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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

Thu, 26 Nov 2009 07:56:20 -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/2009/Nov/26/t1259247579v5pfszkvivaxs9d.htm/, Retrieved Sun, 28 Apr 2024 19:46:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60058, Retrieved Sun, 28 Apr 2024 19:46:01 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

133

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-    D        [(Partial) Autocorrelation Function] [] [2009-11-26 09:49:31] [d181e5359f7da6c8509e4702d1229fb0]
-   PD            [(Partial) Autocorrelation Function] [] [2009-11-26 14:56:20] [5858ea01c9bd81debbf921a11363ad90] [Current]

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Dataseries X:

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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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60058&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60058&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.884578	6.1285	0
2	0.663691	4.5982	1.6e-05
3	0.452038	3.1318	0.001479
4	0.331307	2.2954	0.013062
5	0.311858	2.1606	0.017873
6	0.324216	2.2462	0.014663
7	0.298114	2.0654	0.022154
8	0.204562	1.4172	0.081435
9	0.071096	0.4926	0.312283
10	-0.054144	-0.3751	0.354611
11	-0.157255	-1.0895	0.140687
12	-0.230786	-1.5989	0.058199
13	-0.257611	-1.7848	0.040309
14	-0.258213	-1.789	0.039967
15	-0.257159	-1.7816	0.040567
16	-0.260755	-1.8066	0.038551
17	-0.273747	-1.8966	0.031955
18	-0.291441	-2.0192	0.024537
19	-0.297634	-2.0621	0.022318
20	-0.286839	-1.9873	0.026307
21	-0.281603	-1.951	0.028453
22	-0.297275	-2.0596	0.022442
23	-0.309414	-2.1437	0.018576
24	-0.294153	-2.038	0.023543

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.884578 & 6.1285 & 0 \tabularnewline
2 & 0.663691 & 4.5982 & 1.6e-05 \tabularnewline
3 & 0.452038 & 3.1318 & 0.001479 \tabularnewline
4 & 0.331307 & 2.2954 & 0.013062 \tabularnewline
5 & 0.311858 & 2.1606 & 0.017873 \tabularnewline
6 & 0.324216 & 2.2462 & 0.014663 \tabularnewline
7 & 0.298114 & 2.0654 & 0.022154 \tabularnewline
8 & 0.204562 & 1.4172 & 0.081435 \tabularnewline
9 & 0.071096 & 0.4926 & 0.312283 \tabularnewline
10 & -0.054144 & -0.3751 & 0.354611 \tabularnewline
11 & -0.157255 & -1.0895 & 0.140687 \tabularnewline
12 & -0.230786 & -1.5989 & 0.058199 \tabularnewline
13 & -0.257611 & -1.7848 & 0.040309 \tabularnewline
14 & -0.258213 & -1.789 & 0.039967 \tabularnewline
15 & -0.257159 & -1.7816 & 0.040567 \tabularnewline
16 & -0.260755 & -1.8066 & 0.038551 \tabularnewline
17 & -0.273747 & -1.8966 & 0.031955 \tabularnewline
18 & -0.291441 & -2.0192 & 0.024537 \tabularnewline
19 & -0.297634 & -2.0621 & 0.022318 \tabularnewline
