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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 23 Dec 2014 20:39:53 +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/2014/Dec/23/t1419367248myseajsspjcfhun.htm/, Retrieved Thu, 16 May 2024 04:49:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271428, Retrieved Thu, 16 May 2024 04:49:50 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

180

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

-       [(Partial) Autocorrelation Function] [Gemiddelde consum...] [2014-12-23 20:39:53] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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2,37
2,45
2,53
2,56
2,62
2,67
2,62
2,6
2,53
2,49
2,48
2,44
2,36
2,35
2,44
2,5
2,58
2,55
2,44
2,3
2,24
2,19
2,25
2,28
2,27
2,37
2,47
2,5
2,47
2,61
2,61
2,65
2,43
2,43
2,33
2,27
2,22
2,17
2,28
2,3
2,33
2,44
2,41
2,4
2,34
2,37
2,38
2,3
2,29
2,34
2,35
2,38
2,37
2,45
2,51
2,46
2,42
2,48
2,44
2,43
2,36
2,42
2,42
2,43
2,47
2,54
2,55
2,55
2,49
2,54
2,55
2,5

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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271428&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271428&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271428&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.848501	6.5725	0
2	0.698273	5.4088	1e-06
3	0.486383	3.7675	0.000189
4	0.322655	2.4993	0.007599
5	0.192713	1.4927	0.070372
6	0.047929	0.3713	0.355878
7	-0.070741	-0.548	0.292877
8	-0.165312	-1.2805	0.102649
9	-0.25983	-2.0126	0.024324
10	-0.34873	-2.7012	0.004483
11	-0.400653	-3.1034	0.001458
12	-0.419738	-3.2513	0.000943
13	-0.272326	-2.1094	0.019544
14	-0.149599	-1.1588	0.125566
15	0.009472	0.0734	0.470878
16	0.073289	0.5677	0.28618
17	0.114989	0.8907	0.188323
18	0.173529	1.3442	0.09198

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.848501 & 6.5725 & 0 \tabularnewline
2 & 0.698273 & 5.4088 & 1e-06 \tabularnewline
3 & 0.486383 & 3.7675 & 0.000189 \tabularnewline
4 & 0.322655 & 2.4993 & 0.007599 \tabularnewline
5 & 0.192713 & 1.4927 & 0.070372 \tabularnewline
6 & 0.047929 & 0.3713 & 0.355878 \tabularnewline
7 & -0.070741 & -0.548 & 0.292877 \tabularnewline
8 & -0.165312 & -1.2805 & 0.102649 \tabularnewline
9 & -0.25983 & -2.0126 & 0.024324 \tabularnewline
10 & -0.34873 & -2.7012 & 0.004483 \tabularnewline
11 & -0.400653 & -3.1034 & 0.001458 \tabularnewline
12 & -0.419738 & -3.2513 & 0.000943 \tabularnewline
13 & -0.272326 & -2.1094 & 0.019544 \tabularnewline
14 & -0.149599 & -1.1588 & 0.125566 \tabularnewline
15 & 0.009472 & 0.0734 & 0.470878 \tabularnewline
16 & 0.073289 & 0.5677 & 0.28618 \tabularnewline
17 & 0.114989 & 0.8907 & 0.188323 \tabularnewline
18 & 0.173529 & 1.3442 & 0.09198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271428&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]0.848501[/C][C]6.5725[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.698273[/C][C]5.4088[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.486383[/C][C]3.7675[/C][C]0.000189[/C][/ROW]
[ROW][C]4[/C][C]0.322655[/C][C]2.4993[/C][C]0.007599[/C][/ROW]
[ROW][C]5[/C][C]0.192713[/C][C]1.4927[/C][C]0.070372[/C][/ROW]
[ROW][C]6[/C][C]0.047929[/C][C]0.3713[/C][C]0.355878[/C][/ROW]
[ROW][C]7[/C][C]-0.070741[/C][C]-0.548[/C][C]0.292877[/C][/ROW]
[ROW][C]8[/C][C]-0.165312[/C][C]-1.2805[/C][C]0.102649[/C][/ROW]
[ROW][C]9[/C][C]-0.25983[/C][C]-2.0126[/C][C]0.024324[/C][/ROW]
[ROW][C]10[/C][C]-0.34873[/C][C]-2.7012[/C][C]0.004483[/C][/ROW]
[ROW][C]11[/C][C]-0.400653[/C][C]-3.1034[/C][C]0.001458[/C][/ROW]
[ROW][C]12[/C][C]-0.419738[/C][C]-3.2513[/C][C]0.000943[/C][/ROW]
[ROW][C]13[/C][C]-0.272326[/C][C]-2.1094[/C][C]0.019544[/C][/ROW]
[ROW][C]14[/C][C]-0.149599[/C][C]-1.1588[/C][C]0.125566[/C][/ROW]
[ROW][C]15[/C][C]0.009472[/C][C]0.0734[/C][C]0.470878[/C][/ROW]
[ROW][C]16[/C][C]0.073289[/C][C]0.5677[/C][C]0.28618[/C][/ROW]
[ROW][C]17[/C][C]0.114989[/C][C]0.8907[/C][C]0.188323[/C][/ROW]
[ROW][C]18[/C][C]0.173529[/C][C]1.3442[/C][C]0.09198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271428&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271428&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	0.848501	6.5725	0
2	0.698273	5.4088	1e-06
3	0.486383	3.7675	0.000189
4	0.322655	2.4993	0.007599
5	0.192713	1.4927	0.070372
6	0.047929	0.3713	0.355878
7	-0.070741	-0.548	0.292877
8	-0.165312	-1.2805	0.102649
9	-0.25983	-2.0126	0.024324
10	-0.34873	-2.7012	0.004483
11	-0.400653	-3.1034	0.001458
12	-0.419738	-3.2513	0.000943
13	-0.272326	-2.1094	0.019544
14	-0.149599	-1.1588	0.125566
15	0.009472	0.0734	0.470878
16	0.073289	0.5677	0.28618
17	0.114989	0.8907	0.188323
18	0.173529	1.3442	0.09198

