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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 27 Dec 2010 22:04:02 +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/27/t1293487366xhec5wb3fc7aosx.htm/, Retrieved Mon, 06 May 2024 13:15:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116158, Retrieved Mon, 06 May 2024 13:15:16 +0000

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User-defined keywords

Estimated Impact

128

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-         [(Partial) Autocorrelation Function] [] [2010-12-14 20:34:39] [42f9a5501cee5cbc9edf1c0ec1f66440]
-    D        [(Partial) Autocorrelation Function] [Autocorrelatie] [2010-12-27 22:04:02] [a7b2a0c11f64eef3aa1d49ba29ffb331] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116158&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116158&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116158&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.887356	10.6112	0
2	0.72229	8.6373	0
3	0.628525	7.5161	0
4	0.604254	7.2258	0
5	0.612734	7.3272	0
6	0.601187	7.1892	0
7	0.562157	6.7224	0
8	0.498995	5.9671	0
9	0.468882	5.607	0
10	0.499176	5.9693	0
11	0.599118	7.1644	0
12	0.642807	7.6869	0
13	0.50036	5.9834	0
14	0.315088	3.7679	0.00012
15	0.197845	2.3659	0.009664
16	0.146661	1.7538	0.040803
17	0.130218	1.5572	0.060819
18	0.100496	1.2018	0.115721
19	0.047102	0.5633	0.28707
20	-0.021996	-0.263	0.396452
21	-0.056292	-0.6732	0.250969

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.887356 & 10.6112 & 0 \tabularnewline
2 & 0.72229 & 8.6373 & 0 \tabularnewline
3 & 0.628525 & 7.5161 & 0 \tabularnewline
4 & 0.604254 & 7.2258 & 0 \tabularnewline
5 & 0.612734 & 7.3272 & 0 \tabularnewline
6 & 0.601187 & 7.1892 & 0 \tabularnewline
7 & 0.562157 & 6.7224 & 0 \tabularnewline
8 & 0.498995 & 5.9671 & 0 \tabularnewline
9 & 0.468882 & 5.607 & 0 \tabularnewline
10 & 0.499176 & 5.9693 & 0 \tabularnewline
11 & 0.599118 & 7.1644 & 0 \tabularnewline
12 & 0.642807 & 7.6869 & 0 \tabularnewline
13 & 0.50036 & 5.9834 & 0 \tabularnewline
14 & 0.315088 & 3.7679 & 0.00012 \tabularnewline
15 & 0.197845 & 2.3659 & 0.009664 \tabularnewline
16 & 0.146661 & 1.7538 & 0.040803 \tabularnewline
17 & 0.130218 & 1.5572 & 0.060819 \tabularnewline
18 & 0.100496 & 1.2018 & 0.115721 \tabularnewline
19 & 0.047102 & 0.5633 & 0.28707 \tabularnewline
20 & -0.021996 & -0.263 & 0.396452 \tabularnewline
21 & -0.056292 & -0.6732 & 0.250969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116158&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]0.887356[/C][C]10.6112[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.72229[/C][C]8.6373[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.628525[/C][C]7.5161[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.604254[/C][C]7.2258[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.612734[/C][C]7.3272[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.601187[/C][C]7.1892[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.562157[/C][C]6.7224[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.498995[/C][C]5.9671[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.468882[/C][C]5.607[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.499176[/C][C]5.9693[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.599118[/C][C]7.1644[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.642807[/C][C]7.6869[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.50036[/C][C]5.9834[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.315088[/C][C]3.7679[/C][C]0.00012[/C][/ROW]
[ROW][C]15[/C][C]0.197845[/C][C]2.3659[/C][C]0.009664[/C][/ROW]
[ROW][C]16[/C][C]0.146661[/C][C]1.7538[/C][C]0.040803[/C][/ROW]
[ROW][C]17[/C][C]0.130218[/C][C]1.5572[/C][C]0.060819[/C][/ROW]
[ROW][C]18[/C][C]0.100496[/C][C]1.2018[/C][C]0.115721[/C][/ROW]
[ROW][C]19[/C][C]0.047102[/C][C]0.5633[/C][C]0.28707[/C][/ROW]
[ROW][C]20[/C][C]-0.021996[/C][C]-0.263[/C][C]0.396452[/C][/ROW]
[ROW][C]21[/C][C]-0.056292[/C][C]-0.6732[/C][C]0.250969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116158&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116158&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	0.887356	10.6112	0
2	0.72229	8.6373	0
3	0.628525	7.5161	0
4	0.604254	7.2258	0
5	0.612734	7.3272	0
6	0.601187	7.1892	0
7	0.562157	6.7224	0
8	0.498995	5.9671	0
9	0.468882	5.607	0
10	0.499176	5.9693	0
11	0.599118	7.1644	0
12	0.642807	7.6869	0
13	0.50036	5.9834	0
14	0.315088	3.7679	0.00012
15	0.197845	2.3659	0.009664
16	0.146661	1.7538	0.040803
17	0.130218	1.5572	0.060819
18	0.100496	1.2018	0.115721
19	0.047102	0.5633	0.28707
20	-0.021996	-0.263	0.396452
21	-0.056292	-0.6732	0.250969

