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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, 04 Dec 2009 13:43:56 -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/Dec/04/t1259959477obnlarkf8ql59t2.htm/, Retrieved Sun, 28 Apr 2024 16:16:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64144, Retrieved Sun, 28 Apr 2024 16:16:03 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

127

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] [] [2009-11-27 14:46:03] [b98453cac15ba1066b407e146608df68]
- R PD      [(Partial) Autocorrelation Function] [ws9-3] [2009-12-04 20:43:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   P         [(Partial) Autocorrelation Function] [ws9-4] [2009-12-04 20:46:30] [74be16979710d4c4e7c6647856088456] 
-   PD          [(Partial) Autocorrelation Function] [] [2009-12-04 21:40:54] [badc6a9acdc45286bea7f74742e15a21] 
-   P           [(Partial) Autocorrelation Function] [WS9 acf] [2009-12-09 18:50:44] [626f1d98f4a7f05bcb9f17666b672c60] 
-   P         [(Partial) Autocorrelation Function] [workshop 9 review] [2009-12-06 13:45:43] [309ee52d0058ff0a6f7eec15e07b2d9f] 
-   P         [(Partial) Autocorrelation Function] [Oplossing ACF met...] [2009-12-11 09:39:37] [4395c69e961f9a13a0559fd2f0a72538] 
-   P         [(Partial) Autocorrelation Function] [acf] [2009-12-27 19:56:57] [d8fc2cb19a73ee9b4ebccccec0f2ad7f] 
-   P           [(Partial) Autocorrelation Function] [] [2009-12-27 20:14:54] [d8fc2cb19a73ee9b4ebccccec0f2ad7f] 
-   P             [(Partial) Autocorrelation Function] [acf3] [2009-12-28 09:37:04] [d8fc2cb19a73ee9b4ebccccec0f2ad7f] 
- RMP             [Variance Reduction Matrix] [VRM] [2009-12-28 09:52:00] [d8fc2cb19a73ee9b4ebccccec0f2ad7f] 
- RMP             [Spectral Analysis] [spectrum] [2009-12-28 10:19:24] [d8fc2cb19a73ee9b4ebccccec0f2ad7f] 
-   P               [Spectral Analysis] [spectrum (2)] [2009-12-28 11:46:14] [d8fc2cb19a73ee9b4ebccccec0f2ad7f] 
-   P               [Spectral Analysis] [spectrum (2)] [2009-12-28 11:56:24] [d8fc2cb19a73ee9b4ebccccec0f2ad7f] 

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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=64144&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=64144&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64144&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	0.335464	2.7459	0.003871
2	0.387365	3.1707	0.001147
3	0.422029	3.4545	0.00048
4	0.234628	1.9205	0.029525
5	0.13951	1.1419	0.128773
6	0.120169	0.9836	0.164419
7	0.088688	0.7259	0.235201
8	0.132105	1.0813	0.141714
9	0.135492	1.109	0.135687
10	0.055741	0.4563	0.324838
11	0.083315	0.682	0.248805
12	0.157564	1.2897	0.100791
13	-0.006896	-0.0564	0.477577
14	0.058105	0.4756	0.31795
15	0.052356	0.4286	0.334811
16	-0.047443	-0.3883	0.3495
17	0.033951	0.2779	0.390971
18	-0.073011	-0.5976	0.276053

