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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, 17 Dec 2007 11:57:48 -0700

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/2007/Dec/17/t119791687549yaixuxdi5ux7x.htm/, Retrieved Fri, 03 May 2024 18:52:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4407, Retrieved Fri, 03 May 2024 18:52:25 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

LPG default

Estimated Impact

156

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

-       [(Partial) Autocorrelation Function] [Paper XVI AcorF d...] [2007-12-17 18:57:48] [fd802f308f037a9692de8c23f8b60e49] [Current]

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Dataseries X:

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Histogram

Boxplots

0.4
0.37
0.36
0.36
0.36
0.36
0.32
0.31
0.32
0.33
0.33
0.29
0.33
0.32
0.31
0.33
0.32
0.32
0.3
0.3
0.33
0.35
0.35
0.37
0.38
0.39
0.4
0.32
0.29
0.29
0.3
0.3
0.32
0.32
0.34
0.34
0.34
0.33
0.33
0.33
0.34
0.35
0.34
0.36
0.39
0.43
0.42
0.39
0.37
0.36
0.39
0.39
0.37
0.36
0.38
0.38
0.44
0.49
0.47
0.48

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4407&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4407&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4407&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.6811	0
1	0.070485	0.5414	0.295134
2	-0.103707	-0.7966	0.785558
3	-0.076146	-0.5849	0.719573
4	-0.116022	-0.8912	0.811775
5	0.062956	0.4836	0.315238
6	-0.151161	-1.1611	0.874859
7	-0.171366	-1.3163	0.903416
8	-0.06623	-0.5087	0.693577
9	0.053376	0.41	0.341649
10	0.109409	0.8404	0.202043
11	0.179178	1.3763	0.086967
12	0.063508	0.4878	0.313745
13	0.003193	0.0245	0.490259
14	-0.046872	-0.36	0.639945
15	-0.138502	-1.0639	0.854134
16	-0.035811	-0.2751	0.607888

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & 0.070485 & 0.5414 & 0.295134 \tabularnewline
2 & -0.103707 & -0.7966 & 0.785558 \tabularnewline
3 & -0.076146 & -0.5849 & 0.719573 \tabularnewline
4 & -0.116022 & -0.8912 & 0.811775 \tabularnewline
5 & 0.062956 & 0.4836 & 0.315238 \tabularnewline
6 & -0.151161 & -1.1611 & 0.874859 \tabularnewline
7 & -0.171366 & -1.3163 & 0.903416 \tabularnewline
8 & -0.06623 & -0.5087 & 0.693577 \tabularnewline
9 & 0.053376 & 0.41 & 0.341649 \tabularnewline
10 & 0.109409 & 0.8404 & 0.202043 \tabularnewline
11 & 0.179178 & 1.3763 & 0.086967 \tabularnewline
12 & 0.063508 & 0.4878 & 0.313745 \tabularnewline
13 & 0.003193 & 0.0245 & 0.490259 \tabularnewline
14 & -0.046872 & -0.36 & 0.639945 \tabularnewline
15 & -0.138502 & -1.0639 & 0.854134 \tabularnewline
16 & -0.035811 & -0.2751 & 0.607888 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4407&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]0[/C][C]1[/C][C]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.070485[/C][C]0.5414[/C][C]0.295134[/C][/ROW]
[ROW][C]2[/C][C]-0.103707[/C][C]-0.7966[/C][C]0.785558[/C][/ROW]
[ROW][C]3[/C][C]-0.076146[/C][C]-0.5849[/C][C]0.719573[/C][/ROW]
[ROW][C]4[/C][C]-0.116022[/C][C]-0.8912[/C][C]0.811775[/C][/ROW]
[ROW][C]5[/C][C]0.062956[/C][C]0.4836[/C][C]0.315238[/C][/ROW]
[ROW][C]6[/C][C]-0.151161[/C][C]-1.1611[/C][C]0.874859[/C][/ROW]
[ROW][C]7[/C][C]-0.171366[/C][C]-1.3163[/C][C]0.903416[/C][/ROW]
[ROW][C]8[/C][C]-0.06623[/C][C]-0.5087[/C][C]0.693577[/C][/ROW]
[ROW][C]9[/C][C]0.053376[/C][C]0.41[/C][C]0.341649[/C][/ROW]
[ROW][C]10[/C][C]0.109409[/C][C]0.8404[/C][C]0.202043[/C][/ROW]
[ROW][C]11[/C][C]0.179178[/C][C]1.3763[/C][C]0.086967[/C][/ROW]
[ROW][C]12[/C][C]0.063508[/C][C]0.4878[/C][C]0.313745[/C][/ROW]
[ROW][C]13[/C][C]0.003193[/C][C]0.0245[/C][C]0.490259[/C][/ROW]
[ROW][C]14[/C][C]-0.046872[/C][C]-0.36[/C][C]0.639945[/C][/ROW]
[ROW][C]15[/C][C]-0.138502[/C][C]-1.0639[/C][C]0.854134[/C][/ROW]
[ROW][C]16[/C][C]-0.035811[/C][C]-0.2751[/C][C]0.607888[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4407&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4407&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
0	1	7.6811	0
1	0.070485	0.5414	0.295134
2	-0.103707	-0.7966	0.785558
3	-0.076146	-0.5849	0.719573
4	-0.116022	-0.8912	0.811775
5	0.062956	0.4836	0.315238
6	-0.151161	-1.1611	0.874859
7	-0.171366	-1.3163	0.903416
8	-0.06623	-0.5087	0.693577
9	0.053376	0.41	0.341649
10	0.109409	0.8404	0.202043
11	0.179178	1.3763	0.086967
12	0.063508	0.4878	0.313745
13	0.003193	0.0245	0.490259
14	-0.046872	-0.36	0.639945
15	-0.138502	-1.0639	0.854134
16	-0.035811	-0.2751	0.607888