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.887356	10.6112	0
2	-0.306263	-3.6624	0.000176
3	0.327354	3.9146	7e-05
4	0.101757	1.2168	0.112836
5	0.14585	1.7441	0.041644
6	-0.039986	-0.4782	0.316633
7	0.034477	0.4123	0.340374
8	-0.107284	-1.2829	0.100796
9	0.200854	2.4019	0.008798
10	0.129746	1.5515	0.061491
11	0.419072	5.0114	1e-06
12	-0.351364	-4.2017	2.3e-05
13	-0.682767	-8.1647	0
14	-0.010037	-0.12	0.452315
15	-0.07825	-0.9357	0.175495
16	-0.19403	-2.3203	0.010871
17	0.036957	0.4419	0.329599
18	-0.093544	-1.1186	0.132588
19	0.048827	0.5839	0.280109
20	0.057583	0.6886	0.246097
21	0.064489	0.7712	0.220938

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.887356 & 10.6112 & 0 \tabularnewline
2 & -0.306263 & -3.6624 & 0.000176 \tabularnewline
3 & 0.327354 & 3.9146 & 7e-05 \tabularnewline
4 & 0.101757 & 1.2168 & 0.112836 \tabularnewline
5 & 0.14585 & 1.7441 & 0.041644 \tabularnewline
6 & -0.039986 & -0.4782 & 0.316633 \tabularnewline
7 & 0.034477 & 0.4123 & 0.340374 \tabularnewline
8 & -0.107284 & -1.2829 & 0.100796 \tabularnewline
9 & 0.200854 & 2.4019 & 0.008798 \tabularnewline
10 & 0.129746 & 1.5515 & 0.061491 \tabularnewline
11 & 0.419072 & 5.0114 & 1e-06 \tabularnewline
12 & -0.351364 & -4.2017 & 2.3e-05 \tabularnewline
13 & -0.682767 & -8.1647 & 0 \tabularnewline
14 & -0.010037 & -0.12 & 0.452315 \tabularnewline
15 & -0.07825 & -0.9357 & 0.175495 \tabularnewline
16 & -0.19403 & -2.3203 & 0.010871 \tabularnewline
17 & 0.036957 & 0.4419 & 0.329599 \tabularnewline
18 & -0.093544 & -1.1186 & 0.132588 \tabularnewline
19 & 0.048827 & 0.5839 & 0.280109 \tabularnewline
20 & 0.057583 & 0.6886 & 0.246097 \tabularnewline
21 & 0.064489 & 0.7712 & 0.220938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116158&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]0.887356[/C][C]10.6112[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.306263[/C][C]-3.6624[/C][C]0.000176[/C][/ROW]
[ROW][C]3[/C][C]0.327354[/C][C]3.9146[/C][C]7e-05[/C][/ROW]
[ROW][C]4[/C][C]0.101757[/C][C]1.2168[/C][C]0.112836[/C][/ROW]
[ROW][C]5[/C][C]0.14585[/C][C]1.7441[/C][C]0.041644[/C][/ROW]
[ROW][C]6[/C][C]-0.039986[/C][C]-0.4782[/C][C]0.316633[/C][/ROW]
[ROW][C]7[/C][C]0.034477[/C][C]0.4123[/C][C]0.340374[/C][/ROW]
[ROW][C]8[/C][C]-0.107284[/C][C]-1.2829[/C][C]0.100796[/C][/ROW]
[ROW][C]9[/C][C]0.200854[/C][C]2.4019[/C][C]0.008798[/C][/ROW]
[ROW][C]10[/C][C]0.129746[/C][C]1.5515[/C][C]0.061491[/C][/ROW]
[ROW][C]11[/C][C]0.419072[/C][C]5.0114[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]-0.351364[/C][C]-4.2017[/C][C]2.3e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.682767[/C][C]-8.1647[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.010037[/C][C]-0.12[/C][C]0.452315[/C][/ROW]
[ROW][C]15[/C][C]-0.07825[/C][C]-0.9357[/C][C]0.175495[/C][/ROW]
[ROW][C]16[/C][C]-0.19403[/C][C]-2.3203[/C][C]0.010871[/C][/ROW]
[ROW][C]17[/C][C]0.036957[/C][C]0.4419[/C][C]0.329599[/C][/ROW]
[ROW][C]18[/C][C]-0.093544[/C][C]-1.1186[/C][C]0.132588[/C][/ROW]
[ROW][C]19[/C][C]0.048827[/C][C]0.5839[/C][C]0.280109[/C][/ROW]
[ROW][C]20[/C][C]0.057583[/C][C]0.6886[/C][C]0.246097[/C][/ROW]
[ROW][C]21[/C][C]0.064489[/C][C]0.7712[/C][C]0.220938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116158&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116158&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	0.887356	10.6112	0
2	-0.306263	-3.6624	0.000176
3	0.327354	3.9146	7e-05
4	0.101757	1.2168	0.112836
5	0.14585	1.7441	0.041644
6	-0.039986	-0.4782	0.316633
7	0.034477	0.4123	0.340374
8	-0.107284	-1.2829	0.100796
9	0.200854	2.4019	0.008798
10	0.129746	1.5515	0.061491
11	0.419072	5.0114	1e-06
12	-0.351364	-4.2017	2.3e-05
13	-0.682767	-8.1647	0
14	-0.010037	-0.12	0.452315
15	-0.07825	-0.9357	0.175495
16	-0.19403	-2.3203	0.010871
17	0.036957	0.4419	0.329599
18	-0.093544	-1.1186	0.132588
19	0.048827	0.5839	0.280109
20	0.057583	0.6886	0.246097
21	0.064489	0.7712	0.220938

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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