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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 08 Dec 2007 02:18:50 -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/2007/Dec/08/t1197104736h0i1dwnv09el9mp.htm/, Retrieved Sun, 28 Apr 2024 21:04:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2901, Retrieved Sun, 28 Apr 2024 21:04:54 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

PAF-25D1

Estimated Impact

247

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

-       [(Partial) Autocorrelation Function] [autocorrelation f...] [2007-12-08 09:18:50] [65108f21b143a71c6470aac06bd65b08] [Current]

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Summary of compuational 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 compuational 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=2901&T=0

[TABLE]
[ROW][C]Summary of compuational 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=2901&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2901&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 compuational 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
0	1	7.8102	0
1	0.917161	7.1633	0
2	0.852366	6.6572	0
3	0.777364	6.0714	0
4	0.706191	5.5155	0
5	0.651606	5.0892	2e-06
6	0.618525	4.8308	5e-06
7	0.586191	4.5783	1.2e-05
8	0.533521	4.1669	4.9e-05
9	0.4971	3.8825	0.000128
10	0.422129	3.2969	0.000816
11	0.355951	2.7801	0.003609
12	0.289503	2.2611	0.013666
13	0.248048	1.9373	0.02867
14	0.211458	1.6515	0.051884
15	0.175596	1.3714	0.08763
16	0.151169	1.1807	0.121159
17	0.131487	1.0269	0.15425

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.8102 & 0 \tabularnewline
1 & 0.917161 & 7.1633 & 0 \tabularnewline
2 & 0.852366 & 6.6572 & 0 \tabularnewline
3 & 0.777364 & 6.0714 & 0 \tabularnewline
4 & 0.706191 & 5.5155 & 0 \tabularnewline
5 & 0.651606 & 5.0892 & 2e-06 \tabularnewline
6 & 0.618525 & 4.8308 & 5e-06 \tabularnewline
7 & 0.586191 & 4.5783 & 1.2e-05 \tabularnewline
8 & 0.533521 & 4.1669 & 4.9e-05 \tabularnewline
9 & 0.4971 & 3.8825 & 0.000128 \tabularnewline
10 & 0.422129 & 3.2969 & 0.000816 \tabularnewline
11 & 0.355951 & 2.7801 & 0.003609 \tabularnewline
12 & 0.289503 & 2.2611 & 0.013666 \tabularnewline
13 & 0.248048 & 1.9373 & 0.02867 \tabularnewline
14 & 0.211458 & 1.6515 & 0.051884 \tabularnewline
15 & 0.175596 & 1.3714 & 0.08763 \tabularnewline
16 & 0.151169 & 1.1807 & 0.121159 \tabularnewline
17 & 0.131487 & 1.0269 & 0.15425 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2901&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]0[/C][C]1[/C][C]7.8102[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.917161[/C][C]7.1633[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.852366[/C][C]6.6572[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.777364[/C][C]6.0714[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.706191[/C][C]5.5155[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.651606[/C][C]5.0892[/C][C]2e-06[/C][/ROW]
[ROW][C]6[/C][C]0.618525[/C][C]4.8308[/C][C]5e-06[/C][/ROW]
[ROW][C]7[/C][C]0.586191[/C][C]4.5783[/C][C]1.2e-05[/C][/ROW]
[ROW][C]8[/C][C]0.533521[/C][C]4.1669[/C][C]4.9e-05[/C][/ROW]
[ROW][C]9[/C][C]0.4971[/C][C]3.8825[/C][C]0.000128[/C][/ROW]
[ROW][C]10[/C][C]0.422129[/C][C]3.2969[/C][C]0.000816[/C][/ROW]
[ROW][C]11[/C][C]0.355951[/C][C]2.7801[/C][C]0.003609[/C][/ROW]
[ROW][C]12[/C][C]0.289503[/C][C]2.2611[/C][C]0.013666[/C][/ROW]
[ROW][C]13[/C][C]0.248048[/C][C]1.9373[/C][C]0.02867[/C][/ROW]
[ROW][C]14[/C][C]0.211458[/C][C]1.6515[/C][C]0.051884[/C][/ROW]
[ROW][C]15[/C][C]0.175596[/C][C]1.3714[/C][C]0.08763[/C][/ROW]
[ROW][C]16[/C][C]0.151169[/C][C]1.1807[/C][C]0.121159[/C][/ROW]
[ROW][C]17[/C][C]0.131487[/C][C]1.0269[/C][C]0.15425[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2901&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2901&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
0	1	7.8102	0
1	0.917161	7.1633	0
2	0.852366	6.6572	0
3	0.777364	6.0714	0
4	0.706191	5.5155	0
5	0.651606	5.0892	2e-06
6	0.618525	4.8308	5e-06
7	0.586191	4.5783	1.2e-05
8	0.533521	4.1669	4.9e-05
9	0.4971	3.8825	0.000128
10	0.422129	3.2969	0.000816
11	0.355951	2.7801	0.003609
12	0.289503	2.2611	0.013666
13	0.248048	1.9373	0.02867
14	0.211458	1.6515	0.051884
15	0.175596	1.3714	0.08763
16	0.151169	1.1807	0.121159
17	0.131487	1.0269	0.15425

