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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2011 10:23:33 -0500

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/2011/Dec/20/t13243946234z7cfc92bds177m.htm/, Retrieved Sun, 05 May 2024 21:28:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157985, Retrieved Sun, 05 May 2024 21:28:10 +0000

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User-defined keywords

Estimated Impact

121

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

-     [(Partial) Autocorrelation Function] [] [2011-12-05 11:42:22] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RMPD  [Variance Reduction Matrix] [Variance Reductio...] [2011-12-20 13:59:28] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RMP     [Standard Deviation-Mean Plot] [] [2011-12-20 14:38:17] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RM        [ARIMA Backward Selection] [] [2011-12-20 14:48:06] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RM D          [(Partial) Autocorrelation Function] [] [2011-12-20 15:23:33] [3627de22d386f4cb93d383ef7c1ade7f] [Current]
- R               [(Partial) Autocorrelation Function] [ACF CV] [2011-12-20 15:24:22] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RM              [Spectral Analysis] [] [2011-12-20 15:26:09] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- R                 [Spectral Analysis] [Spectral Analysis CV] [2011-12-20 15:26:40] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RM                [Variance Reduction Matrix] [] [2011-12-20 15:27:08] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- R                   [Variance Reduction Matrix] [VRM CV] [2011-12-20 15:27:35] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RM                  [Standard Deviation-Mean Plot] [] [2011-12-20 15:29:15] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- R                     [Standard Deviation-Mean Plot] [Standard Deviatio...] [2011-12-20 15:29:48] [aba4febe8a2e49e81bdc61a6c01f5c21] 

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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	'Herman Ole Andreas Wold' @ wold.wessa.net

\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' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157985&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' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157985&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157985&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' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.22148	3.7652	0.000101
2	0.241342	4.1028	2.7e-05
3	0.322981	5.4907	0
4	0.246072	4.1832	1.9e-05
5	0.239386	4.0696	3e-05
6	0.304255	5.1723	0
7	0.352072	5.9852	0
8	0.247591	4.209	1.7e-05
9	0.257326	4.3745	9e-06
10	0.326131	5.5442	0
11	0.213657	3.6322	0.000166
12	0.242753	4.1268	2.4e-05
13	0.278017	4.7263	2e-06
14	0.180015	3.0603	0.00121
15	0.237249	4.0332	3.5e-05
16	0.236779	4.0252	3.6e-05
17	0.189341	3.2188	0.000717
18	0.282135	4.7963	1e-06
19	0.25686	4.3666	9e-06
20	0.280591	4.77	1e-06
21	0.190908	3.2454	0.000655
22	0.192918	3.2796	0.000583
23	0.109564	1.8626	0.031767
24	0.16941	2.88	0.002137

