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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Dec 2011 07:45:46 -0500

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/2011/Dec/22/t13245584320nfl7a93s1w8hjr.htm/, Retrieved Fri, 03 May 2024 13:50:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159386, Retrieved Fri, 03 May 2024 13:50:57 +0000

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User-defined keywords

Estimated Impact

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

-     [(Partial) Autocorrelation Function] [Workshop 6: ACF] [2010-12-14 13:10:00] [b9eaf9df71639055b3e2389f5099ca2c]
- R  D    [(Partial) Autocorrelation Function] [ACF] [2011-12-22 12:45:46] [d41d8cd98f00b204e9800998ecf8427e] [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	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159386&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159386&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159386&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.869468	10.2877	0
2	0.75732	8.9607	0
3	0.713891	8.4469	0
4	0.640379	7.5771	0
5	0.558103	6.6036	0
6	0.512037	6.0585	0
7	0.471764	5.582	0
8	0.391617	4.6337	4e-06
9	0.302143	3.575	0.000241
10	0.214506	2.5381	0.006121
11	0.133326	1.5775	0.058464
12	0.058626	0.6937	0.244518
13	-0.003374	-0.0399	0.484109
14	-0.076961	-0.9106	0.182032
15	-0.143325	-1.6959	0.046068
16	-0.204128	-2.4153	0.008507
17	-0.265061	-3.1362	0.001043
18	-0.315301	-3.7307	0.000138
19	-0.363463	-4.3006	1.6e-05
20	-0.409658	-4.8471	2e-06
21	-0.448711	-5.3092	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.869468 & 10.2877 & 0 \tabularnewline
2 & 0.75732 & 8.9607 & 0 \tabularnewline
3 & 0.713891 & 8.4469 & 0 \tabularnewline
4 & 0.640379 & 7.5771 & 0 \tabularnewline
5 & 0.558103 & 6.6036 & 0 \tabularnewline
6 & 0.512037 & 6.0585 & 0 \tabularnewline
7 & 0.471764 & 5.582 & 0 \tabularnewline
8 & 0.391617 & 4.6337 & 4e-06 \tabularnewline
9 & 0.302143 & 3.575 & 0.000241 \tabularnewline
10 & 0.214506 & 2.5381 & 0.006121 \tabularnewline
11 & 0.133326 & 1.5775 & 0.058464 \tabularnewline
12 & 0.058626 & 0.6937 & 0.244518 \tabularnewline
13 & -0.003374 & -0.0399 & 0.484109 \tabularnewline
14 & -0.076961 & -0.9106 & 0.182032 \tabularnewline
15 & -0.143325 & -1.6959 & 0.046068 \tabularnewline
16 & -0.204128 & -2.4153 & 0.008507 \tabularnewline
17 & -0.265061 & -3.1362 & 0.001043 \tabularnewline
18 & -0.315301 & -3.7307 & 0.000138 \tabularnewline
19 & -0.363463 & -4.3006 & 1.6e-05 \tabularnewline
20 & -0.409658 & -4.8471 & 2e-06 \tabularnewline
