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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 21 Dec 2008 15:26:12 -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/2008/Dec/21/t1229898410zd3lp9809m0oneu.htm/, Retrieved Sat, 18 May 2024 21:19:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35885, Retrieved Sat, 18 May 2024 21:19:08 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

136

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

-     [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:13:26] [4ddbf81f78ea7c738951638c7e93f6ee]
-   P   [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:16:00] [4ddbf81f78ea7c738951638c7e93f6ee]
-   PD    [(Partial) Autocorrelation Function] [autocorrelation v...] [2008-12-21 22:17:35] [4ddbf81f78ea7c738951638c7e93f6ee]
-   PD      [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:19:34] [4ddbf81f78ea7c738951638c7e93f6ee]
-             [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:20:27] [4ddbf81f78ea7c738951638c7e93f6ee]
-   P           [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:22:06] [4ddbf81f78ea7c738951638c7e93f6ee]
-   PD            [(Partial) Autocorrelation Function] [autocorrelation t...] [2008-12-21 22:23:36] [4ddbf81f78ea7c738951638c7e93f6ee]
-   PD              [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:24:49] [4ddbf81f78ea7c738951638c7e93f6ee]
-   P                   [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:26:12] [e8f764b122b426f433a1e1038b457077] [Current]

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Dataseries X:

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Histogram

Boxplots

8.3
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35885&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35885&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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.447173	3.0657	0.001797
2	-0.085344	-0.5851	0.280644
3	-0.406285	-2.7853	0.003842
4	-0.531507	-3.6438	0.000335
5	-0.227784	-1.5616	0.062545
6	0.049897	0.3421	0.36691
7	0.164733	1.1294	0.132241
8	0.206868	1.4182	0.081362
9	0.032426	0.2223	0.412521
10	-0.046139	-0.3163	0.376584
11	0.058451	0.4007	0.345221
12	0.017395	0.1193	0.45279
13	0.025376	0.174	0.431319
14	-0.000798	-0.0055	0.497829
15	-0.093147	-0.6386	0.263097
16	-0.132861	-0.9108	0.183512
17	-0.136102	-0.9331	0.177776

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.447173 & 3.0657 & 0.001797 \tabularnewline
2 & -0.085344 & -0.5851 & 0.280644 \tabularnewline
3 & -0.406285 & -2.7853 & 0.003842 \tabularnewline
4 & -0.531507 & -3.6438 & 0.000335 \tabularnewline
5 & -0.227784 & -1.5616 & 0.062545 \tabularnewline
6 & 0.049897 & 0.3421 & 0.36691 \tabularnewline
7 & 0.164733 & 1.1294 & 0.132241 \tabularnewline
8 & 0.206868 & 1.4182 & 0.081362 \tabularnewline
9 & 0.032426 & 0.2223 & 0.412521 \tabularnewline
10 & -0.046139 & -0.3163 & 0.376584 \tabularnewline
11 & 0.058451 & 0.4007 & 0.345221 \tabularnewline
12 & 0.017395 & 0.1193 & 0.45279 \tabularnewline
13 & 0.025376 & 0.174 & 0.431319 \tabularnewline
14 & -0.000798 & -0.0055 & 0.497829 \tabularnewline
15 & -0.093147 & -0.6386 & 0.263097 \tabularnewline
16 & -0.132861 & -0.9108 & 0.183512 \tabularnewline
17 & -0.136102 & -0.9331 & 0.177776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35885&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]0.447173[/C][C]3.0657[/C][C]0.001797[/C][/ROW]
[ROW][C]2[/C][C]-0.085344[/C][C]-0.5851[/C][C]0.280644[/C][/ROW]
[ROW][C]3[/C][C]-0.406285[/C][C]-2.7853[/C][C]0.003842[/C][/ROW]
[ROW][C]4[/C][C]-0.531507[/C][C]-3.6438[/C][C]0.000335[/C][/ROW]
[ROW][C]5[/C][C]-0.227784[/C][C]-1.5616[/C][C]0.062545[/C][/ROW]
[ROW][C]6[/C][C]0.049897[/C][C]0.3421[/C][C]0.36691[/C][/ROW]
[ROW][C]7[/C][C]0.164733[/C][C]1.1294[/C][C]0.132241[/C][/ROW]
[ROW][C]8[/C][C]0.206868[/C][C]1.4182[/C][C]0.081362[/C][/ROW]
[ROW][C]9[/C][C]0.032426[/C][C]0.2223[/C][C]0.412521[/C][/ROW]
[ROW][C]10[/C][C]-0.046139[/C][C]-0.3163[/C][C]0.376584[/C][/ROW]
[ROW][C]11[/C][C]0.058451[/C][C]0.4007[/C][C]0.345221[/C][/ROW]
[ROW][C]12[/C][C]0.017395[/C][C]0.1193[/C][C]0.45279[/C][/ROW]
[ROW][C]13[/C][C]0.025376[/C][C]0.174[/C][C]0.431319[/C][/ROW]
[ROW][C]14[/C][C]-0.000798[/C][C]-0.0055[/C][C]0.497829[/C][/ROW]
[ROW][C]15[/C][C]-0.093147[/C][C]-0.6386[/C][C]0.263097[/C][/ROW]
[ROW][C]16[/C][C]-0.132861[/C][C]-0.9108[/C][C]0.183512[/C][/ROW]
[ROW][C]17[/C][C]-0.136102[/C][C]-0.9331[/C][C]0.177776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35885&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	0.447173	3.0657	0.001797
2	-0.085344	-0.5851	0.280644
3	-0.406285	-2.7853	0.003842
4	-0.531507	-3.6438	0.000335
5	-0.227784	-1.5616	0.062545
6	0.049897	0.3421	0.36691
7	0.164733	1.1294	0.132241
8	0.206868	1.4182	0.081362
9	0.032426	0.2223	0.412521
10	-0.046139	-0.3163	0.376584
11	0.058451	0.4007	0.345221
12	0.017395	0.1193	0.45279
13	0.025376	0.174	0.431319
14	-0.000798	-0.0055	0.497829
15	-0.093147	-0.6386	0.263097
16	-0.132861	-0.9108	0.183512
17	-0.136102	-0.9331	0.177776