20 & -0.286839 & -1.9873 & 0.026307 \tabularnewline
21 & -0.281603 & -1.951 & 0.028453 \tabularnewline
22 & -0.297275 & -2.0596 & 0.022442 \tabularnewline
23 & -0.309414 & -2.1437 & 0.018576 \tabularnewline
24 & -0.294153 & -2.038 & 0.023543 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60058&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]0.884578[/C][C]6.1285[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.663691[/C][C]4.5982[/C][C]1.6e-05[/C][/ROW]
[ROW][C]3[/C][C]0.452038[/C][C]3.1318[/C][C]0.001479[/C][/ROW]
[ROW][C]4[/C][C]0.331307[/C][C]2.2954[/C][C]0.013062[/C][/ROW]
[ROW][C]5[/C][C]0.311858[/C][C]2.1606[/C][C]0.017873[/C][/ROW]
[ROW][C]6[/C][C]0.324216[/C][C]2.2462[/C][C]0.014663[/C][/ROW]
[ROW][C]7[/C][C]0.298114[/C][C]2.0654[/C][C]0.022154[/C][/ROW]
[ROW][C]8[/C][C]0.204562[/C][C]1.4172[/C][C]0.081435[/C][/ROW]
[ROW][C]9[/C][C]0.071096[/C][C]0.4926[/C][C]0.312283[/C][/ROW]
[ROW][C]10[/C][C]-0.054144[/C][C]-0.3751[/C][C]0.354611[/C][/ROW]
[ROW][C]11[/C][C]-0.157255[/C][C]-1.0895[/C][C]0.140687[/C][/ROW]
[ROW][C]12[/C][C]-0.230786[/C][C]-1.5989[/C][C]0.058199[/C][/ROW]
[ROW][C]13[/C][C]-0.257611[/C][C]-1.7848[/C][C]0.040309[/C][/ROW]
[ROW][C]14[/C][C]-0.258213[/C][C]-1.789[/C][C]0.039967[/C][/ROW]
[ROW][C]15[/C][C]-0.257159[/C][C]-1.7816[/C][C]0.040567[/C][/ROW]
[ROW][C]16[/C][C]-0.260755[/C][C]-1.8066[/C][C]0.038551[/C][/ROW]
[ROW][C]17[/C][C]-0.273747[/C][C]-1.8966[/C][C]0.031955[/C][/ROW]
[ROW][C]18[/C][C]-0.291441[/C][C]-2.0192[/C][C]0.024537[/C][/ROW]
[ROW][C]19[/C][C]-0.297634[/C][C]-2.0621[/C][C]0.022318[/C][/ROW]
[ROW][C]20[/C][C]-0.286839[/C][C]-1.9873[/C][C]0.026307[/C][/ROW]
[ROW][C]21[/C][C]-0.281603[/C][C]-1.951[/C][C]0.028453[/C][/ROW]
[ROW][C]22[/C][C]-0.297275[/C][C]-2.0596[/C][C]0.022442[/C][/ROW]
[ROW][C]23[/C][C]-0.309414[/C][C]-2.1437[/C][C]0.018576[/C][/ROW]
[ROW][C]24[/C][C]-0.294153[/C][C]-2.038[/C][C]0.023543[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60058&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	0.884578	6.1285	0
2	0.663691	4.5982	1.6e-05
3	0.452038	3.1318	0.001479
4	0.331307	2.2954	0.013062
5	0.311858	2.1606	0.017873
6	0.324216	2.2462	0.014663
7	0.298114	2.0654	0.022154
8	0.204562	1.4172	0.081435
9	0.071096	0.4926	0.312283
10	-0.054144	-0.3751	0.354611
11	-0.157255	-1.0895	0.140687
12	-0.230786	-1.5989	0.058199
13	-0.257611	-1.7848	0.040309
14	-0.258213	-1.789	0.039967
15	-0.257159	-1.7816	0.040567
16	-0.260755	-1.8066	0.038551
17	-0.273747	-1.8966	0.031955
18	-0.291441	-2.0192	0.024537
19	-0.297634	-2.0621	0.022318
20	-0.286839	-1.9873	0.026307
21	-0.281603	-1.951	0.028453
22	-0.297275	-2.0596	0.022442
23	-0.309414	-2.1437	0.018576
24	-0.294153	-2.038	0.023543

