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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

Fri, 10 Dec 2010 17:42:26 +0000

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/2010/Dec/10/t1292002818yk03r37hxag70mj.htm/, Retrieved Mon, 29 Apr 2024 14:41:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107857, Retrieved Mon, 29 Apr 2024 14:41:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

100

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

-     [(Partial) Autocorrelation Function] [Paper: PACF 1] [2010-12-10 17:20:31] [7d64bf19f34ddcdf2626356c9d5bd60d]
-   P   [(Partial) Autocorrelation Function] [paper ACF 2] [2010-12-10 17:26:39] [7d64bf19f34ddcdf2626356c9d5bd60d]
- R P     [(Partial) Autocorrelation Function] [ACF original] [2010-12-10 17:35:01] [7d64bf19f34ddcdf2626356c9d5bd60d]
-   P       [(Partial) Autocorrelation Function] [ACF 2] [2010-12-10 17:37:10] [7d64bf19f34ddcdf2626356c9d5bd60d]
-   P           [(Partial) Autocorrelation Function] [ACF 4] [2010-12-10 17:42:26] [5842cf9dd57f9603e676e11284d3404a] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107857&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107857&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107857&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.512687	-3.4772	0.000559
2	-0.020957	-0.1421	0.443797
3	0.132837	0.9009	0.186155
4	0.029739	0.2017	0.42052
5	-0.184379	-1.2505	0.108716
6	0.154967	1.051	0.149365
7	-0.146326	-0.9924	0.16309
8	0.135056	0.916	0.182223
9	-0.096374	-0.6536	0.258299
10	-0.120869	-0.8198	0.208286
11	0.30635	2.0778	0.02167
12	-0.204433	-1.3865	0.086134
13	-0.051719	-0.3508	0.363679
14	0.123422	0.8371	0.203435
15	0.002162	0.0147	0.494182
16	-0.101005	-0.685	0.248375
17	0.128104	0.8688	0.194723
18	-0.079015	-0.5359	0.297303
19	0.036387	0.2468	0.403084
20	0.076567	0.5193	0.30302
21	-0.158071	-1.0721	0.144636
22	0.053261	0.3612	0.35979
23	0.013838	0.0939	0.462816
24	-0.110516	-0.7496	0.228669