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.070485	0.5414	0.295134
1	-0.109218	-0.8389	0.797549
2	-0.061373	-0.4714	0.680458
3	-0.119538	-0.9182	0.818871
4	0.066749	0.5127	0.305034
5	-0.1975	-1.517	0.9327
6	-0.156834	-1.2047	0.883428
7	-0.102624	-0.7883	0.783152
8	0.015471	0.1188	0.452904
9	0.012479	0.0959	0.461982
10	0.16279	1.2504	0.108042
11	0.044393	0.341	0.36716
12	0.021356	0.164	0.43513
13	-0.057551	-0.4421	0.669969
14	-0.114658	-0.8807	0.808974
15	-0.027287	-0.2096	0.582647
16	0.012564	0.0965	0.461723

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.070485 & 0.5414 & 0.295134 \tabularnewline
1 & -0.109218 & -0.8389 & 0.797549 \tabularnewline
2 & -0.061373 & -0.4714 & 0.680458 \tabularnewline
3 & -0.119538 & -0.9182 & 0.818871 \tabularnewline
4 & 0.066749 & 0.5127 & 0.305034 \tabularnewline
5 & -0.1975 & -1.517 & 0.9327 \tabularnewline
6 & -0.156834 & -1.2047 & 0.883428 \tabularnewline
7 & -0.102624 & -0.7883 & 0.783152 \tabularnewline
8 & 0.015471 & 0.1188 & 0.452904 \tabularnewline
9 & 0.012479 & 0.0959 & 0.461982 \tabularnewline
10 & 0.16279 & 1.2504 & 0.108042 \tabularnewline
11 & 0.044393 & 0.341 & 0.36716 \tabularnewline
12 & 0.021356 & 0.164 & 0.43513 \tabularnewline
13 & -0.057551 & -0.4421 & 0.669969 \tabularnewline
14 & -0.114658 & -0.8807 & 0.808974 \tabularnewline
15 & -0.027287 & -0.2096 & 0.582647 \tabularnewline
16 & 0.012564 & 0.0965 & 0.461723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4407&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]0[/C][C]0.070485[/C][C]0.5414[/C][C]0.295134[/C][/ROW]
[ROW][C]1[/C][C]-0.109218[/C][C]-0.8389[/C][C]0.797549[/C][/ROW]
[ROW][C]2[/C][C]-0.061373[/C][C]-0.4714[/C][C]0.680458[/C][/ROW]
[ROW][C]3[/C][C]-0.119538[/C][C]-0.9182[/C][C]0.818871[/C][/ROW]
[ROW][C]4[/C][C]0.066749[/C][C]0.5127[/C][C]0.305034[/C][/ROW]
[ROW][C]5[/C][C]-0.1975[/C][C]-1.517[/C][C]0.9327[/C][/ROW]
[ROW][C]6[/C][C]-0.156834[/C][C]-1.2047[/C][C]0.883428[/C][/ROW]
[ROW][C]7[/C][C]-0.102624[/C][C]-0.7883[/C][C]0.783152[/C][/ROW]
[ROW][C]8[/C][C]0.015471[/C][C]0.1188[/C][C]0.452904[/C][/ROW]
[ROW][C]9[/C][C]0.012479[/C][C]0.0959[/C][C]0.461982[/C][/ROW]
[ROW][C]10[/C][C]0.16279[/C][C]1.2504[/C][C]0.108042[/C][/ROW]
[ROW][C]11[/C][C]0.044393[/C][C]0.341[/C][C]0.36716[/C][/ROW]
[ROW][C]12[/C][C]0.021356[/C][C]0.164[/C][C]0.43513[/C][/ROW]
[ROW][C]13[/C][C]-0.057551[/C][C]-0.4421[/C][C]0.669969[/C][/ROW]
[ROW][C]14[/C][C]-0.114658[/C][C]-0.8807[/C][C]0.808974[/C][/ROW]
[ROW][C]15[/C][C]-0.027287[/C][C]-0.2096[/C][C]0.582647[/C][/ROW]
[ROW][C]16[/C][C]0.012564[/C][C]0.0965[/C][C]0.461723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4407&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4407&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
0	0.070485	0.5414	0.295134
1	-0.109218	-0.8389	0.797549
2	-0.061373	-0.4714	0.680458
3	-0.119538	-0.9182	0.818871
4	0.066749	0.5127	0.305034
5	-0.1975	-1.517	0.9327
6	-0.156834	-1.2047	0.883428
7	-0.102624	-0.7883	0.783152
8	0.015471	0.1188	0.452904
9	0.012479	0.0959	0.461982
10	0.16279	1.2504	0.108042
11	0.044393	0.341	0.36716
12	0.021356	0.164	0.43513
13	-0.057551	-0.4421	0.669969
14	-0.114658	-0.8807	0.808974
15	-0.027287	-0.2096	0.582647
16	0.012564	0.0965	0.461723

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -1.8 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -1.8 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code