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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 05:33:04 -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/Nov/25/t1195993433dqnn2li984zvvy8.htm/, Retrieved Sat, 04 May 2024 15:18:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6421, Retrieved Sat, 04 May 2024 15:18:11 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

165

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

-       [(Partial) Autocorrelation Function] [Autocorrelation f...] [2007-11-25 12:33:04] [9fe578921d87f9af8e79a90d6142ba02] [Current]

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Dataseries X:

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Boxplots

8.5
8.6
8.5
8.5
9
9
8.8
8
7.9
8.1
9.3
9.4
9.4
9.3
9
9.1
9.7
9.7
9.6
8.3
8.2
8.4
10.6
10.9
10.9
9.6
9.3
9.3
9.6
9.5
9.5
9
8.9
9
10.1
10.2
10.2
9.5
9.3
9.3
9.4
9.3
9.1
9
8.9
9
9.8
10
9.8
9.4
9
8.9
9.3
9.1
8.8
8.9
8.7
8.6
9.1
9.3
8.9

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=6421&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=6421&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6421&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	6.9282	0
1	0.067542	0.4679	0.320972
2	-0.066164	-0.4584	0.675633
3	-0.57908	-4.012	0.999895
4	-0.073077	-0.5063	0.692515
5	-0.049402	-0.3423	0.633179
6	0.156393	1.0835	0.141995
7	0.023519	0.1629	0.435624
8	0.058836	0.4076	0.34268
9	0.14987	1.0383	0.152159
10	-0.008992	-0.0623	0.524707
11	-0.072427	-0.5018	0.690946
12	-0.189293	-1.3115	0.90203
13	-0.077677	-0.5382	0.703523
14	0.061175	0.4238	0.336791
15	0.163228	1.1309	0.131863
16	0.06341	0.4393	0.331203

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & 0.067542 & 0.4679 & 0.320972 \tabularnewline
2 & -0.066164 & -0.4584 & 0.675633 \tabularnewline
3 & -0.57908 & -4.012 & 0.999895 \tabularnewline
4 & -0.073077 & -0.5063 & 0.692515 \tabularnewline
5 & -0.049402 & -0.3423 & 0.633179 \tabularnewline
6 & 0.156393 & 1.0835 & 0.141995 \tabularnewline
7 & 0.023519 & 0.1629 & 0.435624 \tabularnewline
8 & 0.058836 & 0.4076 & 0.34268 \tabularnewline
9 & 0.14987 & 1.0383 & 0.152159 \tabularnewline
10 & -0.008992 & -0.0623 & 0.524707 \tabularnewline
11 & -0.072427 & -0.5018 & 0.690946 \tabularnewline
12 & -0.189293 & -1.3115 & 0.90203 \tabularnewline
13 & -0.077677 & -0.5382 & 0.703523 \tabularnewline
14 & 0.061175 & 0.4238 & 0.336791 \tabularnewline
15 & 0.163228 & 1.1309 & 0.131863 \tabularnewline
16 & 0.06341 & 0.4393 & 0.331203 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6421&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]6.9282[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.067542[/C][C]0.4679[/C][C]0.320972[/C][/ROW]
[ROW][C]2[/C][C]-0.066164[/C][C]-0.4584[/C][C]0.675633[/C][/ROW]
[ROW][C]3[/C][C]-0.57908[/C][C]-4.012[/C][C]0.999895[/C][/ROW]
[ROW][C]4[/C][C]-0.073077[/C][C]-0.5063[/C][C]0.692515[/C][/ROW]
[ROW][C]5[/C][C]-0.049402[/C][C]-0.3423[/C][C]0.633179[/C][/ROW]
[ROW][C]6[/C][C]0.156393[/C][C]1.0835[/C][C]0.141995[/C][/ROW]
[ROW][C]7[/C][C]0.023519[/C][C]0.1629[/C][C]0.435624[/C][/ROW]
[ROW][C]8[/C][C]0.058836[/C][C]0.4076[/C][C]0.34268[/C][/ROW]
[ROW][C]9[/C][C]0.14987[/C][C]1.0383[/C][C]0.152159[/C][/ROW]
[ROW][C]10[/C][C]-0.008992[/C][C]-0.0623[/C][C]0.524707[/C][/ROW]
[ROW][C]11[/C][C]-0.072427[/C][C]-0.5018[/C][C]0.690946[/C][/ROW]
[ROW][C]12[/C][C]-0.189293[/C][C]-1.3115[/C][C]0.90203[/C][/ROW]
[ROW][C]13[/C][C]-0.077677[/C][C]-0.5382[/C][C]0.703523[/C][/ROW]
[ROW][C]14[/C][C]0.061175[/C][C]0.4238[/C][C]0.336791[/C][/ROW]
[ROW][C]15[/C][C]0.163228[/C][C]1.1309[/C][C]0.131863[/C][/ROW]
[ROW][C]16[/C][C]0.06341[/C][C]0.4393[/C][C]0.331203[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6421&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6421&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	6.9282	0
1	0.067542	0.4679	0.320972
2	-0.066164	-0.4584	0.675633
3	-0.57908	-4.012	0.999895
4	-0.073077	-0.5063	0.692515
5	-0.049402	-0.3423	0.633179
6	0.156393	1.0835	0.141995
7	0.023519	0.1629	0.435624
8	0.058836	0.4076	0.34268
9	0.14987	1.0383	0.152159
10	-0.008992	-0.0623	0.524707
11	-0.072427	-0.5018	0.690946
12	-0.189293	-1.3115	0.90203
13	-0.077677	-0.5382	0.703523
14	0.061175	0.4238	0.336791
15	0.163228	1.1309	0.131863
16	0.06341	0.4393	0.331203

