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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2011 10:43:57 -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/16/t1324050266zj9adeyztyymd6a.htm/, Retrieved Fri, 19 Apr 2024 19:23:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156064, Retrieved Fri, 19 Apr 2024 19:23:29 +0000

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IsPrivate?

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User-defined keywords

Estimated Impact

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

F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Central Tendency] [Workshop 8 STAP 1...] [2011-11-26 13:04:08] [de8512d9b386046939a89973b76869e3]
- RMPD    [Decomposition by Loess] [Workshop 8 STAP 3...] [2011-11-26 14:09:35] [de8512d9b386046939a89973b76869e3]
- RMP       [Structural Time Series Models] [Workshop 8 STAP 3...] [2011-11-26 14:16:57] [de8512d9b386046939a89973b76869e3]
- RMPD        [Multiple Regression] [Workshop 8 STAP 5...] [2011-11-26 14:57:33] [de8512d9b386046939a89973b76869e3]
- RMPD            [(Partial) Autocorrelation Function] [Paper SHW  Deel 2...] [2011-12-16 15:43:57] [5c44e6aad476a1bab98fc6774eca4c08] [Current]
- RM                [Standard Deviation-Mean Plot] [Paper SHW Deel 2 ...] [2011-12-16 15:59:09] [de8512d9b386046939a89973b76869e3] 

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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	'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156064&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156064&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156064&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.210141	3.9816	4.1e-05
2	0.325131	6.1603	0
3	0.153275	2.9041	0.001955
4	0.167252	3.169	0.000831
5	0.099156	1.8787	0.030545
6	0.064513	1.2223	0.111191
7	-0.057203	-1.0838	0.13958
8	-0.023244	-0.4404	0.329956
9	-0.085115	-1.6127	0.053845
10	-0.168424	-3.1912	0.000771
11	-0.075939	-1.4388	0.075533
12	-0.475334	-9.0063	0
13	-0.179215	-3.3956	0.000381
14	-0.162819	-3.085	0.001097
15	-0.106644	-2.0206	0.02203
16	-0.147945	-2.8032	0.002668
17	-0.091478	-1.7333	0.041954
18	-0.089745	-1.7004	0.044958
19	0.027328	0.5178	0.302458
20	-0.012913	-0.2447	0.403425
21	0.024199	0.4585	0.323437
22	-0.018741	-0.3551	0.361367
23	0.009567	0.1813	0.42813
24	-0.022226	-0.4211	0.336957
25	0.091974	1.7427	0.041125