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.22148 & 3.7652 & 0.000101 \tabularnewline
2 & 0.241342 & 4.1028 & 2.7e-05 \tabularnewline
3 & 0.322981 & 5.4907 & 0 \tabularnewline
4 & 0.246072 & 4.1832 & 1.9e-05 \tabularnewline
5 & 0.239386 & 4.0696 & 3e-05 \tabularnewline
6 & 0.304255 & 5.1723 & 0 \tabularnewline
7 & 0.352072 & 5.9852 & 0 \tabularnewline
8 & 0.247591 & 4.209 & 1.7e-05 \tabularnewline
9 & 0.257326 & 4.3745 & 9e-06 \tabularnewline
10 & 0.326131 & 5.5442 & 0 \tabularnewline
11 & 0.213657 & 3.6322 & 0.000166 \tabularnewline
12 & 0.242753 & 4.1268 & 2.4e-05 \tabularnewline
13 & 0.278017 & 4.7263 & 2e-06 \tabularnewline
14 & 0.180015 & 3.0603 & 0.00121 \tabularnewline
15 & 0.237249 & 4.0332 & 3.5e-05 \tabularnewline
16 & 0.236779 & 4.0252 & 3.6e-05 \tabularnewline
17 & 0.189341 & 3.2188 & 0.000717 \tabularnewline
18 & 0.282135 & 4.7963 & 1e-06 \tabularnewline
19 & 0.25686 & 4.3666 & 9e-06 \tabularnewline
20 & 0.280591 & 4.77 & 1e-06 \tabularnewline
21 & 0.190908 & 3.2454 & 0.000655 \tabularnewline
22 & 0.192918 & 3.2796 & 0.000583 \tabularnewline
23 & 0.109564 & 1.8626 & 0.031767 \tabularnewline
24 & 0.16941 & 2.88 & 0.002137 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157985&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]0.22148[/C][C]3.7652[/C][C]0.000101[/C][/ROW]
[ROW][C]2[/C][C]0.241342[/C][C]4.1028[/C][C]2.7e-05[/C][/ROW]
[ROW][C]3[/C][C]0.322981[/C][C]5.4907[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.246072[/C][C]4.1832[/C][C]1.9e-05[/C][/ROW]
[ROW][C]5[/C][C]0.239386[/C][C]4.0696[/C][C]3e-05[/C][/ROW]
[ROW][C]6[/C][C]0.304255[/C][C]5.1723[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.352072[/C][C]5.9852[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.247591[/C][C]4.209[/C][C]1.7e-05[/C][/ROW]
[ROW][C]9[/C][C]0.257326[/C][C]4.3745[/C][C]9e-06[/C][/ROW]
[ROW][C]10[/C][C]0.326131[/C][C]5.5442[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.213657[/C][C]3.6322[/C][C]0.000166[/C][/ROW]
[ROW][C]12[/C][C]0.242753[/C][C]4.1268[/C][C]2.4e-05[/C][/ROW]
[ROW][C]13[/C][C]0.278017[/C][C]4.7263[/C][C]2e-06[/C][/ROW]
[ROW][C]14[/C][C]0.180015[/C][C]3.0603[/C][C]0.00121[/C][/ROW]
[ROW][C]15[/C][C]0.237249[/C][C]4.0332[/C][C]3.5e-05[/C][/ROW]
[ROW][C]16[/C][C]0.236779[/C][C]4.0252[/C][C]3.6e-05[/C][/ROW]
[ROW][C]17[/C][C]0.189341[/C][C]3.2188[/C][C]0.000717[/C][/ROW]
[ROW][C]18[/C][C]0.282135[/C][C]4.7963[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]0.25686[/C][C]4.3666[/C][C]9e-06[/C][/ROW]
[ROW][C]20[/C][C]0.280591[/C][C]4.77[/C][C]1e-06[/C][/ROW]
[ROW][C]21[/C][C]0.190908[/C][C]3.2454[/C][C]0.000655[/C][/ROW]
[ROW][C]22[/C][C]0.192918[/C][C]3.2796[/C][C]0.000583[/C][/ROW]
[ROW][C]23[/C][C]0.109564[/C][C]1.8626[/C][C]0.031767[/C][/ROW]
[ROW][C]24[/C][C]0.16941[/C][C]2.88[/C][C]0.002137[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157985&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157985&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	0.22148	3.7652	0.000101
2	0.241342	4.1028	2.7e-05
3	0.322981	5.4907	0
4	0.246072	4.1832	1.9e-05
5	0.239386	4.0696	3e-05
6	0.304255	5.1723	0
7	0.352072	5.9852	0
8	0.247591	4.209	1.7e-05
9	0.257326	4.3745	9e-06
10	0.326131	5.5442	0
11	0.213657	3.6322	0.000166
12	0.242753	4.1268	2.4e-05
13	0.278017	4.7263	2e-06
14	0.180015	3.0603	0.00121
15	0.237249	4.0332	3.5e-05
16	0.236779	4.0252	3.6e-05
17	0.189341	3.2188	0.000717
18	0.282135	4.7963	1e-06
19	0.25686	4.3666	9e-06
20	0.280591	4.77	1e-06
21	0.190908	3.2454	0.000655
22	0.192918	3.2796	0.000583
23	0.109564	1.8626	0.031767
24	0.16941	2.88	0.002137

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.22148	3.7652	0.000101
2	0.202207	3.4375	0.000337
3	0.258263	4.3905	8e-06
4	0.13026	2.2144	0.01379
5	0.102518	1.7428	0.041216
6	0.160317	2.7254	0.003407
7	0.215449	3.6626	0.000148
8	0.07085	1.2045	0.1147
9	0.054177	0.921	0.178909
10	0.127409	2.1659	0.015566
11	0.005522	0.0939	0.462635
12	0.029151	0.4956	0.310288
13	0.044183	0.7511	0.226598
14	-0.060827	-1.0341	0.150988
15	0.023526	0.3999	0.34475
16	0.009194	0.1563	0.437953
17	-0.037126	-0.6311	0.264225
18	0.104979	1.7846	0.037684
19	0.064186	1.0912	0.138057
20	0.103236	1.755	0.040158
21	-0.005973	-0.1015	0.459598
22	-0.031014	-0.5272	0.299215
23	-0.143697	-2.4428	0.007585
24	-0.023877	-0.4059	0.342556

