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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 14 Dec 2010 12:22:21 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/14/t1292329225ns6pf154mdlvqax.htm/, Retrieved Fri, 03 May 2024 01:00:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109480, Retrieved Fri, 03 May 2024 01:00:36 +0000

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114

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-       [(Partial) Autocorrelation Function] [] [2010-12-14 12:22:21] [4c4b6062b5416bf30d160a3ba34752af] [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=109480&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=109480&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109480&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	-0.750421	-5.5144	1e-06
2	0.450994	3.3141	0.000823
3	-0.303132	-2.2276	0.015049
4	0.140343	1.0313	0.153497
5	-0.048221	-0.3544	0.362227
6	0.086818	0.638	0.263092
7	-0.133082	-0.978	0.16623
8	0.04221	0.3102	0.378811
9	0.091366	0.6714	0.252414
10	-0.177283	-1.3028	0.099093
11	0.326464	2.399	0.009961
12	-0.403364	-2.9641	0.002255
13	0.252852	1.8581	0.034306
14	-0.110645	-0.8131	0.209874
15	0.060657	0.4457	0.328785
16	0.000601	0.0044	0.498245
17	-0.004474	-0.0329	0.486946
18	-0.107461	-0.7897	0.216586
19	0.229143	1.6838	0.048992

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.750421 & -5.5144 & 1e-06 \tabularnewline
2 & 0.450994 & 3.3141 & 0.000823 \tabularnewline
3 & -0.303132 & -2.2276 & 0.015049 \tabularnewline
4 & 0.140343 & 1.0313 & 0.153497 \tabularnewline
5 & -0.048221 & -0.3544 & 0.362227 \tabularnewline
6 & 0.086818 & 0.638 & 0.263092 \tabularnewline
7 & -0.133082 & -0.978 & 0.16623 \tabularnewline
8 & 0.04221 & 0.3102 & 0.378811 \tabularnewline
9 & 0.091366 & 0.6714 & 0.252414 \tabularnewline
10 & -0.177283 & -1.3028 & 0.099093 \tabularnewline
11 & 0.326464 & 2.399 & 0.009961 \tabularnewline
12 & -0.403364 & -2.9641 & 0.002255 \tabularnewline
13 & 0.252852 & 1.8581 & 0.034306 \tabularnewline
14 & -0.110645 & -0.8131 & 0.209874 \tabularnewline
15 & 0.060657 & 0.4457 & 0.328785 \tabularnewline
16 & 0.000601 & 0.0044 & 0.498245 \tabularnewline
17 & -0.004474 & -0.0329 & 0.486946 \tabularnewline
18 & -0.107461 & -0.7897 & 0.216586 \tabularnewline
19 & 0.229143 & 1.6838 & 0.048992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109480&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]-0.750421[/C][C]-5.5144[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.450994[/C][C]3.3141[/C][C]0.000823[/C][/ROW]
[ROW][C]3[/C][C]-0.303132[/C][C]-2.2276[/C][C]0.015049[/C][/ROW]
[ROW][C]4[/C][C]0.140343[/C][C]1.0313[/C][C]0.153497[/C][/ROW]
[ROW][C]5[/C][C]-0.048221[/C][C]-0.3544[/C][C]0.362227[/C][/ROW]
[ROW][C]6[/C][C]0.086818[/C][C]0.638[/C][C]0.263092[/C][/ROW]
[ROW][C]7[/C][C]-0.133082[/C][C]-0.978[/C][C]0.16623[/C][/ROW]
[ROW][C]8[/C][C]0.04221[/C][C]0.3102[/C][C]0.378811[/C][/ROW]
[ROW][C]9[/C][C]0.091366[/C][C]0.6714[/C][C]0.252414[/C][/ROW]
[ROW][C]10[/C][C]-0.177283[/C][C]-1.3028[/C][C]0.099093[/C][/ROW]
[ROW][C]11[/C][C]0.326464[/C][C]2.399[/C][C]0.009961[/C][/ROW]
[ROW][C]12[/C][C]-0.403364[/C][C]-2.9641[/C][C]0.002255[/C][/ROW]
[ROW][C]13[/C][C]0.252852[/C][C]1.8581[/C][C]0.034306[/C][/ROW]
[ROW][C]14[/C][C]-0.110645[/C][C]-0.8131[/C][C]0.209874[/C][/ROW]
[ROW][C]15[/C][C]0.060657[/C][C]0.4457[/C][C]0.328785[/C][/ROW]
[ROW][C]16[/C][C]0.000601[/C][C]0.0044[/C][C]0.498245[/C][/ROW]
[ROW][C]17[/C][C]-0.004474[/C][C]-0.0329[/C][C]0.486946[/C][/ROW]
[ROW][C]18[/C][C]-0.107461[/C][C]-0.7897[/C][C]0.216586[/C][/ROW]
[ROW][C]19[/C][C]0.229143[/C][C]1.6838[/C][C]0.048992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109480&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109480&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	-0.750421	-5.5144	1e-06
2	0.450994	3.3141	0.000823
3	-0.303132	-2.2276	0.015049
4	0.140343	1.0313	0.153497
5	-0.048221	-0.3544	0.362227
6	0.086818	0.638	0.263092
7	-0.133082	-0.978	0.16623
8	0.04221	0.3102	0.378811
9	0.091366	0.6714	0.252414
10	-0.177283	-1.3028	0.099093
11	0.326464	2.399	0.009961
12	-0.403364	-2.9641	0.002255
13	0.252852	1.8581	0.034306
14	-0.110645	-0.8131	0.209874
15	0.060657	0.4457	0.328785
16	0.000601	0.0044	0.498245
17	-0.004474	-0.0329	0.486946
18	-0.107461	-0.7897	0.216586
19	0.229143	1.6838	0.048992