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.067542	0.4679	0.320972
1	-0.07105	-0.4923	0.687607
2	-0.575007	-3.9838	0.999885
3	-0.027085	-0.1876	0.574029
4	-0.153845	-1.0659	0.854093
5	-0.275375	-1.9079	0.968799
6	-0.094311	-0.6534	0.741695
7	-0.11836	-0.82	0.791872
8	0.141253	0.9786	0.166335
9	-0.077869	-0.5395	0.703979
10	-0.067624	-0.4685	0.679231
11	0.028233	0.1956	0.422872
12	-0.162535	-1.1261	0.867134
13	0.027745	0.1922	0.42419
14	0.027896	0.1933	0.423781
15	-0.089799	-0.6221	0.731604
16	0.025595	0.1773	0.43

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.067542 & 0.4679 & 0.320972 \tabularnewline
1 & -0.07105 & -0.4923 & 0.687607 \tabularnewline
2 & -0.575007 & -3.9838 & 0.999885 \tabularnewline
3 & -0.027085 & -0.1876 & 0.574029 \tabularnewline
4 & -0.153845 & -1.0659 & 0.854093 \tabularnewline
5 & -0.275375 & -1.9079 & 0.968799 \tabularnewline
6 & -0.094311 & -0.6534 & 0.741695 \tabularnewline
7 & -0.11836 & -0.82 & 0.791872 \tabularnewline
8 & 0.141253 & 0.9786 & 0.166335 \tabularnewline
9 & -0.077869 & -0.5395 & 0.703979 \tabularnewline
10 & -0.067624 & -0.4685 & 0.679231 \tabularnewline
11 & 0.028233 & 0.1956 & 0.422872 \tabularnewline
12 & -0.162535 & -1.1261 & 0.867134 \tabularnewline
13 & 0.027745 & 0.1922 & 0.42419 \tabularnewline
14 & 0.027896 & 0.1933 & 0.423781 \tabularnewline
15 & -0.089799 & -0.6221 & 0.731604 \tabularnewline
16 & 0.025595 & 0.1773 & 0.43 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6421&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]0.067542[/C][C]0.4679[/C][C]0.320972[/C][/ROW]
[ROW][C]1[/C][C]-0.07105[/C][C]-0.4923[/C][C]0.687607[/C][/ROW]
[ROW][C]2[/C][C]-0.575007[/C][C]-3.9838[/C][C]0.999885[/C][/ROW]
[ROW][C]3[/C][C]-0.027085[/C][C]-0.1876[/C][C]0.574029[/C][/ROW]
[ROW][C]4[/C][C]-0.153845[/C][C]-1.0659[/C][C]0.854093[/C][/ROW]
[ROW][C]5[/C][C]-0.275375[/C][C]-1.9079[/C][C]0.968799[/C][/ROW]
[ROW][C]6[/C][C]-0.094311[/C][C]-0.6534[/C][C]0.741695[/C][/ROW]
[ROW][C]7[/C][C]-0.11836[/C][C]-0.82[/C][C]0.791872[/C][/ROW]
[ROW][C]8[/C][C]0.141253[/C][C]0.9786[/C][C]0.166335[/C][/ROW]
[ROW][C]9[/C][C]-0.077869[/C][C]-0.5395[/C][C]0.703979[/C][/ROW]
[ROW][C]10[/C][C]-0.067624[/C][C]-0.4685[/C][C]0.679231[/C][/ROW]
[ROW][C]11[/C][C]0.028233[/C][C]0.1956[/C][C]0.422872[/C][/ROW]
[ROW][C]12[/C][C]-0.162535[/C][C]-1.1261[/C][C]0.867134[/C][/ROW]
[ROW][C]13[/C][C]0.027745[/C][C]0.1922[/C][C]0.42419[/C][/ROW]
[ROW][C]14[/C][C]0.027896[/C][C]0.1933[/C][C]0.423781[/C][/ROW]
[ROW][C]15[/C][C]-0.089799[/C][C]-0.6221[/C][C]0.731604[/C][/ROW]
[ROW][C]16[/C][C]0.025595[/C][C]0.1773[/C][C]0.43[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6421&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6421&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	0.067542	0.4679	0.320972
1	-0.07105	-0.4923	0.687607
2	-0.575007	-3.9838	0.999885
3	-0.027085	-0.1876	0.574029
4	-0.153845	-1.0659	0.854093
5	-0.275375	-1.9079	0.968799
6	-0.094311	-0.6534	0.741695
7	-0.11836	-0.82	0.791872
8	0.141253	0.9786	0.166335
9	-0.077869	-0.5395	0.703979
10	-0.067624	-0.4685	0.679231
11	0.028233	0.1956	0.422872
12	-0.162535	-1.1261	0.867134
13	0.027745	0.1922	0.42419
14	0.027896	0.1933	0.423781
15	-0.089799	-0.6221	0.731604
16	0.025595	0.1773	0.43

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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

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Input Parameters & R Code