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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

Mon, 06 Dec 2010 21:54:33 +0000

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/2010/Dec/06/t1291672422aiqp5dha1qyrsqw.htm/, Retrieved Sun, 28 Apr 2024 19:55:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105938, Retrieved Sun, 28 Apr 2024 19:55:56 +0000

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User-defined keywords

Estimated Impact

110

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-   PD      [(Partial) Autocorrelation Function] [ACF openstaande V...] [2010-12-06 21:54:33] [be034431ba35f7eb1ce695fc7ca4deb9] [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	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=105938&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=105938&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105938&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	0.242794	2.7469	0.003442
2	0.175667	1.9874	0.024504
3	0.006563	0.0742	0.470465
4	-0.151714	-1.7164	0.044249
5	-0.227556	-2.5745	0.005588
6	-0.361447	-4.0893	3.8e-05
7	-0.222	-2.5116	0.006631
8	-0.181209	-2.0501	0.021196
9	-0.049774	-0.5631	0.287166
10	0.09371	1.0602	0.145523
11	0.299358	3.3868	0.00047
12	0.460166	5.2062	0
13	0.351402	3.9757	5.8e-05
14	0.066288	0.75	0.227327
15	-0.01284	-0.1453	0.442366
16	-0.261855	-2.9625	0.001819
17	-0.28742	-3.2518	0.000733
18	-0.296518	-3.3547	0.000523
19	-0.261708	-2.9609	0.001828
20	-0.233372	-2.6403	0.004657
21	0.010795	0.1221	0.451494

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.242794 & 2.7469 & 0.003442 \tabularnewline
2 & 0.175667 & 1.9874 & 0.024504 \tabularnewline
3 & 0.006563 & 0.0742 & 0.470465 \tabularnewline
4 & -0.151714 & -1.7164 & 0.044249 \tabularnewline
5 & -0.227556 & -2.5745 & 0.005588 \tabularnewline
6 & -0.361447 & -4.0893 & 3.8e-05 \tabularnewline
7 & -0.222 & -2.5116 & 0.006631 \tabularnewline
8 & -0.181209 & -2.0501 & 0.021196 \tabularnewline
9 & -0.049774 & -0.5631 & 0.287166 \tabularnewline
10 & 0.09371 & 1.0602 & 0.145523 \tabularnewline
11 & 0.299358 & 3.3868 & 0.00047 \tabularnewline
12 & 0.460166 & 5.2062 & 0 \tabularnewline
13 & 0.351402 & 3.9757 & 5.8e-05 \tabularnewline
14 & 0.066288 & 0.75 & 0.227327 \tabularnewline
15 & -0.01284 & -0.1453 & 0.442366 \tabularnewline
16 & -0.261855 & -2.9625 & 0.001819 \tabularnewline
17 & -0.28742 & -3.2518 & 0.000733 \tabularnewline
