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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 29 Dec 2010 16:33:21 +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/29/t1293640312v1vng1vsksssvfl.htm/, Retrieved Fri, 03 May 2024 11:25:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116961, Retrieved Fri, 03 May 2024 11:25:16 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

137

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

-     [(Partial) Autocorrelation Function] [autocorrelatie fu...] [2010-12-27 13:56:52] [8e0d27d3447b6ae48398467ddbde7cca]
-         [(Partial) Autocorrelation Function] [] [2010-12-29 16:33:21] [bdfe30dae669994be8da33a8aaee8615] [Current]

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8.3
8.2
8.1
8
8.1
8.1
8
7.8
7.7
7.7
7.7
7.6
7.5
7.3
7.2
7.1
7.2
7.2
7.2
6.9
6.8
6.8
6.8
6.9
7
7.2
7.2
7.2
7
7
7.2
7.4
7.8
8
7.8
7.8
7.9
7.9
8
8
8
8
8.2
8.4
8.6
8.6
8.5
8.5
8.4
8.4
8.4
8.5
8.6
8.6
8.6
8.6
8.6
8.5
8.4
8.4
8.3
8.3
8.3
8.6
8.8
8.8
8.5
8.1
7.9
8
8.4
8.5
8.5
8.4
8.3
8.3
8.2
8.1
8.1
8.2
8.2
8.2
8.1
8.1
8
7.8
7.7
7.7
7.7
7.7
7.7
7.5
7.4
7.3
7.4
7.4
7.3
7.3
7.1
7
6.5
6.3
6.3
6.5
6.6
6.5
6.3
6.3
6.3
6.5
6.7
6.7
6.7
6.8
6.7
6.8
6.8
7
7
7.2
7.4
7.6
7.8
7.9
8.1
8.3
8.5
8.7
8.8
8.9
9
9
9.1
9.1
9.1
9.2
9.4
9.4
9.3
9.4
9.4
9.5
9.5
9.4
9.4
9.4
9.3
9.3
9.3
9.3
9.3
9.2
9.1
9.1
9.1
9.1
9.2
9.2
9.2
9.3
9.4
9.4
9.5
9.6
9.7
9.7
9.8
9.9
9.9
9.9
9.8
9.8
9.7
9.7
9.6
9.6
9.6
9.6
9.6
9.7
9.7
9.7
9.7
9.8
9.8
9.8
9.8
9.9
9.9
9.8
9.7
9.6
9.6
9.5
9.3
9.2
9
8.9
8.7
8.5
8.4
8.2
8.1
7.9
7.8
7.6
7.5
7.4
7.2
7.2
7.1
7
7
6.9
6.8
6.7
6.7
6.6
6.6
6.5
6.5
6.4
6.4
6.4
6.4
6.3
6.4
6.4
6.4
6.4
6.4
6.4
6.4
6.5
6.5
6.6
6.6
6.6
6.7
6.7
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	'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116961&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116961&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116961&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	'Herman Ole Andreas Wold' @ www.yougetit.org

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.991047	15.3852	0
2	0.975616	15.1456	0
3	0.957222	14.8601	0
4	0.938363	14.5673	0
5	0.9187	14.2621	0
6	0.896376	13.9155	0
7	0.869786	13.5027	0
8	0.839136	13.0269	0
9	0.804773	12.4934	0
10	0.767508	11.9149	0
11	0.728652	11.3117	0
12	0.688631	10.6904	0
13	0.647548	10.0526	0
14	0.606242	9.4114	0
15	0.564012	8.7558	0
16	0.520661	8.0828	0
17	0.477256	7.409	0
18	0.433644	6.732	0
19	0.389721	6.0501	0
20	0.345515	5.3638	0
21	0.301033	4.6733	2e-06
22	0.257138	3.9919	4.4e-05
23	0.214997	3.3376	0.000489

