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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 10 Dec 2010 17:29:50 +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/10/t1292002092oc9akk4nroxrcgd.htm/, Retrieved Mon, 29 Apr 2024 12:50:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107852, Retrieved Mon, 29 Apr 2024 12:50:30 +0000

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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)

-     [(Partial) Autocorrelation Function] [Paper: PACF 1] [2010-12-10 17:20:31] [7d64bf19f34ddcdf2626356c9d5bd60d]
-   P   [(Partial) Autocorrelation Function] [paper ACF 2] [2010-12-10 17:26:39] [7d64bf19f34ddcdf2626356c9d5bd60d]
-   P       [(Partial) Autocorrelation Function] [ACF 3] [2010-12-10 17:29:50] [5842cf9dd57f9603e676e11284d3404a] [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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107852&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107852&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107852&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.21522	1.4755	0.073377
2	0.258221	1.7703	0.041584
3	0.337508	2.3138	0.012549
4	0.186229	1.2767	0.103986
5	0.049884	0.342	0.366943
6	0.1687	1.1565	0.126651
7	0.013192	0.0904	0.46416
8	0.063423	0.4348	0.332846
9	-0.05929	-0.4065	0.343122
10	-0.091693	-0.6286	0.266322
11	0.090481	0.6203	0.269026
12	-0.186807	-1.2807	0.103295
13	-0.137569	-0.9431	0.17522
14	-0.0262	-0.1796	0.429114
15	-0.089258	-0.6119	0.27177
16	-0.147677	-1.0124	0.158261
17	-0.041666	-0.2856	0.388202
18	-0.181829	-1.2466	0.109369
19	-0.134388	-0.9213	0.180794
20	-0.156766	-1.0747	0.143991
21	-0.281196	-1.9278	0.029968
22	-0.166198	-1.1394	0.130156
23	-0.166446	-1.1411	0.129806
24	-0.180189	-1.2353	0.111426

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.21522 & 1.4755 & 0.073377 \tabularnewline
2 & 0.258221 & 1.7703 & 0.041584 \tabularnewline
3 & 0.337508 & 2.3138 & 0.012549 \tabularnewline
4 & 0.186229 & 1.2767 & 0.103986 \tabularnewline
5 & 0.049884 & 0.342 & 0.366943 \tabularnewline
6 & 0.1687 & 1.1565 & 0.126651 \tabularnewline
7 & 0.013192 & 0.0904 & 0.46416 \tabularnewline
8 & 0.063423 & 0.4348 & 0.332846 \tabularnewline
9 & -0.05929 & -0.4065 & 0.343122 \tabularnewline
10 & -0.091693 & -0.6286 & 0.266322 \tabularnewline
11 & 0.090481 & 0.6203 & 0.269026 \tabularnewline
12 & -0.186807 & -1.2807 & 0.103295 \tabularnewline
13 & -0.137569 & -0.9431 & 0.17522 \tabularnewline
14 & -0.0262 & -0.1796 & 0.429114 \tabularnewline
15 & -0.089258 & -0.6119 & 0.27177 \tabularnewline
16 & -0.147677 & -1.0124 & 0.158261 \tabularnewline
17 & -0.041666 & -0.2856 & 0.388202 \tabularnewline
18 & -0.181829 & -1.2466 & 0.109369 \tabularnewline
19 & -0.134388 & -0.9213 & 0.180794 \tabularnewline