18 & -0.296518 & -3.3547 & 0.000523 \tabularnewline
19 & -0.261708 & -2.9609 & 0.001828 \tabularnewline
20 & -0.233372 & -2.6403 & 0.004657 \tabularnewline
21 & 0.010795 & 0.1221 & 0.451494 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105938&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]0.242794[/C][C]2.7469[/C][C]0.003442[/C][/ROW]
[ROW][C]2[/C][C]0.175667[/C][C]1.9874[/C][C]0.024504[/C][/ROW]
[ROW][C]3[/C][C]0.006563[/C][C]0.0742[/C][C]0.470465[/C][/ROW]
[ROW][C]4[/C][C]-0.151714[/C][C]-1.7164[/C][C]0.044249[/C][/ROW]
[ROW][C]5[/C][C]-0.227556[/C][C]-2.5745[/C][C]0.005588[/C][/ROW]
[ROW][C]6[/C][C]-0.361447[/C][C]-4.0893[/C][C]3.8e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.222[/C][C]-2.5116[/C][C]0.006631[/C][/ROW]
[ROW][C]8[/C][C]-0.181209[/C][C]-2.0501[/C][C]0.021196[/C][/ROW]
[ROW][C]9[/C][C]-0.049774[/C][C]-0.5631[/C][C]0.287166[/C][/ROW]
[ROW][C]10[/C][C]0.09371[/C][C]1.0602[/C][C]0.145523[/C][/ROW]
[ROW][C]11[/C][C]0.299358[/C][C]3.3868[/C][C]0.00047[/C][/ROW]
[ROW][C]12[/C][C]0.460166[/C][C]5.2062[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.351402[/C][C]3.9757[/C][C]5.8e-05[/C][/ROW]
[ROW][C]14[/C][C]0.066288[/C][C]0.75[/C][C]0.227327[/C][/ROW]
[ROW][C]15[/C][C]-0.01284[/C][C]-0.1453[/C][C]0.442366[/C][/ROW]
[ROW][C]16[/C][C]-0.261855[/C][C]-2.9625[/C][C]0.001819[/C][/ROW]
[ROW][C]17[/C][C]-0.28742[/C][C]-3.2518[/C][C]0.000733[/C][/ROW]
[ROW][C]18[/C][C]-0.296518[/C][C]-3.3547[/C][C]0.000523[/C][/ROW]
[ROW][C]19[/C][C]-0.261708[/C][C]-2.9609[/C][C]0.001828[/C][/ROW]
[ROW][C]20[/C][C]-0.233372[/C][C]-2.6403[/C][C]0.004657[/C][/ROW]
[ROW][C]21[/C][C]0.010795[/C][C]0.1221[/C][C]0.451494[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105938&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105938&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	0.242794	2.7469	0.003442
2	0.175667	1.9874	0.024504
3	0.006563	0.0742	0.470465
4	-0.151714	-1.7164	0.044249
5	-0.227556	-2.5745	0.005588
6	-0.361447	-4.0893	3.8e-05
7	-0.222	-2.5116	0.006631
8	-0.181209	-2.0501	0.021196
9	-0.049774	-0.5631	0.287166
10	0.09371	1.0602	0.145523
11	0.299358	3.3868	0.00047
12	0.460166	5.2062	0
13	0.351402	3.9757	5.8e-05
14	0.066288	0.75	0.227327
15	-0.01284	-0.1453	0.442366
16	-0.261855	-2.9625	0.001819
17	-0.28742	-3.2518	0.000733
18	-0.296518	-3.3547	0.000523
19	-0.261708	-2.9609	0.001828
20	-0.233372	-2.6403	0.004657
21	0.010795	0.1221	0.451494

