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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, 16 Dec 2008 07:24:05 -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/2008/Dec/16/t12294375248it1tpfiutg0n41.htm/, Retrieved Wed, 15 May 2024 21:09:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33961, Retrieved Wed, 15 May 2024 21:09:45 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

194

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

-     [Standard Deviation-Mean Plot] [Paper Hoofdstuk 4...] [2008-12-05 10:14:55] [6fea0e9a9b3b29a63badf2c274e82506]
- RM D  [Variance Reduction Matrix] [Paper, hoofdstuk ...] [2008-12-06 15:48:43] [79c17183721a40a589db5f9f561947d8]
- RMP     [(Partial) Autocorrelation Function] [Paper, hoofdstuk ...] [2008-12-06 16:56:09] [79c17183721a40a589db5f9f561947d8]
-   P       [(Partial) Autocorrelation Function] [Paper, hoofdstuk ...] [2008-12-06 17:05:19] [79c17183721a40a589db5f9f561947d8]
-   P         [(Partial) Autocorrelation Function] [Paper 4.3 (P)ACF ...] [2008-12-16 14:21:32] [79c17183721a40a589db5f9f561947d8]
-   P             [(Partial) Autocorrelation Function] [Paper 4.3 (P)ACF ...] [2008-12-16 14:24:05] [3bb0537fcae9c337e49b9ce75ff3d4da] [Current]

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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=33961&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=33961&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33961&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	-0.211378	-1.2505	0.109701
2	0.121527	0.719	0.238469
3	-0.27595	-1.6325	0.055766
4	-0.090454	-0.5351	0.29797
5	0.015836	0.0937	0.462947
6	0.016221	0.096	0.462049
7	0.047286	0.2797	0.39066
8	-0.039658	-0.2346	0.407935
9	0.262388	1.5523	0.064792
10	-0.151738	-0.8977	0.187741
11	0.123414	0.7301	0.235086
12	-0.471938	-2.792	0.004215
13	0.087435	0.5173	0.30411
14	-0.213733	-1.2645	0.10721
15	0.316776	1.8741	0.034644
16	-0.049204	-0.2911	0.386349
17	0.007232	0.0428	0.483058
18	0.085612	0.5065	0.307845
19	-0.153932	-0.9107	0.184348
20	0.119947	0.7096	0.241322
21	-0.180273	-1.0665	0.146747
22	0.031218	0.1847	0.42727
23	-0.034138	-0.202	0.420557
24	0.205379	1.215	0.116243

