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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 17 Dec 2010 20:42:49 +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/17/t1292618505lix39x1qrjiufi2.htm/, Retrieved Fri, 03 May 2024 19:20:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111729, Retrieved Fri, 03 May 2024 19:20:39 +0000

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User-defined keywords

Estimated Impact

158

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

-     [Univariate Data Series] [Bouwvergunningen] [2009-11-02 16:57:06] [11ac052cc87d77b9933b02bea117068e]
-   P   [Univariate Data Series] [Bouwvergunningen ...] [2009-11-11 14:29:30] [11ac052cc87d77b9933b02bea117068e]
- RMPD    [Variance Reduction Matrix] [Workshop 6] [2010-12-16 20:00:53] [29e492448d11757ae0fad5ef6e7f8e86]
- RMPD        [(Partial) Autocorrelation Function] [] [2010-12-17 20:42:49] [0956ee981dded61b2e7128dae94e5715] [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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111729&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111729&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111729&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.354152	2.6025	0.005961
2	0.07594	0.558	0.289561
3	0.188512	1.3853	0.085833
4	0.358312	2.633	0.005507
5	0.264693	1.9451	0.028489
6	0.046301	0.3402	0.367499
7	-0.200801	-1.4756	0.072932
8	-0.054702	-0.402	0.344645
9	-0.004869	-0.0358	0.485795
10	-0.063227	-0.4646	0.322034
11	-0.0981	-0.7209	0.237044
12	-0.41042	-3.016	0.00195
13	-0.177946	-1.3076	0.09827
14	0.067606	0.4968	0.310672
15	-0.06652	-0.4888	0.313474
16	-0.230051	-1.6905	0.048347
17	-0.139392	-1.0243	0.155125
18	-0.082314	-0.6049	0.273896

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.354152 & 2.6025 & 0.005961 \tabularnewline
2 & 0.07594 & 0.558 & 0.289561 \tabularnewline
3 & 0.188512 & 1.3853 & 0.085833 \tabularnewline
4 & 0.358312 & 2.633 & 0.005507 \tabularnewline
5 & 0.264693 & 1.9451 & 0.028489 \tabularnewline
6 & 0.046301 & 0.3402 & 0.367499 \tabularnewline
7 & -0.200801 & -1.4756 & 0.072932 \tabularnewline
8 & -0.054702 & -0.402 & 0.344645 \tabularnewline
9 & -0.004869 & -0.0358 & 0.485795 \tabularnewline
10 & -0.063227 & -0.4646 & 0.322034 \tabularnewline
11 & -0.0981 & -0.7209 & 0.237044 \tabularnewline
12 & -0.41042 & -3.016 & 0.00195 \tabularnewline
13 & -0.177946 & -1.3076 & 0.09827 \tabularnewline
14 & 0.067606 & 0.4968 & 0.310672 \tabularnewline
15 & -0.06652 & -0.4888 & 0.313474 \tabularnewline
16 & -0.230051 & -1.6905 & 0.048347 \tabularnewline
17 & -0.139392 & -1.0243 & 0.155125 \tabularnewline
18 & -0.082314 & -0.6049 & 0.273896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111729&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]0.354152[/C][C]2.6025[/C][C]0.005961[/C][/ROW]
[ROW][C]2[/C][C]0.07594[/C][C]0.558[/C][C]0.289561[/C][/ROW]
[ROW][C]3[/C][C]0.188512[/C][C]1.3853[/C][C]0.085833[/C][/ROW]
[ROW][C]4[/C][C]0.358312[/C][C]2.633[/C][C]0.005507[/C][/ROW]
[ROW][C]5[/C][C]0.264693[/C][C]1.9451[/C][C]0.028489[/C][/ROW]
[ROW][C]6[/C][C]0.046301[/C][C]0.3402[/C][C]0.367499[/C][/ROW]
[ROW][C]7[/C][C]-0.200801[/C][C]-1.4756[/C][C]0.072932[/C][/ROW]
[ROW][C]8[/C][C]-0.054702[/C][C]-0.402[/C][C]0.344645[/C][/ROW]
[ROW][C]9[/C][C]-0.004869[/C][C]-0.0358[/C][C]0.485795[/C][/ROW]
[ROW][C]10[/C][C]-0.063227[/C][C]-0.4646[/C][C]0.322034[/C][/ROW]
[ROW][C]11[/C][C]-0.0981[/C][C]-0.7209[/C][C]0.237044[/C][/ROW]
[ROW][C]12[/C][C]-0.41042[/C][C]-3.016[/C][C]0.00195[/C][/ROW]
[ROW][C]13[/C][C]-0.177946[/C][C]-1.3076[/C][C]0.09827[/C][/ROW]
[ROW][C]14[/C][C]0.067606[/C][C]0.4968[/C][C]0.310672[/C][/ROW]
[ROW][C]15[/C][C]-0.06652[/C][C]-0.4888[/C][C]0.313474[/C][/ROW]
[ROW][C]16[/C][C]-0.230051[/C][C]-1.6905[/C][C]0.048347[/C][/ROW]
[ROW][C]17[/C][C]-0.139392[/C][C]-1.0243[/C][C]0.155125[/C][/ROW]
[ROW][C]18[/C][C]-0.082314[/C][C]-0.6049[/C][C]0.273896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111729&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111729&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	0.354152	2.6025	0.005961
2	0.07594	0.558	0.289561
3	0.188512	1.3853	0.085833
4	0.358312	2.633	0.005507
5	0.264693	1.9451	0.028489
6	0.046301	0.3402	0.367499
7	-0.200801	-1.4756	0.072932
8	-0.054702	-0.402	0.344645
9	-0.004869	-0.0358	0.485795
10	-0.063227	-0.4646	0.322034
11	-0.0981	-0.7209	0.237044
12	-0.41042	-3.016	0.00195
13	-0.177946	-1.3076	0.09827
14	0.067606	0.4968	0.310672
15	-0.06652	-0.4888	0.313474
16	-0.230051	-1.6905	0.048347
17	-0.139392	-1.0243	0.155125
18	-0.082314	-0.6049	0.273896

