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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, 21 Nov 2007 12:52:08 -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/21/t1195674436zdlbqa1ufom5qkm.htm/, Retrieved Tue, 07 May 2024 06:10:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5878, Retrieved Tue, 07 May 2024 06:10:55 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

218

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

-       [(Partial) Autocorrelation Function] [inducing stationa...] [2007-11-21 19:52:08] [2127dfc39c0d0690439ab654f5655d7e] [Current]

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Dataseries X:

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Histogram

Boxplots

7.4
7.2
7
6.6
6.4
6.4
6.8
7.3
7
7
6.7
6.7
6.3
6.2
6
6.3
6.2
6.1
6.2
6.6
6.6
7.8
7.4
7.4
7.5
7.4
7.4
7
6.9
6.9
7.6
7.7
7.6
8.2
8
8.1
8.3
8.2
8.1
7.7
7.6
7.7
8.2
8.4
8.4
8.6
8.4
8.5
8.7
8.7
8.6
7.4
7.3
7.4
9
9.2
9.2
8.5
8.3
8.3
8.6
8.6
8.5
8.1
8.1
8
8.6
8.7
8.7
8.6
8.4
8.4
8.7
8.7
8.5
8.3
8.3
8.3
8.1
8.2
8.1
8.1
7.9
7.7
8.1
8
7.7
7.8
7.6
7.4
7.7
7.9
7.6

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=5878&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=5878&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5878&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	9.6437	0
1	0.903488	8.7129	0
2	0.794999	7.6667	0
3	0.691242	6.6661	0
4	0.656283	6.329	0
5	0.65331	6.3003	0
6	0.64701	6.2395	0
7	0.608454	5.8677	0
8	0.571274	5.5092	0
9	0.560666	5.4069	0
10	0.57961	5.5896	0
11	0.600216	5.7883	0
12	0.609806	5.8808	0
13	0.529216	5.1036	1e-06
14	0.440061	4.2438	2.6e-05
15	0.34104	3.2889	0.000711
16	0.272505	2.6279	0.005025
17	0.239367	2.3084	0.011597
18	0.202474	1.9526	0.026938

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.6437 & 0 \tabularnewline
1 & 0.903488 & 8.7129 & 0 \tabularnewline
2 & 0.794999 & 7.6667 & 0 \tabularnewline
3 & 0.691242 & 6.6661 & 0 \tabularnewline
4 & 0.656283 & 6.329 & 0 \tabularnewline
5 & 0.65331 & 6.3003 & 0 \tabularnewline
6 & 0.64701 & 6.2395 & 0 \tabularnewline
7 & 0.608454 & 5.8677 & 0 \tabularnewline
8 & 0.571274 & 5.5092 & 0 \tabularnewline
9 & 0.560666 & 5.4069 & 0 \tabularnewline
10 & 0.57961 & 5.5896 & 0 \tabularnewline
11 & 0.600216 & 5.7883 & 0 \tabularnewline
12 & 0.609806 & 5.8808 & 0 \tabularnewline
13 & 0.529216 & 5.1036 & 1e-06 \tabularnewline
14 & 0.440061 & 4.2438 & 2.6e-05 \tabularnewline
15 & 0.34104 & 3.2889 & 0.000711 \tabularnewline
16 & 0.272505 & 2.6279 & 0.005025 \tabularnewline
17 & 0.239367 & 2.3084 & 0.011597 \tabularnewline
18 & 0.202474 & 1.9526 & 0.026938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5878&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]9.6437[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.903488[/C][C]8.7129[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.794999[/C][C]7.6667[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.691242[/C][C]6.6661[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.656283[/C][C]6.329[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.65331[/C][C]6.3003[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.64701[/C][C]6.2395[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.608454[/C][C]5.8677[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.571274[/C][C]5.5092[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.560666[/C][C]5.4069[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.57961[/C][C]5.5896[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.600216[/C][C]5.7883[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.609806[/C][C]5.8808[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.529216[/C][C]5.1036[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]0.440061[/C][C]4.2438[/C][C]2.6e-05[/C][/ROW]
[ROW][C]15[/C][C]0.34104[/C][C]3.2889[/C][C]0.000711[/C][/ROW]
[ROW][C]16[/C][C]0.272505[/C][C]2.6279[/C][C]0.005025[/C][/ROW]
[ROW][C]17[/C][C]0.239367[/C][C]2.3084[/C][C]0.011597[/C][/ROW]
[ROW][C]18[/C][C]0.202474[/C][C]1.9526[/C][C]0.026938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5878&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5878&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	9.6437	0
1	0.903488	8.7129	0
2	0.794999	7.6667	0
3	0.691242	6.6661	0
4	0.656283	6.329	0
5	0.65331	6.3003	0
6	0.64701	6.2395	0
7	0.608454	5.8677	0
8	0.571274	5.5092	0
9	0.560666	5.4069	0
10	0.57961	5.5896	0
11	0.600216	5.7883	0
12	0.609806	5.8808	0
13	0.529216	5.1036	1e-06
14	0.440061	4.2438	2.6e-05
15	0.34104	3.2889	0.000711
16	0.272505	2.6279	0.005025
17	0.239367	2.3084	0.011597
18	0.202474	1.9526	0.026938

