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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 09 Dec 2008 07:06:56 -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/09/t122883167584fpkx595dw7o4r.htm/, Retrieved Sun, 19 May 2024 09:22:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31416, Retrieved Sun, 19 May 2024 09:22:48 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

180

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Variance Reduction Matrix] [] [2008-12-02 14:53:11] [3ba9e05a140f75dbe22af2042ab9e185]
F RMP       [(Partial) Autocorrelation Function] [] [2008-12-09 14:06:56] [84357e896eab491ec515599b43df427d] [Current]

Feedback Forum

2008-12-16 09:12:12 [Katja van Hek] [reply] 
De ACF grafiek laat een op en neergaand patroon zien dat enkel significant is bij lag 12. Je kunt er vanuit gaan dat bij meerdere observaties seizoenaliteit zichtbaar is. Als je volgens de VRM D gelijkstelt aan 1 zul je zien dat die seizoenaliteit verdwenen is en er geen significante waarden meer zijn.

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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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31416&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31416&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31416&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.037867	0.2958	0.384211
2	-0.123003	-0.9607	0.170252
3	-0.219043	-1.7108	0.046101
4	-0.254627	-1.9887	0.025613
5	0.163618	1.2779	0.103063
6	0.144868	1.1315	0.131146
7	0.189303	1.4785	0.072209
8	-0.16722	-1.306	0.098223
9	-0.257042	-2.0076	0.024563
10	-0.167133	-1.3054	0.098338
11	0.023876	0.1865	0.426344
12	0.579929	4.5294	1.4e-05
13	0.066283	0.5177	0.303275
14	-0.110755	-0.865	0.195207
15	-0.11709	-0.9145	0.182027
16	-0.25903	-2.0231	0.023726
17	0.070771	0.5527	0.29123

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.037867 & 0.2958 & 0.384211 \tabularnewline
2 & -0.123003 & -0.9607 & 0.170252 \tabularnewline
3 & -0.219043 & -1.7108 & 0.046101 \tabularnewline
4 & -0.254627 & -1.9887 & 0.025613 \tabularnewline
5 & 0.163618 & 1.2779 & 0.103063 \tabularnewline
6 & 0.144868 & 1.1315 & 0.131146 \tabularnewline
7 & 0.189303 & 1.4785 & 0.072209 \tabularnewline
8 & -0.16722 & -1.306 & 0.098223 \tabularnewline
9 & -0.257042 & -2.0076 & 0.024563 \tabularnewline
10 & -0.167133 & -1.3054 & 0.098338 \tabularnewline
11 & 0.023876 & 0.1865 & 0.426344 \tabularnewline
12 & 0.579929 & 4.5294 & 1.4e-05 \tabularnewline
13 & 0.066283 & 0.5177 & 0.303275 \tabularnewline
14 & -0.110755 & -0.865 & 0.195207 \tabularnewline
15 & -0.11709 & -0.9145 & 0.182027 \tabularnewline
16 & -0.25903 & -2.0231 & 0.023726 \tabularnewline
17 & 0.070771 & 0.5527 & 0.29123 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31416&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]0.037867[/C][C]0.2958[/C][C]0.384211[/C][/ROW]
[ROW][C]2[/C][C]-0.123003[/C][C]-0.9607[/C][C]0.170252[/C][/ROW]
[ROW][C]3[/C][C]-0.219043[/C][C]-1.7108[/C][C]0.046101[/C][/ROW]
[ROW][C]4[/C][C]-0.254627[/C][C]-1.9887[/C][C]0.025613[/C][/ROW]
[ROW][C]5[/C][C]0.163618[/C][C]1.2779[/C][C]0.103063[/C][/ROW]
[ROW][C]6[/C][C]0.144868[/C][C]1.1315[/C][C]0.131146[/C][/ROW]
[ROW][C]7[/C][C]0.189303[/C][C]1.4785[/C][C]0.072209[/C][/ROW]
[ROW][C]8[/C][C]-0.16722[/C][C]-1.306[/C][C]0.098223[/C][/ROW]
[ROW][C]9[/C][C]-0.257042[/C][C]-2.0076[/C][C]0.024563[/C][/ROW]
[ROW][C]10[/C][C]-0.167133[/C][C]-1.3054[/C][C]0.098338[/C][/ROW]
[ROW][C]11[/C][C]0.023876[/C][C]0.1865[/C][C]0.426344[/C][/ROW]
[ROW][C]12[/C][C]0.579929[/C][C]4.5294[/C][C]1.4e-05[/C][/ROW]
[ROW][C]13[/C][C]0.066283[/C][C]0.5177[/C][C]0.303275[/C][/ROW]
[ROW][C]14[/C][C]-0.110755[/C][C]-0.865[/C][C]0.195207[/C][/ROW]
[ROW][C]15[/C][C]-0.11709[/C][C]-0.9145[/C][C]0.182027[/C][/ROW]
[ROW][C]16[/C][C]-0.25903[/C][C]-2.0231[/C][C]0.023726[/C][/ROW]
[ROW][C]17[/C][C]0.070771[/C][C]0.5527[/C][C]0.29123[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31416&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31416&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	0.037867	0.2958	0.384211
2	-0.123003	-0.9607	0.170252
3	-0.219043	-1.7108	0.046101
4	-0.254627	-1.9887	0.025613
5	0.163618	1.2779	0.103063
6	0.144868	1.1315	0.131146
7	0.189303	1.4785	0.072209
8	-0.16722	-1.306	0.098223
9	-0.257042	-2.0076	0.024563
10	-0.167133	-1.3054	0.098338
11	0.023876	0.1865	0.426344
12	0.579929	4.5294	1.4e-05
13	0.066283	0.5177	0.303275
14	-0.110755	-0.865	0.195207
15	-0.11709	-0.9145	0.182027
16	-0.25903	-2.0231	0.023726
17	0.070771	0.5527	0.29123

