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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 08 Dec 2008 12:55:18 -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/08/t1228766192r9x5kst3u9wxsz0.htm/, Retrieved Thu, 16 May 2024 14:40:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30881, Retrieved Thu, 16 May 2024 14:40:15 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

176

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

F     [Spectral Analysis] [Diff Spectral] [2008-12-06 12:07:42] [74be16979710d4c4e7c6647856088456]
F RMP   [ARIMA Backward Selection] [Arima backward] [2008-12-06 14:19:09] [74be16979710d4c4e7c6647856088456]
- RMPD      [(Partial) Autocorrelation Function] [ACF int prod] [2008-12-08 19:55:18] [e1dd70d3b1099218056e8ae5041dcc2f] [Current]
-   P         [(Partial) Autocorrelation Function] [ACF en PACF inter...] [2008-12-08 20:06:19] [11edab5c4db3615abbf782b1c6e7cacf] 

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30881&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30881&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30881&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.283853	2.4252	0.008886
2	0.235655	2.0134	0.023878
3	0.133923	1.1442	0.128131
4	0.023528	0.201	0.420621
5	0.064061	0.5473	0.292909
6	0.117212	1.0015	0.159956
7	-0.046173	-0.3945	0.34718
8	-0.135043	-1.1538	0.126172
9	0.001983	0.0169	0.493265
10	-0.142207	-1.215	0.114138
11	-0.027037	-0.231	0.40898
12	-0.123137	-1.0521	0.148116
13	-0.111564	-0.9532	0.171815
14	-0.092674	-0.7918	0.21552
15	-0.029006	-0.2478	0.402481
16	-0.078346	-0.6694	0.25268
17	0.018841	0.161	0.436278
18	-0.055498	-0.4742	0.318397
19	0.000487	0.0042	0.498346