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.335464 & 2.7459 & 0.003871 \tabularnewline
2 & 0.387365 & 3.1707 & 0.001147 \tabularnewline
3 & 0.422029 & 3.4545 & 0.00048 \tabularnewline
4 & 0.234628 & 1.9205 & 0.029525 \tabularnewline
5 & 0.13951 & 1.1419 & 0.128773 \tabularnewline
6 & 0.120169 & 0.9836 & 0.164419 \tabularnewline
7 & 0.088688 & 0.7259 & 0.235201 \tabularnewline
8 & 0.132105 & 1.0813 & 0.141714 \tabularnewline
9 & 0.135492 & 1.109 & 0.135687 \tabularnewline
10 & 0.055741 & 0.4563 & 0.324838 \tabularnewline
11 & 0.083315 & 0.682 & 0.248805 \tabularnewline
12 & 0.157564 & 1.2897 & 0.100791 \tabularnewline
13 & -0.006896 & -0.0564 & 0.477577 \tabularnewline
14 & 0.058105 & 0.4756 & 0.31795 \tabularnewline
15 & 0.052356 & 0.4286 & 0.334811 \tabularnewline
16 & -0.047443 & -0.3883 & 0.3495 \tabularnewline
17 & 0.033951 & 0.2779 & 0.390971 \tabularnewline
18 & -0.073011 & -0.5976 & 0.276053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64144&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]0.335464[/C][C]2.7459[/C][C]0.003871[/C][/ROW]
[ROW][C]2[/C][C]0.387365[/C][C]3.1707[/C][C]0.001147[/C][/ROW]
[ROW][C]3[/C][C]0.422029[/C][C]3.4545[/C][C]0.00048[/C][/ROW]
[ROW][C]4[/C][C]0.234628[/C][C]1.9205[/C][C]0.029525[/C][/ROW]
[ROW][C]5[/C][C]0.13951[/C][C]1.1419[/C][C]0.128773[/C][/ROW]
[ROW][C]6[/C][C]0.120169[/C][C]0.9836[/C][C]0.164419[/C][/ROW]
[ROW][C]7[/C][C]0.088688[/C][C]0.7259[/C][C]0.235201[/C][/ROW]
[ROW][C]8[/C][C]0.132105[/C][C]1.0813[/C][C]0.141714[/C][/ROW]
[ROW][C]9[/C][C]0.135492[/C][C]1.109[/C][C]0.135687[/C][/ROW]
[ROW][C]10[/C][C]0.055741[/C][C]0.4563[/C][C]0.324838[/C][/ROW]
[ROW][C]11[/C][C]0.083315[/C][C]0.682[/C][C]0.248805[/C][/ROW]
[ROW][C]12[/C][C]0.157564[/C][C]1.2897[/C][C]0.100791[/C][/ROW]
[ROW][C]13[/C][C]-0.006896[/C][C]-0.0564[/C][C]0.477577[/C][/ROW]
[ROW][C]14[/C][C]0.058105[/C][C]0.4756[/C][C]0.31795[/C][/ROW]
[ROW][C]15[/C][C]0.052356[/C][C]0.4286[/C][C]0.334811[/C][/ROW]
[ROW][C]16[/C][C]-0.047443[/C][C]-0.3883[/C][C]0.3495[/C][/ROW]
[ROW][C]17[/C][C]0.033951[/C][C]0.2779[/C][C]0.390971[/C][/ROW]
[ROW][C]18[/C][C]-0.073011[/C][C]-0.5976[/C][C]0.276053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64144&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64144&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	0.335464	2.7459	0.003871
2	0.387365	3.1707	0.001147
3	0.422029	3.4545	0.00048
4	0.234628	1.9205	0.029525
5	0.13951	1.1419	0.128773
6	0.120169	0.9836	0.164419
7	0.088688	0.7259	0.235201
8	0.132105	1.0813	0.141714
9	0.135492	1.109	0.135687
10	0.055741	0.4563	0.324838
11	0.083315	0.682	0.248805
12	0.157564	1.2897	0.100791
13	-0.006896	-0.0564	0.477577
14	0.058105	0.4756	0.31795
15	0.052356	0.4286	0.334811
16	-0.047443	-0.3883	0.3495
17	0.033951	0.2779	0.390971
18	-0.073011	-0.5976	0.276053

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.335464	2.7459	0.003871
2	0.309679	2.5348	0.006796
3	0.284709	2.3304	0.011401
4	-0.021461	-0.1757	0.430544
5	-0.142374	-1.1654	0.123998
6	-0.078778	-0.6448	0.260621
7	0.024686	0.2021	0.42024
8	0.159813	1.3081	0.09765
9	0.128462	1.0515	0.148402
10	-0.077034	-0.6305	0.265241
11	-0.096014	-0.7859	0.217346
12	0.082112	0.6721	0.25191
13	-0.059396	-0.4862	0.314215
14	0.034417	0.2817	0.389516
15	0.001047	0.0086	0.496594
16	-0.098586	-0.807	0.211272
17	0.032231	0.2638	0.396362
18	-0.085871	-0.7029	0.24228

