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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 10:29:27 -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/2009/Nov/26/t1259256647a4qlwilpqsfgx1b.htm/, Retrieved Sun, 28 Apr 2024 22:07:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60192, Retrieved Sun, 28 Apr 2024 22:07:15 +0000

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No (this computation is public)

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Estimated Impact

114

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

-       [(Partial) Autocorrelation Function] [] [2009-11-26 17:29:27] [14869f38c4320b00c96ca15cc00142de] [Current]
-    D    [(Partial) Autocorrelation Function] [] [2009-12-15 20:51:15] [73863f7f907331e734eff34b7de6fc83] 

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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=60192&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=60192&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60192&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	0.870597	6.7436	0
2	0.750049	5.8099	0
3	0.648834	5.0258	2e-06
4	0.600912	4.6546	9e-06
5	0.559976	4.3376	2.8e-05
6	0.514331	3.984	9.3e-05
7	0.487459	3.7758	0.000184
8	0.456237	3.534	0.000398
9	0.398648	3.0879	0.001525
10	0.30665	2.3753	0.010374
11	0.243373	1.8852	0.032126
12	0.194521	1.5067	0.068561
13	0.164811	1.2766	0.103327
14	0.117867	0.913	0.182449
15	0.037242	0.2885	0.38699
16	-0.017583	-0.1362	0.44606
17	-0.06827	-0.5288	0.299442
18	-0.083821	-0.6493	0.25932

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.870597 & 6.7436 & 0 \tabularnewline
2 & 0.750049 & 5.8099 & 0 \tabularnewline
3 & 0.648834 & 5.0258 & 2e-06 \tabularnewline
4 & 0.600912 & 4.6546 & 9e-06 \tabularnewline
5 & 0.559976 & 4.3376 & 2.8e-05 \tabularnewline
6 & 0.514331 & 3.984 & 9.3e-05 \tabularnewline
7 & 0.487459 & 3.7758 & 0.000184 \tabularnewline
8 & 0.456237 & 3.534 & 0.000398 \tabularnewline
9 & 0.398648 & 3.0879 & 0.001525 \tabularnewline
10 & 0.30665 & 2.3753 & 0.010374 \tabularnewline
11 & 0.243373 & 1.8852 & 0.032126 \tabularnewline
12 & 0.194521 & 1.5067 & 0.068561 \tabularnewline
13 & 0.164811 & 1.2766 & 0.103327 \tabularnewline
14 & 0.117867 & 0.913 & 0.182449 \tabularnewline
15 & 0.037242 & 0.2885 & 0.38699 \tabularnewline
16 & -0.017583 & -0.1362 & 0.44606 \tabularnewline
17 & -0.06827 & -0.5288 & 0.299442 \tabularnewline
18 & -0.083821 & -0.6493 & 0.25932 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60192&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]0.870597[/C][C]6.7436[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.750049[/C][C]5.8099[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.648834[/C][C]5.0258[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.600912[/C][C]4.6546[/C][C]9e-06[/C][/ROW]
[ROW][C]5[/C][C]0.559976[/C][C]4.3376[/C][C]2.8e-05[/C][/ROW]
[ROW][C]6[/C][C]0.514331[/C][C]3.984[/C][C]9.3e-05[/C][/ROW]
[ROW][C]7[/C][C]0.487459[/C][C]3.7758[/C][C]0.000184[/C][/ROW]
[ROW][C]8[/C][C]0.456237[/C][C]3.534[/C][C]0.000398[/C][/ROW]
[ROW][C]9[/C][C]0.398648[/C][C]3.0879[/C][C]0.001525[/C][/ROW]
[ROW][C]10[/C][C]0.30665[/C][C]2.3753[/C][C]0.010374[/C][/ROW]
[ROW][C]11[/C][C]0.243373[/C][C]1.8852[/C][C]0.032126[/C][/ROW]
[ROW][C]12[/C][C]0.194521[/C][C]1.5067[/C][C]0.068561[/C][/ROW]
[ROW][C]13[/C][C]0.164811[/C][C]1.2766[/C][C]0.103327[/C][/ROW]
[ROW][C]14[/C][C]0.117867[/C][C]0.913[/C][C]0.182449[/C][/ROW]
[ROW][C]15[/C][C]0.037242[/C][C]0.2885[/C][C]0.38699[/C][/ROW]
[ROW][C]16[/C][C]-0.017583[/C][C]-0.1362[/C][C]0.44606[/C][/ROW]
[ROW][C]17[/C][C]-0.06827[/C][C]-0.5288[/C][C]0.299442[/C][/ROW]
[ROW][C]18[/C][C]-0.083821[/C][C]-0.6493[/C][C]0.25932[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60192&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60192&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	0.870597	6.7436	0
2	0.750049	5.8099	0
3	0.648834	5.0258	2e-06
4	0.600912	4.6546	9e-06
5	0.559976	4.3376	2.8e-05
6	0.514331	3.984	9.3e-05
7	0.487459	3.7758	0.000184
8	0.456237	3.534	0.000398
9	0.398648	3.0879	0.001525
10	0.30665	2.3753	0.010374
11	0.243373	1.8852	0.032126
12	0.194521	1.5067	0.068561
13	0.164811	1.2766	0.103327
14	0.117867	0.913	0.182449
15	0.037242	0.2885	0.38699
16	-0.017583	-0.1362	0.44606
17	-0.06827	-0.5288	0.299442
18	-0.083821	-0.6493	0.25932

