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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

Tue, 06 Dec 2011 15:39:00 -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/06/t1323203986i4rk9ymhe3ke96w.htm/, Retrieved Mon, 29 Apr 2024 03:48:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151920, Retrieved Mon, 29 Apr 2024 03:48:10 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

104

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]
- R  D    [(Partial) Autocorrelation Function] [WS9 - ACF] [2010-12-07 08:36:37] [1f5baf2b24e732d76900bb8178fc04e7]
- R         [(Partial) Autocorrelation Function] [Autocorrelatie] [2011-12-06 20:26:10] [19d77e37efa419fdc040c74a96874aff]
-   P           [(Partial) Autocorrelation Function] [Autocorrelatie d=1] [2011-12-06 20:39:00] [0f9b7c3b8d01420b2751adc6f98a35df] [Current]

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Dataseries X:

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Histogram

Boxplots

2.4
2.4
2.5
2.6
2.4
2.6
2.4
2.3
2.4
2.4
2.4
2.4
2.4
2.4
2.4
2.4
2.5
2.1
2.1
2
2
2
1.9
1.9
2
1.8
1.6
1.3
1.4
1.4
1.5
1.7
1.6
1.5
1.6
1.5
1.1
1.1
1.1
1.4
1.3
1.4
1.3
1.1
1
0.9
0.8
0.8
0.8
0.8
1
1.1
1
0.9
1.1
1.2
1.2
1.4
1.5
1.7
1.9
1.9
1.9
1.7
1.7
2.1
2
2
2.5
2.4
2.5
2.5
2
1.9
2.2
2.7
3.1
2.8
2.6
2.3
2.2
2.2
2
2
2.6
2.5
2.5
2.3
2
1.9
2
2.1
2.1
2.3
2.3
2.3
2.1
2.4
2.5
2.1
1.8
1.9
1.9
2.1
2.2
2
2.2
2
1.9
1.6
1.7
2
2.5
2.4
2.3
2.3
2.1
2.4
2.2
2.4
1.9
2.1
2.1
2.1
2
2.1
2.2
2.2
2.6
2.5
2.3
2.2
2.4
2.3
2.2
2.5
2.5
2.5
2.4
2.3
1.7
1.6
1.9
1.9
1.8
1.8
1.9
1.9
1.9
1.9
1.8
1.7
2.1
2.6
3.1
3.1
3.2
3.3
3.6
3.3
3.7
4
4
3.8
3.6
3.2
2.1
1.6
1.1
1.2
0.6
0.6
0
-0.1
-0.6
-0.2
-0.3
-0.1
0.5
0.9

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' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151920&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151920&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151920&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' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.189231	2.5317	0.006105
2	0.14881	1.9909	0.024005
3	-0.040286	-0.539	0.295281
4	0.048203	0.6449	0.259907
5	-0.099376	-1.3296	0.092678
6	0.051116	0.6839	0.247467
7	0.056962	0.7621	0.223501
8	0.035526	0.4753	0.317574
9	0.041213	0.5514	0.291024
10	-0.006715	-0.0898	0.464258
11	-0.021985	-0.2941	0.384496
12	-0.46098	-6.1675	0
13	-0.216697	-2.8992	0.002105
14	-0.1959	-2.621	0.004761
15	-0.040902	-0.5472	0.292453
16	-0.007614	-0.1019	0.459489
17	0.029868	0.3996	0.344963
18	-0.012844	-0.1718	0.431879
19	0.018307	0.2449	0.403394
20	-0.009538	-0.1276	0.449298
21	-0.011205	-0.1499	0.440504
22	-0.017064	-0.2283	0.409835