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.512687 & -3.4772 & 0.000559 \tabularnewline
2 & -0.020957 & -0.1421 & 0.443797 \tabularnewline
3 & 0.132837 & 0.9009 & 0.186155 \tabularnewline
4 & 0.029739 & 0.2017 & 0.42052 \tabularnewline
5 & -0.184379 & -1.2505 & 0.108716 \tabularnewline
6 & 0.154967 & 1.051 & 0.149365 \tabularnewline
7 & -0.146326 & -0.9924 & 0.16309 \tabularnewline
8 & 0.135056 & 0.916 & 0.182223 \tabularnewline
9 & -0.096374 & -0.6536 & 0.258299 \tabularnewline
10 & -0.120869 & -0.8198 & 0.208286 \tabularnewline
11 & 0.30635 & 2.0778 & 0.02167 \tabularnewline
12 & -0.204433 & -1.3865 & 0.086134 \tabularnewline
13 & -0.051719 & -0.3508 & 0.363679 \tabularnewline
14 & 0.123422 & 0.8371 & 0.203435 \tabularnewline
15 & 0.002162 & 0.0147 & 0.494182 \tabularnewline
16 & -0.101005 & -0.685 & 0.248375 \tabularnewline
17 & 0.128104 & 0.8688 & 0.194723 \tabularnewline
18 & -0.079015 & -0.5359 & 0.297303 \tabularnewline
19 & 0.036387 & 0.2468 & 0.403084 \tabularnewline
20 & 0.076567 & 0.5193 & 0.30302 \tabularnewline
21 & -0.158071 & -1.0721 & 0.144636 \tabularnewline
22 & 0.053261 & 0.3612 & 0.35979 \tabularnewline
23 & 0.013838 & 0.0939 & 0.462816 \tabularnewline
24 & -0.110516 & -0.7496 & 0.228669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107857&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]-0.512687[/C][C]-3.4772[/C][C]0.000559[/C][/ROW]
[ROW][C]2[/C][C]-0.020957[/C][C]-0.1421[/C][C]0.443797[/C][/ROW]
[ROW][C]3[/C][C]0.132837[/C][C]0.9009[/C][C]0.186155[/C][/ROW]
[ROW][C]4[/C][C]0.029739[/C][C]0.2017[/C][C]0.42052[/C][/ROW]
[ROW][C]5[/C][C]-0.184379[/C][C]-1.2505[/C][C]0.108716[/C][/ROW]
[ROW][C]6[/C][C]0.154967[/C][C]1.051[/C][C]0.149365[/C][/ROW]
[ROW][C]7[/C][C]-0.146326[/C][C]-0.9924[/C][C]0.16309[/C][/ROW]
[ROW][C]8[/C][C]0.135056[/C][C]0.916[/C][C]0.182223[/C][/ROW]
[ROW][C]9[/C][C]-0.096374[/C][C]-0.6536[/C][C]0.258299[/C][/ROW]
[ROW][C]10[/C][C]-0.120869[/C][C]-0.8198[/C][C]0.208286[/C][/ROW]
[ROW][C]11[/C][C]0.30635[/C][C]2.0778[/C][C]0.02167[/C][/ROW]
[ROW][C]12[/C][C]-0.204433[/C][C]-1.3865[/C][C]0.086134[/C][/ROW]
[ROW][C]13[/C][C]-0.051719[/C][C]-0.3508[/C][C]0.363679[/C][/ROW]
[ROW][C]14[/C][C]0.123422[/C][C]0.8371[/C][C]0.203435[/C][/ROW]
[ROW][C]15[/C][C]0.002162[/C][C]0.0147[/C][C]0.494182[/C][/ROW]
[ROW][C]16[/C][C]-0.101005[/C][C]-0.685[/C][C]0.248375[/C][/ROW]
[ROW][C]17[/C][C]0.128104[/C][C]0.8688[/C][C]0.194723[/C][/ROW]
[ROW][C]18[/C][C]-0.079015[/C][C]-0.5359[/C][C]0.297303[/C][/ROW]
[ROW][C]19[/C][C]0.036387[/C][C]0.2468[/C][C]0.403084[/C][/ROW]
[ROW][C]20[/C][C]0.076567[/C][C]0.5193[/C][C]0.30302[/C][/ROW]
[ROW][C]21[/C][C]-0.158071[/C][C]-1.0721[/C][C]0.144636[/C][/ROW]
[ROW][C]22[/C][C]0.053261[/C][C]0.3612[/C][C]0.35979[/C][/ROW]
[ROW][C]23[/C][C]0.013838[/C][C]0.0939[/C][C]0.462816[/C][/ROW]
[ROW][C]24[/C][C]-0.110516[/C][C]-0.7496[/C][C]0.228669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107857&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107857&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	-0.512687	-3.4772	0.000559
2	-0.020957	-0.1421	0.443797
3	0.132837	0.9009	0.186155
4	0.029739	0.2017	0.42052
5	-0.184379	-1.2505	0.108716
6	0.154967	1.051	0.149365
7	-0.146326	-0.9924	0.16309
8	0.135056	0.916	0.182223
9	-0.096374	-0.6536	0.258299
10	-0.120869	-0.8198	0.208286
11	0.30635	2.0778	0.02167
12	-0.204433	-1.3865	0.086134
13	-0.051719	-0.3508	0.363679
14	0.123422	0.8371	0.203435
15	0.002162	0.0147	0.494182
16	-0.101005	-0.685	0.248375
17	0.128104	0.8688	0.194723
18	-0.079015	-0.5359	0.297303
19	0.036387	0.2468	0.403084
20	0.076567	0.5193	0.30302
21	-0.158071	-1.0721	0.144636
22	0.053261	0.3612	0.35979
23	0.013838	0.0939	0.462816
24	-0.110516	-0.7496	0.228669

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.512687	-3.4772	0.000559
2	-0.385001	-2.6112	0.006071
3	-0.126501	-0.858	0.197678
4	0.090196	0.6117	0.27186
5	-0.097488	-0.6612	0.255892
6	-0.007422	-0.0503	0.480036
7	-0.1932	-1.3103	0.098292
8	0.003964	0.0269	0.489333
9	-0.044235	-0.3	0.382759
10	-0.287678	-1.9511	0.028574
11	0.126991	0.8613	0.196771
12	-0.024648	-0.1672	0.433983
13	-0.069968	-0.4745	0.318678
14	-0.099755	-0.6766	0.251033
15	-0.046104	-0.3127	0.377963
16	0.010282	0.0697	0.472354
17	0.018792	0.1275	0.449568
18	0.027805	0.1886	0.425626
19	-0.04121	-0.2795	0.390558
20	0.171563	1.1636	0.125294
21	0.000428	0.0029	0.498848
22	-0.167105	-1.1334	0.131467
23	-0.120579	-0.8178	0.208841
24	-0.177124	-1.2013	0.11789