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.354152	2.6025	0.005961
2	-0.05658	-0.4158	0.33961
3	0.206628	1.5184	0.067373
4	0.26668	1.9597	0.027601
5	0.080443	0.5911	0.278449
6	-0.084609	-0.6217	0.268362
7	-0.336984	-2.4763	0.00822
8	-0.061407	-0.4512	0.326809
9	-0.11199	-0.823	0.207076
10	0.02542	0.1868	0.426261
11	0.148325	1.09	0.140286
12	-0.395272	-2.9046	0.002659
13	0.166594	1.2242	0.113093
14	0.05801	0.4263	0.335797
15	-0.041547	-0.3053	0.380653
16	0.051022	0.3749	0.35459
17	-0.05567	-0.4091	0.342047
18	-0.085566	-0.6288	0.266072

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.354152 & 2.6025 & 0.005961 \tabularnewline
2 & -0.05658 & -0.4158 & 0.33961 \tabularnewline
3 & 0.206628 & 1.5184 & 0.067373 \tabularnewline
4 & 0.26668 & 1.9597 & 0.027601 \tabularnewline
5 & 0.080443 & 0.5911 & 0.278449 \tabularnewline
6 & -0.084609 & -0.6217 & 0.268362 \tabularnewline
7 & -0.336984 & -2.4763 & 0.00822 \tabularnewline
8 & -0.061407 & -0.4512 & 0.326809 \tabularnewline
9 & -0.11199 & -0.823 & 0.207076 \tabularnewline
10 & 0.02542 & 0.1868 & 0.426261 \tabularnewline
11 & 0.148325 & 1.09 & 0.140286 \tabularnewline
12 & -0.395272 & -2.9046 & 0.002659 \tabularnewline
13 & 0.166594 & 1.2242 & 0.113093 \tabularnewline
14 & 0.05801 & 0.4263 & 0.335797 \tabularnewline
15 & -0.041547 & -0.3053 & 0.380653 \tabularnewline
16 & 0.051022 & 0.3749 & 0.35459 \tabularnewline
17 & -0.05567 & -0.4091 & 0.342047 \tabularnewline
18 & -0.085566 & -0.6288 & 0.266072 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111729&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]0.354152[/C][C]2.6025[/C][C]0.005961[/C][/ROW]
[ROW][C]2[/C][C]-0.05658[/C][C]-0.4158[/C][C]0.33961[/C][/ROW]
[ROW][C]3[/C][C]0.206628[/C][C]1.5184[/C][C]0.067373[/C][/ROW]
[ROW][C]4[/C][C]0.26668[/C][C]1.9597[/C][C]0.027601[/C][/ROW]
[ROW][C]5[/C][C]0.080443[/C][C]0.5911[/C][C]0.278449[/C][/ROW]
[ROW][C]6[/C][C]-0.084609[/C][C]-0.6217[/C][C]0.268362[/C][/ROW]
[ROW][C]7[/C][C]-0.336984[/C][C]-2.4763[/C][C]0.00822[/C][/ROW]
[ROW][C]8[/C][C]-0.061407[/C][C]-0.4512[/C][C]0.326809[/C][/ROW]
[ROW][C]9[/C][C]-0.11199[/C][C]-0.823[/C][C]0.207076[/C][/ROW]
[ROW][C]10[/C][C]0.02542[/C][C]0.1868[/C][C]0.426261[/C][/ROW]
[ROW][C]11[/C][C]0.148325[/C][C]1.09[/C][C]0.140286[/C][/ROW]
[ROW][C]12[/C][C]-0.395272[/C][C]-2.9046[/C][C]0.002659[/C][/ROW]
[ROW][C]13[/C][C]0.166594[/C][C]1.2242[/C][C]0.113093[/C][/ROW]
[ROW][C]14[/C][C]0.05801[/C][C]0.4263[/C][C]0.335797[/C][/ROW]
[ROW][C]15[/C][C]-0.041547[/C][C]-0.3053[/C][C]0.380653[/C][/ROW]
[ROW][C]16[/C][C]0.051022[/C][C]0.3749[/C][C]0.35459[/C][/ROW]
[ROW][C]17[/C][C]-0.05567[/C][C]-0.4091[/C][C]0.342047[/C][/ROW]
[ROW][C]18[/C][C]-0.085566[/C][C]-0.6288[/C][C]0.266072[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111729&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111729&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	0.354152	2.6025	0.005961
2	-0.05658	-0.4158	0.33961
3	0.206628	1.5184	0.067373
4	0.26668	1.9597	0.027601
5	0.080443	0.5911	0.278449
6	-0.084609	-0.6217	0.268362
7	-0.336984	-2.4763	0.00822
8	-0.061407	-0.4512	0.326809
9	-0.11199	-0.823	0.207076
10	0.02542	0.1868	0.426261
11	0.148325	1.09	0.140286
12	-0.395272	-2.9046	0.002659
13	0.166594	1.2242	0.113093
14	0.05801	0.4263	0.335797
15	-0.041547	-0.3053	0.380653
16	0.051022	0.3749	0.35459
17	-0.05567	-0.4091	0.342047
18	-0.085566	-0.6288	0.266072

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 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code