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.211378 & -1.2505 & 0.109701 \tabularnewline
2 & 0.121527 & 0.719 & 0.238469 \tabularnewline
3 & -0.27595 & -1.6325 & 0.055766 \tabularnewline
4 & -0.090454 & -0.5351 & 0.29797 \tabularnewline
5 & 0.015836 & 0.0937 & 0.462947 \tabularnewline
6 & 0.016221 & 0.096 & 0.462049 \tabularnewline
7 & 0.047286 & 0.2797 & 0.39066 \tabularnewline
8 & -0.039658 & -0.2346 & 0.407935 \tabularnewline
9 & 0.262388 & 1.5523 & 0.064792 \tabularnewline
10 & -0.151738 & -0.8977 & 0.187741 \tabularnewline
11 & 0.123414 & 0.7301 & 0.235086 \tabularnewline
12 & -0.471938 & -2.792 & 0.004215 \tabularnewline
13 & 0.087435 & 0.5173 & 0.30411 \tabularnewline
14 & -0.213733 & -1.2645 & 0.10721 \tabularnewline
15 & 0.316776 & 1.8741 & 0.034644 \tabularnewline
16 & -0.049204 & -0.2911 & 0.386349 \tabularnewline
17 & 0.007232 & 0.0428 & 0.483058 \tabularnewline
18 & 0.085612 & 0.5065 & 0.307845 \tabularnewline
19 & -0.153932 & -0.9107 & 0.184348 \tabularnewline
20 & 0.119947 & 0.7096 & 0.241322 \tabularnewline
21 & -0.180273 & -1.0665 & 0.146747 \tabularnewline
22 & 0.031218 & 0.1847 & 0.42727 \tabularnewline
23 & -0.034138 & -0.202 & 0.420557 \tabularnewline
24 & 0.205379 & 1.215 & 0.116243 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33961&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]-0.211378[/C][C]-1.2505[/C][C]0.109701[/C][/ROW]
[ROW][C]2[/C][C]0.121527[/C][C]0.719[/C][C]0.238469[/C][/ROW]
[ROW][C]3[/C][C]-0.27595[/C][C]-1.6325[/C][C]0.055766[/C][/ROW]
[ROW][C]4[/C][C]-0.090454[/C][C]-0.5351[/C][C]0.29797[/C][/ROW]
[ROW][C]5[/C][C]0.015836[/C][C]0.0937[/C][C]0.462947[/C][/ROW]
[ROW][C]6[/C][C]0.016221[/C][C]0.096[/C][C]0.462049[/C][/ROW]
[ROW][C]7[/C][C]0.047286[/C][C]0.2797[/C][C]0.39066[/C][/ROW]
[ROW][C]8[/C][C]-0.039658[/C][C]-0.2346[/C][C]0.407935[/C][/ROW]
[ROW][C]9[/C][C]0.262388[/C][C]1.5523[/C][C]0.064792[/C][/ROW]
[ROW][C]10[/C][C]-0.151738[/C][C]-0.8977[/C][C]0.187741[/C][/ROW]
[ROW][C]11[/C][C]0.123414[/C][C]0.7301[/C][C]0.235086[/C][/ROW]
[ROW][C]12[/C][C]-0.471938[/C][C]-2.792[/C][C]0.004215[/C][/ROW]
[ROW][C]13[/C][C]0.087435[/C][C]0.5173[/C][C]0.30411[/C][/ROW]
[ROW][C]14[/C][C]-0.213733[/C][C]-1.2645[/C][C]0.10721[/C][/ROW]
[ROW][C]15[/C][C]0.316776[/C][C]1.8741[/C][C]0.034644[/C][/ROW]
[ROW][C]16[/C][C]-0.049204[/C][C]-0.2911[/C][C]0.386349[/C][/ROW]
[ROW][C]17[/C][C]0.007232[/C][C]0.0428[/C][C]0.483058[/C][/ROW]
[ROW][C]18[/C][C]0.085612[/C][C]0.5065[/C][C]0.307845[/C][/ROW]
[ROW][C]19[/C][C]-0.153932[/C][C]-0.9107[/C][C]0.184348[/C][/ROW]
[ROW][C]20[/C][C]0.119947[/C][C]0.7096[/C][C]0.241322[/C][/ROW]
[ROW][C]21[/C][C]-0.180273[/C][C]-1.0665[/C][C]0.146747[/C][/ROW]
[ROW][C]22[/C][C]0.031218[/C][C]0.1847[/C][C]0.42727[/C][/ROW]
[ROW][C]23[/C][C]-0.034138[/C][C]-0.202[/C][C]0.420557[/C][/ROW]
[ROW][C]24[/C][C]0.205379[/C][C]1.215[/C][C]0.116243[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33961&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33961&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	-0.211378	-1.2505	0.109701
2	0.121527	0.719	0.238469
3	-0.27595	-1.6325	0.055766
4	-0.090454	-0.5351	0.29797
5	0.015836	0.0937	0.462947
6	0.016221	0.096	0.462049
7	0.047286	0.2797	0.39066
8	-0.039658	-0.2346	0.407935
9	0.262388	1.5523	0.064792
10	-0.151738	-0.8977	0.187741
11	0.123414	0.7301	0.235086
12	-0.471938	-2.792	0.004215
13	0.087435	0.5173	0.30411
14	-0.213733	-1.2645	0.10721
15	0.316776	1.8741	0.034644
16	-0.049204	-0.2911	0.386349
17	0.007232	0.0428	0.483058
18	0.085612	0.5065	0.307845
19	-0.153932	-0.9107	0.184348
20	0.119947	0.7096	0.241322
21	-0.180273	-1.0665	0.146747
22	0.031218	0.1847	0.42727
23	-0.034138	-0.202	0.420557
24	0.205379	1.215	0.116243

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.211378	-1.2505	0.109701
2	0.08044	0.4759	0.318555
3	-0.247935	-1.4668	0.075679
4	-0.218811	-1.2945	0.101983
5	-0.006469	-0.0383	0.484845
6	-0.035637	-0.2108	0.417121
7	-0.050052	-0.2961	0.384446
8	-0.06382	-0.3776	0.354017
9	0.284843	1.6852	0.050428
10	-0.041468	-0.2453	0.403817
11	0.039281	0.2324	0.408794
12	-0.368998	-2.183	0.017915
13	-0.057969	-0.343	0.366843
14	-0.259563	-1.5356	0.066814
15	0.086583	0.5122	0.305852
16	-0.156605	-0.9265	0.180269
17	-0.097795	-0.5786	0.283294
18	0.072351	0.428	0.335624
19	-0.04725	-0.2795	0.390741
20	-0.005191	-0.0307	0.487837
21	0.033746	0.1996	0.421458
22	-0.110749	-0.6552	0.258312
23	0.070388	0.4164	0.339823
24	-0.121291	-0.7176	0.238893