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.447173	3.0657	0.001797
2	-0.356618	-2.4449	0.009147
3	-0.279313	-1.9149	0.030803
4	-0.336402	-2.3063	0.012777
5	0.0548	0.3757	0.354418
6	-0.13238	-0.9076	0.184372
7	-0.127066	-0.8711	0.194058
8	-0.034934	-0.2395	0.405882
9	-0.159624	-1.0943	0.139694
10	0.003964	0.0272	0.489219
11	0.146978	1.0076	0.159396
12	-0.078987	-0.5415	0.295359
13	0.029909	0.205	0.419211
14	0.024801	0.17	0.43286
15	0.013995	0.0959	0.461987
16	-0.121225	-0.8311	0.205066
17	-0.079392	-0.5443	0.294408

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.447173 & 3.0657 & 0.001797 \tabularnewline
2 & -0.356618 & -2.4449 & 0.009147 \tabularnewline
3 & -0.279313 & -1.9149 & 0.030803 \tabularnewline
4 & -0.336402 & -2.3063 & 0.012777 \tabularnewline
5 & 0.0548 & 0.3757 & 0.354418 \tabularnewline
6 & -0.13238 & -0.9076 & 0.184372 \tabularnewline
7 & -0.127066 & -0.8711 & 0.194058 \tabularnewline
8 & -0.034934 & -0.2395 & 0.405882 \tabularnewline
9 & -0.159624 & -1.0943 & 0.139694 \tabularnewline
10 & 0.003964 & 0.0272 & 0.489219 \tabularnewline
11 & 0.146978 & 1.0076 & 0.159396 \tabularnewline
12 & -0.078987 & -0.5415 & 0.295359 \tabularnewline
13 & 0.029909 & 0.205 & 0.419211 \tabularnewline
14 & 0.024801 & 0.17 & 0.43286 \tabularnewline
15 & 0.013995 & 0.0959 & 0.461987 \tabularnewline
16 & -0.121225 & -0.8311 & 0.205066 \tabularnewline
17 & -0.079392 & -0.5443 & 0.294408 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35885&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]0.447173[/C][C]3.0657[/C][C]0.001797[/C][/ROW]
[ROW][C]2[/C][C]-0.356618[/C][C]-2.4449[/C][C]0.009147[/C][/ROW]
[ROW][C]3[/C][C]-0.279313[/C][C]-1.9149[/C][C]0.030803[/C][/ROW]
[ROW][C]4[/C][C]-0.336402[/C][C]-2.3063[/C][C]0.012777[/C][/ROW]
[ROW][C]5[/C][C]0.0548[/C][C]0.3757[/C][C]0.354418[/C][/ROW]
[ROW][C]6[/C][C]-0.13238[/C][C]-0.9076[/C][C]0.184372[/C][/ROW]
[ROW][C]7[/C][C]-0.127066[/C][C]-0.8711[/C][C]0.194058[/C][/ROW]
[ROW][C]8[/C][C]-0.034934[/C][C]-0.2395[/C][C]0.405882[/C][/ROW]
[ROW][C]9[/C][C]-0.159624[/C][C]-1.0943[/C][C]0.139694[/C][/ROW]
[ROW][C]10[/C][C]0.003964[/C][C]0.0272[/C][C]0.489219[/C][/ROW]
[ROW][C]11[/C][C]0.146978[/C][C]1.0076[/C][C]0.159396[/C][/ROW]
[ROW][C]12[/C][C]-0.078987[/C][C]-0.5415[/C][C]0.295359[/C][/ROW]
[ROW][C]13[/C][C]0.029909[/C][C]0.205[/C][C]0.419211[/C][/ROW]
[ROW][C]14[/C][C]0.024801[/C][C]0.17[/C][C]0.43286[/C][/ROW]
[ROW][C]15[/C][C]0.013995[/C][C]0.0959[/C][C]0.461987[/C][/ROW]
[ROW][C]16[/C][C]-0.121225[/C][C]-0.8311[/C][C]0.205066[/C][/ROW]
[ROW][C]17[/C][C]-0.079392[/C][C]-0.5443[/C][C]0.294408[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35885&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35885&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	0.447173	3.0657	0.001797
2	-0.356618	-2.4449	0.009147
3	-0.279313	-1.9149	0.030803
4	-0.336402	-2.3063	0.012777
5	0.0548	0.3757	0.354418
6	-0.13238	-0.9076	0.184372
7	-0.127066	-0.8711	0.194058
8	-0.034934	-0.2395	0.405882
9	-0.159624	-1.0943	0.139694
10	0.003964	0.0272	0.489219
11	0.146978	1.0076	0.159396
12	-0.078987	-0.5415	0.295359
13	0.029909	0.205	0.419211
14	0.024801	0.17	0.43286
15	0.013995	0.0959	0.461987
16	-0.121225	-0.8311	0.205066
17	-0.079392	-0.5443	0.294408

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 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