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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 14 Dec 2009 02:39:23 -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/Dec/14/t1260783801j1pejmmfby1his2.htm/, Retrieved Sun, 05 May 2024 19:03:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67475, Retrieved Sun, 05 May 2024 19:03:40 +0000

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User-defined keywords

Estimated Impact

150

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

-     [Variance Reduction Matrix] [VRM invoer] [2008-12-17 15:09:52] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [Autocorrelation F...] [2009-12-14 09:39:23] [91da2e1ebdd83187f2515f461585cbee] [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=67475&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=67475&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67475&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	0.812487	10.0499	0
2	0.736354	9.1082	0
3	0.782314	9.6767	0
4	0.774818	9.584	0
5	0.753904	9.3253	0
6	0.762627	9.4332	0
7	0.697965	8.6334	0
8	0.698155	8.6357	0
9	0.646345	7.9948	0
10	0.581313	7.1904	0
11	0.647721	8.0119	0
12	0.742568	9.1851	0
13	0.587706	7.2695	0
14	0.52434	6.4857	0
15	0.551626	6.8232	0
16	0.548768	6.7879	0
17	0.54258	6.7113	0
18	0.537101	6.6436	0
19	0.491219	6.076	0
20	0.484126	5.9883	0
21	0.416267	5.1489	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.812487 & 10.0499 & 0 \tabularnewline
2 & 0.736354 & 9.1082 & 0 \tabularnewline
3 & 0.782314 & 9.6767 & 0 \tabularnewline
4 & 0.774818 & 9.584 & 0 \tabularnewline
5 & 0.753904 & 9.3253 & 0 \tabularnewline
6 & 0.762627 & 9.4332 & 0 \tabularnewline
7 & 0.697965 & 8.6334 & 0 \tabularnewline
8 & 0.698155 & 8.6357 & 0 \tabularnewline
9 & 0.646345 & 7.9948 & 0 \tabularnewline
10 & 0.581313 & 7.1904 & 0 \tabularnewline
11 & 0.647721 & 8.0119 & 0 \tabularnewline
12 & 0.742568 & 9.1851 & 0 \tabularnewline
13 & 0.587706 & 7.2695 & 0 \tabularnewline
14 & 0.52434 & 6.4857 & 0 \tabularnewline
15 & 0.551626 & 6.8232 & 0 \tabularnewline
16 & 0.548768 & 6.7879 & 0 \tabularnewline
17 & 0.54258 & 6.7113 & 0 \tabularnewline
18 & 0.537101 & 6.6436 & 0 \tabularnewline
19 & 0.491219 & 6.076 & 0 \tabularnewline
20 & 0.484126 & 5.9883 & 0 \tabularnewline
21 & 0.416267 & 5.1489 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67475&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]0.812487[/C][C]10.0499[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.736354[/C][C]9.1082[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.782314[/C][C]9.6767[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.774818[/C][C]9.584[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.753904[/C][C]9.3253[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.762627[/C][C]9.4332[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.697965[/C][C]8.6334[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.698155[/C][C]8.6357[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.646345[/C][C]7.9948[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.581313[/C][C]7.1904[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.647721[/C][C]8.0119[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.742568[/C][C]9.1851[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.587706[/C][C]7.2695[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.52434[/C][C]6.4857[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.551626[/C][C]6.8232[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.548768[/C][C]6.7879[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.54258[/C][C]6.7113[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.537101[/C][C]6.6436[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.491219[/C][C]6.076[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.484126[/C][C]5.9883[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.416267[/C][C]5.1489[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67475&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67475&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	0.812487	10.0499	0
2	0.736354	9.1082	0
3	0.782314	9.6767	0
4	0.774818	9.584	0
5	0.753904	9.3253	0
6	0.762627	9.4332	0
7	0.697965	8.6334	0
8	0.698155	8.6357	0
9	0.646345	7.9948	0
10	0.581313	7.1904	0
11	0.647721	8.0119	0
12	0.742568	9.1851	0
13	0.587706	7.2695	0
14	0.52434	6.4857	0
15	0.551626	6.8232	0
16	0.548768	6.7879	0
17	0.54258	6.7113	0
18	0.537101	6.6436	0
19	0.491219	6.076	0
20	0.484126	5.9883	0
21	0.416267	5.1489	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.812487	10.0499	0
2	0.224263	2.774	0.003114
3	0.42134	5.2117	0
4	0.164773	2.0381	0.021629
5	0.156508	1.9359	0.027362
6	0.151101	1.869	0.031766
7	-0.153892	-1.9035	0.029424
8	0.087292	1.0797	0.140978
9	-0.279274	-3.4544	0.000357
10	-0.182387	-2.256	0.012744
11	0.229297	2.8362	0.002591
12	0.485403	6.0041	0
13	-0.310249	-3.8376	9.1e-05
14	-0.196769	-2.4339	0.008044
15	-0.11789	-1.4582	0.073416
16	0.028256	0.3495	0.363595
17	0.059223	0.7326	0.232476
18	0.032614	0.4034	0.343605
19	0.081061	1.0027	0.158801
20	-0.089387	-1.1057	0.135305
21	-0.113986	-1.4099	0.080294