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.750421	-5.5144	1e-06
2	-0.256687	-1.8863	0.032322
3	-0.172632	-1.2686	0.105016
4	-0.250852	-1.8434	0.035382
5	-0.165279	-1.2146	0.114911
6	0.085177	0.6259	0.267002
7	-0.050559	-0.3715	0.355849
8	-0.280977	-2.0648	0.021881
9	0.071286	0.5238	0.301265
10	-0.085825	-0.6307	0.265454
11	0.240065	1.7641	0.041685
12	0.073101	0.5372	0.296675
13	-0.220591	-1.621	0.055421
14	-0.058575	-0.4304	0.334295
15	-0.022549	-0.1657	0.434505
16	0.011222	0.0825	0.467292
17	0.070324	0.5168	0.303711
18	-0.11621	-0.854	0.198447
19	0.154448	1.135	0.130704

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.750421 & -5.5144 & 1e-06 \tabularnewline
2 & -0.256687 & -1.8863 & 0.032322 \tabularnewline
3 & -0.172632 & -1.2686 & 0.105016 \tabularnewline
4 & -0.250852 & -1.8434 & 0.035382 \tabularnewline
5 & -0.165279 & -1.2146 & 0.114911 \tabularnewline
6 & 0.085177 & 0.6259 & 0.267002 \tabularnewline
7 & -0.050559 & -0.3715 & 0.355849 \tabularnewline
8 & -0.280977 & -2.0648 & 0.021881 \tabularnewline
9 & 0.071286 & 0.5238 & 0.301265 \tabularnewline
10 & -0.085825 & -0.6307 & 0.265454 \tabularnewline
11 & 0.240065 & 1.7641 & 0.041685 \tabularnewline
12 & 0.073101 & 0.5372 & 0.296675 \tabularnewline
13 & -0.220591 & -1.621 & 0.055421 \tabularnewline
14 & -0.058575 & -0.4304 & 0.334295 \tabularnewline
15 & -0.022549 & -0.1657 & 0.434505 \tabularnewline
16 & 0.011222 & 0.0825 & 0.467292 \tabularnewline
17 & 0.070324 & 0.5168 & 0.303711 \tabularnewline
18 & -0.11621 & -0.854 & 0.198447 \tabularnewline
19 & 0.154448 & 1.135 & 0.130704 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109480&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]-0.750421[/C][C]-5.5144[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.256687[/C][C]-1.8863[/C][C]0.032322[/C][/ROW]
[ROW][C]3[/C][C]-0.172632[/C][C]-1.2686[/C][C]0.105016[/C][/ROW]
[ROW][C]4[/C][C]-0.250852[/C][C]-1.8434[/C][C]0.035382[/C][/ROW]
[ROW][C]5[/C][C]-0.165279[/C][C]-1.2146[/C][C]0.114911[/C][/ROW]
[ROW][C]6[/C][C]0.085177[/C][C]0.6259[/C][C]0.267002[/C][/ROW]
[ROW][C]7[/C][C]-0.050559[/C][C]-0.3715[/C][C]0.355849[/C][/ROW]
[ROW][C]8[/C][C]-0.280977[/C][C]-2.0648[/C][C]0.021881[/C][/ROW]
[ROW][C]9[/C][C]0.071286[/C][C]0.5238[/C][C]0.301265[/C][/ROW]
[ROW][C]10[/C][C]-0.085825[/C][C]-0.6307[/C][C]0.265454[/C][/ROW]
[ROW][C]11[/C][C]0.240065[/C][C]1.7641[/C][C]0.041685[/C][/ROW]
[ROW][C]12[/C][C]0.073101[/C][C]0.5372[/C][C]0.296675[/C][/ROW]
[ROW][C]13[/C][C]-0.220591[/C][C]-1.621[/C][C]0.055421[/C][/ROW]
[ROW][C]14[/C][C]-0.058575[/C][C]-0.4304[/C][C]0.334295[/C][/ROW]
[ROW][C]15[/C][C]-0.022549[/C][C]-0.1657[/C][C]0.434505[/C][/ROW]
[ROW][C]16[/C][C]0.011222[/C][C]0.0825[/C][C]0.467292[/C][/ROW]
[ROW][C]17[/C][C]0.070324[/C][C]0.5168[/C][C]0.303711[/C][/ROW]
[ROW][C]18[/C][C]-0.11621[/C][C]-0.854[/C][C]0.198447[/C][/ROW]
[ROW][C]19[/C][C]0.154448[/C][C]1.135[/C][C]0.130704[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109480&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109480&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	-0.750421	-5.5144	1e-06
2	-0.256687	-1.8863	0.032322
3	-0.172632	-1.2686	0.105016
4	-0.250852	-1.8434	0.035382
5	-0.165279	-1.2146	0.114911
6	0.085177	0.6259	0.267002
7	-0.050559	-0.3715	0.355849
8	-0.280977	-2.0648	0.021881
9	0.071286	0.5238	0.301265
10	-0.085825	-0.6307	0.265454
11	0.240065	1.7641	0.041685
12	0.073101	0.5372	0.296675
13	-0.220591	-1.621	0.055421
14	-0.058575	-0.4304	0.334295
15	-0.022549	-0.1657	0.434505
16	0.011222	0.0825	0.467292
17	0.070324	0.5168	0.303711
18	-0.11621	-0.854	0.198447
19	0.154448	1.135	0.130704

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 2 ; 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code