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.991047 & 15.3852 & 0 \tabularnewline
2 & 0.975616 & 15.1456 & 0 \tabularnewline
3 & 0.957222 & 14.8601 & 0 \tabularnewline
4 & 0.938363 & 14.5673 & 0 \tabularnewline
5 & 0.9187 & 14.2621 & 0 \tabularnewline
6 & 0.896376 & 13.9155 & 0 \tabularnewline
7 & 0.869786 & 13.5027 & 0 \tabularnewline
8 & 0.839136 & 13.0269 & 0 \tabularnewline
9 & 0.804773 & 12.4934 & 0 \tabularnewline
10 & 0.767508 & 11.9149 & 0 \tabularnewline
11 & 0.728652 & 11.3117 & 0 \tabularnewline
12 & 0.688631 & 10.6904 & 0 \tabularnewline
13 & 0.647548 & 10.0526 & 0 \tabularnewline
14 & 0.606242 & 9.4114 & 0 \tabularnewline
15 & 0.564012 & 8.7558 & 0 \tabularnewline
16 & 0.520661 & 8.0828 & 0 \tabularnewline
17 & 0.477256 & 7.409 & 0 \tabularnewline
18 & 0.433644 & 6.732 & 0 \tabularnewline
19 & 0.389721 & 6.0501 & 0 \tabularnewline
20 & 0.345515 & 5.3638 & 0 \tabularnewline
21 & 0.301033 & 4.6733 & 2e-06 \tabularnewline
22 & 0.257138 & 3.9919 & 4.4e-05 \tabularnewline
23 & 0.214997 & 3.3376 & 0.000489 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116961&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]0.991047[/C][C]15.3852[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.975616[/C][C]15.1456[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.957222[/C][C]14.8601[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.938363[/C][C]14.5673[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.9187[/C][C]14.2621[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.896376[/C][C]13.9155[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.869786[/C][C]13.5027[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.839136[/C][C]13.0269[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.804773[/C][C]12.4934[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.767508[/C][C]11.9149[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.728652[/C][C]11.3117[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.688631[/C][C]10.6904[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.647548[/C][C]10.0526[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.606242[/C][C]9.4114[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.564012[/C][C]8.7558[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.520661[/C][C]8.0828[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.477256[/C][C]7.409[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.433644[/C][C]6.732[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.389721[/C][C]6.0501[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.345515[/C][C]5.3638[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.301033[/C][C]4.6733[/C][C]2e-06[/C][/ROW]
[ROW][C]22[/C][C]0.257138[/C][C]3.9919[/C][C]4.4e-05[/C][/ROW]
[ROW][C]23[/C][C]0.214997[/C][C]3.3376[/C][C]0.000489[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116961&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116961&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	0.991047	15.3852	0
2	0.975616	15.1456	0
3	0.957222	14.8601	0
4	0.938363	14.5673	0
5	0.9187	14.2621	0
6	0.896376	13.9155	0
7	0.869786	13.5027	0
8	0.839136	13.0269	0
9	0.804773	12.4934	0
10	0.767508	11.9149	0
11	0.728652	11.3117	0
12	0.688631	10.6904	0
13	0.647548	10.0526	0
14	0.606242	9.4114	0
15	0.564012	8.7558	0
16	0.520661	8.0828	0
17	0.477256	7.409	0
18	0.433644	6.732	0
19	0.389721	6.0501	0
20	0.345515	5.3638	0
21	0.301033	4.6733	2e-06
22	0.257138	3.9919	4.4e-05
23	0.214997	3.3376	0.000489

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.991047	15.3852	0
2	-0.367913	-5.7115	0
3	-0.049841	-0.7737	0.219921
4	0.04286	0.6654	0.253226
5	-0.062557	-0.9712	0.166224
6	-0.156265	-2.4259	0.008003
7	-0.175315	-2.7216	0.003485
8	-0.109104	-1.6937	0.045803
9	-0.123705	-1.9204	0.027993
10	-0.103018	-1.5993	0.055535
11	-0.03149	-0.4889	0.312693
12	-0.033608	-0.5217	0.301165
13	-0.025237	-0.3918	0.347782
14	0.051029	0.7922	0.214516
15	-0.023607	-0.3665	0.357163
16	-0.022195	-0.3446	0.365361
17	0.056202	0.8725	0.191905
18	-0.016557	-0.257	0.398685
19	-0.043296	-0.6721	0.251071
20	-0.037132	-0.5765	0.282424
21	-0.037637	-0.5843	0.279788
22	0.003017	0.0468	0.481341
23	0.042272	0.6562	0.256148