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.903488	8.7129	0
1	-0.115891	-1.1176	0.866695
2	-0.030707	-0.2961	0.616104
3	0.315354	3.0412	0.001531
4	0.117664	1.1347	0.129707
5	-0.041824	-0.4033	0.656187
6	-0.070889	-0.6836	0.752044
7	0.113176	1.0914	0.138952
8	0.159728	1.5404	0.063434
9	0.079654	0.7682	0.222171
10	0.012307	0.1187	0.452892
11	0.07577	0.7307	0.2334
12	-0.41635	-4.0151	0.99994
13	-0.048507	-0.4678	0.679484
14	-0.125858	-1.2137	0.886038
15	-0.201483	-1.943	0.972482
16	0.032526	0.3137	0.377236
17	-0.150459	-1.451	0.924924
18	-0.009968	-0.0961	0.538187

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.903488 & 8.7129 & 0 \tabularnewline
1 & -0.115891 & -1.1176 & 0.866695 \tabularnewline
2 & -0.030707 & -0.2961 & 0.616104 \tabularnewline
3 & 0.315354 & 3.0412 & 0.001531 \tabularnewline
4 & 0.117664 & 1.1347 & 0.129707 \tabularnewline
5 & -0.041824 & -0.4033 & 0.656187 \tabularnewline
6 & -0.070889 & -0.6836 & 0.752044 \tabularnewline
7 & 0.113176 & 1.0914 & 0.138952 \tabularnewline
8 & 0.159728 & 1.5404 & 0.063434 \tabularnewline
9 & 0.079654 & 0.7682 & 0.222171 \tabularnewline
10 & 0.012307 & 0.1187 & 0.452892 \tabularnewline
11 & 0.07577 & 0.7307 & 0.2334 \tabularnewline
12 & -0.41635 & -4.0151 & 0.99994 \tabularnewline
13 & -0.048507 & -0.4678 & 0.679484 \tabularnewline
14 & -0.125858 & -1.2137 & 0.886038 \tabularnewline
15 & -0.201483 & -1.943 & 0.972482 \tabularnewline
16 & 0.032526 & 0.3137 & 0.377236 \tabularnewline
17 & -0.150459 & -1.451 & 0.924924 \tabularnewline
18 & -0.009968 & -0.0961 & 0.538187 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5878&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]0.903488[/C][C]8.7129[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.115891[/C][C]-1.1176[/C][C]0.866695[/C][/ROW]
[ROW][C]2[/C][C]-0.030707[/C][C]-0.2961[/C][C]0.616104[/C][/ROW]
[ROW][C]3[/C][C]0.315354[/C][C]3.0412[/C][C]0.001531[/C][/ROW]
[ROW][C]4[/C][C]0.117664[/C][C]1.1347[/C][C]0.129707[/C][/ROW]
[ROW][C]5[/C][C]-0.041824[/C][C]-0.4033[/C][C]0.656187[/C][/ROW]
[ROW][C]6[/C][C]-0.070889[/C][C]-0.6836[/C][C]0.752044[/C][/ROW]
[ROW][C]7[/C][C]0.113176[/C][C]1.0914[/C][C]0.138952[/C][/ROW]
[ROW][C]8[/C][C]0.159728[/C][C]1.5404[/C][C]0.063434[/C][/ROW]
[ROW][C]9[/C][C]0.079654[/C][C]0.7682[/C][C]0.222171[/C][/ROW]
[ROW][C]10[/C][C]0.012307[/C][C]0.1187[/C][C]0.452892[/C][/ROW]
[ROW][C]11[/C][C]0.07577[/C][C]0.7307[/C][C]0.2334[/C][/ROW]
[ROW][C]12[/C][C]-0.41635[/C][C]-4.0151[/C][C]0.99994[/C][/ROW]
[ROW][C]13[/C][C]-0.048507[/C][C]-0.4678[/C][C]0.679484[/C][/ROW]
[ROW][C]14[/C][C]-0.125858[/C][C]-1.2137[/C][C]0.886038[/C][/ROW]
[ROW][C]15[/C][C]-0.201483[/C][C]-1.943[/C][C]0.972482[/C][/ROW]
[ROW][C]16[/C][C]0.032526[/C][C]0.3137[/C][C]0.377236[/C][/ROW]
[ROW][C]17[/C][C]-0.150459[/C][C]-1.451[/C][C]0.924924[/C][/ROW]
[ROW][C]18[/C][C]-0.009968[/C][C]-0.0961[/C][C]0.538187[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5878&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5878&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	0.903488	8.7129	0
1	-0.115891	-1.1176	0.866695
2	-0.030707	-0.2961	0.616104
3	0.315354	3.0412	0.001531
4	0.117664	1.1347	0.129707
5	-0.041824	-0.4033	0.656187
6	-0.070889	-0.6836	0.752044
7	0.113176	1.0914	0.138952
8	0.159728	1.5404	0.063434
9	0.079654	0.7682	0.222171
10	0.012307	0.1187	0.452892
11	0.07577	0.7307	0.2334
12	-0.41635	-4.0151	0.99994
13	-0.048507	-0.4678	0.679484
14	-0.125858	-1.2137	0.886038
15	-0.201483	-1.943	0.972482
16	0.032526	0.3137	0.377236
17	-0.150459	-1.451	0.924924
18	-0.009968	-0.0961	0.538187

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code