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.283853 & 2.4252 & 0.008886 \tabularnewline
2 & 0.235655 & 2.0134 & 0.023878 \tabularnewline
3 & 0.133923 & 1.1442 & 0.128131 \tabularnewline
4 & 0.023528 & 0.201 & 0.420621 \tabularnewline
5 & 0.064061 & 0.5473 & 0.292909 \tabularnewline
6 & 0.117212 & 1.0015 & 0.159956 \tabularnewline
7 & -0.046173 & -0.3945 & 0.34718 \tabularnewline
8 & -0.135043 & -1.1538 & 0.126172 \tabularnewline
9 & 0.001983 & 0.0169 & 0.493265 \tabularnewline
10 & -0.142207 & -1.215 & 0.114138 \tabularnewline
11 & -0.027037 & -0.231 & 0.40898 \tabularnewline
12 & -0.123137 & -1.0521 & 0.148116 \tabularnewline
13 & -0.111564 & -0.9532 & 0.171815 \tabularnewline
14 & -0.092674 & -0.7918 & 0.21552 \tabularnewline
15 & -0.029006 & -0.2478 & 0.402481 \tabularnewline
16 & -0.078346 & -0.6694 & 0.25268 \tabularnewline
17 & 0.018841 & 0.161 & 0.436278 \tabularnewline
18 & -0.055498 & -0.4742 & 0.318397 \tabularnewline
19 & 0.000487 & 0.0042 & 0.498346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30881&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]0.283853[/C][C]2.4252[/C][C]0.008886[/C][/ROW]
[ROW][C]2[/C][C]0.235655[/C][C]2.0134[/C][C]0.023878[/C][/ROW]
[ROW][C]3[/C][C]0.133923[/C][C]1.1442[/C][C]0.128131[/C][/ROW]
[ROW][C]4[/C][C]0.023528[/C][C]0.201[/C][C]0.420621[/C][/ROW]
[ROW][C]5[/C][C]0.064061[/C][C]0.5473[/C][C]0.292909[/C][/ROW]
[ROW][C]6[/C][C]0.117212[/C][C]1.0015[/C][C]0.159956[/C][/ROW]
[ROW][C]7[/C][C]-0.046173[/C][C]-0.3945[/C][C]0.34718[/C][/ROW]
[ROW][C]8[/C][C]-0.135043[/C][C]-1.1538[/C][C]0.126172[/C][/ROW]
[ROW][C]9[/C][C]0.001983[/C][C]0.0169[/C][C]0.493265[/C][/ROW]
[ROW][C]10[/C][C]-0.142207[/C][C]-1.215[/C][C]0.114138[/C][/ROW]
[ROW][C]11[/C][C]-0.027037[/C][C]-0.231[/C][C]0.40898[/C][/ROW]
[ROW][C]12[/C][C]-0.123137[/C][C]-1.0521[/C][C]0.148116[/C][/ROW]
[ROW][C]13[/C][C]-0.111564[/C][C]-0.9532[/C][C]0.171815[/C][/ROW]
[ROW][C]14[/C][C]-0.092674[/C][C]-0.7918[/C][C]0.21552[/C][/ROW]
[ROW][C]15[/C][C]-0.029006[/C][C]-0.2478[/C][C]0.402481[/C][/ROW]
[ROW][C]16[/C][C]-0.078346[/C][C]-0.6694[/C][C]0.25268[/C][/ROW]
[ROW][C]17[/C][C]0.018841[/C][C]0.161[/C][C]0.436278[/C][/ROW]
[ROW][C]18[/C][C]-0.055498[/C][C]-0.4742[/C][C]0.318397[/C][/ROW]
[ROW][C]19[/C][C]0.000487[/C][C]0.0042[/C][C]0.498346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30881&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30881&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	0.283853	2.4252	0.008886
2	0.235655	2.0134	0.023878
3	0.133923	1.1442	0.128131
4	0.023528	0.201	0.420621
5	0.064061	0.5473	0.292909
6	0.117212	1.0015	0.159956
7	-0.046173	-0.3945	0.34718
8	-0.135043	-1.1538	0.126172
9	0.001983	0.0169	0.493265
10	-0.142207	-1.215	0.114138
11	-0.027037	-0.231	0.40898
12	-0.123137	-1.0521	0.148116
13	-0.111564	-0.9532	0.171815
14	-0.092674	-0.7918	0.21552
15	-0.029006	-0.2478	0.402481
16	-0.078346	-0.6694	0.25268
17	0.018841	0.161	0.436278
18	-0.055498	-0.4742	0.318397
19	0.000487	0.0042	0.498346

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.283853	2.4252	0.008886
2	0.168673	1.4411	0.07691
3	0.034073	0.2911	0.385893
4	-0.061453	-0.5251	0.300567
5	0.047072	0.4022	0.344362
6	0.108807	0.9296	0.177808
7	-0.124451	-1.0633	0.145573
8	-0.170565	-1.4573	0.07466
9	0.105546	0.9018	0.185068
10	-0.095355	-0.8147	0.208942
11	0.011868	0.1014	0.459754
12	-0.125321	-1.0707	0.143907
13	-0.002928	-0.025	0.490054
14	0.001168	0.01	0.496032
15	0.006798	0.0581	0.47692
16	-0.063229	-0.5402	0.295341
17	0.073709	0.6298	0.265406
18	-0.068796	-0.5878	0.279243
19	0.053539	0.4574	0.324358

