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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 21 Dec 2008 12:05:34 -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/t1229886356k3e9yj6jyhlrdrl.htm/, Retrieved Sun, 19 May 2024 12:41:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35764, Retrieved Sun, 19 May 2024 12:41:41 +0000

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Original text written by user:

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No (this computation is public)

User-defined keywords

Estimated Impact

142

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

F       [(Partial) Autocorrelation Function] [] [2008-12-21 19:05:34] [d41d8cd98f00b204e9800998ecf8427e] [Current]

Feedback Forum

2009-01-08 13:04:33 [Aurélie Van Impe] [reply] 
Je conclusie is correct maar uitermate kort. Die had uitgebreider gemogen. Zie commentaar bij ACF van de werkloosheid.

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Dataseries X:

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Histogram

Boxplots

1.8
1.7
1.4
1.2
1
1.7
2.4
2
2.1
2
1.8
2.7
2.3
1.9
2
2.3
2.8
2.4
2.3
2.7
2.7
2.9
3
2.2
2.3
2.8
2.8
2.8
2.2
2.6
2.8
2.5
2.4
2.3
1.9
1.7
2
2.1
1.7
1.8
1.8
1.8
1.3
1.3
1.3
1.2
1.4
2.2
2.9
3.1
3.5
3.6
4.4
4.1
5.1
5.8
5.9
5.4
5.5
4.8
3.2

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35764&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]0 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=35764&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35764&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	0 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.917746	7.1678	0
2	0.801812	6.2623	0
3	0.686775	5.3639	1e-06
4	0.553946	4.3265	2.9e-05
5	0.411153	3.2112	0.001055
6	0.275331	2.1504	0.017748
7	0.160907	1.2567	0.106822
8	0.054346	0.4245	0.336365
9	-0.042759	-0.334	0.369777
10	-0.116329	-0.9086	0.183579
11	-0.192774	-1.5056	0.068664
12	-0.269563	-2.1054	0.019693
13	-0.294388	-2.2992	0.012465
14	-0.284022	-2.2183	0.015134
15	-0.269114	-2.1018	0.019852
16	-0.258995	-2.0228	0.023741
17	-0.240681	-1.8798	0.032458

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.917746 & 7.1678 & 0 \tabularnewline
2 & 0.801812 & 6.2623 & 0 \tabularnewline
3 & 0.686775 & 5.3639 & 1e-06 \tabularnewline
4 & 0.553946 & 4.3265 & 2.9e-05 \tabularnewline
5 & 0.411153 & 3.2112 & 0.001055 \tabularnewline
6 & 0.275331 & 2.1504 & 0.017748 \tabularnewline
7 & 0.160907 & 1.2567 & 0.106822 \tabularnewline
8 & 0.054346 & 0.4245 & 0.336365 \tabularnewline
9 & -0.042759 & -0.334 & 0.369777 \tabularnewline
10 & -0.116329 & -0.9086 & 0.183579 \tabularnewline
11 & -0.192774 & -1.5056 & 0.068664 \tabularnewline
12 & -0.269563 & -2.1054 & 0.019693 \tabularnewline
13 & -0.294388 & -2.2992 & 0.012465 \tabularnewline
14 & -0.284022 & -2.2183 & 0.015134 \tabularnewline
15 & -0.269114 & -2.1018 & 0.019852 \tabularnewline
16 & -0.258995 & -2.0228 & 0.023741 \tabularnewline
17 & -0.240681 & -1.8798 & 0.032458 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35764&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]0.917746[/C][C]7.1678[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.801812[/C][C]6.2623[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.686775[/C][C]5.3639[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.553946[/C][C]4.3265[/C][C]2.9e-05[/C][/ROW]
[ROW][C]5[/C][C]0.411153[/C][C]3.2112[/C][C]0.001055[/C][/ROW]
[ROW][C]6[/C][C]0.275331[/C][C]2.1504[/C][C]0.017748[/C][/ROW]
[ROW][C]7[/C][C]0.160907[/C][C]1.2567[/C][C]0.106822[/C][/ROW]
[ROW][C]8[/C][C]0.054346[/C][C]0.4245[/C][C]0.336365[/C][/ROW]
[ROW][C]9[/C][C]-0.042759[/C][C]-0.334[/C][C]0.369777[/C][/ROW]
[ROW][C]10[/C][C]-0.116329[/C][C]-0.9086[/C][C]0.183579[/C][/ROW]
[ROW][C]11[/C][C]-0.192774[/C][C]-1.5056[/C][C]0.068664[/C][/ROW]
[ROW][C]12[/C][C]-0.269563[/C][C]-2.1054[/C][C]0.019693[/C][/ROW]
[ROW][C]13[/C][C]-0.294388[/C][C]-2.2992[/C][C]0.012465[/C][/ROW]
[ROW][C]14[/C][C]-0.284022[/C][C]-2.2183[/C][C]0.015134[/C][/ROW]
[ROW][C]15[/C][C]-0.269114[/C][C]-2.1018[/C][C]0.019852[/C][/ROW]
[ROW][C]16[/C][C]-0.258995[/C][C]-2.0228[/C][C]0.023741[/C][/ROW]
[ROW][C]17[/C][C]-0.240681[/C][C]-1.8798[/C][C]0.032458[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35764&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35764&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	0.917746	7.1678	0
2	0.801812	6.2623	0
3	0.686775	5.3639	1e-06
4	0.553946	4.3265	2.9e-05
5	0.411153	3.2112	0.001055
6	0.275331	2.1504	0.017748
7	0.160907	1.2567	0.106822
8	0.054346	0.4245	0.336365
9	-0.042759	-0.334	0.369777
10	-0.116329	-0.9086	0.183579
11	-0.192774	-1.5056	0.068664
12	-0.269563	-2.1054	0.019693
13	-0.294388	-2.2992	0.012465
14	-0.284022	-2.2183	0.015134
15	-0.269114	-2.1018	0.019852
16	-0.258995	-2.0228	0.023741
17	-0.240681	-1.8798	0.032458