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.870597	6.7436	0
2	-0.032597	-0.2525	0.40076
3	0.012145	0.0941	0.462681
4	0.163106	1.2634	0.105664
5	0.013896	0.1076	0.457322
6	-0.018139	-0.1405	0.444367
7	0.096179	0.745	0.229591
8	-0.016393	-0.127	0.449689
9	-0.122225	-0.9467	0.173782
10	-0.153879	-1.1919	0.118989
11	0.045346	0.3513	0.363316
12	-0.039507	-0.306	0.380325
13	-0.000899	-0.007	0.497232
14	-0.068481	-0.5305	0.298878
15	-0.186414	-1.444	0.076976
16	0.031432	0.2435	0.404236
17	-0.033379	-0.2585	0.398434
18	0.084063	0.6511	0.258719

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.870597 & 6.7436 & 0 \tabularnewline
2 & -0.032597 & -0.2525 & 0.40076 \tabularnewline
3 & 0.012145 & 0.0941 & 0.462681 \tabularnewline
4 & 0.163106 & 1.2634 & 0.105664 \tabularnewline
5 & 0.013896 & 0.1076 & 0.457322 \tabularnewline
6 & -0.018139 & -0.1405 & 0.444367 \tabularnewline
7 & 0.096179 & 0.745 & 0.229591 \tabularnewline
8 & -0.016393 & -0.127 & 0.449689 \tabularnewline
9 & -0.122225 & -0.9467 & 0.173782 \tabularnewline
10 & -0.153879 & -1.1919 & 0.118989 \tabularnewline
11 & 0.045346 & 0.3513 & 0.363316 \tabularnewline
12 & -0.039507 & -0.306 & 0.380325 \tabularnewline
13 & -0.000899 & -0.007 & 0.497232 \tabularnewline
14 & -0.068481 & -0.5305 & 0.298878 \tabularnewline
15 & -0.186414 & -1.444 & 0.076976 \tabularnewline
16 & 0.031432 & 0.2435 & 0.404236 \tabularnewline
17 & -0.033379 & -0.2585 & 0.398434 \tabularnewline
18 & 0.084063 & 0.6511 & 0.258719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60192&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]0.870597[/C][C]6.7436[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.032597[/C][C]-0.2525[/C][C]0.40076[/C][/ROW]
[ROW][C]3[/C][C]0.012145[/C][C]0.0941[/C][C]0.462681[/C][/ROW]
[ROW][C]4[/C][C]0.163106[/C][C]1.2634[/C][C]0.105664[/C][/ROW]
[ROW][C]5[/C][C]0.013896[/C][C]0.1076[/C][C]0.457322[/C][/ROW]
[ROW][C]6[/C][C]-0.018139[/C][C]-0.1405[/C][C]0.444367[/C][/ROW]
[ROW][C]7[/C][C]0.096179[/C][C]0.745[/C][C]0.229591[/C][/ROW]
[ROW][C]8[/C][C]-0.016393[/C][C]-0.127[/C][C]0.449689[/C][/ROW]
[ROW][C]9[/C][C]-0.122225[/C][C]-0.9467[/C][C]0.173782[/C][/ROW]
[ROW][C]10[/C][C]-0.153879[/C][C]-1.1919[/C][C]0.118989[/C][/ROW]
[ROW][C]11[/C][C]0.045346[/C][C]0.3513[/C][C]0.363316[/C][/ROW]
[ROW][C]12[/C][C]-0.039507[/C][C]-0.306[/C][C]0.380325[/C][/ROW]
[ROW][C]13[/C][C]-0.000899[/C][C]-0.007[/C][C]0.497232[/C][/ROW]
[ROW][C]14[/C][C]-0.068481[/C][C]-0.5305[/C][C]0.298878[/C][/ROW]
[ROW][C]15[/C][C]-0.186414[/C][C]-1.444[/C][C]0.076976[/C][/ROW]
[ROW][C]16[/C][C]0.031432[/C][C]0.2435[/C][C]0.404236[/C][/ROW]
[ROW][C]17[/C][C]-0.033379[/C][C]-0.2585[/C][C]0.398434[/C][/ROW]
[ROW][C]18[/C][C]0.084063[/C][C]0.6511[/C][C]0.258719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60192&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60192&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	0.870597	6.7436	0
2	-0.032597	-0.2525	0.40076
3	0.012145	0.0941	0.462681
4	0.163106	1.2634	0.105664
5	0.013896	0.1076	0.457322
6	-0.018139	-0.1405	0.444367
7	0.096179	0.745	0.229591
8	-0.016393	-0.127	0.449689
9	-0.122225	-0.9467	0.173782
10	-0.153879	-1.1919	0.118989
11	0.045346	0.3513	0.363316
12	-0.039507	-0.306	0.380325
13	-0.000899	-0.007	0.497232
14	-0.068481	-0.5305	0.298878
15	-0.186414	-1.444	0.076976
16	0.031432	0.2435	0.404236
17	-0.033379	-0.2585	0.398434
18	0.084063	0.6511	0.258719

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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