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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 12:05:48 -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/Nov/25/t1196017019xke10cch9d4iwy7.htm/, Retrieved Sat, 04 May 2024 07:26:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6531, Retrieved Sat, 04 May 2024 07:26:33 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

174

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

-       [(Partial) Autocorrelation Function] [inducing stationa...] [2007-11-25 19:05:48] [a04acf73ce4b7e85f8287f21ada159c8] [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=6531&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=6531&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6531&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	9	0
1	0.951663	8.565	0
2	0.912399	8.2116	0
3	0.870574	7.8352	0
4	0.835295	7.5177	0
5	0.803323	7.2299	0
6	0.767606	6.9085	0
7	0.742696	6.6843	0
8	0.720204	6.4818	0
9	0.709247	6.3832	0
10	0.688954	6.2006	0
11	0.662959	5.9666	0
12	0.630059	5.6705	0
13	0.59152	5.3237	0
14	0.541386	4.8725	3e-06
15	0.491839	4.4266	1.5e-05
16	0.44446	4.0001	7e-05
17	0.398295	3.5847	0.000288
18	0.350694	3.1562	0.001122

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9 & 0 \tabularnewline
1 & 0.951663 & 8.565 & 0 \tabularnewline
2 & 0.912399 & 8.2116 & 0 \tabularnewline
3 & 0.870574 & 7.8352 & 0 \tabularnewline
4 & 0.835295 & 7.5177 & 0 \tabularnewline
5 & 0.803323 & 7.2299 & 0 \tabularnewline
6 & 0.767606 & 6.9085 & 0 \tabularnewline
7 & 0.742696 & 6.6843 & 0 \tabularnewline
8 & 0.720204 & 6.4818 & 0 \tabularnewline
9 & 0.709247 & 6.3832 & 0 \tabularnewline
10 & 0.688954 & 6.2006 & 0 \tabularnewline
11 & 0.662959 & 5.9666 & 0 \tabularnewline
12 & 0.630059 & 5.6705 & 0 \tabularnewline
13 & 0.59152 & 5.3237 & 0 \tabularnewline
14 & 0.541386 & 4.8725 & 3e-06 \tabularnewline
15 & 0.491839 & 4.4266 & 1.5e-05 \tabularnewline
16 & 0.44446 & 4.0001 & 7e-05 \tabularnewline
17 & 0.398295 & 3.5847 & 0.000288 \tabularnewline
18 & 0.350694 & 3.1562 & 0.001122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6531&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]9[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.951663[/C][C]8.565[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.912399[/C][C]8.2116[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.870574[/C][C]7.8352[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.835295[/C][C]7.5177[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.803323[/C][C]7.2299[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.767606[/C][C]6.9085[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.742696[/C][C]6.6843[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.720204[/C][C]6.4818[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.709247[/C][C]6.3832[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.688954[/C][C]6.2006[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.662959[/C][C]5.9666[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.630059[/C][C]5.6705[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.59152[/C][C]5.3237[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.541386[/C][C]4.8725[/C][C]3e-06[/C][/ROW]
[ROW][C]15[/C][C]0.491839[/C][C]4.4266[/C][C]1.5e-05[/C][/ROW]
[ROW][C]16[/C][C]0.44446[/C][C]4.0001[/C][C]7e-05[/C][/ROW]
[ROW][C]17[/C][C]0.398295[/C][C]3.5847[/C][C]0.000288[/C][/ROW]
[ROW][C]18[/C][C]0.350694[/C][C]3.1562[/C][C]0.001122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6531&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6531&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	9	0
1	0.951663	8.565	0
2	0.912399	8.2116	0
3	0.870574	7.8352	0
4	0.835295	7.5177	0
5	0.803323	7.2299	0
6	0.767606	6.9085	0
7	0.742696	6.6843	0
8	0.720204	6.4818	0
9	0.709247	6.3832	0
10	0.688954	6.2006	0
11	0.662959	5.9666	0
12	0.630059	5.6705	0
13	0.59152	5.3237	0
14	0.541386	4.8725	3e-06
15	0.491839	4.4266	1.5e-05
16	0.44446	4.0001	7e-05
17	0.398295	3.5847	0.000288
18	0.350694	3.1562	0.001122

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.951663	8.565	0
1	0.071404	0.6426	0.261136
2	-0.039155	-0.3524	0.637273
3	0.043417	0.3908	0.348502
4	0.028374	0.2554	0.399544
5	-0.053335	-0.48	0.683745
6	0.091874	0.8269	0.205372
7	0.037714	0.3394	0.367583
8	0.109958	0.9896	0.162653
9	-0.076541	-0.6889	0.753562
10	-0.078463	-0.7062	0.758945
11	-0.088342	-0.7951	0.785554
12	-0.086054	-0.7745	0.77955
13	-0.177593	-1.5983	0.943069
14	-0.035581	-0.3202	0.625191
15	-0.025101	-0.2259	0.589081
16	-0.042346	-0.3811	0.647943
17	-0.100584	-0.9053	0.815994
18	0.066604	0.5994	0.275278

