][C]3.5101[/C][C]0.000362[/C][/ROW]
[ROW][C]11[/C][C]0.405182[/C][C]3.7136[/C][C]0.000183[/C][/ROW]
[ROW][C]12[/C][C]0.448073[/C][C]4.1067[/C][C]4.6e-05[/C][/ROW]
[ROW][C]13[/C][C]0.311779[/C][C]2.8575[/C][C]0.002691[/C][/ROW]
[ROW][C]14[/C][C]0.248215[/C][C]2.2749[/C][C]0.012729[/C][/ROW]
[ROW][C]15[/C][C]0.21245[/C][C]1.9471[/C][C]0.02743[/C][/ROW]
[ROW][C]16[/C][C]0.148721[/C][C]1.3631[/C][C]0.088254[/C][/ROW]
[ROW][C]17[/C][C]0.159551[/C][C]1.4623[/C][C]0.073694[/C][/ROW]
[ROW][C]18[/C][C]0.133719[/C][C]1.2256[/C][C]0.111895[/C][/ROW]
[ROW][C]19[/C][C]0.066149[/C][C]0.6063[/C][C]0.272987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282922&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282922&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	0.801025	7.3415	0
2	0.72039	6.6025	0
3	0.731018	6.6999	0
4	0.663451	6.0806	0
5	0.643322	5.8961	0
6	0.650918	5.9658	0
7	0.551896	5.0582	1e-06
8	0.498454	4.5684	8e-06
9	0.477985	4.3808	1.7e-05
10	0.382978	3.5101	0.000362
11	0.405182	3.7136	0.000183
12	0.448073	4.1067	4.6e-05
13	0.311779	2.8575	0.002691
14	0.248215	2.2749	0.012729
15	0.21245	1.9471	0.02743
16	0.148721	1.3631	0.088254
17	0.159551	1.4623	0.073694
18	0.133719	1.2256	0.111895
19	0.066149	0.6063	0.272987

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.801025	7.3415	0
2	0.219749	2.014	0.023603
3	0.307134	2.8149	0.003038
4	-0.032826	-0.3009	0.382135
5	0.121945	1.1176	0.133453
6	0.101902	0.9339	0.176504
7	-0.190358	-1.7447	0.042351
8	-0.054012	-0.495	0.310936
9	-0.039468	-0.3617	0.359231
10	-0.16161	-1.4812	0.07115
11	0.201624	1.8479	0.034067
12	0.180673	1.6559	0.050738
13	-0.274021	-2.5114	0.006969
14	-0.113556	-1.0408	0.150488
15	-0.138774	-1.2719	0.103462
16	0.012094	0.1108	0.456002
17	0.088602	0.8121	0.209529
18	-0.078953	-0.7236	0.235655
19	0.057476	0.5268	0.299869

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.801025 & 7.3415 & 0 \tabularnewline
2 & 0.219749 & 2.014 & 0.023603 \tabularnewline
3 & 0.307134 & 2.8149 & 0.003038 \tabularnewline
4 & -0.032826 & -0.3009 & 0.382135 \tabularnewline
5 & 0.121945 & 1.1176 & 0.133453 \tabularnewline
6 & 0.101902 & 0.9339 & 0.176504 \tabularnewline
7 & -0.190358 & -1.7447 & 0.042351 \tabularnewline
8 & -0.054012 & -0.495 & 0.310936 \tabularnewline
9 & -0.039468 & -0.3617 & 0.359231 \tabularnewline
10 & -0.16161 & -1.4812 & 0.07115 \tabularnewline
11 & 0.201624 & 1.8479 & 0.034067 \tabularnewline
12 & 0.180673 & 1.6559 & 0.050738 \tabularnewline
13 & -0.274021 & -2.5114 & 0.006969 \tabularnewline
14 & -0.113556 & -1.0408 & 0.150488 \tabularnewline
15 & -0.138774 & -1.2719 & 0.103462 \tabularnewline
16 & 0.012094 & 0.1108 & 0.456002 \tabularnewline
17 & 0.088602 & 0.8121 & 0.209529 \tabularnewline
18 & -0.078953 & -0.7236 & 0.235655 \tabularnewline
19 & 0.057476 & 0.5268 & 0.299869 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282922&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]0.801025[/C][C]7.3415[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.219749[/C][C]2.014[/C][C]0.023603[/C][/ROW]
[ROW][C]3[/C][C]0.307134[/C][C]2.8149[/C][C]0.003038[/C][/ROW]
[ROW][C]4[/C][C]-0.032826[/C][C]-0.3009[/C][C]0.382135[/C][/ROW]
[ROW][C]5[/C][C]0.121945[/C][C]1.1176[/C][C]0.133453[/C][/ROW]
[ROW][C]6[/C][C]0.101902[/C][C]0.9339[/C][C]0.176504[/C][/ROW]
[ROW][C]7[/C][C]-0.190358[/C][C]-1.7447[/C][C]0.042351[/C][/ROW]
[ROW][C]8[/C][C]-0.054012[/C][C]-0.495[/C][C]0.310936[/C][/ROW]
[ROW][C]9[/C][C]-0.039468[/C][C]-0.3617[/C][C]0.359231[/C][/ROW]
[ROW][C]10[/C][C]-0.16161[/C][C]-1.4812[/C][C]0.07115[/C][/ROW]
[ROW][C]11[/C][C]0.201624[/C][C]1.8479[/C][C]0.034067[/C][/ROW]
[ROW][C]12[/C][C]0.180673[/C][C]1.6559[/C][C]0.050738[/C][/ROW]
[ROW][C]13[/C][C]-0.274021[/C][C]-2.5114[/C][C]0.006969[/C][/ROW]
[ROW][C]14[/C][C]-0.113556[/C][C]-1.0408[/C][C]0.150488[/C][/ROW]
[ROW][C]15[/C][C]-0.138774[/C][C]-1.2719[/C][C]0.103462[/C][/ROW]
[ROW][C]16[/C][C]0.012094[/C][C]0.1108[/C][C]0.456002[/C][/ROW]
[ROW][C]17[/C][C]0.088602[/C][C]0.8121[/C][C]0.209529[/C][/ROW]
[ROW][C]18[/C][C]-0.078953[/C][C]-0.7236[/C][C]0.235655[/C][/ROW]
[ROW][C]19[/C][C]0.057476[/C][C]0.5268[/C][C]0.299869[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282922&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282922&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	0.801025	7.3415	0
2	0.219749	2.014	0.023603
3	0.307134	2.8149	0.003038
4	-0.032826	-0.3009	0.382135
5	0.121945	1.1176	0.133453
6	0.101902	0.9339	0.176504
7	-0.190358	-1.7447	0.042351
8	-0.054012	-0.495	0.310936
9	-0.039468	-0.3617	0.359231
10	-0.16161	-1.4812	0.07115
11	0.201624	1.8479	0.034067
12	0.180673	1.6559	0.050738
13	-0.274021	-2.5114	0.006969
14	-0.113556	-1.0408	0.150488
15	-0.138774	-1.2719	0.103462
16	0.012094	0.1108	0.456002
17	0.088602	0.8121	0.209529
18	-0.078953	-0.7236	0.235655
19	0.057476	0.5268	0.299869

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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