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.211378 & -1.2505 & 0.109701 \tabularnewline
2 & 0.08044 & 0.4759 & 0.318555 \tabularnewline
3 & -0.247935 & -1.4668 & 0.075679 \tabularnewline
4 & -0.218811 & -1.2945 & 0.101983 \tabularnewline
5 & -0.006469 & -0.0383 & 0.484845 \tabularnewline
6 & -0.035637 & -0.2108 & 0.417121 \tabularnewline
7 & -0.050052 & -0.2961 & 0.384446 \tabularnewline
8 & -0.06382 & -0.3776 & 0.354017 \tabularnewline
9 & 0.284843 & 1.6852 & 0.050428 \tabularnewline
10 & -0.041468 & -0.2453 & 0.403817 \tabularnewline
11 & 0.039281 & 0.2324 & 0.408794 \tabularnewline
12 & -0.368998 & -2.183 & 0.017915 \tabularnewline
13 & -0.057969 & -0.343 & 0.366843 \tabularnewline
14 & -0.259563 & -1.5356 & 0.066814 \tabularnewline
15 & 0.086583 & 0.5122 & 0.305852 \tabularnewline
16 & -0.156605 & -0.9265 & 0.180269 \tabularnewline
17 & -0.097795 & -0.5786 & 0.283294 \tabularnewline
18 & 0.072351 & 0.428 & 0.335624 \tabularnewline
19 & -0.04725 & -0.2795 & 0.390741 \tabularnewline
20 & -0.005191 & -0.0307 & 0.487837 \tabularnewline
21 & 0.033746 & 0.1996 & 0.421458 \tabularnewline
22 & -0.110749 & -0.6552 & 0.258312 \tabularnewline
23 & 0.070388 & 0.4164 & 0.339823 \tabularnewline
24 & -0.121291 & -0.7176 & 0.238893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33961&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]-0.211378[/C][C]-1.2505[/C][C]0.109701[/C][/ROW]
[ROW][C]2[/C][C]0.08044[/C][C]0.4759[/C][C]0.318555[/C][/ROW]
[ROW][C]3[/C][C]-0.247935[/C][C]-1.4668[/C][C]0.075679[/C][/ROW]
[ROW][C]4[/C][C]-0.218811[/C][C]-1.2945[/C][C]0.101983[/C][/ROW]
[ROW][C]5[/C][C]-0.006469[/C][C]-0.0383[/C][C]0.484845[/C][/ROW]
[ROW][C]6[/C][C]-0.035637[/C][C]-0.2108[/C][C]0.417121[/C][/ROW]
[ROW][C]7[/C][C]-0.050052[/C][C]-0.2961[/C][C]0.384446[/C][/ROW]
[ROW][C]8[/C][C]-0.06382[/C][C]-0.3776[/C][C]0.354017[/C][/ROW]
[ROW][C]9[/C][C]0.284843[/C][C]1.6852[/C][C]0.050428[/C][/ROW]
[ROW][C]10[/C][C]-0.041468[/C][C]-0.2453[/C][C]0.403817[/C][/ROW]
[ROW][C]11[/C][C]0.039281[/C][C]0.2324[/C][C]0.408794[/C][/ROW]
[ROW][C]12[/C][C]-0.368998[/C][C]-2.183[/C][C]0.017915[/C][/ROW]
[ROW][C]13[/C][C]-0.057969[/C][C]-0.343[/C][C]0.366843[/C][/ROW]
[ROW][C]14[/C][C]-0.259563[/C][C]-1.5356[/C][C]0.066814[/C][/ROW]
[ROW][C]15[/C][C]0.086583[/C][C]0.5122[/C][C]0.305852[/C][/ROW]
[ROW][C]16[/C][C]-0.156605[/C][C]-0.9265[/C][C]0.180269[/C][/ROW]
[ROW][C]17[/C][C]-0.097795[/C][C]-0.5786[/C][C]0.283294[/C][/ROW]
[ROW][C]18[/C][C]0.072351[/C][C]0.428[/C][C]0.335624[/C][/ROW]
[ROW][C]19[/C][C]-0.04725[/C][C]-0.2795[/C][C]0.390741[/C][/ROW]
[ROW][C]20[/C][C]-0.005191[/C][C]-0.0307[/C][C]0.487837[/C][/ROW]
[ROW][C]21[/C][C]0.033746[/C][C]0.1996[/C][C]0.421458[/C][/ROW]
[ROW][C]22[/C][C]-0.110749[/C][C]-0.6552[/C][C]0.258312[/C][/ROW]
[ROW][C]23[/C][C]0.070388[/C][C]0.4164[/C][C]0.339823[/C][/ROW]
[ROW][C]24[/C][C]-0.121291[/C][C]-0.7176[/C][C]0.238893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33961&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33961&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	-0.211378	-1.2505	0.109701
2	0.08044	0.4759	0.318555
3	-0.247935	-1.4668	0.075679
4	-0.218811	-1.2945	0.101983
5	-0.006469	-0.0383	0.484845
6	-0.035637	-0.2108	0.417121
7	-0.050052	-0.2961	0.384446
8	-0.06382	-0.3776	0.354017
9	0.284843	1.6852	0.050428
10	-0.041468	-0.2453	0.403817
11	0.039281	0.2324	0.408794
12	-0.368998	-2.183	0.017915
13	-0.057969	-0.343	0.366843
14	-0.259563	-1.5356	0.066814
15	0.086583	0.5122	0.305852
16	-0.156605	-0.9265	0.180269
17	-0.097795	-0.5786	0.283294
18	0.072351	0.428	0.335624
19	-0.04725	-0.2795	0.390741
20	-0.005191	-0.0307	0.487837
21	0.033746	0.1996	0.421458
22	-0.110749	-0.6552	0.258312
23	0.070388	0.4164	0.339823
24	-0.121291	-0.7176	0.238893

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 2 ; par5 = 12 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 2 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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