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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 21 Dec 2008 06:24:41 -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/21/t12298660527zw8ypgwkqwtk99.htm/, Retrieved Sun, 19 May 2024 10:21:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35566, Retrieved Sun, 19 May 2024 10:21:03 +0000

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User-defined keywords

Estimated Impact

179

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

-     [(Partial) Autocorrelation Function] [(Partial) autocor...] [2008-12-21 10:44:06] [8b0d202c3a0c4ea223fd8b8e731dacd8]
-   P   [(Partial) Autocorrelation Function] [ACF werkloosheid] [2008-12-21 11:01:48] [8b0d202c3a0c4ea223fd8b8e731dacd8]
-   PD      [(Partial) Autocorrelation Function] [ACF, PACF inschri...] [2008-12-21 13:24:41] [9ba97de59bb4d2edf0cfeac4ca7d2b73] [Current]
-   P         [(Partial) Autocorrelation Function] [ACF inschr. perso...] [2008-12-21 13:57:40] [8b0d202c3a0c4ea223fd8b8e731dacd8] 

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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=35566&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=35566&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35566&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	0.475262	4.0327	6.8e-05
2	0.393173	3.3362	0.000673
3	0.14831	1.2585	0.106147
4	0.063649	0.5401	0.295406
5	0.088046	0.7471	0.228719
6	0.10976	0.9313	0.177394
7	0.053224	0.4516	0.32645
8	0.084552	0.7174	0.23771
9	0.047654	0.4044	0.343574
10	-0.244977	-2.0787	0.020604
11	-0.3637	-3.0861	0.001439
12	-0.48208	-4.0906	5.5e-05
13	-0.3697	-3.137	0.001236
14	-0.178271	-1.5127	0.067369
15	-0.079298	-0.6729	0.251594
16	-0.093431	-0.7928	0.215252
17	-0.037305	-0.3165	0.376253
18	-0.047235	-0.4008	0.344876
19	-0.108901	-0.9241	0.179272