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.512687 & -3.4772 & 0.000559 \tabularnewline
2 & -0.385001 & -2.6112 & 0.006071 \tabularnewline
3 & -0.126501 & -0.858 & 0.197678 \tabularnewline
4 & 0.090196 & 0.6117 & 0.27186 \tabularnewline
5 & -0.097488 & -0.6612 & 0.255892 \tabularnewline
6 & -0.007422 & -0.0503 & 0.480036 \tabularnewline
7 & -0.1932 & -1.3103 & 0.098292 \tabularnewline
8 & 0.003964 & 0.0269 & 0.489333 \tabularnewline
9 & -0.044235 & -0.3 & 0.382759 \tabularnewline
10 & -0.287678 & -1.9511 & 0.028574 \tabularnewline
11 & 0.126991 & 0.8613 & 0.196771 \tabularnewline
12 & -0.024648 & -0.1672 & 0.433983 \tabularnewline
13 & -0.069968 & -0.4745 & 0.318678 \tabularnewline
14 & -0.099755 & -0.6766 & 0.251033 \tabularnewline
15 & -0.046104 & -0.3127 & 0.377963 \tabularnewline
16 & 0.010282 & 0.0697 & 0.472354 \tabularnewline
17 & 0.018792 & 0.1275 & 0.449568 \tabularnewline
18 & 0.027805 & 0.1886 & 0.425626 \tabularnewline
19 & -0.04121 & -0.2795 & 0.390558 \tabularnewline
20 & 0.171563 & 1.1636 & 0.125294 \tabularnewline
21 & 0.000428 & 0.0029 & 0.498848 \tabularnewline
22 & -0.167105 & -1.1334 & 0.131467 \tabularnewline
23 & -0.120579 & -0.8178 & 0.208841 \tabularnewline
24 & -0.177124 & -1.2013 & 0.11789 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107857&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]-0.512687[/C][C]-3.4772[/C][C]0.000559[/C][/ROW]
[ROW][C]2[/C][C]-0.385001[/C][C]-2.6112[/C][C]0.006071[/C][/ROW]
[ROW][C]3[/C][C]-0.126501[/C][C]-0.858[/C][C]0.197678[/C][/ROW]
[ROW][C]4[/C][C]0.090196[/C][C]0.6117[/C][C]0.27186[/C][/ROW]
[ROW][C]5[/C][C]-0.097488[/C][C]-0.6612[/C][C]0.255892[/C][/ROW]
[ROW][C]6[/C][C]-0.007422[/C][C]-0.0503[/C][C]0.480036[/C][/ROW]
[ROW][C]7[/C][C]-0.1932[/C][C]-1.3103[/C][C]0.098292[/C][/ROW]
[ROW][C]8[/C][C]0.003964[/C][C]0.0269[/C][C]0.489333[/C][/ROW]
[ROW][C]9[/C][C]-0.044235[/C][C]-0.3[/C][C]0.382759[/C][/ROW]
[ROW][C]10[/C][C]-0.287678[/C][C]-1.9511[/C][C]0.028574[/C][/ROW]
[ROW][C]11[/C][C]0.126991[/C][C]0.8613[/C][C]0.196771[/C][/ROW]
[ROW][C]12[/C][C]-0.024648[/C][C]-0.1672[/C][C]0.433983[/C][/ROW]
[ROW][C]13[/C][C]-0.069968[/C][C]-0.4745[/C][C]0.318678[/C][/ROW]
[ROW][C]14[/C][C]-0.099755[/C][C]-0.6766[/C][C]0.251033[/C][/ROW]
[ROW][C]15[/C][C]-0.046104[/C][C]-0.3127[/C][C]0.377963[/C][/ROW]
[ROW][C]16[/C][C]0.010282[/C][C]0.0697[/C][C]0.472354[/C][/ROW]
[ROW][C]17[/C][C]0.018792[/C][C]0.1275[/C][C]0.449568[/C][/ROW]
[ROW][C]18[/C][C]0.027805[/C][C]0.1886[/C][C]0.425626[/C][/ROW]
[ROW][C]19[/C][C]-0.04121[/C][C]-0.2795[/C][C]0.390558[/C][/ROW]
[ROW][C]20[/C][C]0.171563[/C][C]1.1636[/C][C]0.125294[/C][/ROW]
[ROW][C]21[/C][C]0.000428[/C][C]0.0029[/C][C]0.498848[/C][/ROW]
[ROW][C]22[/C][C]-0.167105[/C][C]-1.1334[/C][C]0.131467[/C][/ROW]
[ROW][C]23[/C][C]-0.120579[/C][C]-0.8178[/C][C]0.208841[/C][/ROW]
[ROW][C]24[/C][C]-0.177124[/C][C]-1.2013[/C][C]0.11789[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107857&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107857&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	-0.512687	-3.4772	0.000559
2	-0.385001	-2.6112	0.006071
3	-0.126501	-0.858	0.197678
4	0.090196	0.6117	0.27186
5	-0.097488	-0.6612	0.255892
6	-0.007422	-0.0503	0.480036
7	-0.1932	-1.3103	0.098292
8	0.003964	0.0269	0.489333
9	-0.044235	-0.3	0.382759
10	-0.287678	-1.9511	0.028574
11	0.126991	0.8613	0.196771
12	-0.024648	-0.1672	0.433983
13	-0.069968	-0.4745	0.318678
14	-0.099755	-0.6766	0.251033
15	-0.046104	-0.3127	0.377963
16	0.010282	0.0697	0.472354
17	0.018792	0.1275	0.449568
18	0.027805	0.1886	0.425626
19	-0.04121	-0.2795	0.390558
20	0.171563	1.1636	0.125294
21	0.000428	0.0029	0.498848
22	-0.167105	-1.1334	0.131467
23	-0.120579	-0.8178	0.208841
24	-0.177124	-1.2013	0.11789

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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