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.210141 & 3.9816 & 4.1e-05 \tabularnewline
2 & 0.325131 & 6.1603 & 0 \tabularnewline
3 & 0.153275 & 2.9041 & 0.001955 \tabularnewline
4 & 0.167252 & 3.169 & 0.000831 \tabularnewline
5 & 0.099156 & 1.8787 & 0.030545 \tabularnewline
6 & 0.064513 & 1.2223 & 0.111191 \tabularnewline
7 & -0.057203 & -1.0838 & 0.13958 \tabularnewline
8 & -0.023244 & -0.4404 & 0.329956 \tabularnewline
9 & -0.085115 & -1.6127 & 0.053845 \tabularnewline
10 & -0.168424 & -3.1912 & 0.000771 \tabularnewline
11 & -0.075939 & -1.4388 & 0.075533 \tabularnewline
12 & -0.475334 & -9.0063 & 0 \tabularnewline
13 & -0.179215 & -3.3956 & 0.000381 \tabularnewline
14 & -0.162819 & -3.085 & 0.001097 \tabularnewline
15 & -0.106644 & -2.0206 & 0.02203 \tabularnewline
16 & -0.147945 & -2.8032 & 0.002668 \tabularnewline
17 & -0.091478 & -1.7333 & 0.041954 \tabularnewline
18 & -0.089745 & -1.7004 & 0.044958 \tabularnewline
19 & 0.027328 & 0.5178 & 0.302458 \tabularnewline
20 & -0.012913 & -0.2447 & 0.403425 \tabularnewline
21 & 0.024199 & 0.4585 & 0.323437 \tabularnewline
22 & -0.018741 & -0.3551 & 0.361367 \tabularnewline
23 & 0.009567 & 0.1813 & 0.42813 \tabularnewline
24 & -0.022226 & -0.4211 & 0.336957 \tabularnewline
25 & 0.091974 & 1.7427 & 0.041125 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156064&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]0.210141[/C][C]3.9816[/C][C]4.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.325131[/C][C]6.1603[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.153275[/C][C]2.9041[/C][C]0.001955[/C][/ROW]
[ROW][C]4[/C][C]0.167252[/C][C]3.169[/C][C]0.000831[/C][/ROW]
[ROW][C]5[/C][C]0.099156[/C][C]1.8787[/C][C]0.030545[/C][/ROW]
[ROW][C]6[/C][C]0.064513[/C][C]1.2223[/C][C]0.111191[/C][/ROW]
[ROW][C]7[/C][C]-0.057203[/C][C]-1.0838[/C][C]0.13958[/C][/ROW]
[ROW][C]8[/C][C]-0.023244[/C][C]-0.4404[/C][C]0.329956[/C][/ROW]
[ROW][C]9[/C][C]-0.085115[/C][C]-1.6127[/C][C]0.053845[/C][/ROW]
[ROW][C]10[/C][C]-0.168424[/C][C]-3.1912[/C][C]0.000771[/C][/ROW]
[ROW][C]11[/C][C]-0.075939[/C][C]-1.4388[/C][C]0.075533[/C][/ROW]
[ROW][C]12[/C][C]-0.475334[/C][C]-9.0063[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.179215[/C][C]-3.3956[/C][C]0.000381[/C][/ROW]
[ROW][C]14[/C][C]-0.162819[/C][C]-3.085[/C][C]0.001097[/C][/ROW]
[ROW][C]15[/C][C]-0.106644[/C][C]-2.0206[/C][C]0.02203[/C][/ROW]
[ROW][C]16[/C][C]-0.147945[/C][C]-2.8032[/C][C]0.002668[/C][/ROW]
[ROW][C]17[/C][C]-0.091478[/C][C]-1.7333[/C][C]0.041954[/C][/ROW]
[ROW][C]18[/C][C]-0.089745[/C][C]-1.7004[/C][C]0.044958[/C][/ROW]
[ROW][C]19[/C][C]0.027328[/C][C]0.5178[/C][C]0.302458[/C][/ROW]
[ROW][C]20[/C][C]-0.012913[/C][C]-0.2447[/C][C]0.403425[/C][/ROW]
[ROW][C]21[/C][C]0.024199[/C][C]0.4585[/C][C]0.323437[/C][/ROW]
[ROW][C]22[/C][C]-0.018741[/C][C]-0.3551[/C][C]0.361367[/C][/ROW]
[ROW][C]23[/C][C]0.009567[/C][C]0.1813[/C][C]0.42813[/C][/ROW]
[ROW][C]24[/C][C]-0.022226[/C][C]-0.4211[/C][C]0.336957[/C][/ROW]
[ROW][C]25[/C][C]0.091974[/C][C]1.7427[/C][C]0.041125[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156064&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156064&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	0.210141	3.9816	4.1e-05
2	0.325131	6.1603	0
3	0.153275	2.9041	0.001955
4	0.167252	3.169	0.000831
5	0.099156	1.8787	0.030545
6	0.064513	1.2223	0.111191
7	-0.057203	-1.0838	0.13958
8	-0.023244	-0.4404	0.329956
9	-0.085115	-1.6127	0.053845
10	-0.168424	-3.1912	0.000771
11	-0.075939	-1.4388	0.075533
12	-0.475334	-9.0063	0
13	-0.179215	-3.3956	0.000381
14	-0.162819	-3.085	0.001097
15	-0.106644	-2.0206	0.02203
16	-0.147945	-2.8032	0.002668
17	-0.091478	-1.7333	0.041954
18	-0.089745	-1.7004	0.044958
19	0.027328	0.5178	0.302458
20	-0.012913	-0.2447	0.403425
21	0.024199	0.4585	0.323437
22	-0.018741	-0.3551	0.361367
23	0.009567	0.1813	0.42813
24	-0.022226	-0.4211	0.336957
25	0.091974	1.7427	0.041125

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.210141	3.9816	4.1e-05
2	0.293952	5.5696	0
3	0.049544	0.9387	0.174253
4	0.049534	0.9385	0.174302
5	0.012741	0.2414	0.404686
6	-0.02095	-0.3969	0.34582
7	-0.124687	-2.3625	0.009343
8	-0.032709	-0.6197	0.267912
9	-0.045438	-0.8609	0.194928
10	-0.146092	-2.768	0.002966
11	0.023631	0.4477	0.327306
12	-0.42914	-8.131	0
13	-0.0237	-0.449	0.326836
14	0.150889	2.8589	0.002249
15	0.029791	0.5645	0.286395
16	-0.044612	-0.8453	0.199257
17	-0.012037	-0.2281	0.40986
18	0.004648	0.0881	0.464938
19	0.011303	0.2142	0.415271
20	0.009823	0.1861	0.426229
21	-0.009818	-0.186	0.426268
22	-0.15669	-2.9689	0.001595
23	0.012173	0.2306	0.408859
24	-0.273087	-5.1743	0
25	0.053216	1.0083	0.156993