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.884578	6.1285	0
2	-0.546092	-3.7834	0.000215
3	0.179552	1.244	0.109776
4	0.239252	1.6576	0.051962
5	0.105318	0.7297	0.23457
6	-0.158877	-1.1007	0.138252
7	-0.12278	-0.8506	0.199595
8	-0.088733	-0.6148	0.270807
9	-0.030859	-0.2138	0.415805
10	-0.071398	-0.4947	0.311549
11	-0.224442	-1.555	0.06326
12	-0.059528	-0.4124	0.340932
13	0.176795	1.2249	0.113301
14	-0.067269	-0.4661	0.321644
15	-0.125213	-0.8675	0.194991
16	0.050564	0.3503	0.363817
17	0.042595	0.2951	0.384592
18	-0.041187	-0.2853	0.388302
19	-0.028938	-0.2005	0.420972
20	-0.071444	-0.495	0.311437
21	-0.172402	-1.1944	0.119088
22	-0.077878	-0.5396	0.295999
23	0.081055	0.5616	0.288512
24	-0.005846	-0.0405	0.483929

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.884578 & 6.1285 & 0 \tabularnewline
2 & -0.546092 & -3.7834 & 0.000215 \tabularnewline
3 & 0.179552 & 1.244 & 0.109776 \tabularnewline
4 & 0.239252 & 1.6576 & 0.051962 \tabularnewline
5 & 0.105318 & 0.7297 & 0.23457 \tabularnewline
6 & -0.158877 & -1.1007 & 0.138252 \tabularnewline
7 & -0.12278 & -0.8506 & 0.199595 \tabularnewline
8 & -0.088733 & -0.6148 & 0.270807 \tabularnewline
9 & -0.030859 & -0.2138 & 0.415805 \tabularnewline
10 & -0.071398 & -0.4947 & 0.311549 \tabularnewline
11 & -0.224442 & -1.555 & 0.06326 \tabularnewline
12 & -0.059528 & -0.4124 & 0.340932 \tabularnewline
13 & 0.176795 & 1.2249 & 0.113301 \tabularnewline
14 & -0.067269 & -0.4661 & 0.321644 \tabularnewline
15 & -0.125213 & -0.8675 & 0.194991 \tabularnewline
16 & 0.050564 & 0.3503 & 0.363817 \tabularnewline
17 & 0.042595 & 0.2951 & 0.384592 \tabularnewline
18 & -0.041187 & -0.2853 & 0.388302 \tabularnewline
19 & -0.028938 & -0.2005 & 0.420972 \tabularnewline
20 & -0.071444 & -0.495 & 0.311437 \tabularnewline
21 & -0.172402 & -1.1944 & 0.119088 \tabularnewline
22 & -0.077878 & -0.5396 & 0.295999 \tabularnewline
23 & 0.081055 & 0.5616 & 0.288512 \tabularnewline
24 & -0.005846 & -0.0405 & 0.483929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60058&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]0.884578[/C][C]6.1285[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.546092[/C][C]-3.7834[/C][C]0.000215[/C][/ROW]
[ROW][C]3[/C][C]0.179552[/C][C]1.244[/C][C]0.109776[/C][/ROW]
[ROW][C]4[/C][C]0.239252[/C][C]1.6576[/C][C]0.051962[/C][/ROW]
[ROW][C]5[/C][C]0.105318[/C][C]0.7297[/C][C]0.23457[/C][/ROW]
[ROW][C]6[/C][C]-0.158877[/C][C]-1.1007[/C][C]0.138252[/C][/ROW]
[ROW][C]7[/C][C]-0.12278[/C][C]-0.8506[/C][C]0.199595[/C][/ROW]
[ROW][C]8[/C][C]-0.088733[/C][C]-0.6148[/C][C]0.270807[/C][/ROW]
[ROW][C]9[/C][C]-0.030859[/C][C]-0.2138[/C][C]0.415805[/C][/ROW]
[ROW][C]10[/C][C]-0.071398[/C][C]-0.4947[/C][C]0.311549[/C][/ROW]
[ROW][C]11[/C][C]-0.224442[/C][C]-1.555[/C][C]0.06326[/C][/ROW]
[ROW][C]12[/C][C]-0.059528[/C][C]-0.4124[/C][C]0.340932[/C][/ROW]
[ROW][C]13[/C][C]0.176795[/C][C]1.2249[/C][C]0.113301[/C][/ROW]
[ROW][C]14[/C][C]-0.067269[/C][C]-0.4661[/C][C]0.321644[/C][/ROW]
[ROW][C]15[/C][C]-0.125213[/C][C]-0.8675[/C][C]0.194991[/C][/ROW]
[ROW][C]16[/C][C]0.050564[/C][C]0.3503[/C][C]0.363817[/C][/ROW]
[ROW][C]17[/C][C]0.042595[/C][C]0.2951[/C][C]0.384592[/C][/ROW]
[ROW][C]18[/C][C]-0.041187[/C][C]-0.2853[/C][C]0.388302[/C][/ROW]
[ROW][C]19[/C][C]-0.028938[/C][C]-0.2005[/C][C]0.420972[/C][/ROW]
[ROW][C]20[/C][C]-0.071444[/C][C]-0.495[/C][C]0.311437[/C][/ROW]
[ROW][C]21[/C][C]-0.172402[/C][C]-1.1944[/C][C]0.119088[/C][/ROW]
[ROW][C]22[/C][C]-0.077878[/C][C]-0.5396[/C][C]0.295999[/C][/ROW]
[ROW][C]23[/C][C]0.081055[/C][C]0.5616[/C][C]0.288512[/C][/ROW]
[ROW][C]24[/C][C]-0.005846[/C][C]-0.0405[/C][C]0.483929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60058&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60058&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	0.884578	6.1285	0
2	-0.546092	-3.7834	0.000215
3	0.179552	1.244	0.109776
4	0.239252	1.6576	0.051962
5	0.105318	0.7297	0.23457
6	-0.158877	-1.1007	0.138252
7	-0.12278	-0.8506	0.199595
8	-0.088733	-0.6148	0.270807
9	-0.030859	-0.2138	0.415805
10	-0.071398	-0.4947	0.311549
11	-0.224442	-1.555	0.06326
12	-0.059528	-0.4124	0.340932
13	0.176795	1.2249	0.113301
14	-0.067269	-0.4661	0.321644
15	-0.125213	-0.8675	0.194991
16	0.050564	0.3503	0.363817
17	0.042595	0.2951	0.384592
18	-0.041187	-0.2853	0.388302
19	-0.028938	-0.2005	0.420972
20	-0.071444	-0.495	0.311437
21	-0.172402	-1.1944	0.119088
22	-0.077878	-0.5396	0.295999
23	0.081055	0.5616	0.288512
24	-0.005846	-0.0405	0.483929

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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