21 & -0.448711 & -5.3092 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159386&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]0.869468[/C][C]10.2877[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.75732[/C][C]8.9607[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.713891[/C][C]8.4469[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.640379[/C][C]7.5771[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.558103[/C][C]6.6036[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.512037[/C][C]6.0585[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.471764[/C][C]5.582[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.391617[/C][C]4.6337[/C][C]4e-06[/C][/ROW]
[ROW][C]9[/C][C]0.302143[/C][C]3.575[/C][C]0.000241[/C][/ROW]
[ROW][C]10[/C][C]0.214506[/C][C]2.5381[/C][C]0.006121[/C][/ROW]
[ROW][C]11[/C][C]0.133326[/C][C]1.5775[/C][C]0.058464[/C][/ROW]
[ROW][C]12[/C][C]0.058626[/C][C]0.6937[/C][C]0.244518[/C][/ROW]
[ROW][C]13[/C][C]-0.003374[/C][C]-0.0399[/C][C]0.484109[/C][/ROW]
[ROW][C]14[/C][C]-0.076961[/C][C]-0.9106[/C][C]0.182032[/C][/ROW]
[ROW][C]15[/C][C]-0.143325[/C][C]-1.6959[/C][C]0.046068[/C][/ROW]
[ROW][C]16[/C][C]-0.204128[/C][C]-2.4153[/C][C]0.008507[/C][/ROW]
[ROW][C]17[/C][C]-0.265061[/C][C]-3.1362[/C][C]0.001043[/C][/ROW]
[ROW][C]18[/C][C]-0.315301[/C][C]-3.7307[/C][C]0.000138[/C][/ROW]
[ROW][C]19[/C][C]-0.363463[/C][C]-4.3006[/C][C]1.6e-05[/C][/ROW]
[ROW][C]20[/C][C]-0.409658[/C][C]-4.8471[/C][C]2e-06[/C][/ROW]
[ROW][C]21[/C][C]-0.448711[/C][C]-5.3092[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159386&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159386&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	0.869468	10.2877	0
2	0.75732	8.9607	0
3	0.713891	8.4469	0
4	0.640379	7.5771	0
5	0.558103	6.6036	0
6	0.512037	6.0585	0
7	0.471764	5.582	0
8	0.391617	4.6337	4e-06
9	0.302143	3.575	0.000241
10	0.214506	2.5381	0.006121
11	0.133326	1.5775	0.058464
12	0.058626	0.6937	0.244518
13	-0.003374	-0.0399	0.484109
14	-0.076961	-0.9106	0.182032
15	-0.143325	-1.6959	0.046068
16	-0.204128	-2.4153	0.008507
17	-0.265061	-3.1362	0.001043
18	-0.315301	-3.7307	0.000138
19	-0.363463	-4.3006	1.6e-05
20	-0.409658	-4.8471	2e-06
21	-0.448711	-5.3092	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.869468	10.2877	0
2	0.005515	0.0653	0.474032
3	0.22237	2.6311	0.004732
4	-0.120424	-1.4249	0.078209
5	-0.022051	-0.2609	0.397271
6	0.052066	0.6161	0.269428
7	0.009279	0.1098	0.456367
8	-0.139811	-1.6543	0.050157
9	-0.112881	-1.3356	0.09192
10	-0.136194	-1.6115	0.054664
11	-0.040009	-0.4734	0.318334
12	-0.043144	-0.5105	0.305256
13	-0.017222	-0.2038	0.419413
14	-0.126409	-1.4957	0.068492
15	-0.028035	-0.3317	0.370302
16	-0.066495	-0.7868	0.21637
17	-0.027946	-0.3307	0.370698
18	-0.02484	-0.2939	0.384631
19	-0.07365	-0.8714	0.192503
20	-0.070718	-0.8368	0.202079
21	-0.048306	-0.5716	0.284265