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.189231 & 2.5317 & 0.006105 \tabularnewline
2 & 0.14881 & 1.9909 & 0.024005 \tabularnewline
3 & -0.040286 & -0.539 & 0.295281 \tabularnewline
4 & 0.048203 & 0.6449 & 0.259907 \tabularnewline
5 & -0.099376 & -1.3296 & 0.092678 \tabularnewline
6 & 0.051116 & 0.6839 & 0.247467 \tabularnewline
7 & 0.056962 & 0.7621 & 0.223501 \tabularnewline
8 & 0.035526 & 0.4753 & 0.317574 \tabularnewline
9 & 0.041213 & 0.5514 & 0.291024 \tabularnewline
10 & -0.006715 & -0.0898 & 0.464258 \tabularnewline
11 & -0.021985 & -0.2941 & 0.384496 \tabularnewline
12 & -0.46098 & -6.1675 & 0 \tabularnewline
13 & -0.216697 & -2.8992 & 0.002105 \tabularnewline
14 & -0.1959 & -2.621 & 0.004761 \tabularnewline
15 & -0.040902 & -0.5472 & 0.292453 \tabularnewline
16 & -0.007614 & -0.1019 & 0.459489 \tabularnewline
17 & 0.029868 & 0.3996 & 0.344963 \tabularnewline
18 & -0.012844 & -0.1718 & 0.431879 \tabularnewline
19 & 0.018307 & 0.2449 & 0.403394 \tabularnewline
20 & -0.009538 & -0.1276 & 0.449298 \tabularnewline
21 & -0.011205 & -0.1499 & 0.440504 \tabularnewline
22 & -0.017064 & -0.2283 & 0.409835 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151920&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]0.189231[/C][C]2.5317[/C][C]0.006105[/C][/ROW]
[ROW][C]2[/C][C]0.14881[/C][C]1.9909[/C][C]0.024005[/C][/ROW]
[ROW][C]3[/C][C]-0.040286[/C][C]-0.539[/C][C]0.295281[/C][/ROW]
[ROW][C]4[/C][C]0.048203[/C][C]0.6449[/C][C]0.259907[/C][/ROW]
[ROW][C]5[/C][C]-0.099376[/C][C]-1.3296[/C][C]0.092678[/C][/ROW]
[ROW][C]6[/C][C]0.051116[/C][C]0.6839[/C][C]0.247467[/C][/ROW]
[ROW][C]7[/C][C]0.056962[/C][C]0.7621[/C][C]0.223501[/C][/ROW]
[ROW][C]8[/C][C]0.035526[/C][C]0.4753[/C][C]0.317574[/C][/ROW]
[ROW][C]9[/C][C]0.041213[/C][C]0.5514[/C][C]0.291024[/C][/ROW]
[ROW][C]10[/C][C]-0.006715[/C][C]-0.0898[/C][C]0.464258[/C][/ROW]
[ROW][C]11[/C][C]-0.021985[/C][C]-0.2941[/C][C]0.384496[/C][/ROW]
[ROW][C]12[/C][C]-0.46098[/C][C]-6.1675[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.216697[/C][C]-2.8992[/C][C]0.002105[/C][/ROW]
[ROW][C]14[/C][C]-0.1959[/C][C]-2.621[/C][C]0.004761[/C][/ROW]
[ROW][C]15[/C][C]-0.040902[/C][C]-0.5472[/C][C]0.292453[/C][/ROW]
[ROW][C]16[/C][C]-0.007614[/C][C]-0.1019[/C][C]0.459489[/C][/ROW]
[ROW][C]17[/C][C]0.029868[/C][C]0.3996[/C][C]0.344963[/C][/ROW]
[ROW][C]18[/C][C]-0.012844[/C][C]-0.1718[/C][C]0.431879[/C][/ROW]
[ROW][C]19[/C][C]0.018307[/C][C]0.2449[/C][C]0.403394[/C][/ROW]
[ROW][C]20[/C][C]-0.009538[/C][C]-0.1276[/C][C]0.449298[/C][/ROW]
[ROW][C]21[/C][C]-0.011205[/C][C]-0.1499[/C][C]0.440504[/C][/ROW]
[ROW][C]22[/C][C]-0.017064[/C][C]-0.2283[/C][C]0.409835[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151920&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151920&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	0.189231	2.5317	0.006105
2	0.14881	1.9909	0.024005
3	-0.040286	-0.539	0.295281
4	0.048203	0.6449	0.259907
5	-0.099376	-1.3296	0.092678
6	0.051116	0.6839	0.247467
7	0.056962	0.7621	0.223501
8	0.035526	0.4753	0.317574
9	0.041213	0.5514	0.291024
10	-0.006715	-0.0898	0.464258
11	-0.021985	-0.2941	0.384496
12	-0.46098	-6.1675	0
13	-0.216697	-2.8992	0.002105
14	-0.1959	-2.621	0.004761
15	-0.040902	-0.5472	0.292453
16	-0.007614	-0.1019	0.459489
17	0.029868	0.3996	0.344963
18	-0.012844	-0.1718	0.431879
19	0.018307	0.2449	0.403394
20	-0.009538	-0.1276	0.449298
21	-0.011205	-0.1499	0.440504
22	-0.017064	-0.2283	0.409835

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.189231	2.5317	0.006105
2	0.117198	1.568	0.059323
3	-0.091827	-1.2286	0.110424
4	0.056229	0.7523	0.226433
5	-0.104947	-1.4041	0.081012
6	0.074691	0.9993	0.1595
7	0.073505	0.9834	0.163362
8	-0.02341	-0.3132	0.377243
9	0.044819	0.5996	0.274755
10	-0.037958	-0.5078	0.306092
11	-0.019597	-0.2622	0.39674
12	-0.471323	-6.3059	0
13	-0.077067	-1.0311	0.151945
14	-0.041892	-0.5605	0.287929
15	-0.03941	-0.5273	0.29933
16	0.096591	1.2923	0.098961
17	-0.08889	-1.1893	0.117955
18	0.048096	0.6435	0.260366
19	0.083364	1.1153	0.133102
20	0.008051	0.1077	0.45717
21	0.052952	0.7084	0.239794
22	-0.020654	-0.2763	0.391304

