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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 13 May 2009 12:54:52 -0600

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/2009/May/13/t1242240957ydkm157xims680z.htm/, Retrieved Thu, 09 May 2024 01:12:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39910, Retrieved Thu, 09 May 2024 01:12:55 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

147

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

-     [(Partial) Autocorrelation Function] [] [2008-12-16 08:41:39] [a18c43c8b63fa6800a53bb187b9ddd45]
-    D    [(Partial) Autocorrelation Function] [Maxime Jonckheere...] [2009-05-13 18:54:52] [d41d8cd98f00b204e9800998ecf8427e] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39910&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39910&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39910&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.980794	9.0425	0
2	0.957303	8.8259	0
3	0.932617	8.5983	0
4	0.90483	8.3421	0
5	0.878339	8.0979	0
6	0.849196	7.8292	0
7	0.818099	7.5425	0
8	0.783533	7.2238	0
9	0.749928	6.914	0
10	0.716216	6.6032	0
11	0.682833	6.2954	0
12	0.649529	5.9884	0
13	0.617454	5.6926	0
14	0.582294	5.3685	0
15	0.544762	5.0225	1e-06
16	0.503934	4.646	6e-06
17	0.457771	4.2204	3e-05
18	0.410416	3.7838	0.000143
19	0.360203	3.3209	0.000662

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.980794 & 9.0425 & 0 \tabularnewline
2 & 0.957303 & 8.8259 & 0 \tabularnewline
3 & 0.932617 & 8.5983 & 0 \tabularnewline
4 & 0.90483 & 8.3421 & 0 \tabularnewline
5 & 0.878339 & 8.0979 & 0 \tabularnewline
6 & 0.849196 & 7.8292 & 0 \tabularnewline
7 & 0.818099 & 7.5425 & 0 \tabularnewline
8 & 0.783533 & 7.2238 & 0 \tabularnewline
9 & 0.749928 & 6.914 & 0 \tabularnewline
10 & 0.716216 & 6.6032 & 0 \tabularnewline
11 & 0.682833 & 6.2954 & 0 \tabularnewline
12 & 0.649529 & 5.9884 & 0 \tabularnewline
13 & 0.617454 & 5.6926 & 0 \tabularnewline
14 & 0.582294 & 5.3685 & 0 \tabularnewline
15 & 0.544762 & 5.0225 & 1e-06 \tabularnewline
16 & 0.503934 & 4.646 & 6e-06 \tabularnewline
17 & 0.457771 & 4.2204 & 3e-05 \tabularnewline
18 & 0.410416 & 3.7838 & 0.000143 \tabularnewline
19 & 0.360203 & 3.3209 & 0.000662 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39910&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]0.980794[/C][C]9.0425[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.957303[/C][C]8.8259[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.932617[/C][C]8.5983[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.90483[/C][C]8.3421[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.878339[/C][C]8.0979[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.849196[/C][C]7.8292[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.818099[/C][C]7.5425[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.783533[/C][C]7.2238[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.749928[/C][C]6.914[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.716216[/C][C]6.6032[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.682833[/C][C]6.2954[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.649529[/C][C]5.9884[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.617454[/C][C]5.6926[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.582294[/C][C]5.3685[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.544762[/C][C]5.0225[/C][C]1e-06[/C][/ROW]
[ROW][C]16[/C][C]0.503934[/C][C]4.646[/C][C]6e-06[/C][/ROW]
[ROW][C]17[/C][C]0.457771[/C][C]4.2204[/C][C]3e-05[/C][/ROW]
[ROW][C]18[/C][C]0.410416[/C][C]3.7838[/C][C]0.000143[/C][/ROW]
[ROW][C]19[/C][C]0.360203[/C][C]3.3209[/C][C]0.000662[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39910&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39910&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	0.980794	9.0425	0
2	0.957303	8.8259	0
3	0.932617	8.5983	0
4	0.90483	8.3421	0
5	0.878339	8.0979	0
6	0.849196	7.8292	0
7	0.818099	7.5425	0
8	0.783533	7.2238	0
9	0.749928	6.914	0
10	0.716216	6.6032	0
11	0.682833	6.2954	0
12	0.649529	5.9884	0
13	0.617454	5.6926	0
14	0.582294	5.3685	0
15	0.544762	5.0225	1e-06
16	0.503934	4.646	6e-06
17	0.457771	4.2204	3e-05
18	0.410416	3.7838	0.000143
19	0.360203	3.3209	0.000662

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.980794	9.0425	0
2	-0.122364	-1.1281	0.131217
3	-0.031391	-0.2894	0.386485
4	-0.090086	-0.8306	0.204277
5	0.037753	0.3481	0.364326
6	-0.091832	-0.8466	0.199785
7	-0.047713	-0.4399	0.330565
8	-0.107872	-0.9945	0.161394
9	0.041168	0.3796	0.352612
10	-0.031267	-0.2883	0.38692
11	0.005852	0.054	0.478548
12	-0.033924	-0.3128	0.377614
13	0.035209	0.3246	0.373135
14	-0.118653	-1.0939	0.138539
15	-0.058621	-0.5405	0.295148
16	-0.125705	-1.1589	0.124862
17	-0.135685	-1.251	0.107191
18	-0.060492	-0.5577	0.289256
19	-0.097258	-0.8967	0.186214