20 & -0.156766 & -1.0747 & 0.143991 \tabularnewline
21 & -0.281196 & -1.9278 & 0.029968 \tabularnewline
22 & -0.166198 & -1.1394 & 0.130156 \tabularnewline
23 & -0.166446 & -1.1411 & 0.129806 \tabularnewline
24 & -0.180189 & -1.2353 & 0.111426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107852&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]0.21522[/C][C]1.4755[/C][C]0.073377[/C][/ROW]
[ROW][C]2[/C][C]0.258221[/C][C]1.7703[/C][C]0.041584[/C][/ROW]
[ROW][C]3[/C][C]0.337508[/C][C]2.3138[/C][C]0.012549[/C][/ROW]
[ROW][C]4[/C][C]0.186229[/C][C]1.2767[/C][C]0.103986[/C][/ROW]
[ROW][C]5[/C][C]0.049884[/C][C]0.342[/C][C]0.366943[/C][/ROW]
[ROW][C]6[/C][C]0.1687[/C][C]1.1565[/C][C]0.126651[/C][/ROW]
[ROW][C]7[/C][C]0.013192[/C][C]0.0904[/C][C]0.46416[/C][/ROW]
[ROW][C]8[/C][C]0.063423[/C][C]0.4348[/C][C]0.332846[/C][/ROW]
[ROW][C]9[/C][C]-0.05929[/C][C]-0.4065[/C][C]0.343122[/C][/ROW]
[ROW][C]10[/C][C]-0.091693[/C][C]-0.6286[/C][C]0.266322[/C][/ROW]
[ROW][C]11[/C][C]0.090481[/C][C]0.6203[/C][C]0.269026[/C][/ROW]
[ROW][C]12[/C][C]-0.186807[/C][C]-1.2807[/C][C]0.103295[/C][/ROW]
[ROW][C]13[/C][C]-0.137569[/C][C]-0.9431[/C][C]0.17522[/C][/ROW]
[ROW][C]14[/C][C]-0.0262[/C][C]-0.1796[/C][C]0.429114[/C][/ROW]
[ROW][C]15[/C][C]-0.089258[/C][C]-0.6119[/C][C]0.27177[/C][/ROW]
[ROW][C]16[/C][C]-0.147677[/C][C]-1.0124[/C][C]0.158261[/C][/ROW]
[ROW][C]17[/C][C]-0.041666[/C][C]-0.2856[/C][C]0.388202[/C][/ROW]
[ROW][C]18[/C][C]-0.181829[/C][C]-1.2466[/C][C]0.109369[/C][/ROW]
[ROW][C]19[/C][C]-0.134388[/C][C]-0.9213[/C][C]0.180794[/C][/ROW]
[ROW][C]20[/C][C]-0.156766[/C][C]-1.0747[/C][C]0.143991[/C][/ROW]
[ROW][C]21[/C][C]-0.281196[/C][C]-1.9278[/C][C]0.029968[/C][/ROW]
[ROW][C]22[/C][C]-0.166198[/C][C]-1.1394[/C][C]0.130156[/C][/ROW]
[ROW][C]23[/C][C]-0.166446[/C][C]-1.1411[/C][C]0.129806[/C][/ROW]
[ROW][C]24[/C][C]-0.180189[/C][C]-1.2353[/C][C]0.111426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107852&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107852&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	0.21522	1.4755	0.073377
2	0.258221	1.7703	0.041584
3	0.337508	2.3138	0.012549
4	0.186229	1.2767	0.103986
5	0.049884	0.342	0.366943
6	0.1687	1.1565	0.126651
7	0.013192	0.0904	0.46416
8	0.063423	0.4348	0.332846
9	-0.05929	-0.4065	0.343122
10	-0.091693	-0.6286	0.266322
11	0.090481	0.6203	0.269026
12	-0.186807	-1.2807	0.103295
13	-0.137569	-0.9431	0.17522
14	-0.0262	-0.1796	0.429114
15	-0.089258	-0.6119	0.27177
16	-0.147677	-1.0124	0.158261
17	-0.041666	-0.2856	0.388202
18	-0.181829	-1.2466	0.109369
19	-0.134388	-0.9213	0.180794
20	-0.156766	-1.0747	0.143991
21	-0.281196	-1.9278	0.029968
22	-0.166198	-1.1394	0.130156
23	-0.166446	-1.1411	0.129806
24	-0.180189	-1.2353	0.111426