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.991047 & 15.3852 & 0 \tabularnewline
2 & -0.367913 & -5.7115 & 0 \tabularnewline
3 & -0.049841 & -0.7737 & 0.219921 \tabularnewline
4 & 0.04286 & 0.6654 & 0.253226 \tabularnewline
5 & -0.062557 & -0.9712 & 0.166224 \tabularnewline
6 & -0.156265 & -2.4259 & 0.008003 \tabularnewline
7 & -0.175315 & -2.7216 & 0.003485 \tabularnewline
8 & -0.109104 & -1.6937 & 0.045803 \tabularnewline
9 & -0.123705 & -1.9204 & 0.027993 \tabularnewline
10 & -0.103018 & -1.5993 & 0.055535 \tabularnewline
11 & -0.03149 & -0.4889 & 0.312693 \tabularnewline
12 & -0.033608 & -0.5217 & 0.301165 \tabularnewline
13 & -0.025237 & -0.3918 & 0.347782 \tabularnewline
14 & 0.051029 & 0.7922 & 0.214516 \tabularnewline
15 & -0.023607 & -0.3665 & 0.357163 \tabularnewline
16 & -0.022195 & -0.3446 & 0.365361 \tabularnewline
17 & 0.056202 & 0.8725 & 0.191905 \tabularnewline
18 & -0.016557 & -0.257 & 0.398685 \tabularnewline
19 & -0.043296 & -0.6721 & 0.251071 \tabularnewline
20 & -0.037132 & -0.5765 & 0.282424 \tabularnewline
21 & -0.037637 & -0.5843 & 0.279788 \tabularnewline
22 & 0.003017 & 0.0468 & 0.481341 \tabularnewline
23 & 0.042272 & 0.6562 & 0.256148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116961&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]0.991047[/C][C]15.3852[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.367913[/C][C]-5.7115[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.049841[/C][C]-0.7737[/C][C]0.219921[/C][/ROW]
[ROW][C]4[/C][C]0.04286[/C][C]0.6654[/C][C]0.253226[/C][/ROW]
[ROW][C]5[/C][C]-0.062557[/C][C]-0.9712[/C][C]0.166224[/C][/ROW]
[ROW][C]6[/C][C]-0.156265[/C][C]-2.4259[/C][C]0.008003[/C][/ROW]
[ROW][C]7[/C][C]-0.175315[/C][C]-2.7216[/C][C]0.003485[/C][/ROW]
[ROW][C]8[/C][C]-0.109104[/C][C]-1.6937[/C][C]0.045803[/C][/ROW]
[ROW][C]9[/C][C]-0.123705[/C][C]-1.9204[/C][C]0.027993[/C][/ROW]
[ROW][C]10[/C][C]-0.103018[/C][C]-1.5993[/C][C]0.055535[/C][/ROW]
[ROW][C]11[/C][C]-0.03149[/C][C]-0.4889[/C][C]0.312693[/C][/ROW]
[ROW][C]12[/C][C]-0.033608[/C][C]-0.5217[/C][C]0.301165[/C][/ROW]
[ROW][C]13[/C][C]-0.025237[/C][C]-0.3918[/C][C]0.347782[/C][/ROW]
[ROW][C]14[/C][C]0.051029[/C][C]0.7922[/C][C]0.214516[/C][/ROW]
[ROW][C]15[/C][C]-0.023607[/C][C]-0.3665[/C][C]0.357163[/C][/ROW]
[ROW][C]16[/C][C]-0.022195[/C][C]-0.3446[/C][C]0.365361[/C][/ROW]
[ROW][C]17[/C][C]0.056202[/C][C]0.8725[/C][C]0.191905[/C][/ROW]
[ROW][C]18[/C][C]-0.016557[/C][C]-0.257[/C][C]0.398685[/C][/ROW]
[ROW][C]19[/C][C]-0.043296[/C][C]-0.6721[/C][C]0.251071[/C][/ROW]
[ROW][C]20[/C][C]-0.037132[/C][C]-0.5765[/C][C]0.282424[/C][/ROW]
[ROW][C]21[/C][C]-0.037637[/C][C]-0.5843[/C][C]0.279788[/C][/ROW]
[ROW][C]22[/C][C]0.003017[/C][C]0.0468[/C][C]0.481341[/C][/ROW]
[ROW][C]23[/C][C]0.042272[/C][C]0.6562[/C][C]0.256148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116961&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116961&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	0.991047	15.3852	0
2	-0.367913	-5.7115	0
3	-0.049841	-0.7737	0.219921
4	0.04286	0.6654	0.253226
5	-0.062557	-0.9712	0.166224
6	-0.156265	-2.4259	0.008003
7	-0.175315	-2.7216	0.003485
8	-0.109104	-1.6937	0.045803
9	-0.123705	-1.9204	0.027993
10	-0.103018	-1.5993	0.055535
11	-0.03149	-0.4889	0.312693
12	-0.033608	-0.5217	0.301165
13	-0.025237	-0.3918	0.347782
14	0.051029	0.7922	0.214516
15	-0.023607	-0.3665	0.357163
16	-0.022195	-0.3446	0.365361
17	0.056202	0.8725	0.191905
18	-0.016557	-0.257	0.398685
19	-0.043296	-0.6721	0.251071
20	-0.037132	-0.5765	0.282424
21	-0.037637	-0.5843	0.279788
22	0.003017	0.0468	0.481341
23	0.042272	0.6562	0.256148

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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