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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

Wed, 05 Dec 2007 09:27:01 -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/05/t1196871335zh2gri1a5gga2o1.htm/, Retrieved Thu, 02 May 2024 17:57:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2488, Retrieved Thu, 02 May 2024 17:57:46 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

235

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

-       [(Partial) Autocorrelation Function] [Opdracht 5 Estima...] [2007-12-05 16:27:01] [cb172450b25aceeff04d58e88e905157] [Current]

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Dataseries X:

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Histogram

Boxplots

2.6
2.5
2.5
1.6
1.4
0.8
1.1
1.3
1.2
1.3
1.1
1.3
1.2
1.6
1.7
1.5
0.9
1.5
1.4
1.6
1.7
1.4
1.8
1.7
1.4
1.2
1
1.7
2.4
2
2.1
2
1.8
2.7
2.3
1.9
2
2.3
2.8
2.4
2.3
2.7
2.7
2.9
3
2.2
2.3
2.8
2.8
2.8
2.2
2.6
2.8
2.5
2.4
2.3
1.9
1.7
2
2.1

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2488&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2488&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2488&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.6811	0
1	-0.11457	-0.88	0.808794
2	-0.207145	-1.5911	0.941535
3	-0.063757	-0.4897	0.686929
4	-0.123327	-0.9473	0.826323
5	0.324529	2.4928	0.007751
6	0.033492	0.2573	0.398937
7	-0.225191	-1.7297	0.955546
8	-0.007521	-0.0578	0.522938
9	-0.070848	-0.5442	0.705819
10	0.175984	1.3518	0.090806
11	0.296181	2.275	0.013277
12	-0.467258	-3.5891	0.999662
13	0.067258	0.5166	0.303677
14	0.099059	0.7609	0.224877
15	0.009177	0.0705	0.472021
16	0.157038	1.2062	0.116272

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & -0.11457 & -0.88 & 0.808794 \tabularnewline
2 & -0.207145 & -1.5911 & 0.941535 \tabularnewline
3 & -0.063757 & -0.4897 & 0.686929 \tabularnewline
4 & -0.123327 & -0.9473 & 0.826323 \tabularnewline
5 & 0.324529 & 2.4928 & 0.007751 \tabularnewline
6 & 0.033492 & 0.2573 & 0.398937 \tabularnewline
7 & -0.225191 & -1.7297 & 0.955546 \tabularnewline
8 & -0.007521 & -0.0578 & 0.522938 \tabularnewline
9 & -0.070848 & -0.5442 & 0.705819 \tabularnewline
10 & 0.175984 & 1.3518 & 0.090806 \tabularnewline
11 & 0.296181 & 2.275 & 0.013277 \tabularnewline
12 & -0.467258 & -3.5891 & 0.999662 \tabularnewline
13 & 0.067258 & 0.5166 & 0.303677 \tabularnewline
14 & 0.099059 & 0.7609 & 0.224877 \tabularnewline
15 & 0.009177 & 0.0705 & 0.472021 \tabularnewline
16 & 0.157038 & 1.2062 & 0.116272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2488&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]-0.11457[/C][C]-0.88[/C][C]0.808794[/C][/ROW]
[ROW][C]2[/C][C]-0.207145[/C][C]-1.5911[/C][C]0.941535[/C][/ROW]
[ROW][C]3[/C][C]-0.063757[/C][C]-0.4897[/C][C]0.686929[/C][/ROW]
[ROW][C]4[/C][C]-0.123327[/C][C]-0.9473[/C][C]0.826323[/C][/ROW]
[ROW][C]5[/C][C]0.324529[/C][C]2.4928[/C][C]0.007751[/C][/ROW]
[ROW][C]6[/C][C]0.033492[/C][C]0.2573[/C][C]0.398937[/C][/ROW]
[ROW][C]7[/C][C]-0.225191[/C][C]-1.7297[/C][C]0.955546[/C][/ROW]
[ROW][C]8[/C][C]-0.007521[/C][C]-0.0578[/C][C]0.522938[/C][/ROW]
[ROW][C]9[/C][C]-0.070848[/C][C]-0.5442[/C][C]0.705819[/C][/ROW]
[ROW][C]10[/C][C]0.175984[/C][C]1.3518[/C][C]0.090806[/C][/ROW]
[ROW][C]11[/C][C]0.296181[/C][C]2.275[/C][C]0.013277[/C][/ROW]
[ROW][C]12[/C][C]-0.467258[/C][C]-3.5891[/C][C]0.999662[/C][/ROW]
[ROW][C]13[/C][C]0.067258[/C][C]0.5166[/C][C]0.303677[/C][/ROW]
[ROW][C]14[/C][C]0.099059[/C][C]0.7609[/C][C]0.224877[/C][/ROW]
[ROW][C]15[/C][C]0.009177[/C][C]0.0705[/C][C]0.472021[/C][/ROW]
[ROW][C]16[/C][C]0.157038[/C][C]1.2062[/C][C]0.116272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2488&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2488&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	-0.11457	-0.88	0.808794
2	-0.207145	-1.5911	0.941535
3	-0.063757	-0.4897	0.686929
4	-0.123327	-0.9473	0.826323
5	0.324529	2.4928	0.007751
6	0.033492	0.2573	0.398937
7	-0.225191	-1.7297	0.955546
8	-0.007521	-0.0578	0.522938
9	-0.070848	-0.5442	0.705819
10	0.175984	1.3518	0.090806
11	0.296181	2.275	0.013277
12	-0.467258	-3.5891	0.999662
13	0.067258	0.5166	0.303677
14	0.099059	0.7609	0.224877
15	0.009177	0.0705	0.472021
16	0.157038	1.2062	0.116272