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.869468 & 10.2877 & 0 \tabularnewline
2 & 0.005515 & 0.0653 & 0.474032 \tabularnewline
3 & 0.22237 & 2.6311 & 0.004732 \tabularnewline
4 & -0.120424 & -1.4249 & 0.078209 \tabularnewline
5 & -0.022051 & -0.2609 & 0.397271 \tabularnewline
6 & 0.052066 & 0.6161 & 0.269428 \tabularnewline
7 & 0.009279 & 0.1098 & 0.456367 \tabularnewline
8 & -0.139811 & -1.6543 & 0.050157 \tabularnewline
9 & -0.112881 & -1.3356 & 0.09192 \tabularnewline
10 & -0.136194 & -1.6115 & 0.054664 \tabularnewline
11 & -0.040009 & -0.4734 & 0.318334 \tabularnewline
12 & -0.043144 & -0.5105 & 0.305256 \tabularnewline
13 & -0.017222 & -0.2038 & 0.419413 \tabularnewline
14 & -0.126409 & -1.4957 & 0.068492 \tabularnewline
15 & -0.028035 & -0.3317 & 0.370302 \tabularnewline
16 & -0.066495 & -0.7868 & 0.21637 \tabularnewline
17 & -0.027946 & -0.3307 & 0.370698 \tabularnewline
18 & -0.02484 & -0.2939 & 0.384631 \tabularnewline
19 & -0.07365 & -0.8714 & 0.192503 \tabularnewline
20 & -0.070718 & -0.8368 & 0.202079 \tabularnewline
21 & -0.048306 & -0.5716 & 0.284265 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159386&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]0.869468[/C][C]10.2877[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.005515[/C][C]0.0653[/C][C]0.474032[/C][/ROW]
[ROW][C]3[/C][C]0.22237[/C][C]2.6311[/C][C]0.004732[/C][/ROW]
[ROW][C]4[/C][C]-0.120424[/C][C]-1.4249[/C][C]0.078209[/C][/ROW]
[ROW][C]5[/C][C]-0.022051[/C][C]-0.2609[/C][C]0.397271[/C][/ROW]
[ROW][C]6[/C][C]0.052066[/C][C]0.6161[/C][C]0.269428[/C][/ROW]
[ROW][C]7[/C][C]0.009279[/C][C]0.1098[/C][C]0.456367[/C][/ROW]
[ROW][C]8[/C][C]-0.139811[/C][C]-1.6543[/C][C]0.050157[/C][/ROW]
[ROW][C]9[/C][C]-0.112881[/C][C]-1.3356[/C][C]0.09192[/C][/ROW]
[ROW][C]10[/C][C]-0.136194[/C][C]-1.6115[/C][C]0.054664[/C][/ROW]
[ROW][C]11[/C][C]-0.040009[/C][C]-0.4734[/C][C]0.318334[/C][/ROW]
[ROW][C]12[/C][C]-0.043144[/C][C]-0.5105[/C][C]0.305256[/C][/ROW]
[ROW][C]13[/C][C]-0.017222[/C][C]-0.2038[/C][C]0.419413[/C][/ROW]
[ROW][C]14[/C][C]-0.126409[/C][C]-1.4957[/C][C]0.068492[/C][/ROW]
[ROW][C]15[/C][C]-0.028035[/C][C]-0.3317[/C][C]0.370302[/C][/ROW]
[ROW][C]16[/C][C]-0.066495[/C][C]-0.7868[/C][C]0.21637[/C][/ROW]
[ROW][C]17[/C][C]-0.027946[/C][C]-0.3307[/C][C]0.370698[/C][/ROW]
[ROW][C]18[/C][C]-0.02484[/C][C]-0.2939[/C][C]0.384631[/C][/ROW]
[ROW][C]19[/C][C]-0.07365[/C][C]-0.8714[/C][C]0.192503[/C][/ROW]
[ROW][C]20[/C][C]-0.070718[/C][C]-0.8368[/C][C]0.202079[/C][/ROW]
[ROW][C]21[/C][C]-0.048306[/C][C]-0.5716[/C][C]0.284265[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159386&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159386&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	0.869468	10.2877	0
2	0.005515	0.0653	0.474032
3	0.22237	2.6311	0.004732
4	-0.120424	-1.4249	0.078209
5	-0.022051	-0.2609	0.397271
6	0.052066	0.6161	0.269428
7	0.009279	0.1098	0.456367
8	-0.139811	-1.6543	0.050157
9	-0.112881	-1.3356	0.09192
10	-0.136194	-1.6115	0.054664
11	-0.040009	-0.4734	0.318334
12	-0.043144	-0.5105	0.305256
13	-0.017222	-0.2038	0.419413
14	-0.126409	-1.4957	0.068492
15	-0.028035	-0.3317	0.370302
16	-0.066495	-0.7868	0.21637
17	-0.027946	-0.3307	0.370698
18	-0.02484	-0.2939	0.384631
19	-0.07365	-0.8714	0.192503
20	-0.070718	-0.8368	0.202079
21	-0.048306	-0.5716	0.284265

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 ; par8 = ;

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