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Author's title

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

Fri, 12 Dec 2008 04:14:36 -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/2008/Dec/12/t1229080546q1rya15e5hs71q8.htm/, Retrieved Tue, 14 May 2024 04:43:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32552, Retrieved Tue, 14 May 2024 04:43:32 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

203

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

-     [Variance Reduction Matrix] [VRM - vaste rente...] [2008-12-12 10:51:08] [c5a66f1c8528a963efc2b82a8519f117]
- RM D  [Standard Deviation-Mean Plot] [SDMP inschrijving...] [2008-12-12 11:03:14] [c5a66f1c8528a963efc2b82a8519f117]
- RM      [Variance Reduction Matrix] [VRM - inschrijvin...] [2008-12-12 11:08:27] [c5a66f1c8528a963efc2b82a8519f117]
- RMP         [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 11:14:36] [b4fc5040f26b33db57f84cfb8d1d2b82] [Current]
- RMP           [Spectral Analysis] [SA - inschrijving...] [2008-12-12 11:17:12] [c5a66f1c8528a963efc2b82a8519f117] 
-                 [Spectral Analysis] [SA - inschrijving...] [2008-12-12 11:25:51] [c5a66f1c8528a963efc2b82a8519f117] 
-  M D            [Spectral Analysis] [spectraalanalyse ...] [2009-12-11 14:10:59] [37a8d600db9abe09a2528d150ccff095] 
-  MPD            [Spectral Analysis] [spectraalanalyse ...] [2009-12-11 14:34:45] [37a8d600db9abe09a2528d150ccff095] 
-   P           [(Partial) Autocorrelation Function] [SA - inschrijving...] [2008-12-12 11:30:34] [c5a66f1c8528a963efc2b82a8519f117] 
-   P           [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 11:32:48] [c5a66f1c8528a963efc2b82a8519f117] 
-                 [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 11:37:19] [c5a66f1c8528a963efc2b82a8519f117] 
- RM                [ARIMA Backward Selection] [ARIMA backward se...] [2008-12-12 11:51:13] [c5a66f1c8528a963efc2b82a8519f117] 
- RM                  [ARIMA Forecasting] [ARIMA forecasting...] [2008-12-12 11:57:42] [c5a66f1c8528a963efc2b82a8519f117] 
F                       [ARIMA Forecasting] [ARIMA forecasting...] [2008-12-12 12:06:55] [c5a66f1c8528a963efc2b82a8519f117] 
-  MPD                    [ARIMA Forecasting] [ARIMA forecasting...] [2009-12-16 20:44:06] [37a8d600db9abe09a2528d150ccff095] 
-  MPD                    [ARIMA Forecasting] [Arima forecast - ...] [2009-12-16 20:56:07] [37a8d600db9abe09a2528d150ccff095] 
-  MPD                [ARIMA Backward Selection] [Arima backward se...] [2009-12-16 15:42:38] [37a8d600db9abe09a2528d150ccff095] 
-  MPD              [(Partial) Autocorrelation Function] [ACF en PACF - uit...] [2009-12-11 15:34:04] [37a8d600db9abe09a2528d150ccff095] 
-   P           [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 14:06:23] [c5a66f1c8528a963efc2b82a8519f117] 
-   P             [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 14:09:53] [c5a66f1c8528a963efc2b82a8519f117] 
-   P               [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 14:13:00] [c5a66f1c8528a963efc2b82a8519f117] 
-   P                 [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 14:23:53] [c5a66f1c8528a963efc2b82a8519f117] 

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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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32552&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32552&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32552&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.358795	2.8023	0.003396
2	0.150112	1.1724	0.122795
3	-0.073328	-0.5727	0.284472
4	-0.250143	-1.9537	0.027664
5	-0.311067	-2.4295	0.009039
6	-0.505276	-3.9463	0.000104
7	-0.272217	-2.1261	0.018776
8	-0.178059	-1.3907	0.084687
9	-0.089394	-0.6982	0.243856
10	0.067825	0.5297	0.29911
11	0.257824	2.0137	0.024231
12	0.698356	5.4543	0
13	0.228982	1.7884	0.039338
14	0.098314	0.7679	0.222767
15	-0.036394	-0.2842	0.388591
16	-0.164865	-1.2876	0.101369
17	-0.241	-1.8823	0.032286