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.917746	7.1678	0
2	-0.256414	-2.0027	0.024832
3	-0.016603	-0.1297	0.448625
4	-0.200546	-1.5663	0.061224
5	-0.10692	-0.8351	0.203468
6	-0.049166	-0.384	0.351159
7	0.033168	0.2591	0.398234
8	-0.082326	-0.643	0.261322
9	-0.040869	-0.3192	0.375334
10	0.011756	0.0918	0.463571
11	-0.177915	-1.3896	0.084857
12	-0.08265	-0.6455	0.260507
13	0.242741	1.8959	0.031359
14	0.058887	0.4599	0.323604
15	-0.041846	-0.3268	0.372459
16	-0.126284	-0.9863	0.163938
17	-0.057248	-0.4471	0.328185

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.917746 & 7.1678 & 0 \tabularnewline
2 & -0.256414 & -2.0027 & 0.024832 \tabularnewline
3 & -0.016603 & -0.1297 & 0.448625 \tabularnewline
4 & -0.200546 & -1.5663 & 0.061224 \tabularnewline
5 & -0.10692 & -0.8351 & 0.203468 \tabularnewline
6 & -0.049166 & -0.384 & 0.351159 \tabularnewline
7 & 0.033168 & 0.2591 & 0.398234 \tabularnewline
8 & -0.082326 & -0.643 & 0.261322 \tabularnewline
9 & -0.040869 & -0.3192 & 0.375334 \tabularnewline
10 & 0.011756 & 0.0918 & 0.463571 \tabularnewline
11 & -0.177915 & -1.3896 & 0.084857 \tabularnewline
12 & -0.08265 & -0.6455 & 0.260507 \tabularnewline
13 & 0.242741 & 1.8959 & 0.031359 \tabularnewline
14 & 0.058887 & 0.4599 & 0.323604 \tabularnewline
15 & -0.041846 & -0.3268 & 0.372459 \tabularnewline
16 & -0.126284 & -0.9863 & 0.163938 \tabularnewline
17 & -0.057248 & -0.4471 & 0.328185 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35764&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]0.917746[/C][C]7.1678[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.256414[/C][C]-2.0027[/C][C]0.024832[/C][/ROW]
[ROW][C]3[/C][C]-0.016603[/C][C]-0.1297[/C][C]0.448625[/C][/ROW]
[ROW][C]4[/C][C]-0.200546[/C][C]-1.5663[/C][C]0.061224[/C][/ROW]
[ROW][C]5[/C][C]-0.10692[/C][C]-0.8351[/C][C]0.203468[/C][/ROW]
[ROW][C]6[/C][C]-0.049166[/C][C]-0.384[/C][C]0.351159[/C][/ROW]
[ROW][C]7[/C][C]0.033168[/C][C]0.2591[/C][C]0.398234[/C][/ROW]
[ROW][C]8[/C][C]-0.082326[/C][C]-0.643[/C][C]0.261322[/C][/ROW]
[ROW][C]9[/C][C]-0.040869[/C][C]-0.3192[/C][C]0.375334[/C][/ROW]
[ROW][C]10[/C][C]0.011756[/C][C]0.0918[/C][C]0.463571[/C][/ROW]
[ROW][C]11[/C][C]-0.177915[/C][C]-1.3896[/C][C]0.084857[/C][/ROW]
[ROW][C]12[/C][C]-0.08265[/C][C]-0.6455[/C][C]0.260507[/C][/ROW]
[ROW][C]13[/C][C]0.242741[/C][C]1.8959[/C][C]0.031359[/C][/ROW]
[ROW][C]14[/C][C]0.058887[/C][C]0.4599[/C][C]0.323604[/C][/ROW]
[ROW][C]15[/C][C]-0.041846[/C][C]-0.3268[/C][C]0.372459[/C][/ROW]
[ROW][C]16[/C][C]-0.126284[/C][C]-0.9863[/C][C]0.163938[/C][/ROW]
[ROW][C]17[/C][C]-0.057248[/C][C]-0.4471[/C][C]0.328185[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35764&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35764&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	0.917746	7.1678	0
2	-0.256414	-2.0027	0.024832
3	-0.016603	-0.1297	0.448625
4	-0.200546	-1.5663	0.061224
5	-0.10692	-0.8351	0.203468
6	-0.049166	-0.384	0.351159
7	0.033168	0.2591	0.398234
8	-0.082326	-0.643	0.261322
9	-0.040869	-0.3192	0.375334
10	0.011756	0.0918	0.463571
11	-0.177915	-1.3896	0.084857
12	-0.08265	-0.6455	0.260507
13	0.242741	1.8959	0.031359
14	0.058887	0.4599	0.323604
15	-0.041846	-0.3268	0.372459
16	-0.126284	-0.9863	0.163938
17	-0.057248	-0.4471	0.328185

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