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.951663 & 8.565 & 0 \tabularnewline
1 & 0.071404 & 0.6426 & 0.261136 \tabularnewline
2 & -0.039155 & -0.3524 & 0.637273 \tabularnewline
3 & 0.043417 & 0.3908 & 0.348502 \tabularnewline
4 & 0.028374 & 0.2554 & 0.399544 \tabularnewline
5 & -0.053335 & -0.48 & 0.683745 \tabularnewline
6 & 0.091874 & 0.8269 & 0.205372 \tabularnewline
7 & 0.037714 & 0.3394 & 0.367583 \tabularnewline
8 & 0.109958 & 0.9896 & 0.162653 \tabularnewline
9 & -0.076541 & -0.6889 & 0.753562 \tabularnewline
10 & -0.078463 & -0.7062 & 0.758945 \tabularnewline
11 & -0.088342 & -0.7951 & 0.785554 \tabularnewline
12 & -0.086054 & -0.7745 & 0.77955 \tabularnewline
13 & -0.177593 & -1.5983 & 0.943069 \tabularnewline
14 & -0.035581 & -0.3202 & 0.625191 \tabularnewline
15 & -0.025101 & -0.2259 & 0.589081 \tabularnewline
16 & -0.042346 & -0.3811 & 0.647943 \tabularnewline
17 & -0.100584 & -0.9053 & 0.815994 \tabularnewline
18 & 0.066604 & 0.5994 & 0.275278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6531&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]0.951663[/C][C]8.565[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.071404[/C][C]0.6426[/C][C]0.261136[/C][/ROW]
[ROW][C]2[/C][C]-0.039155[/C][C]-0.3524[/C][C]0.637273[/C][/ROW]
[ROW][C]3[/C][C]0.043417[/C][C]0.3908[/C][C]0.348502[/C][/ROW]
[ROW][C]4[/C][C]0.028374[/C][C]0.2554[/C][C]0.399544[/C][/ROW]
[ROW][C]5[/C][C]-0.053335[/C][C]-0.48[/C][C]0.683745[/C][/ROW]
[ROW][C]6[/C][C]0.091874[/C][C]0.8269[/C][C]0.205372[/C][/ROW]
[ROW][C]7[/C][C]0.037714[/C][C]0.3394[/C][C]0.367583[/C][/ROW]
[ROW][C]8[/C][C]0.109958[/C][C]0.9896[/C][C]0.162653[/C][/ROW]
[ROW][C]9[/C][C]-0.076541[/C][C]-0.6889[/C][C]0.753562[/C][/ROW]
[ROW][C]10[/C][C]-0.078463[/C][C]-0.7062[/C][C]0.758945[/C][/ROW]
[ROW][C]11[/C][C]-0.088342[/C][C]-0.7951[/C][C]0.785554[/C][/ROW]
[ROW][C]12[/C][C]-0.086054[/C][C]-0.7745[/C][C]0.77955[/C][/ROW]
[ROW][C]13[/C][C]-0.177593[/C][C]-1.5983[/C][C]0.943069[/C][/ROW]
[ROW][C]14[/C][C]-0.035581[/C][C]-0.3202[/C][C]0.625191[/C][/ROW]
[ROW][C]15[/C][C]-0.025101[/C][C]-0.2259[/C][C]0.589081[/C][/ROW]
[ROW][C]16[/C][C]-0.042346[/C][C]-0.3811[/C][C]0.647943[/C][/ROW]
[ROW][C]17[/C][C]-0.100584[/C][C]-0.9053[/C][C]0.815994[/C][/ROW]
[ROW][C]18[/C][C]0.066604[/C][C]0.5994[/C][C]0.275278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6531&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6531&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	0.951663	8.565	0
1	0.071404	0.6426	0.261136
2	-0.039155	-0.3524	0.637273
3	0.043417	0.3908	0.348502
4	0.028374	0.2554	0.399544
5	-0.053335	-0.48	0.683745
6	0.091874	0.8269	0.205372
7	0.037714	0.3394	0.367583
8	0.109958	0.9896	0.162653
9	-0.076541	-0.6889	0.753562
10	-0.078463	-0.7062	0.758945
11	-0.088342	-0.7951	0.785554
12	-0.086054	-0.7745	0.77955
13	-0.177593	-1.5983	0.943069
14	-0.035581	-0.3202	0.625191
15	-0.025101	-0.2259	0.589081
16	-0.042346	-0.3811	0.647943
17	-0.100584	-0.9053	0.815994
18	0.066604	0.5994	0.275278

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 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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Dataset

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