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.11457	-0.88	0.808794
1	-0.223201	-1.7144	0.954151
2	-0.126222	-0.9695	0.83188
3	-0.215025	-1.6516	0.948039
4	0.25393	1.9505	0.027938
5	0.045436	0.349	0.364165
6	-0.124115	-0.9533	0.827848
7	-0.017706	-0.136	0.553859
8	-0.074902	-0.5753	0.716373
9	0.068412	0.5255	0.30061
10	0.29144	2.2386	0.014484
11	-0.351945	-2.7033	0.995523
12	0.156774	1.2042	0.11666
13	0.057671	0.443	0.329701
14	-0.010234	-0.0786	0.531195
15	-0.037489	-0.288	0.612805
16	-0.113794	-0.8741	0.807188

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.11457 & -0.88 & 0.808794 \tabularnewline
1 & -0.223201 & -1.7144 & 0.954151 \tabularnewline
2 & -0.126222 & -0.9695 & 0.83188 \tabularnewline
3 & -0.215025 & -1.6516 & 0.948039 \tabularnewline
4 & 0.25393 & 1.9505 & 0.027938 \tabularnewline
5 & 0.045436 & 0.349 & 0.364165 \tabularnewline
6 & -0.124115 & -0.9533 & 0.827848 \tabularnewline
7 & -0.017706 & -0.136 & 0.553859 \tabularnewline
8 & -0.074902 & -0.5753 & 0.716373 \tabularnewline
9 & 0.068412 & 0.5255 & 0.30061 \tabularnewline
10 & 0.29144 & 2.2386 & 0.014484 \tabularnewline
11 & -0.351945 & -2.7033 & 0.995523 \tabularnewline
12 & 0.156774 & 1.2042 & 0.11666 \tabularnewline
13 & 0.057671 & 0.443 & 0.329701 \tabularnewline
14 & -0.010234 & -0.0786 & 0.531195 \tabularnewline
15 & -0.037489 & -0.288 & 0.612805 \tabularnewline
16 & -0.113794 & -0.8741 & 0.807188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2488&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]-0.11457[/C][C]-0.88[/C][C]0.808794[/C][/ROW]
[ROW][C]1[/C][C]-0.223201[/C][C]-1.7144[/C][C]0.954151[/C][/ROW]
[ROW][C]2[/C][C]-0.126222[/C][C]-0.9695[/C][C]0.83188[/C][/ROW]
[ROW][C]3[/C][C]-0.215025[/C][C]-1.6516[/C][C]0.948039[/C][/ROW]
[ROW][C]4[/C][C]0.25393[/C][C]1.9505[/C][C]0.027938[/C][/ROW]
[ROW][C]5[/C][C]0.045436[/C][C]0.349[/C][C]0.364165[/C][/ROW]
[ROW][C]6[/C][C]-0.124115[/C][C]-0.9533[/C][C]0.827848[/C][/ROW]
[ROW][C]7[/C][C]-0.017706[/C][C]-0.136[/C][C]0.553859[/C][/ROW]
[ROW][C]8[/C][C]-0.074902[/C][C]-0.5753[/C][C]0.716373[/C][/ROW]
[ROW][C]9[/C][C]0.068412[/C][C]0.5255[/C][C]0.30061[/C][/ROW]
[ROW][C]10[/C][C]0.29144[/C][C]2.2386[/C][C]0.014484[/C][/ROW]
[ROW][C]11[/C][C]-0.351945[/C][C]-2.7033[/C][C]0.995523[/C][/ROW]
[ROW][C]12[/C][C]0.156774[/C][C]1.2042[/C][C]0.11666[/C][/ROW]
[ROW][C]13[/C][C]0.057671[/C][C]0.443[/C][C]0.329701[/C][/ROW]
[ROW][C]14[/C][C]-0.010234[/C][C]-0.0786[/C][C]0.531195[/C][/ROW]
[ROW][C]15[/C][C]-0.037489[/C][C]-0.288[/C][C]0.612805[/C][/ROW]
[ROW][C]16[/C][C]-0.113794[/C][C]-0.8741[/C][C]0.807188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2488&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2488&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	-0.11457	-0.88	0.808794
1	-0.223201	-1.7144	0.954151
2	-0.126222	-0.9695	0.83188
3	-0.215025	-1.6516	0.948039
4	0.25393	1.9505	0.027938
5	0.045436	0.349	0.364165
6	-0.124115	-0.9533	0.827848
7	-0.017706	-0.136	0.553859
8	-0.074902	-0.5753	0.716373
9	0.068412	0.5255	0.30061
10	0.29144	2.2386	0.014484
11	-0.351945	-2.7033	0.995523
12	0.156774	1.2042	0.11666
13	0.057671	0.443	0.329701
14	-0.010234	-0.0786	0.531195
15	-0.037489	-0.288	0.612805
16	-0.113794	-0.8741	0.807188

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code