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.21522	1.4755	0.073377
2	0.222193	1.5233	0.067195
3	0.271854	1.8637	0.034306
4	0.054771	0.3755	0.354492
5	-0.124371	-0.8526	0.19909
6	0.047788	0.3276	0.372327
7	-0.074487	-0.5107	0.305991
8	0.051997	0.3565	0.361541
9	-0.125388	-0.8596	0.197181
10	-0.111046	-0.7613	0.225143
11	0.175097	1.2004	0.117998
12	-0.189317	-1.2979	0.100329
13	-0.05852	-0.4012	0.345048
14	-0.001854	-0.0127	0.494956
15	0.041529	0.2847	0.38856
16	-0.015554	-0.1066	0.457766
17	-0.058659	-0.4021	0.344699
18	-0.113369	-0.7772	0.220462
19	-0.074846	-0.5131	0.305136
20	-0.037377	-0.2562	0.399441
21	-0.209842	-1.4386	0.078444
22	-0.079661	-0.5461	0.29378
23	0.031495	0.2159	0.414992
24	0.031909	0.2188	0.413893

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.21522 & 1.4755 & 0.073377 \tabularnewline
2 & 0.222193 & 1.5233 & 0.067195 \tabularnewline
3 & 0.271854 & 1.8637 & 0.034306 \tabularnewline
4 & 0.054771 & 0.3755 & 0.354492 \tabularnewline
5 & -0.124371 & -0.8526 & 0.19909 \tabularnewline
6 & 0.047788 & 0.3276 & 0.372327 \tabularnewline
7 & -0.074487 & -0.5107 & 0.305991 \tabularnewline
8 & 0.051997 & 0.3565 & 0.361541 \tabularnewline
9 & -0.125388 & -0.8596 & 0.197181 \tabularnewline
10 & -0.111046 & -0.7613 & 0.225143 \tabularnewline
11 & 0.175097 & 1.2004 & 0.117998 \tabularnewline
12 & -0.189317 & -1.2979 & 0.100329 \tabularnewline
13 & -0.05852 & -0.4012 & 0.345048 \tabularnewline
14 & -0.001854 & -0.0127 & 0.494956 \tabularnewline
15 & 0.041529 & 0.2847 & 0.38856 \tabularnewline
16 & -0.015554 & -0.1066 & 0.457766 \tabularnewline
17 & -0.058659 & -0.4021 & 0.344699 \tabularnewline
18 & -0.113369 & -0.7772 & 0.220462 \tabularnewline
19 & -0.074846 & -0.5131 & 0.305136 \tabularnewline
20 & -0.037377 & -0.2562 & 0.399441 \tabularnewline
21 & -0.209842 & -1.4386 & 0.078444 \tabularnewline
22 & -0.079661 & -0.5461 & 0.29378 \tabularnewline
23 & 0.031495 & 0.2159 & 0.414992 \tabularnewline
24 & 0.031909 & 0.2188 & 0.413893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107852&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]0.21522[/C][C]1.4755[/C][C]0.073377[/C][/ROW]
[ROW][C]2[/C][C]0.222193[/C][C]1.5233[/C][C]0.067195[/C][/ROW]
[ROW][C]3[/C][C]0.271854[/C][C]1.8637[/C][C]0.034306[/C][/ROW]
[ROW][C]4[/C][C]0.054771[/C][C]0.3755[/C][C]0.354492[/C][/ROW]
[ROW][C]5[/C][C]-0.124371[/C][C]-0.8526[/C][C]0.19909[/C][/ROW]
[ROW][C]6[/C][C]0.047788[/C][C]0.3276[/C][C]0.372327[/C][/ROW]
[ROW][C]7[/C][C]-0.074487[/C][C]-0.5107[/C][C]0.305991[/C][/ROW]
[ROW][C]8[/C][C]0.051997[/C][C]0.3565[/C][C]0.361541[/C][/ROW]
[ROW][C]9[/C][C]-0.125388[/C][C]-0.8596[/C][C]0.197181[/C][/ROW]
[ROW][C]10[/C][C]-0.111046[/C][C]-0.7613[/C][C]0.225143[/C][/ROW]
[ROW][C]11[/C][C]0.175097[/C][C]1.2004[/C][C]0.117998[/C][/ROW]
[ROW][C]12[/C][C]-0.189317[/C][C]-1.2979[/C][C]0.100329[/C][/ROW]
[ROW][C]13[/C][C]-0.05852[/C][C]-0.4012[/C][C]0.345048[/C][/ROW]
[ROW][C]14[/C][C]-0.001854[/C][C]-0.0127[/C][C]0.494956[/C][/ROW]
[ROW][C]15[/C][C]0.041529[/C][C]0.2847[/C][C]0.38856[/C][/ROW]
[ROW][C]16[/C][C]-0.015554[/C][C]-0.1066[/C][C]0.457766[/C][/ROW]
[ROW][C]17[/C][C]-0.058659[/C][C]-0.4021[/C][C]0.344699[/C][/ROW]
[ROW][C]18[/C][C]-0.113369[/C][C]-0.7772[/C][C]0.220462[/C][/ROW]
[ROW][C]19[/C][C]-0.074846[/C][C]-0.5131[/C][C]0.305136[/C][/ROW]
[ROW][C]20[/C][C]-0.037377[/C][C]-0.2562[/C][C]0.399441[/C][/ROW]
[ROW][C]21[/C][C]-0.209842[/C][C]-1.4386[/C][C]0.078444[/C][/ROW]
[ROW][C]22[/C][C]-0.079661[/C][C]-0.5461[/C][C]0.29378[/C][/ROW]
[ROW][C]23[/C][C]0.031495[/C][C]0.2159[/C][C]0.414992[/C][/ROW]
[ROW][C]24[/C][C]0.031909[/C][C]0.2188[/C][C]0.413893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107852&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107852&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	0.21522	1.4755	0.073377
2	0.222193	1.5233	0.067195
3	0.271854	1.8637	0.034306
4	0.054771	0.3755	0.354492
5	-0.124371	-0.8526	0.19909
6	0.047788	0.3276	0.372327
7	-0.074487	-0.5107	0.305991
8	0.051997	0.3565	0.361541
9	-0.125388	-0.8596	0.197181
10	-0.111046	-0.7613	0.225143
11	0.175097	1.2004	0.117998
12	-0.189317	-1.2979	0.100329
13	-0.05852	-0.4012	0.345048
14	-0.001854	-0.0127	0.494956
15	0.041529	0.2847	0.38856
16	-0.015554	-0.1066	0.457766
17	-0.058659	-0.4021	0.344699
18	-0.113369	-0.7772	0.220462
19	-0.074846	-0.5131	0.305136
20	-0.037377	-0.2562	0.399441
21	-0.209842	-1.4386	0.078444
22	-0.079661	-0.5461	0.29378
23	0.031495	0.2159	0.414992
24	0.031909	0.2188	0.413893

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

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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