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.037867	0.2958	0.384211
2	-0.124616	-0.9733	0.167129
3	-0.212689	-1.6612	0.050907
4	-0.274097	-2.1408	0.018149
5	0.121394	0.9481	0.173406
6	0.041963	0.3277	0.372113
7	0.138898	1.0848	0.141133
8	-0.181152	-1.4148	0.0811
9	-0.140331	-1.096	0.138689
10	-0.163531	-1.2772	0.103183
11	-0.02308	-0.1803	0.428773
12	0.467147	3.6485	0.000274
13	-0.019095	-0.1491	0.440969
14	-0.08124	-0.6345	0.264062
15	0.105183	0.8215	0.207279
16	-0.032599	-0.2546	0.399943
17	-0.081941	-0.64	0.262291

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.037867 & 0.2958 & 0.384211 \tabularnewline
2 & -0.124616 & -0.9733 & 0.167129 \tabularnewline
3 & -0.212689 & -1.6612 & 0.050907 \tabularnewline
4 & -0.274097 & -2.1408 & 0.018149 \tabularnewline
5 & 0.121394 & 0.9481 & 0.173406 \tabularnewline
6 & 0.041963 & 0.3277 & 0.372113 \tabularnewline
7 & 0.138898 & 1.0848 & 0.141133 \tabularnewline
8 & -0.181152 & -1.4148 & 0.0811 \tabularnewline
9 & -0.140331 & -1.096 & 0.138689 \tabularnewline
10 & -0.163531 & -1.2772 & 0.103183 \tabularnewline
11 & -0.02308 & -0.1803 & 0.428773 \tabularnewline
12 & 0.467147 & 3.6485 & 0.000274 \tabularnewline
13 & -0.019095 & -0.1491 & 0.440969 \tabularnewline
14 & -0.08124 & -0.6345 & 0.264062 \tabularnewline
15 & 0.105183 & 0.8215 & 0.207279 \tabularnewline
16 & -0.032599 & -0.2546 & 0.399943 \tabularnewline
17 & -0.081941 & -0.64 & 0.262291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31416&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]0.037867[/C][C]0.2958[/C][C]0.384211[/C][/ROW]
[ROW][C]2[/C][C]-0.124616[/C][C]-0.9733[/C][C]0.167129[/C][/ROW]
[ROW][C]3[/C][C]-0.212689[/C][C]-1.6612[/C][C]0.050907[/C][/ROW]
[ROW][C]4[/C][C]-0.274097[/C][C]-2.1408[/C][C]0.018149[/C][/ROW]
[ROW][C]5[/C][C]0.121394[/C][C]0.9481[/C][C]0.173406[/C][/ROW]
[ROW][C]6[/C][C]0.041963[/C][C]0.3277[/C][C]0.372113[/C][/ROW]
[ROW][C]7[/C][C]0.138898[/C][C]1.0848[/C][C]0.141133[/C][/ROW]
[ROW][C]8[/C][C]-0.181152[/C][C]-1.4148[/C][C]0.0811[/C][/ROW]
[ROW][C]9[/C][C]-0.140331[/C][C]-1.096[/C][C]0.138689[/C][/ROW]
[ROW][C]10[/C][C]-0.163531[/C][C]-1.2772[/C][C]0.103183[/C][/ROW]
[ROW][C]11[/C][C]-0.02308[/C][C]-0.1803[/C][C]0.428773[/C][/ROW]
[ROW][C]12[/C][C]0.467147[/C][C]3.6485[/C][C]0.000274[/C][/ROW]
[ROW][C]13[/C][C]-0.019095[/C][C]-0.1491[/C][C]0.440969[/C][/ROW]
[ROW][C]14[/C][C]-0.08124[/C][C]-0.6345[/C][C]0.264062[/C][/ROW]
[ROW][C]15[/C][C]0.105183[/C][C]0.8215[/C][C]0.207279[/C][/ROW]
[ROW][C]16[/C][C]-0.032599[/C][C]-0.2546[/C][C]0.399943[/C][/ROW]
[ROW][C]17[/C][C]-0.081941[/C][C]-0.64[/C][C]0.262291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31416&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31416&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	0.037867	0.2958	0.384211
2	-0.124616	-0.9733	0.167129
3	-0.212689	-1.6612	0.050907
4	-0.274097	-2.1408	0.018149
5	0.121394	0.9481	0.173406
6	0.041963	0.3277	0.372113
7	0.138898	1.0848	0.141133
8	-0.181152	-1.4148	0.0811
9	-0.140331	-1.096	0.138689
10	-0.163531	-1.2772	0.103183
11	-0.02308	-0.1803	0.428773
12	0.467147	3.6485	0.000274
13	-0.019095	-0.1491	0.440969
14	-0.08124	-0.6345	0.264062
15	0.105183	0.8215	0.207279
16	-0.032599	-0.2546	0.399943
17	-0.081941	-0.64	0.262291

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

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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Input Parameters & R Code