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.917161	7.1633	0
1	0.07041	0.5499	0.292191
2	-0.088125	-0.6883	0.753057
3	-0.029544	-0.2307	0.590857
4	0.070712	0.5523	0.291388
5	0.123603	0.9654	0.169085
6	-0.000104	-8e-04	0.500324
7	-0.167128	-1.3053	0.901656
8	0.056845	0.444	0.329315
9	-0.211469	-1.6516	0.948125
10	-0.024415	-0.1907	0.575297
11	-0.038767	-0.3028	0.618455
12	0.10025	0.783	0.218336
13	0.005492	0.0429	0.482963
14	-0.078045	-0.6096	0.727789
15	0.023194	0.1812	0.428424
16	0.113456	0.8861	0.189516
17	-0.049779	-0.3888	0.650607

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.917161 & 7.1633 & 0 \tabularnewline
1 & 0.07041 & 0.5499 & 0.292191 \tabularnewline
2 & -0.088125 & -0.6883 & 0.753057 \tabularnewline
3 & -0.029544 & -0.2307 & 0.590857 \tabularnewline
4 & 0.070712 & 0.5523 & 0.291388 \tabularnewline
5 & 0.123603 & 0.9654 & 0.169085 \tabularnewline
6 & -0.000104 & -8e-04 & 0.500324 \tabularnewline
7 & -0.167128 & -1.3053 & 0.901656 \tabularnewline
8 & 0.056845 & 0.444 & 0.329315 \tabularnewline
9 & -0.211469 & -1.6516 & 0.948125 \tabularnewline
10 & -0.024415 & -0.1907 & 0.575297 \tabularnewline
11 & -0.038767 & -0.3028 & 0.618455 \tabularnewline
12 & 0.10025 & 0.783 & 0.218336 \tabularnewline
13 & 0.005492 & 0.0429 & 0.482963 \tabularnewline
14 & -0.078045 & -0.6096 & 0.727789 \tabularnewline
15 & 0.023194 & 0.1812 & 0.428424 \tabularnewline
16 & 0.113456 & 0.8861 & 0.189516 \tabularnewline
17 & -0.049779 & -0.3888 & 0.650607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2901&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]0[/C][C]0.917161[/C][C]7.1633[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.07041[/C][C]0.5499[/C][C]0.292191[/C][/ROW]
[ROW][C]2[/C][C]-0.088125[/C][C]-0.6883[/C][C]0.753057[/C][/ROW]
[ROW][C]3[/C][C]-0.029544[/C][C]-0.2307[/C][C]0.590857[/C][/ROW]
[ROW][C]4[/C][C]0.070712[/C][C]0.5523[/C][C]0.291388[/C][/ROW]
[ROW][C]5[/C][C]0.123603[/C][C]0.9654[/C][C]0.169085[/C][/ROW]
[ROW][C]6[/C][C]-0.000104[/C][C]-8e-04[/C][C]0.500324[/C][/ROW]
[ROW][C]7[/C][C]-0.167128[/C][C]-1.3053[/C][C]0.901656[/C][/ROW]
[ROW][C]8[/C][C]0.056845[/C][C]0.444[/C][C]0.329315[/C][/ROW]
[ROW][C]9[/C][C]-0.211469[/C][C]-1.6516[/C][C]0.948125[/C][/ROW]
[ROW][C]10[/C][C]-0.024415[/C][C]-0.1907[/C][C]0.575297[/C][/ROW]
[ROW][C]11[/C][C]-0.038767[/C][C]-0.3028[/C][C]0.618455[/C][/ROW]
[ROW][C]12[/C][C]0.10025[/C][C]0.783[/C][C]0.218336[/C][/ROW]
[ROW][C]13[/C][C]0.005492[/C][C]0.0429[/C][C]0.482963[/C][/ROW]
[ROW][C]14[/C][C]-0.078045[/C][C]-0.6096[/C][C]0.727789[/C][/ROW]
[ROW][C]15[/C][C]0.023194[/C][C]0.1812[/C][C]0.428424[/C][/ROW]
[ROW][C]16[/C][C]0.113456[/C][C]0.8861[/C][C]0.189516[/C][/ROW]
[ROW][C]17[/C][C]-0.049779[/C][C]-0.3888[/C][C]0.650607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2901&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2901&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
0	0.917161	7.1633	0
1	0.07041	0.5499	0.292191
2	-0.088125	-0.6883	0.753057
3	-0.029544	-0.2307	0.590857
4	0.070712	0.5523	0.291388
5	0.123603	0.9654	0.169085
6	-0.000104	-8e-04	0.500324
7	-0.167128	-1.3053	0.901656
8	0.056845	0.444	0.329315
9	-0.211469	-1.6516	0.948125
10	-0.024415	-0.1907	0.575297
11	-0.038767	-0.3028	0.618455
12	0.10025	0.783	0.218336
13	0.005492	0.0429	0.482963
14	-0.078045	-0.6096	0.727789
15	0.023194	0.1812	0.428424
16	0.113456	0.8861	0.189516
17	-0.049779	-0.3888	0.650607

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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