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.335464 & 2.7459 & 0.003871 \tabularnewline
2 & 0.309679 & 2.5348 & 0.006796 \tabularnewline
3 & 0.284709 & 2.3304 & 0.011401 \tabularnewline
4 & -0.021461 & -0.1757 & 0.430544 \tabularnewline
5 & -0.142374 & -1.1654 & 0.123998 \tabularnewline
6 & -0.078778 & -0.6448 & 0.260621 \tabularnewline
7 & 0.024686 & 0.2021 & 0.42024 \tabularnewline
8 & 0.159813 & 1.3081 & 0.09765 \tabularnewline
9 & 0.128462 & 1.0515 & 0.148402 \tabularnewline
10 & -0.077034 & -0.6305 & 0.265241 \tabularnewline
11 & -0.096014 & -0.7859 & 0.217346 \tabularnewline
12 & 0.082112 & 0.6721 & 0.25191 \tabularnewline
13 & -0.059396 & -0.4862 & 0.314215 \tabularnewline
14 & 0.034417 & 0.2817 & 0.389516 \tabularnewline
15 & 0.001047 & 0.0086 & 0.496594 \tabularnewline
16 & -0.098586 & -0.807 & 0.211272 \tabularnewline
17 & 0.032231 & 0.2638 & 0.396362 \tabularnewline
18 & -0.085871 & -0.7029 & 0.24228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64144&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]0.335464[/C][C]2.7459[/C][C]0.003871[/C][/ROW]
[ROW][C]2[/C][C]0.309679[/C][C]2.5348[/C][C]0.006796[/C][/ROW]
[ROW][C]3[/C][C]0.284709[/C][C]2.3304[/C][C]0.011401[/C][/ROW]
[ROW][C]4[/C][C]-0.021461[/C][C]-0.1757[/C][C]0.430544[/C][/ROW]
[ROW][C]5[/C][C]-0.142374[/C][C]-1.1654[/C][C]0.123998[/C][/ROW]
[ROW][C]6[/C][C]-0.078778[/C][C]-0.6448[/C][C]0.260621[/C][/ROW]
[ROW][C]7[/C][C]0.024686[/C][C]0.2021[/C][C]0.42024[/C][/ROW]
[ROW][C]8[/C][C]0.159813[/C][C]1.3081[/C][C]0.09765[/C][/ROW]
[ROW][C]9[/C][C]0.128462[/C][C]1.0515[/C][C]0.148402[/C][/ROW]
[ROW][C]10[/C][C]-0.077034[/C][C]-0.6305[/C][C]0.265241[/C][/ROW]
[ROW][C]11[/C][C]-0.096014[/C][C]-0.7859[/C][C]0.217346[/C][/ROW]
[ROW][C]12[/C][C]0.082112[/C][C]0.6721[/C][C]0.25191[/C][/ROW]
[ROW][C]13[/C][C]-0.059396[/C][C]-0.4862[/C][C]0.314215[/C][/ROW]
[ROW][C]14[/C][C]0.034417[/C][C]0.2817[/C][C]0.389516[/C][/ROW]
[ROW][C]15[/C][C]0.001047[/C][C]0.0086[/C][C]0.496594[/C][/ROW]
[ROW][C]16[/C][C]-0.098586[/C][C]-0.807[/C][C]0.211272[/C][/ROW]
[ROW][C]17[/C][C]0.032231[/C][C]0.2638[/C][C]0.396362[/C][/ROW]
[ROW][C]18[/C][C]-0.085871[/C][C]-0.7029[/C][C]0.24228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64144&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64144&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	0.335464	2.7459	0.003871
2	0.309679	2.5348	0.006796
3	0.284709	2.3304	0.011401
4	-0.021461	-0.1757	0.430544
5	-0.142374	-1.1654	0.123998
6	-0.078778	-0.6448	0.260621
7	0.024686	0.2021	0.42024
8	0.159813	1.3081	0.09765
9	0.128462	1.0515	0.148402
10	-0.077034	-0.6305	0.265241
11	-0.096014	-0.7859	0.217346
12	0.082112	0.6721	0.25191
13	-0.059396	-0.4862	0.314215
14	0.034417	0.2817	0.389516
15	0.001047	0.0086	0.496594
16	-0.098586	-0.807	0.211272
17	0.032231	0.2638	0.396362
18	-0.085871	-0.7029	0.24228

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.5 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.5 ; par3 = 0 ; par4 = 0 ; 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