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.189231 & 2.5317 & 0.006105 \tabularnewline
2 & 0.117198 & 1.568 & 0.059323 \tabularnewline
3 & -0.091827 & -1.2286 & 0.110424 \tabularnewline
4 & 0.056229 & 0.7523 & 0.226433 \tabularnewline
5 & -0.104947 & -1.4041 & 0.081012 \tabularnewline
6 & 0.074691 & 0.9993 & 0.1595 \tabularnewline
7 & 0.073505 & 0.9834 & 0.163362 \tabularnewline
8 & -0.02341 & -0.3132 & 0.377243 \tabularnewline
9 & 0.044819 & 0.5996 & 0.274755 \tabularnewline
10 & -0.037958 & -0.5078 & 0.306092 \tabularnewline
11 & -0.019597 & -0.2622 & 0.39674 \tabularnewline
12 & -0.471323 & -6.3059 & 0 \tabularnewline
13 & -0.077067 & -1.0311 & 0.151945 \tabularnewline
14 & -0.041892 & -0.5605 & 0.287929 \tabularnewline
15 & -0.03941 & -0.5273 & 0.29933 \tabularnewline
16 & 0.096591 & 1.2923 & 0.098961 \tabularnewline
17 & -0.08889 & -1.1893 & 0.117955 \tabularnewline
18 & 0.048096 & 0.6435 & 0.260366 \tabularnewline
19 & 0.083364 & 1.1153 & 0.133102 \tabularnewline
20 & 0.008051 & 0.1077 & 0.45717 \tabularnewline
21 & 0.052952 & 0.7084 & 0.239794 \tabularnewline
22 & -0.020654 & -0.2763 & 0.391304 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151920&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]0.189231[/C][C]2.5317[/C][C]0.006105[/C][/ROW]
[ROW][C]2[/C][C]0.117198[/C][C]1.568[/C][C]0.059323[/C][/ROW]
[ROW][C]3[/C][C]-0.091827[/C][C]-1.2286[/C][C]0.110424[/C][/ROW]
[ROW][C]4[/C][C]0.056229[/C][C]0.7523[/C][C]0.226433[/C][/ROW]
[ROW][C]5[/C][C]-0.104947[/C][C]-1.4041[/C][C]0.081012[/C][/ROW]
[ROW][C]6[/C][C]0.074691[/C][C]0.9993[/C][C]0.1595[/C][/ROW]
[ROW][C]7[/C][C]0.073505[/C][C]0.9834[/C][C]0.163362[/C][/ROW]
[ROW][C]8[/C][C]-0.02341[/C][C]-0.3132[/C][C]0.377243[/C][/ROW]
[ROW][C]9[/C][C]0.044819[/C][C]0.5996[/C][C]0.274755[/C][/ROW]
[ROW][C]10[/C][C]-0.037958[/C][C]-0.5078[/C][C]0.306092[/C][/ROW]
[ROW][C]11[/C][C]-0.019597[/C][C]-0.2622[/C][C]0.39674[/C][/ROW]
[ROW][C]12[/C][C]-0.471323[/C][C]-6.3059[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.077067[/C][C]-1.0311[/C][C]0.151945[/C][/ROW]
[ROW][C]14[/C][C]-0.041892[/C][C]-0.5605[/C][C]0.287929[/C][/ROW]
[ROW][C]15[/C][C]-0.03941[/C][C]-0.5273[/C][C]0.29933[/C][/ROW]
[ROW][C]16[/C][C]0.096591[/C][C]1.2923[/C][C]0.098961[/C][/ROW]
[ROW][C]17[/C][C]-0.08889[/C][C]-1.1893[/C][C]0.117955[/C][/ROW]
[ROW][C]18[/C][C]0.048096[/C][C]0.6435[/C][C]0.260366[/C][/ROW]
[ROW][C]19[/C][C]0.083364[/C][C]1.1153[/C][C]0.133102[/C][/ROW]
[ROW][C]20[/C][C]0.008051[/C][C]0.1077[/C][C]0.45717[/C][/ROW]
[ROW][C]21[/C][C]0.052952[/C][C]0.7084[/C][C]0.239794[/C][/ROW]
[ROW][C]22[/C][C]-0.020654[/C][C]-0.2763[/C][C]0.391304[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151920&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151920&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	0.189231	2.5317	0.006105
2	0.117198	1.568	0.059323
3	-0.091827	-1.2286	0.110424
4	0.056229	0.7523	0.226433
5	-0.104947	-1.4041	0.081012
6	0.074691	0.9993	0.1595
7	0.073505	0.9834	0.163362
8	-0.02341	-0.3132	0.377243
9	0.044819	0.5996	0.274755
10	-0.037958	-0.5078	0.306092
11	-0.019597	-0.2622	0.39674
12	-0.471323	-6.3059	0
13	-0.077067	-1.0311	0.151945
14	-0.041892	-0.5605	0.287929
15	-0.03941	-0.5273	0.29933
16	0.096591	1.2923	0.098961
17	-0.08889	-1.1893	0.117955
18	0.048096	0.6435	0.260366
19	0.083364	1.1153	0.133102
20	0.008051	0.1077	0.45717
21	0.052952	0.7084	0.239794
22	-0.020654	-0.2763	0.391304

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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