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.242794	2.7469	0.003442
2	0.12403	1.4032	0.081484
3	-0.065739	-0.7438	0.229195
4	-0.174996	-1.9799	0.024932
5	-0.167295	-1.8927	0.030326
6	-0.26614	-3.011	0.001569
7	-0.07352	-0.8318	0.203539
8	-0.08471	-0.9584	0.169839
9	-0.029569	-0.3345	0.369261
10	0.035728	0.4042	0.343366
11	0.202126	2.2868	0.011925
12	0.312622	3.5369	0.000282
13	0.183525	2.0763	0.019931
14	-0.1632	-1.8464	0.033572
15	-0.098943	-1.1194	0.13253
16	-0.233863	-2.6459	0.004585
17	-0.096829	-1.0955	0.137679
18	0.008079	0.0914	0.463657
19	0.016624	0.1881	0.425558
20	-0.14118	-1.5973	0.056336
21	0.104959	1.1875	0.11862

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.242794 & 2.7469 & 0.003442 \tabularnewline
2 & 0.12403 & 1.4032 & 0.081484 \tabularnewline
3 & -0.065739 & -0.7438 & 0.229195 \tabularnewline
4 & -0.174996 & -1.9799 & 0.024932 \tabularnewline
5 & -0.167295 & -1.8927 & 0.030326 \tabularnewline
6 & -0.26614 & -3.011 & 0.001569 \tabularnewline
7 & -0.07352 & -0.8318 & 0.203539 \tabularnewline
8 & -0.08471 & -0.9584 & 0.169839 \tabularnewline
9 & -0.029569 & -0.3345 & 0.369261 \tabularnewline
10 & 0.035728 & 0.4042 & 0.343366 \tabularnewline
11 & 0.202126 & 2.2868 & 0.011925 \tabularnewline
12 & 0.312622 & 3.5369 & 0.000282 \tabularnewline
13 & 0.183525 & 2.0763 & 0.019931 \tabularnewline
14 & -0.1632 & -1.8464 & 0.033572 \tabularnewline
15 & -0.098943 & -1.1194 & 0.13253 \tabularnewline
16 & -0.233863 & -2.6459 & 0.004585 \tabularnewline
17 & -0.096829 & -1.0955 & 0.137679 \tabularnewline
18 & 0.008079 & 0.0914 & 0.463657 \tabularnewline
19 & 0.016624 & 0.1881 & 0.425558 \tabularnewline
20 & -0.14118 & -1.5973 & 0.056336 \tabularnewline
21 & 0.104959 & 1.1875 & 0.11862 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105938&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]0.242794[/C][C]2.7469[/C][C]0.003442[/C][/ROW]
[ROW][C]2[/C][C]0.12403[/C][C]1.4032[/C][C]0.081484[/C][/ROW]
[ROW][C]3[/C][C]-0.065739[/C][C]-0.7438[/C][C]0.229195[/C][/ROW]
[ROW][C]4[/C][C]-0.174996[/C][C]-1.9799[/C][C]0.024932[/C][/ROW]
[ROW][C]5[/C][C]-0.167295[/C][C]-1.8927[/C][C]0.030326[/C][/ROW]
[ROW][C]6[/C][C]-0.26614[/C][C]-3.011[/C][C]0.001569[/C][/ROW]
[ROW][C]7[/C][C]-0.07352[/C][C]-0.8318[/C][C]0.203539[/C][/ROW]
[ROW][C]8[/C][C]-0.08471[/C][C]-0.9584[/C][C]0.169839[/C][/ROW]
[ROW][C]9[/C][C]-0.029569[/C][C]-0.3345[/C][C]0.369261[/C][/ROW]
[ROW][C]10[/C][C]0.035728[/C][C]0.4042[/C][C]0.343366[/C][/ROW]
[ROW][C]11[/C][C]0.202126[/C][C]2.2868[/C][C]0.011925[/C][/ROW]
[ROW][C]12[/C][C]0.312622[/C][C]3.5369[/C][C]0.000282[/C][/ROW]
[ROW][C]13[/C][C]0.183525[/C][C]2.0763[/C][C]0.019931[/C][/ROW]
[ROW][C]14[/C][C]-0.1632[/C][C]-1.8464[/C][C]0.033572[/C][/ROW]
[ROW][C]15[/C][C]-0.098943[/C][C]-1.1194[/C][C]0.13253[/C][/ROW]
[ROW][C]16[/C][C]-0.233863[/C][C]-2.6459[/C][C]0.004585[/C][/ROW]
[ROW][C]17[/C][C]-0.096829[/C][C]-1.0955[/C][C]0.137679[/C][/ROW]
[ROW][C]18[/C][C]0.008079[/C][C]0.0914[/C][C]0.463657[/C][/ROW]
[ROW][C]19[/C][C]0.016624[/C][C]0.1881[/C][C]0.425558[/C][/ROW]
[ROW][C]20[/C][C]-0.14118[/C][C]-1.5973[/C][C]0.056336[/C][/ROW]
[ROW][C]21[/C][C]0.104959[/C][C]1.1875[/C][C]0.11862[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105938&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105938&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	0.242794	2.7469	0.003442
2	0.12403	1.4032	0.081484
3	-0.065739	-0.7438	0.229195
4	-0.174996	-1.9799	0.024932
5	-0.167295	-1.8927	0.030326
6	-0.26614	-3.011	0.001569
7	-0.07352	-0.8318	0.203539
8	-0.08471	-0.9584	0.169839
9	-0.029569	-0.3345	0.369261
10	0.035728	0.4042	0.343366
11	0.202126	2.2868	0.011925
12	0.312622	3.5369	0.000282
13	0.183525	2.0763	0.019931
14	-0.1632	-1.8464	0.033572
15	-0.098943	-1.1194	0.13253
16	-0.233863	-2.6459	0.004585
17	-0.096829	-1.0955	0.137679
18	0.008079	0.0914	0.463657
19	0.016624	0.1881	0.425558
20	-0.14118	-1.5973	0.056336
21	0.104959	1.1875	0.11862

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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