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.22148 & 3.7652 & 0.000101 \tabularnewline
2 & 0.202207 & 3.4375 & 0.000337 \tabularnewline
3 & 0.258263 & 4.3905 & 8e-06 \tabularnewline
4 & 0.13026 & 2.2144 & 0.01379 \tabularnewline
5 & 0.102518 & 1.7428 & 0.041216 \tabularnewline
6 & 0.160317 & 2.7254 & 0.003407 \tabularnewline
7 & 0.215449 & 3.6626 & 0.000148 \tabularnewline
8 & 0.07085 & 1.2045 & 0.1147 \tabularnewline
9 & 0.054177 & 0.921 & 0.178909 \tabularnewline
10 & 0.127409 & 2.1659 & 0.015566 \tabularnewline
11 & 0.005522 & 0.0939 & 0.462635 \tabularnewline
12 & 0.029151 & 0.4956 & 0.310288 \tabularnewline
13 & 0.044183 & 0.7511 & 0.226598 \tabularnewline
14 & -0.060827 & -1.0341 & 0.150988 \tabularnewline
15 & 0.023526 & 0.3999 & 0.34475 \tabularnewline
16 & 0.009194 & 0.1563 & 0.437953 \tabularnewline
17 & -0.037126 & -0.6311 & 0.264225 \tabularnewline
18 & 0.104979 & 1.7846 & 0.037684 \tabularnewline
19 & 0.064186 & 1.0912 & 0.138057 \tabularnewline
20 & 0.103236 & 1.755 & 0.040158 \tabularnewline
21 & -0.005973 & -0.1015 & 0.459598 \tabularnewline
22 & -0.031014 & -0.5272 & 0.299215 \tabularnewline
23 & -0.143697 & -2.4428 & 0.007585 \tabularnewline
24 & -0.023877 & -0.4059 & 0.342556 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157985&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]0.22148[/C][C]3.7652[/C][C]0.000101[/C][/ROW]
[ROW][C]2[/C][C]0.202207[/C][C]3.4375[/C][C]0.000337[/C][/ROW]
[ROW][C]3[/C][C]0.258263[/C][C]4.3905[/C][C]8e-06[/C][/ROW]
[ROW][C]4[/C][C]0.13026[/C][C]2.2144[/C][C]0.01379[/C][/ROW]
[ROW][C]5[/C][C]0.102518[/C][C]1.7428[/C][C]0.041216[/C][/ROW]
[ROW][C]6[/C][C]0.160317[/C][C]2.7254[/C][C]0.003407[/C][/ROW]
[ROW][C]7[/C][C]0.215449[/C][C]3.6626[/C][C]0.000148[/C][/ROW]
[ROW][C]8[/C][C]0.07085[/C][C]1.2045[/C][C]0.1147[/C][/ROW]
[ROW][C]9[/C][C]0.054177[/C][C]0.921[/C][C]0.178909[/C][/ROW]
[ROW][C]10[/C][C]0.127409[/C][C]2.1659[/C][C]0.015566[/C][/ROW]
[ROW][C]11[/C][C]0.005522[/C][C]0.0939[/C][C]0.462635[/C][/ROW]
[ROW][C]12[/C][C]0.029151[/C][C]0.4956[/C][C]0.310288[/C][/ROW]
[ROW][C]13[/C][C]0.044183[/C][C]0.7511[/C][C]0.226598[/C][/ROW]
[ROW][C]14[/C][C]-0.060827[/C][C]-1.0341[/C][C]0.150988[/C][/ROW]
[ROW][C]15[/C][C]0.023526[/C][C]0.3999[/C][C]0.34475[/C][/ROW]
[ROW][C]16[/C][C]0.009194[/C][C]0.1563[/C][C]0.437953[/C][/ROW]
[ROW][C]17[/C][C]-0.037126[/C][C]-0.6311[/C][C]0.264225[/C][/ROW]
[ROW][C]18[/C][C]0.104979[/C][C]1.7846[/C][C]0.037684[/C][/ROW]
[ROW][C]19[/C][C]0.064186[/C][C]1.0912[/C][C]0.138057[/C][/ROW]
[ROW][C]20[/C][C]0.103236[/C][C]1.755[/C][C]0.040158[/C][/ROW]
[ROW][C]21[/C][C]-0.005973[/C][C]-0.1015[/C][C]0.459598[/C][/ROW]
[ROW][C]22[/C][C]-0.031014[/C][C]-0.5272[/C][C]0.299215[/C][/ROW]
[ROW][C]23[/C][C]-0.143697[/C][C]-2.4428[/C][C]0.007585[/C][/ROW]
[ROW][C]24[/C][C]-0.023877[/C][C]-0.4059[/C][C]0.342556[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157985&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157985&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	0.22148	3.7652	0.000101
2	0.202207	3.4375	0.000337
3	0.258263	4.3905	8e-06
4	0.13026	2.2144	0.01379
5	0.102518	1.7428	0.041216
6	0.160317	2.7254	0.003407
7	0.215449	3.6626	0.000148
8	0.07085	1.2045	0.1147
9	0.054177	0.921	0.178909
10	0.127409	2.1659	0.015566
11	0.005522	0.0939	0.462635
12	0.029151	0.4956	0.310288
13	0.044183	0.7511	0.226598
14	-0.060827	-1.0341	0.150988
15	0.023526	0.3999	0.34475
16	0.009194	0.1563	0.437953
17	-0.037126	-0.6311	0.264225
18	0.104979	1.7846	0.037684
19	0.064186	1.0912	0.138057
20	0.103236	1.755	0.040158
21	-0.005973	-0.1015	0.459598
22	-0.031014	-0.5272	0.299215
23	-0.143697	-2.4428	0.007585
24	-0.023877	-0.4059	0.342556

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 = 4 ;

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