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.358795 & 2.8023 & 0.003396 \tabularnewline
2 & 0.150112 & 1.1724 & 0.122795 \tabularnewline
3 & -0.073328 & -0.5727 & 0.284472 \tabularnewline
4 & -0.250143 & -1.9537 & 0.027664 \tabularnewline
5 & -0.311067 & -2.4295 & 0.009039 \tabularnewline
6 & -0.505276 & -3.9463 & 0.000104 \tabularnewline
7 & -0.272217 & -2.1261 & 0.018776 \tabularnewline
8 & -0.178059 & -1.3907 & 0.084687 \tabularnewline
9 & -0.089394 & -0.6982 & 0.243856 \tabularnewline
10 & 0.067825 & 0.5297 & 0.29911 \tabularnewline
11 & 0.257824 & 2.0137 & 0.024231 \tabularnewline
12 & 0.698356 & 5.4543 & 0 \tabularnewline
13 & 0.228982 & 1.7884 & 0.039338 \tabularnewline
14 & 0.098314 & 0.7679 & 0.222767 \tabularnewline
15 & -0.036394 & -0.2842 & 0.388591 \tabularnewline
16 & -0.164865 & -1.2876 & 0.101369 \tabularnewline
17 & -0.241 & -1.8823 & 0.032286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32552&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]0.358795[/C][C]2.8023[/C][C]0.003396[/C][/ROW]
[ROW][C]2[/C][C]0.150112[/C][C]1.1724[/C][C]0.122795[/C][/ROW]
[ROW][C]3[/C][C]-0.073328[/C][C]-0.5727[/C][C]0.284472[/C][/ROW]
[ROW][C]4[/C][C]-0.250143[/C][C]-1.9537[/C][C]0.027664[/C][/ROW]
[ROW][C]5[/C][C]-0.311067[/C][C]-2.4295[/C][C]0.009039[/C][/ROW]
[ROW][C]6[/C][C]-0.505276[/C][C]-3.9463[/C][C]0.000104[/C][/ROW]
[ROW][C]7[/C][C]-0.272217[/C][C]-2.1261[/C][C]0.018776[/C][/ROW]
[ROW][C]8[/C][C]-0.178059[/C][C]-1.3907[/C][C]0.084687[/C][/ROW]
[ROW][C]9[/C][C]-0.089394[/C][C]-0.6982[/C][C]0.243856[/C][/ROW]
[ROW][C]10[/C][C]0.067825[/C][C]0.5297[/C][C]0.29911[/C][/ROW]
[ROW][C]11[/C][C]0.257824[/C][C]2.0137[/C][C]0.024231[/C][/ROW]
[ROW][C]12[/C][C]0.698356[/C][C]5.4543[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.228982[/C][C]1.7884[/C][C]0.039338[/C][/ROW]
[ROW][C]14[/C][C]0.098314[/C][C]0.7679[/C][C]0.222767[/C][/ROW]
[ROW][C]15[/C][C]-0.036394[/C][C]-0.2842[/C][C]0.388591[/C][/ROW]
[ROW][C]16[/C][C]-0.164865[/C][C]-1.2876[/C][C]0.101369[/C][/ROW]
[ROW][C]17[/C][C]-0.241[/C][C]-1.8823[/C][C]0.032286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32552&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32552&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	0.358795	2.8023	0.003396
2	0.150112	1.1724	0.122795
3	-0.073328	-0.5727	0.284472
4	-0.250143	-1.9537	0.027664
5	-0.311067	-2.4295	0.009039
6	-0.505276	-3.9463	0.000104
7	-0.272217	-2.1261	0.018776
8	-0.178059	-1.3907	0.084687
9	-0.089394	-0.6982	0.243856
10	0.067825	0.5297	0.29911
11	0.257824	2.0137	0.024231
12	0.698356	5.4543	0
13	0.228982	1.7884	0.039338
14	0.098314	0.7679	0.222767
15	-0.036394	-0.2842	0.388591
16	-0.164865	-1.2876	0.101369
17	-0.241	-1.8823	0.032286

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.358795	2.8023	0.003396
2	0.024537	0.1916	0.424329
3	-0.154661	-1.2079	0.115866
4	-0.212396	-1.6589	0.051138
5	-0.167145	-1.3054	0.098322
6	-0.40159	-3.1365	0.001316
7	-0.054028	-0.422	0.337263
8	-0.159292	-1.2441	0.109109
9	-0.237724	-1.8567	0.034093
10	-0.166452	-1.3	0.09924
11	0.021009	0.1641	0.435104
12	0.536267	4.1884	4.6e-05
13	-0.353997	-2.7648	0.003762
14	-0.147315	-1.1506	0.1272
15	0.036816	0.2875	0.387336
16	0.080298	0.6271	0.266452
17	-0.10292	-0.8038	0.212308