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.475262 & 4.0327 & 6.8e-05 \tabularnewline
2 & 0.393173 & 3.3362 & 0.000673 \tabularnewline
3 & 0.14831 & 1.2585 & 0.106147 \tabularnewline
4 & 0.063649 & 0.5401 & 0.295406 \tabularnewline
5 & 0.088046 & 0.7471 & 0.228719 \tabularnewline
6 & 0.10976 & 0.9313 & 0.177394 \tabularnewline
7 & 0.053224 & 0.4516 & 0.32645 \tabularnewline
8 & 0.084552 & 0.7174 & 0.23771 \tabularnewline
9 & 0.047654 & 0.4044 & 0.343574 \tabularnewline
10 & -0.244977 & -2.0787 & 0.020604 \tabularnewline
11 & -0.3637 & -3.0861 & 0.001439 \tabularnewline
12 & -0.48208 & -4.0906 & 5.5e-05 \tabularnewline
13 & -0.3697 & -3.137 & 0.001236 \tabularnewline
14 & -0.178271 & -1.5127 & 0.067369 \tabularnewline
15 & -0.079298 & -0.6729 & 0.251594 \tabularnewline
16 & -0.093431 & -0.7928 & 0.215252 \tabularnewline
17 & -0.037305 & -0.3165 & 0.376253 \tabularnewline
18 & -0.047235 & -0.4008 & 0.344876 \tabularnewline
19 & -0.108901 & -0.9241 & 0.179272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35566&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]0.475262[/C][C]4.0327[/C][C]6.8e-05[/C][/ROW]
[ROW][C]2[/C][C]0.393173[/C][C]3.3362[/C][C]0.000673[/C][/ROW]
[ROW][C]3[/C][C]0.14831[/C][C]1.2585[/C][C]0.106147[/C][/ROW]
[ROW][C]4[/C][C]0.063649[/C][C]0.5401[/C][C]0.295406[/C][/ROW]
[ROW][C]5[/C][C]0.088046[/C][C]0.7471[/C][C]0.228719[/C][/ROW]
[ROW][C]6[/C][C]0.10976[/C][C]0.9313[/C][C]0.177394[/C][/ROW]
[ROW][C]7[/C][C]0.053224[/C][C]0.4516[/C][C]0.32645[/C][/ROW]
[ROW][C]8[/C][C]0.084552[/C][C]0.7174[/C][C]0.23771[/C][/ROW]
[ROW][C]9[/C][C]0.047654[/C][C]0.4044[/C][C]0.343574[/C][/ROW]
[ROW][C]10[/C][C]-0.244977[/C][C]-2.0787[/C][C]0.020604[/C][/ROW]
[ROW][C]11[/C][C]-0.3637[/C][C]-3.0861[/C][C]0.001439[/C][/ROW]
[ROW][C]12[/C][C]-0.48208[/C][C]-4.0906[/C][C]5.5e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.3697[/C][C]-3.137[/C][C]0.001236[/C][/ROW]
[ROW][C]14[/C][C]-0.178271[/C][C]-1.5127[/C][C]0.067369[/C][/ROW]
[ROW][C]15[/C][C]-0.079298[/C][C]-0.6729[/C][C]0.251594[/C][/ROW]
[ROW][C]16[/C][C]-0.093431[/C][C]-0.7928[/C][C]0.215252[/C][/ROW]
[ROW][C]17[/C][C]-0.037305[/C][C]-0.3165[/C][C]0.376253[/C][/ROW]
[ROW][C]18[/C][C]-0.047235[/C][C]-0.4008[/C][C]0.344876[/C][/ROW]
[ROW][C]19[/C][C]-0.108901[/C][C]-0.9241[/C][C]0.179272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35566&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35566&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	0.475262	4.0327	6.8e-05
2	0.393173	3.3362	0.000673
3	0.14831	1.2585	0.106147
4	0.063649	0.5401	0.295406
5	0.088046	0.7471	0.228719
6	0.10976	0.9313	0.177394
7	0.053224	0.4516	0.32645
8	0.084552	0.7174	0.23771
9	0.047654	0.4044	0.343574
10	-0.244977	-2.0787	0.020604
11	-0.3637	-3.0861	0.001439
12	-0.48208	-4.0906	5.5e-05
13	-0.3697	-3.137	0.001236
14	-0.178271	-1.5127	0.067369
15	-0.079298	-0.6729	0.251594
16	-0.093431	-0.7928	0.215252
17	-0.037305	-0.3165	0.376253
18	-0.047235	-0.4008	0.344876
19	-0.108901	-0.9241	0.179272

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.475262	4.0327	6.8e-05
2	0.216114	1.8338	0.035409
3	-0.136696	-1.1599	0.12496
4	-0.049728	-0.422	0.337157
5	0.125735	1.0669	0.144792
6	0.080877	0.6863	0.247376
7	-0.091099	-0.773	0.221025
8	0.04373	0.3711	0.35584
9	0.034903	0.2962	0.383979
10	-0.424121	-3.5988	0.000292
11	-0.298418	-2.5322	0.006759
12	-0.110835	-0.9405	0.175062
13	0.050349	0.4272	0.335245
14	0.109409	0.9284	0.178159
15	0.067955	0.5766	0.282998
16	-0.037629	-0.3193	0.375215
17	0.059832	0.5077	0.306611
18	0.116228	0.9862	0.163662
19	-0.046738	-0.3966	0.346422