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.812487 & 10.0499 & 0 \tabularnewline
2 & 0.224263 & 2.774 & 0.003114 \tabularnewline
3 & 0.42134 & 5.2117 & 0 \tabularnewline
4 & 0.164773 & 2.0381 & 0.021629 \tabularnewline
5 & 0.156508 & 1.9359 & 0.027362 \tabularnewline
6 & 0.151101 & 1.869 & 0.031766 \tabularnewline
7 & -0.153892 & -1.9035 & 0.029424 \tabularnewline
8 & 0.087292 & 1.0797 & 0.140978 \tabularnewline
9 & -0.279274 & -3.4544 & 0.000357 \tabularnewline
10 & -0.182387 & -2.256 & 0.012744 \tabularnewline
11 & 0.229297 & 2.8362 & 0.002591 \tabularnewline
12 & 0.485403 & 6.0041 & 0 \tabularnewline
13 & -0.310249 & -3.8376 & 9.1e-05 \tabularnewline
14 & -0.196769 & -2.4339 & 0.008044 \tabularnewline
15 & -0.11789 & -1.4582 & 0.073416 \tabularnewline
16 & 0.028256 & 0.3495 & 0.363595 \tabularnewline
17 & 0.059223 & 0.7326 & 0.232476 \tabularnewline
18 & 0.032614 & 0.4034 & 0.343605 \tabularnewline
19 & 0.081061 & 1.0027 & 0.158801 \tabularnewline
20 & -0.089387 & -1.1057 & 0.135305 \tabularnewline
21 & -0.113986 & -1.4099 & 0.080294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67475&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]0.812487[/C][C]10.0499[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.224263[/C][C]2.774[/C][C]0.003114[/C][/ROW]
[ROW][C]3[/C][C]0.42134[/C][C]5.2117[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.164773[/C][C]2.0381[/C][C]0.021629[/C][/ROW]
[ROW][C]5[/C][C]0.156508[/C][C]1.9359[/C][C]0.027362[/C][/ROW]
[ROW][C]6[/C][C]0.151101[/C][C]1.869[/C][C]0.031766[/C][/ROW]
[ROW][C]7[/C][C]-0.153892[/C][C]-1.9035[/C][C]0.029424[/C][/ROW]
[ROW][C]8[/C][C]0.087292[/C][C]1.0797[/C][C]0.140978[/C][/ROW]
[ROW][C]9[/C][C]-0.279274[/C][C]-3.4544[/C][C]0.000357[/C][/ROW]
[ROW][C]10[/C][C]-0.182387[/C][C]-2.256[/C][C]0.012744[/C][/ROW]
[ROW][C]11[/C][C]0.229297[/C][C]2.8362[/C][C]0.002591[/C][/ROW]
[ROW][C]12[/C][C]0.485403[/C][C]6.0041[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.310249[/C][C]-3.8376[/C][C]9.1e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.196769[/C][C]-2.4339[/C][C]0.008044[/C][/ROW]
[ROW][C]15[/C][C]-0.11789[/C][C]-1.4582[/C][C]0.073416[/C][/ROW]
[ROW][C]16[/C][C]0.028256[/C][C]0.3495[/C][C]0.363595[/C][/ROW]
[ROW][C]17[/C][C]0.059223[/C][C]0.7326[/C][C]0.232476[/C][/ROW]
[ROW][C]18[/C][C]0.032614[/C][C]0.4034[/C][C]0.343605[/C][/ROW]
[ROW][C]19[/C][C]0.081061[/C][C]1.0027[/C][C]0.158801[/C][/ROW]
[ROW][C]20[/C][C]-0.089387[/C][C]-1.1057[/C][C]0.135305[/C][/ROW]
[ROW][C]21[/C][C]-0.113986[/C][C]-1.4099[/C][C]0.080294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67475&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67475&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	0.812487	10.0499	0
2	0.224263	2.774	0.003114
3	0.42134	5.2117	0
4	0.164773	2.0381	0.021629
5	0.156508	1.9359	0.027362
6	0.151101	1.869	0.031766
7	-0.153892	-1.9035	0.029424
8	0.087292	1.0797	0.140978
9	-0.279274	-3.4544	0.000357
10	-0.182387	-2.256	0.012744
11	0.229297	2.8362	0.002591
12	0.485403	6.0041	0
13	-0.310249	-3.8376	9.1e-05
14	-0.196769	-2.4339	0.008044
15	-0.11789	-1.4582	0.073416
16	0.028256	0.3495	0.363595
17	0.059223	0.7326	0.232476
18	0.032614	0.4034	0.343605
19	0.081061	1.0027	0.158801
20	-0.089387	-1.1057	0.135305
21	-0.113986	-1.4099	0.080294

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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