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.358795 & 2.8023 & 0.003396 \tabularnewline
2 & 0.024537 & 0.1916 & 0.424329 \tabularnewline
3 & -0.154661 & -1.2079 & 0.115866 \tabularnewline
4 & -0.212396 & -1.6589 & 0.051138 \tabularnewline
5 & -0.167145 & -1.3054 & 0.098322 \tabularnewline
6 & -0.40159 & -3.1365 & 0.001316 \tabularnewline
7 & -0.054028 & -0.422 & 0.337263 \tabularnewline
8 & -0.159292 & -1.2441 & 0.109109 \tabularnewline
9 & -0.237724 & -1.8567 & 0.034093 \tabularnewline
10 & -0.166452 & -1.3 & 0.09924 \tabularnewline
11 & 0.021009 & 0.1641 & 0.435104 \tabularnewline
12 & 0.536267 & 4.1884 & 4.6e-05 \tabularnewline
13 & -0.353997 & -2.7648 & 0.003762 \tabularnewline
14 & -0.147315 & -1.1506 & 0.1272 \tabularnewline
15 & 0.036816 & 0.2875 & 0.387336 \tabularnewline
16 & 0.080298 & 0.6271 & 0.266452 \tabularnewline
17 & -0.10292 & -0.8038 & 0.212308 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32552&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]0.358795[/C][C]2.8023[/C][C]0.003396[/C][/ROW]
[ROW][C]2[/C][C]0.024537[/C][C]0.1916[/C][C]0.424329[/C][/ROW]
[ROW][C]3[/C][C]-0.154661[/C][C]-1.2079[/C][C]0.115866[/C][/ROW]
[ROW][C]4[/C][C]-0.212396[/C][C]-1.6589[/C][C]0.051138[/C][/ROW]
[ROW][C]5[/C][C]-0.167145[/C][C]-1.3054[/C][C]0.098322[/C][/ROW]
[ROW][C]6[/C][C]-0.40159[/C][C]-3.1365[/C][C]0.001316[/C][/ROW]
[ROW][C]7[/C][C]-0.054028[/C][C]-0.422[/C][C]0.337263[/C][/ROW]
[ROW][C]8[/C][C]-0.159292[/C][C]-1.2441[/C][C]0.109109[/C][/ROW]
[ROW][C]9[/C][C]-0.237724[/C][C]-1.8567[/C][C]0.034093[/C][/ROW]
[ROW][C]10[/C][C]-0.166452[/C][C]-1.3[/C][C]0.09924[/C][/ROW]
[ROW][C]11[/C][C]0.021009[/C][C]0.1641[/C][C]0.435104[/C][/ROW]
[ROW][C]12[/C][C]0.536267[/C][C]4.1884[/C][C]4.6e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.353997[/C][C]-2.7648[/C][C]0.003762[/C][/ROW]
[ROW][C]14[/C][C]-0.147315[/C][C]-1.1506[/C][C]0.1272[/C][/ROW]
[ROW][C]15[/C][C]0.036816[/C][C]0.2875[/C][C]0.387336[/C][/ROW]
[ROW][C]16[/C][C]0.080298[/C][C]0.6271[/C][C]0.266452[/C][/ROW]
[ROW][C]17[/C][C]-0.10292[/C][C]-0.8038[/C][C]0.212308[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32552&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32552&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	0.358795	2.8023	0.003396
2	0.024537	0.1916	0.424329
3	-0.154661	-1.2079	0.115866
4	-0.212396	-1.6589	0.051138
5	-0.167145	-1.3054	0.098322
6	-0.40159	-3.1365	0.001316
7	-0.054028	-0.422	0.337263
8	-0.159292	-1.2441	0.109109
9	-0.237724	-1.8567	0.034093
10	-0.166452	-1.3	0.09924
11	0.021009	0.1641	0.435104
12	0.536267	4.1884	4.6e-05
13	-0.353997	-2.7648	0.003762
14	-0.147315	-1.1506	0.1272
15	0.036816	0.2875	0.387336
16	0.080298	0.6271	0.266452
17	-0.10292	-0.8038	0.212308

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 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