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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Dec 2010 21:25:36 +0000

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/2010/Dec/19/t1292793822w3ok2yxqfyigqqi.htm/, Retrieved Sun, 05 May 2024 07:42:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112754, Retrieved Sun, 05 May 2024 07:42:53 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

135

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D    [(Partial) Autocorrelation Function] [Workshop 9, Stati...] [2010-12-03 13:18:27] [d946de7cca328fbcf207448a112523ab]
-    D      [(Partial) Autocorrelation Function] [Autocorrelatie Fu...] [2010-12-19 14:18:56] [d946de7cca328fbcf207448a112523ab]
- R PD        [(Partial) Autocorrelation Function] [Paper ACF] [2010-12-19 14:22:07] [3635fb7041b1998c5a1332cf9de22bce]
-   PD            [(Partial) Autocorrelation Function] [Paper ACF poging 2] [2010-12-19 21:25:36] [23a9b79f355c69a75648521a893cf584] [Current]
-   P               [(Partial) Autocorrelation Function] [Autocorrelationfu...] [2010-12-22 08:46:14] [8081b8996d5947580de3eb171e82db4f] 
-   P               [(Partial) Autocorrelation Function] [Paper Autocorrela...] [2010-12-22 09:08:40] [d946de7cca328fbcf207448a112523ab] 
-   P               [(Partial) Autocorrelation Function] [Paper Autocorrela...] [2010-12-22 09:08:40] [d946de7cca328fbcf207448a112523ab] 
-   P               [(Partial) Autocorrelation Function] [Paper Autocorrela...] [2010-12-22 09:08:40] [d946de7cca328fbcf207448a112523ab] 
-   P               [(Partial) Autocorrelation Function] [Paper ACF poging 3] [2010-12-22 09:12:13] [3635fb7041b1998c5a1332cf9de22bce] 

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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	2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112754&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]2 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=112754&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112754&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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.947038	8.6797	0
2	0.884419	8.1058	0
3	0.811776	7.4401	0
4	0.735927	6.7449	0
5	0.674106	6.1783	0
6	0.630785	5.7812	0
7	0.612521	5.6138	0
8	0.60992	5.59	0
9	0.61484	5.6351	0
10	0.622251	5.703	0
11	0.622022	5.7009	0
12	0.597705	5.4781	0
13	0.544057	4.9864	2e-06
14	0.469337	4.3015	2.3e-05
15	0.39414	3.6124	0.000258
16	0.314699	2.8843	0.002491
17	0.250804	2.2987	0.012004
18	0.213332	1.9552	0.026941
19	0.192581	1.765	0.040597

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.947038 & 8.6797 & 0 \tabularnewline
2 & 0.884419 & 8.1058 & 0 \tabularnewline
3 & 0.811776 & 7.4401 & 0 \tabularnewline
4 & 0.735927 & 6.7449 & 0 \tabularnewline
5 & 0.674106 & 6.1783 & 0 \tabularnewline
6 & 0.630785 & 5.7812 & 0 \tabularnewline
7 & 0.612521 & 5.6138 & 0 \tabularnewline
8 & 0.60992 & 5.59 & 0 \tabularnewline
9 & 0.61484 & 5.6351 & 0 \tabularnewline
10 & 0.622251 & 5.703 & 0 \tabularnewline
11 & 0.622022 & 5.7009 & 0 \tabularnewline
12 & 0.597705 & 5.4781 & 0 \tabularnewline
13 & 0.544057 & 4.9864 & 2e-06 \tabularnewline
14 & 0.469337 & 4.3015 & 2.3e-05 \tabularnewline
15 & 0.39414 & 3.6124 & 0.000258 \tabularnewline
16 & 0.314699 & 2.8843 & 0.002491 \tabularnewline
17 & 0.250804 & 2.2987 & 0.012004 \tabularnewline
18 & 0.213332 & 1.9552 & 0.026941 \tabularnewline
19 & 0.192581 & 1.765 & 0.040597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112754&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]0.947038[/C][C]8.6797[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.884419[/C][C]8.1058[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.811776[/C][C]7.4401[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.735927[/C][C]6.7449[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.674106[/C][C]6.1783[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.630785[/C][C]5.7812[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.612521[/C][C]5.6138[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.60992[/C][C]5.59[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.61484[/C][C]5.6351[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.622251[/C][C]5.703[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.622022[/C][C]5.7009[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.597705[/C][C]5.4781[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.544057[/C][C]4.9864[/C][C]2e-06[/C][/ROW]
[ROW][C]14[/C][C]0.469337[/C][C]4.3015[/C][C]2.3e-05[/C][/ROW]
[ROW][C]15[/C][C]0.39414[/C][C]3.6124[/C][C]0.000258[/C][/ROW]
[ROW][C]16[/C][C]0.314699[/C][C]2.8843[/C][C]0.002491[/C][/ROW]
[ROW][C]17[/C][C]0.250804[/C][C]2.2987[/C][C]0.012004[/C][/ROW]
[ROW][C]18[/C][C]0.213332[/C][C]1.9552[/C][C]0.026941[/C][/ROW]
[ROW][C]19[/C][C]0.192581[/C][C]1.765[/C][C]0.040597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112754&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112754&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	0.947038	8.6797	0
2	0.884419	8.1058	0
3	0.811776	7.4401	0
4	0.735927	6.7449	0
5	0.674106	6.1783	0
6	0.630785	5.7812	0
7	0.612521	5.6138	0
8	0.60992	5.59	0
9	0.61484	5.6351	0
10	0.622251	5.703	0
11	0.622022	5.7009	0
12	0.597705	5.4781	0
13	0.544057	4.9864	2e-06
14	0.469337	4.3015	2.3e-05
15	0.39414	3.6124	0.000258
16	0.314699	2.8843	0.002491
17	0.250804	2.2987	0.012004
18	0.213332	1.9552	0.026941
19	0.192581	1.765	0.040597