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.475262 & 4.0327 & 6.8e-05 \tabularnewline
2 & 0.216114 & 1.8338 & 0.035409 \tabularnewline
3 & -0.136696 & -1.1599 & 0.12496 \tabularnewline
4 & -0.049728 & -0.422 & 0.337157 \tabularnewline
5 & 0.125735 & 1.0669 & 0.144792 \tabularnewline
6 & 0.080877 & 0.6863 & 0.247376 \tabularnewline
7 & -0.091099 & -0.773 & 0.221025 \tabularnewline
8 & 0.04373 & 0.3711 & 0.35584 \tabularnewline
9 & 0.034903 & 0.2962 & 0.383979 \tabularnewline
10 & -0.424121 & -3.5988 & 0.000292 \tabularnewline
11 & -0.298418 & -2.5322 & 0.006759 \tabularnewline
12 & -0.110835 & -0.9405 & 0.175062 \tabularnewline
13 & 0.050349 & 0.4272 & 0.335245 \tabularnewline
14 & 0.109409 & 0.9284 & 0.178159 \tabularnewline
15 & 0.067955 & 0.5766 & 0.282998 \tabularnewline
16 & -0.037629 & -0.3193 & 0.375215 \tabularnewline
17 & 0.059832 & 0.5077 & 0.306611 \tabularnewline
18 & 0.116228 & 0.9862 & 0.163662 \tabularnewline
19 & -0.046738 & -0.3966 & 0.346422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35566&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]0.475262[/C][C]4.0327[/C][C]6.8e-05[/C][/ROW]
[ROW][C]2[/C][C]0.216114[/C][C]1.8338[/C][C]0.035409[/C][/ROW]
[ROW][C]3[/C][C]-0.136696[/C][C]-1.1599[/C][C]0.12496[/C][/ROW]
[ROW][C]4[/C][C]-0.049728[/C][C]-0.422[/C][C]0.337157[/C][/ROW]
[ROW][C]5[/C][C]0.125735[/C][C]1.0669[/C][C]0.144792[/C][/ROW]
[ROW][C]6[/C][C]0.080877[/C][C]0.6863[/C][C]0.247376[/C][/ROW]
[ROW][C]7[/C][C]-0.091099[/C][C]-0.773[/C][C]0.221025[/C][/ROW]
[ROW][C]8[/C][C]0.04373[/C][C]0.3711[/C][C]0.35584[/C][/ROW]
[ROW][C]9[/C][C]0.034903[/C][C]0.2962[/C][C]0.383979[/C][/ROW]
[ROW][C]10[/C][C]-0.424121[/C][C]-3.5988[/C][C]0.000292[/C][/ROW]
[ROW][C]11[/C][C]-0.298418[/C][C]-2.5322[/C][C]0.006759[/C][/ROW]
[ROW][C]12[/C][C]-0.110835[/C][C]-0.9405[/C][C]0.175062[/C][/ROW]
[ROW][C]13[/C][C]0.050349[/C][C]0.4272[/C][C]0.335245[/C][/ROW]
[ROW][C]14[/C][C]0.109409[/C][C]0.9284[/C][C]0.178159[/C][/ROW]
[ROW][C]15[/C][C]0.067955[/C][C]0.5766[/C][C]0.282998[/C][/ROW]
[ROW][C]16[/C][C]-0.037629[/C][C]-0.3193[/C][C]0.375215[/C][/ROW]
[ROW][C]17[/C][C]0.059832[/C][C]0.5077[/C][C]0.306611[/C][/ROW]
[ROW][C]18[/C][C]0.116228[/C][C]0.9862[/C][C]0.163662[/C][/ROW]
[ROW][C]19[/C][C]-0.046738[/C][C]-0.3966[/C][C]0.346422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35566&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35566&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	0.475262	4.0327	6.8e-05
2	0.216114	1.8338	0.035409
3	-0.136696	-1.1599	0.12496
4	-0.049728	-0.422	0.337157
5	0.125735	1.0669	0.144792
6	0.080877	0.6863	0.247376
7	-0.091099	-0.773	0.221025
8	0.04373	0.3711	0.35584
9	0.034903	0.2962	0.383979
10	-0.424121	-3.5988	0.000292
11	-0.298418	-2.5322	0.006759
12	-0.110835	-0.9405	0.175062
13	0.050349	0.4272	0.335245
14	0.109409	0.9284	0.178159
15	0.067955	0.5766	0.282998
16	-0.037629	-0.3193	0.375215
17	0.059832	0.5077	0.306611
18	0.116228	0.9862	0.163662
19	-0.046738	-0.3966	0.346422

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code