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.210141 & 3.9816 & 4.1e-05 \tabularnewline
2 & 0.293952 & 5.5696 & 0 \tabularnewline
3 & 0.049544 & 0.9387 & 0.174253 \tabularnewline
4 & 0.049534 & 0.9385 & 0.174302 \tabularnewline
5 & 0.012741 & 0.2414 & 0.404686 \tabularnewline
6 & -0.02095 & -0.3969 & 0.34582 \tabularnewline
7 & -0.124687 & -2.3625 & 0.009343 \tabularnewline
8 & -0.032709 & -0.6197 & 0.267912 \tabularnewline
9 & -0.045438 & -0.8609 & 0.194928 \tabularnewline
10 & -0.146092 & -2.768 & 0.002966 \tabularnewline
11 & 0.023631 & 0.4477 & 0.327306 \tabularnewline
12 & -0.42914 & -8.131 & 0 \tabularnewline
13 & -0.0237 & -0.449 & 0.326836 \tabularnewline
14 & 0.150889 & 2.8589 & 0.002249 \tabularnewline
15 & 0.029791 & 0.5645 & 0.286395 \tabularnewline
16 & -0.044612 & -0.8453 & 0.199257 \tabularnewline
17 & -0.012037 & -0.2281 & 0.40986 \tabularnewline
18 & 0.004648 & 0.0881 & 0.464938 \tabularnewline
19 & 0.011303 & 0.2142 & 0.415271 \tabularnewline
20 & 0.009823 & 0.1861 & 0.426229 \tabularnewline
21 & -0.009818 & -0.186 & 0.426268 \tabularnewline
22 & -0.15669 & -2.9689 & 0.001595 \tabularnewline
23 & 0.012173 & 0.2306 & 0.408859 \tabularnewline
24 & -0.273087 & -5.1743 & 0 \tabularnewline
25 & 0.053216 & 1.0083 & 0.156993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156064&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]0.210141[/C][C]3.9816[/C][C]4.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.293952[/C][C]5.5696[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.049544[/C][C]0.9387[/C][C]0.174253[/C][/ROW]
[ROW][C]4[/C][C]0.049534[/C][C]0.9385[/C][C]0.174302[/C][/ROW]
[ROW][C]5[/C][C]0.012741[/C][C]0.2414[/C][C]0.404686[/C][/ROW]
[ROW][C]6[/C][C]-0.02095[/C][C]-0.3969[/C][C]0.34582[/C][/ROW]
[ROW][C]7[/C][C]-0.124687[/C][C]-2.3625[/C][C]0.009343[/C][/ROW]
[ROW][C]8[/C][C]-0.032709[/C][C]-0.6197[/C][C]0.267912[/C][/ROW]
[ROW][C]9[/C][C]-0.045438[/C][C]-0.8609[/C][C]0.194928[/C][/ROW]
[ROW][C]10[/C][C]-0.146092[/C][C]-2.768[/C][C]0.002966[/C][/ROW]
[ROW][C]11[/C][C]0.023631[/C][C]0.4477[/C][C]0.327306[/C][/ROW]
[ROW][C]12[/C][C]-0.42914[/C][C]-8.131[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.0237[/C][C]-0.449[/C][C]0.326836[/C][/ROW]
[ROW][C]14[/C][C]0.150889[/C][C]2.8589[/C][C]0.002249[/C][/ROW]
[ROW][C]15[/C][C]0.029791[/C][C]0.5645[/C][C]0.286395[/C][/ROW]
[ROW][C]16[/C][C]-0.044612[/C][C]-0.8453[/C][C]0.199257[/C][/ROW]
[ROW][C]17[/C][C]-0.012037[/C][C]-0.2281[/C][C]0.40986[/C][/ROW]
[ROW][C]18[/C][C]0.004648[/C][C]0.0881[/C][C]0.464938[/C][/ROW]
[ROW][C]19[/C][C]0.011303[/C][C]0.2142[/C][C]0.415271[/C][/ROW]
[ROW][C]20[/C][C]0.009823[/C][C]0.1861[/C][C]0.426229[/C][/ROW]
[ROW][C]21[/C][C]-0.009818[/C][C]-0.186[/C][C]0.426268[/C][/ROW]
[ROW][C]22[/C][C]-0.15669[/C][C]-2.9689[/C][C]0.001595[/C][/ROW]
[ROW][C]23[/C][C]0.012173[/C][C]0.2306[/C][C]0.408859[/C][/ROW]
[ROW][C]24[/C][C]-0.273087[/C][C]-5.1743[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.053216[/C][C]1.0083[/C][C]0.156993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156064&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156064&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	0.210141	3.9816	4.1e-05
2	0.293952	5.5696	0
3	0.049544	0.9387	0.174253
4	0.049534	0.9385	0.174302
5	0.012741	0.2414	0.404686
6	-0.02095	-0.3969	0.34582
7	-0.124687	-2.3625	0.009343
8	-0.032709	-0.6197	0.267912
9	-0.045438	-0.8609	0.194928
10	-0.146092	-2.768	0.002966
11	0.023631	0.4477	0.327306
12	-0.42914	-8.131	0
13	-0.0237	-0.449	0.326836
14	0.150889	2.8589	0.002249
15	0.029791	0.5645	0.286395
16	-0.044612	-0.8453	0.199257
17	-0.012037	-0.2281	0.40986
18	0.004648	0.0881	0.464938
19	0.011303	0.2142	0.415271
20	0.009823	0.1861	0.426229
21	-0.009818	-0.186	0.426268
22	-0.15669	-2.9689	0.001595
23	0.012173	0.2306	0.408859
24	-0.273087	-5.1743	0
25	0.053216	1.0083	0.156993

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 = additive ; par2 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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