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.848501	6.5725	0
2	-0.077419	-0.5997	0.275487
3	-0.309955	-2.4009	0.009736
4	0.035271	0.2732	0.392816
5	0.05474	0.424	0.336535
6	-0.242675	-1.8798	0.0325
7	-0.076258	-0.5907	0.278472
8	0.058098	0.45	0.327158
9	-0.187286	-1.4507	0.076034
10	-0.203154	-1.5736	0.060417
11	0.102816	0.7964	0.214467
12	0.0139	0.1077	0.457309
13	0.473474	3.6675	0.000261
14	-0.072896	-0.5646	0.287209
15	-0.04762	-0.3689	0.356764
16	-0.150224	-1.1636	0.12459
17	0.003788	0.0293	0.488345
18	0.139137	1.0777	0.14273

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.848501 & 6.5725 & 0 \tabularnewline
2 & -0.077419 & -0.5997 & 0.275487 \tabularnewline
3 & -0.309955 & -2.4009 & 0.009736 \tabularnewline
4 & 0.035271 & 0.2732 & 0.392816 \tabularnewline
5 & 0.05474 & 0.424 & 0.336535 \tabularnewline
6 & -0.242675 & -1.8798 & 0.0325 \tabularnewline
7 & -0.076258 & -0.5907 & 0.278472 \tabularnewline
8 & 0.058098 & 0.45 & 0.327158 \tabularnewline
9 & -0.187286 & -1.4507 & 0.076034 \tabularnewline
10 & -0.203154 & -1.5736 & 0.060417 \tabularnewline
11 & 0.102816 & 0.7964 & 0.214467 \tabularnewline
12 & 0.0139 & 0.1077 & 0.457309 \tabularnewline
13 & 0.473474 & 3.6675 & 0.000261 \tabularnewline
14 & -0.072896 & -0.5646 & 0.287209 \tabularnewline
15 & -0.04762 & -0.3689 & 0.356764 \tabularnewline
16 & -0.150224 & -1.1636 & 0.12459 \tabularnewline
17 & 0.003788 & 0.0293 & 0.488345 \tabularnewline
18 & 0.139137 & 1.0777 & 0.14273 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271428&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]0.848501[/C][C]6.5725[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.077419[/C][C]-0.5997[/C][C]0.275487[/C][/ROW]
[ROW][C]3[/C][C]-0.309955[/C][C]-2.4009[/C][C]0.009736[/C][/ROW]
[ROW][C]4[/C][C]0.035271[/C][C]0.2732[/C][C]0.392816[/C][/ROW]
[ROW][C]5[/C][C]0.05474[/C][C]0.424[/C][C]0.336535[/C][/ROW]
[ROW][C]6[/C][C]-0.242675[/C][C]-1.8798[/C][C]0.0325[/C][/ROW]
[ROW][C]7[/C][C]-0.076258[/C][C]-0.5907[/C][C]0.278472[/C][/ROW]
[ROW][C]8[/C][C]0.058098[/C][C]0.45[/C][C]0.327158[/C][/ROW]
[ROW][C]9[/C][C]-0.187286[/C][C]-1.4507[/C][C]0.076034[/C][/ROW]
[ROW][C]10[/C][C]-0.203154[/C][C]-1.5736[/C][C]0.060417[/C][/ROW]
[ROW][C]11[/C][C]0.102816[/C][C]0.7964[/C][C]0.214467[/C][/ROW]
[ROW][C]12[/C][C]0.0139[/C][C]0.1077[/C][C]0.457309[/C][/ROW]
[ROW][C]13[/C][C]0.473474[/C][C]3.6675[/C][C]0.000261[/C][/ROW]
[ROW][C]14[/C][C]-0.072896[/C][C]-0.5646[/C][C]0.287209[/C][/ROW]
[ROW][C]15[/C][C]-0.04762[/C][C]-0.3689[/C][C]0.356764[/C][/ROW]
[ROW][C]16[/C][C]-0.150224[/C][C]-1.1636[/C][C]0.12459[/C][/ROW]
[ROW][C]17[/C][C]0.003788[/C][C]0.0293[/C][C]0.488345[/C][/ROW]
[ROW][C]18[/C][C]0.139137[/C][C]1.0777[/C][C]0.14273[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271428&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271428&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	0.848501	6.5725	0
2	-0.077419	-0.5997	0.275487
3	-0.309955	-2.4009	0.009736
4	0.035271	0.2732	0.392816
5	0.05474	0.424	0.336535
6	-0.242675	-1.8798	0.0325
7	-0.076258	-0.5907	0.278472
8	0.058098	0.45	0.327158
9	-0.187286	-1.4507	0.076034
10	-0.203154	-1.5736	0.060417
11	0.102816	0.7964	0.214467
12	0.0139	0.1077	0.457309
13	0.473474	3.6675	0.000261
14	-0.072896	-0.5646	0.287209
15	-0.04762	-0.3689	0.356764
16	-0.150224	-1.1636	0.12459
17	0.003788	0.0293	0.488345
18	0.139137	1.0777	0.14273

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code