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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 08:02:00 -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/t125924803151sjbhjuc16gsxa.htm/, Retrieved Mon, 29 Apr 2024 06:49:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60066, Retrieved Mon, 29 Apr 2024 06:49:57 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

100

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [] [2009-11-26 15:02:00] [bcaf453a09027aa0f995cb78bdc3c98a] [Current]

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Dataseries X:

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Histogram

Boxplots

9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.2

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60066&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]2 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=60066&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60066&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.84266	6.5814	0
2	0.636226	4.9691	3e-06
3	0.529187	4.1331	5.5e-05
4	0.548333	4.2826	3.3e-05
5	0.638853	4.9896	3e-06
6	0.683904	5.3415	1e-06
7	0.604917	4.7245	7e-06
8	0.459583	3.5895	0.000331
9	0.338687	2.6452	0.005184
10	0.317357	2.4786	0.007985
11	0.336308	2.6267	0.005444
12	0.346642	2.7074	0.004393

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.84266 & 6.5814 & 0 \tabularnewline
2 & 0.636226 & 4.9691 & 3e-06 \tabularnewline
3 & 0.529187 & 4.1331 & 5.5e-05 \tabularnewline
4 & 0.548333 & 4.2826 & 3.3e-05 \tabularnewline
5 & 0.638853 & 4.9896 & 3e-06 \tabularnewline
6 & 0.683904 & 5.3415 & 1e-06 \tabularnewline
7 & 0.604917 & 4.7245 & 7e-06 \tabularnewline
8 & 0.459583 & 3.5895 & 0.000331 \tabularnewline
9 & 0.338687 & 2.6452 & 0.005184 \tabularnewline
10 & 0.317357 & 2.4786 & 0.007985 \tabularnewline
11 & 0.336308 & 2.6267 & 0.005444 \tabularnewline
12 & 0.346642 & 2.7074 & 0.004393 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60066&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]0.84266[/C][C]6.5814[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.636226[/C][C]4.9691[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]0.529187[/C][C]4.1331[/C][C]5.5e-05[/C][/ROW]
[ROW][C]4[/C][C]0.548333[/C][C]4.2826[/C][C]3.3e-05[/C][/ROW]
[ROW][C]5[/C][C]0.638853[/C][C]4.9896[/C][C]3e-06[/C][/ROW]
[ROW][C]6[/C][C]0.683904[/C][C]5.3415[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.604917[/C][C]4.7245[/C][C]7e-06[/C][/ROW]
[ROW][C]8[/C][C]0.459583[/C][C]3.5895[/C][C]0.000331[/C][/ROW]
[ROW][C]9[/C][C]0.338687[/C][C]2.6452[/C][C]0.005184[/C][/ROW]
[ROW][C]10[/C][C]0.317357[/C][C]2.4786[/C][C]0.007985[/C][/ROW]
[ROW][C]11[/C][C]0.336308[/C][C]2.6267[/C][C]0.005444[/C][/ROW]
[ROW][C]12[/C][C]0.346642[/C][C]2.7074[/C][C]0.004393[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60066&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60066&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	0.84266	6.5814	0
2	0.636226	4.9691	3e-06
3	0.529187	4.1331	5.5e-05
4	0.548333	4.2826	3.3e-05
5	0.638853	4.9896	3e-06
6	0.683904	5.3415	1e-06
7	0.604917	4.7245	7e-06
8	0.459583	3.5895	0.000331
9	0.338687	2.6452	0.005184
10	0.317357	2.4786	0.007985
11	0.336308	2.6267	0.005444
12	0.346642	2.7074	0.004393

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.84266	6.5814	0
2	-0.254719	-1.9894	0.025572
3	0.262423	2.0496	0.022356
4	0.280867	2.1936	0.016041
5	0.269342	2.1036	0.019771
6	0.051683	0.4037	0.343939
7	-0.161316	-1.2599	0.106249
8	-0.116504	-0.9099	0.183222
9	-0.127042	-0.9922	0.162503
10	0.018476	0.1443	0.44287
11	-0.146335	-1.1429	0.12877
12	0.015751	0.123	0.451247

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.84266 & 6.5814 & 0 \tabularnewline
2 & -0.254719 & -1.9894 & 0.025572 \tabularnewline
3 & 0.262423 & 2.0496 & 0.022356 \tabularnewline
4 & 0.280867 & 2.1936 & 0.016041 \tabularnewline
5 & 0.269342 & 2.1036 & 0.019771 \tabularnewline
6 & 0.051683 & 0.4037 & 0.343939 \tabularnewline
7 & -0.161316 & -1.2599 & 0.106249 \tabularnewline
8 & -0.116504 & -0.9099 & 0.183222 \tabularnewline
9 & -0.127042 & -0.9922 & 0.162503 \tabularnewline
10 & 0.018476 & 0.1443 & 0.44287 \tabularnewline
11 & -0.146335 & -1.1429 & 0.12877 \tabularnewline
12 & 0.015751 & 0.123 & 0.451247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60066&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]0.84266[/C][C]6.5814[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.254719[/C][C]-1.9894[/C][C]0.025572[/C][/ROW]
[ROW][C]3[/C][C]0.262423[/C][C]2.0496[/C][C]0.022356[/C][/ROW]
[ROW][C]4[/C][C]0.280867[/C][C]2.1936[/C][C]0.016041[/C][/ROW]
[ROW][C]5[/C][C]0.269342[/C][C]2.1036[/C][C]0.019771[/C][/ROW]
[ROW][C]6[/C][C]0.051683[/C][C]0.4037[/C][C]0.343939[/C][/ROW]
[ROW][C]7[/C][C]-0.161316[/C][C]-1.2599[/C][C]0.106249[/C][/ROW]
[ROW][C]8[/C][C]-0.116504[/C][C]-0.9099[/C][C]0.183222[/C][/ROW]
[ROW][C]9[/C][C]-0.127042[/C][C]-0.9922[/C][C]0.162503[/C][/ROW]
[ROW][C]10[/C][C]0.018476[/C][C]0.1443[/C][C]0.44287[/C][/ROW]
[ROW][C]11[/C][C]-0.146335[/C][C]-1.1429[/C][C]0.12877[/C][/ROW]
[ROW][C]12[/C][C]0.015751[/C][C]0.123[/C][C]0.451247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60066&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60066&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	0.84266	6.5814	0
2	-0.254719	-1.9894	0.025572
3	0.262423	2.0496	0.022356
4	0.280867	2.1936	0.016041
5	0.269342	2.1036	0.019771
6	0.051683	0.4037	0.343939
7	-0.161316	-1.2599	0.106249
8	-0.116504	-0.9099	0.183222
9	-0.127042	-0.9922	0.162503
10	0.018476	0.1443	0.44287
11	-0.146335	-1.1429	0.12877
12	0.015751	0.123	0.451247

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code