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.980794 & 9.0425 & 0 \tabularnewline
2 & -0.122364 & -1.1281 & 0.131217 \tabularnewline
3 & -0.031391 & -0.2894 & 0.386485 \tabularnewline
4 & -0.090086 & -0.8306 & 0.204277 \tabularnewline
5 & 0.037753 & 0.3481 & 0.364326 \tabularnewline
6 & -0.091832 & -0.8466 & 0.199785 \tabularnewline
7 & -0.047713 & -0.4399 & 0.330565 \tabularnewline
8 & -0.107872 & -0.9945 & 0.161394 \tabularnewline
9 & 0.041168 & 0.3796 & 0.352612 \tabularnewline
10 & -0.031267 & -0.2883 & 0.38692 \tabularnewline
11 & 0.005852 & 0.054 & 0.478548 \tabularnewline
12 & -0.033924 & -0.3128 & 0.377614 \tabularnewline
13 & 0.035209 & 0.3246 & 0.373135 \tabularnewline
14 & -0.118653 & -1.0939 & 0.138539 \tabularnewline
15 & -0.058621 & -0.5405 & 0.295148 \tabularnewline
16 & -0.125705 & -1.1589 & 0.124862 \tabularnewline
17 & -0.135685 & -1.251 & 0.107191 \tabularnewline
18 & -0.060492 & -0.5577 & 0.289256 \tabularnewline
19 & -0.097258 & -0.8967 & 0.186214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39910&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]0.980794[/C][C]9.0425[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.122364[/C][C]-1.1281[/C][C]0.131217[/C][/ROW]
[ROW][C]3[/C][C]-0.031391[/C][C]-0.2894[/C][C]0.386485[/C][/ROW]
[ROW][C]4[/C][C]-0.090086[/C][C]-0.8306[/C][C]0.204277[/C][/ROW]
[ROW][C]5[/C][C]0.037753[/C][C]0.3481[/C][C]0.364326[/C][/ROW]
[ROW][C]6[/C][C]-0.091832[/C][C]-0.8466[/C][C]0.199785[/C][/ROW]
[ROW][C]7[/C][C]-0.047713[/C][C]-0.4399[/C][C]0.330565[/C][/ROW]
[ROW][C]8[/C][C]-0.107872[/C][C]-0.9945[/C][C]0.161394[/C][/ROW]
[ROW][C]9[/C][C]0.041168[/C][C]0.3796[/C][C]0.352612[/C][/ROW]
[ROW][C]10[/C][C]-0.031267[/C][C]-0.2883[/C][C]0.38692[/C][/ROW]
[ROW][C]11[/C][C]0.005852[/C][C]0.054[/C][C]0.478548[/C][/ROW]
[ROW][C]12[/C][C]-0.033924[/C][C]-0.3128[/C][C]0.377614[/C][/ROW]
[ROW][C]13[/C][C]0.035209[/C][C]0.3246[/C][C]0.373135[/C][/ROW]
[ROW][C]14[/C][C]-0.118653[/C][C]-1.0939[/C][C]0.138539[/C][/ROW]
[ROW][C]15[/C][C]-0.058621[/C][C]-0.5405[/C][C]0.295148[/C][/ROW]
[ROW][C]16[/C][C]-0.125705[/C][C]-1.1589[/C][C]0.124862[/C][/ROW]
[ROW][C]17[/C][C]-0.135685[/C][C]-1.251[/C][C]0.107191[/C][/ROW]
[ROW][C]18[/C][C]-0.060492[/C][C]-0.5577[/C][C]0.289256[/C][/ROW]
[ROW][C]19[/C][C]-0.097258[/C][C]-0.8967[/C][C]0.186214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39910&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39910&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	0.980794	9.0425	0
2	-0.122364	-1.1281	0.131217
3	-0.031391	-0.2894	0.386485
4	-0.090086	-0.8306	0.204277
5	0.037753	0.3481	0.364326
6	-0.091832	-0.8466	0.199785
7	-0.047713	-0.4399	0.330565
8	-0.107872	-0.9945	0.161394
9	0.041168	0.3796	0.352612
10	-0.031267	-0.2883	0.38692
11	0.005852	0.054	0.478548
12	-0.033924	-0.3128	0.377614
13	0.035209	0.3246	0.373135
14	-0.118653	-1.0939	0.138539
15	-0.058621	-0.5405	0.295148
16	-0.125705	-1.1589	0.124862
17	-0.135685	-1.251	0.107191
18	-0.060492	-0.5577	0.289256
19	-0.097258	-0.8967	0.186214

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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')

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Dataset

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Figures (Output of Computation)

Input Parameters & R Code