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.283853 & 2.4252 & 0.008886 \tabularnewline
2 & 0.168673 & 1.4411 & 0.07691 \tabularnewline
3 & 0.034073 & 0.2911 & 0.385893 \tabularnewline
4 & -0.061453 & -0.5251 & 0.300567 \tabularnewline
5 & 0.047072 & 0.4022 & 0.344362 \tabularnewline
6 & 0.108807 & 0.9296 & 0.177808 \tabularnewline
7 & -0.124451 & -1.0633 & 0.145573 \tabularnewline
8 & -0.170565 & -1.4573 & 0.07466 \tabularnewline
9 & 0.105546 & 0.9018 & 0.185068 \tabularnewline
10 & -0.095355 & -0.8147 & 0.208942 \tabularnewline
11 & 0.011868 & 0.1014 & 0.459754 \tabularnewline
12 & -0.125321 & -1.0707 & 0.143907 \tabularnewline
13 & -0.002928 & -0.025 & 0.490054 \tabularnewline
14 & 0.001168 & 0.01 & 0.496032 \tabularnewline
15 & 0.006798 & 0.0581 & 0.47692 \tabularnewline
16 & -0.063229 & -0.5402 & 0.295341 \tabularnewline
17 & 0.073709 & 0.6298 & 0.265406 \tabularnewline
18 & -0.068796 & -0.5878 & 0.279243 \tabularnewline
19 & 0.053539 & 0.4574 & 0.324358 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30881&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]0.283853[/C][C]2.4252[/C][C]0.008886[/C][/ROW]
[ROW][C]2[/C][C]0.168673[/C][C]1.4411[/C][C]0.07691[/C][/ROW]
[ROW][C]3[/C][C]0.034073[/C][C]0.2911[/C][C]0.385893[/C][/ROW]
[ROW][C]4[/C][C]-0.061453[/C][C]-0.5251[/C][C]0.300567[/C][/ROW]
[ROW][C]5[/C][C]0.047072[/C][C]0.4022[/C][C]0.344362[/C][/ROW]
[ROW][C]6[/C][C]0.108807[/C][C]0.9296[/C][C]0.177808[/C][/ROW]
[ROW][C]7[/C][C]-0.124451[/C][C]-1.0633[/C][C]0.145573[/C][/ROW]
[ROW][C]8[/C][C]-0.170565[/C][C]-1.4573[/C][C]0.07466[/C][/ROW]
[ROW][C]9[/C][C]0.105546[/C][C]0.9018[/C][C]0.185068[/C][/ROW]
[ROW][C]10[/C][C]-0.095355[/C][C]-0.8147[/C][C]0.208942[/C][/ROW]
[ROW][C]11[/C][C]0.011868[/C][C]0.1014[/C][C]0.459754[/C][/ROW]
[ROW][C]12[/C][C]-0.125321[/C][C]-1.0707[/C][C]0.143907[/C][/ROW]
[ROW][C]13[/C][C]-0.002928[/C][C]-0.025[/C][C]0.490054[/C][/ROW]
[ROW][C]14[/C][C]0.001168[/C][C]0.01[/C][C]0.496032[/C][/ROW]
[ROW][C]15[/C][C]0.006798[/C][C]0.0581[/C][C]0.47692[/C][/ROW]
[ROW][C]16[/C][C]-0.063229[/C][C]-0.5402[/C][C]0.295341[/C][/ROW]
[ROW][C]17[/C][C]0.073709[/C][C]0.6298[/C][C]0.265406[/C][/ROW]
[ROW][C]18[/C][C]-0.068796[/C][C]-0.5878[/C][C]0.279243[/C][/ROW]
[ROW][C]19[/C][C]0.053539[/C][C]0.4574[/C][C]0.324358[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30881&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30881&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	0.283853	2.4252	0.008886
2	0.168673	1.4411	0.07691
3	0.034073	0.2911	0.385893
4	-0.061453	-0.5251	0.300567
5	0.047072	0.4022	0.344362
6	0.108807	0.9296	0.177808
7	-0.124451	-1.0633	0.145573
8	-0.170565	-1.4573	0.07466
9	0.105546	0.9018	0.185068
10	-0.095355	-0.8147	0.208942
11	0.011868	0.1014	0.459754
12	-0.125321	-1.0707	0.143907
13	-0.002928	-0.025	0.490054
14	0.001168	0.01	0.496032
15	0.006798	0.0581	0.47692
16	-0.063229	-0.5402	0.295341
17	0.073709	0.6298	0.265406
18	-0.068796	-0.5878	0.279243
19	0.053539	0.4574	0.324358

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 ;

Parameters (R input):

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

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Input Parameters & R Code