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.947038	8.6797	0
2	-0.120861	-1.1077	0.135575
3	-0.123732	-1.134	0.130005
4	-0.057197	-0.5242	0.300753
5	0.108274	0.9924	0.161938
6	0.132568	1.215	0.113883
7	0.178173	1.633	0.053108
8	0.079011	0.7241	0.235494
9	0.020192	0.1851	0.426813
10	0.0165	0.1512	0.440079
11	-0.025734	-0.2359	0.40706
12	-0.169631	-1.5547	0.061889
13	-0.226	-2.0713	0.020698
14	-0.161748	-1.4824	0.070982
15	0.034985	0.3206	0.37464
16	-0.073998	-0.6782	0.249754
17	0.028391	0.2602	0.39767
18	0.091451	0.8382	0.202158
19	-0.003513	-0.0322	0.487194

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.947038 & 8.6797 & 0 \tabularnewline
2 & -0.120861 & -1.1077 & 0.135575 \tabularnewline
3 & -0.123732 & -1.134 & 0.130005 \tabularnewline
4 & -0.057197 & -0.5242 & 0.300753 \tabularnewline
5 & 0.108274 & 0.9924 & 0.161938 \tabularnewline
6 & 0.132568 & 1.215 & 0.113883 \tabularnewline
7 & 0.178173 & 1.633 & 0.053108 \tabularnewline
8 & 0.079011 & 0.7241 & 0.235494 \tabularnewline
9 & 0.020192 & 0.1851 & 0.426813 \tabularnewline
10 & 0.0165 & 0.1512 & 0.440079 \tabularnewline
11 & -0.025734 & -0.2359 & 0.40706 \tabularnewline
12 & -0.169631 & -1.5547 & 0.061889 \tabularnewline
13 & -0.226 & -2.0713 & 0.020698 \tabularnewline
14 & -0.161748 & -1.4824 & 0.070982 \tabularnewline
15 & 0.034985 & 0.3206 & 0.37464 \tabularnewline
16 & -0.073998 & -0.6782 & 0.249754 \tabularnewline
17 & 0.028391 & 0.2602 & 0.39767 \tabularnewline
18 & 0.091451 & 0.8382 & 0.202158 \tabularnewline
19 & -0.003513 & -0.0322 & 0.487194 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112754&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]0.947038[/C][C]8.6797[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.120861[/C][C]-1.1077[/C][C]0.135575[/C][/ROW]
[ROW][C]3[/C][C]-0.123732[/C][C]-1.134[/C][C]0.130005[/C][/ROW]
[ROW][C]4[/C][C]-0.057197[/C][C]-0.5242[/C][C]0.300753[/C][/ROW]
[ROW][C]5[/C][C]0.108274[/C][C]0.9924[/C][C]0.161938[/C][/ROW]
[ROW][C]6[/C][C]0.132568[/C][C]1.215[/C][C]0.113883[/C][/ROW]
[ROW][C]7[/C][C]0.178173[/C][C]1.633[/C][C]0.053108[/C][/ROW]
[ROW][C]8[/C][C]0.079011[/C][C]0.7241[/C][C]0.235494[/C][/ROW]
[ROW][C]9[/C][C]0.020192[/C][C]0.1851[/C][C]0.426813[/C][/ROW]
[ROW][C]10[/C][C]0.0165[/C][C]0.1512[/C][C]0.440079[/C][/ROW]
[ROW][C]11[/C][C]-0.025734[/C][C]-0.2359[/C][C]0.40706[/C][/ROW]
[ROW][C]12[/C][C]-0.169631[/C][C]-1.5547[/C][C]0.061889[/C][/ROW]
[ROW][C]13[/C][C]-0.226[/C][C]-2.0713[/C][C]0.020698[/C][/ROW]
[ROW][C]14[/C][C]-0.161748[/C][C]-1.4824[/C][C]0.070982[/C][/ROW]
[ROW][C]15[/C][C]0.034985[/C][C]0.3206[/C][C]0.37464[/C][/ROW]
[ROW][C]16[/C][C]-0.073998[/C][C]-0.6782[/C][C]0.249754[/C][/ROW]
[ROW][C]17[/C][C]0.028391[/C][C]0.2602[/C][C]0.39767[/C][/ROW]
[ROW][C]18[/C][C]0.091451[/C][C]0.8382[/C][C]0.202158[/C][/ROW]
[ROW][C]19[/C][C]-0.003513[/C][C]-0.0322[/C][C]0.487194[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112754&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112754&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	0.947038	8.6797	0
2	-0.120861	-1.1077	0.135575
3	-0.123732	-1.134	0.130005
4	-0.057197	-0.5242	0.300753
5	0.108274	0.9924	0.161938
6	0.132568	1.215	0.113883
7	0.178173	1.633	0.053108
8	0.079011	0.7241	0.235494
9	0.020192	0.1851	0.426813
10	0.0165	0.1512	0.440079
11	-0.025734	-0.2359	0.40706
12	-0.169631	-1.5547	0.061889
13	-0.226	-2.0713	0.020698
14	-0.161748	-1.4824	0.070982
15	0.034985	0.3206	0.37464
16	-0.073998	-0.6782	0.249754
17	0.028391	0.2602	0.39767
18	0.091451	0.8382	0.202158
19	-0.003513	-0.0322	0.487194

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 2 ; par2 = equal ; par3 = 4 ; par4 = no ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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