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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 03 Sep 2015 08:11:42 +0100

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/2015/Sep/03/t1441264313yy8rai39m72ua9b.htm/, Retrieved Thu, 16 May 2024 08:35:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280453, Retrieved Thu, 16 May 2024 08:35:52 +0000

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User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2015-09-03 07:11:42] [3e99441ea7f7f69c8fa4628f6be951c3] [Current]

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Dataseries X:

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Histogram

Boxplots

1.4
1.5
1.8
1.8
1.8
1.7
1.5
1.1
1.3
1.6
1.9
1.9
2
2.2
2.2
2
2.3
2.6
3.2
3.2
3.1
2.8
2.3
1.9
1.9
2
2
1.8
1.6
1.4
0.2
0.3
0.4
0.7
1
1.1
0.8
0.8
1
1.1
1
0.8
1.6
1.5
1.6
1.6
1.6
1.9
2
1.9
2
2.1
2.3
2.3
2.6
2.6
2.7
2.6
2.6
2.4
2.5
2.5
2.5
2.4
2.1
2.1
2.3
2.3
2.3
2.9
2.8
2.9
3
3
2.9
2.6
2.8
2.9
3.1
2.8
2.4
1.6
1.5
1.7

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=280453&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=280453&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280453&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	0.214661	1.9557	0.026935
2	0.038273	0.3487	0.364104
3	-0.14346	-1.307	0.097414
4	-0.11666	-1.0628	0.145472
5	-0.08827	-0.8042	0.211795
6	0.043706	0.3982	0.345761
7	0.162789	1.4831	0.070921
8	0.180508	1.6445	0.051928
9	0.072379	0.6594	0.255732
10	-0.081748	-0.7448	0.22926
11	-0.148534	-1.3532	0.089831
12	-0.428279	-3.9018	9.7e-05
13	-0.1244	-1.1333	0.130169
14	-0.041774	-0.3806	0.352244
15	0.099973	0.9108	0.182521
16	0.136715	1.2455	0.10822
17	0.001727	0.0157	0.493742
18	-0.020076	-0.1829	0.427659
19	-0.075732	-0.69	0.246075

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.214661 & 1.9557 & 0.026935 \tabularnewline
2 & 0.038273 & 0.3487 & 0.364104 \tabularnewline
3 & -0.14346 & -1.307 & 0.097414 \tabularnewline
4 & -0.11666 & -1.0628 & 0.145472 \tabularnewline
5 & -0.08827 & -0.8042 & 0.211795 \tabularnewline
6 & 0.043706 & 0.3982 & 0.345761 \tabularnewline
7 & 0.162789 & 1.4831 & 0.070921 \tabularnewline
8 & 0.180508 & 1.6445 & 0.051928 \tabularnewline
9 & 0.072379 & 0.6594 & 0.255732 \tabularnewline
10 & -0.081748 & -0.7448 & 0.22926 \tabularnewline
11 & -0.148534 & -1.3532 & 0.089831 \tabularnewline
12 & -0.428279 & -3.9018 & 9.7e-05 \tabularnewline
13 & -0.1244 & -1.1333 & 0.130169 \tabularnewline
14 & -0.041774 & -0.3806 & 0.352244 \tabularnewline
15 & 0.099973 & 0.9108 & 0.182521 \tabularnewline
16 & 0.136715 & 1.2455 & 0.10822 \tabularnewline
17 & 0.001727 & 0.0157 & 0.493742 \tabularnewline
18 & -0.020076 & -0.1829 & 0.427659 \tabularnewline
19 & -0.075732 & -0.69 & 0.246075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280453&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]0.214661[/C][C]1.9557[/C][C]0.026935[/C][/ROW]
[ROW][C]2[/C][C]0.038273[/C][C]0.3487[/C][C]0.364104[/C][/ROW]
[ROW][C]3[/C][C]-0.14346[/C][C]-1.307[/C][C]0.097414[/C][/ROW]
[ROW][C]4[/C][C]-0.11666[/C][C]-1.0628[/C][C]0.145472[/C][/ROW]
[ROW][C]5[/C][C]-0.08827[/C][C]-0.8042[/C][C]0.211795[/C][/ROW]
[ROW][C]6[/C][C]0.043706[/C][C]0.3982[/C][C]0.345761[/C][/ROW]
[ROW][C]7[/C][C]0.162789[/C][C]1.4831[/C][C]0.070921[/C][/ROW]
[ROW][C]8[/C][C]0.180508[/C][C]1.6445[/C][C]0.051928[/C][/ROW]
[ROW][C]9[/C][C]0.072379[/C][C]0.6594[/C][C]0.255732[/C][/ROW]
[ROW][C]10[/C][C]-0.081748[/C][C]-0.7448[/C][C]0.22926[/C][/ROW]
[ROW][C]11[/C][C]-0.148534[/C][C]-1.3532[/C][C]0.089831[/C][/ROW]
[ROW][C]12[/C][C]-0.428279[/C][C]-3.9018[/C][C]9.7e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.1244[/C][C]-1.1333[/C][C]0.130169[/C][/ROW]
[ROW][C]14[/C][C]-0.041774[/C][C]-0.3806[/C][C]0.352244[/C][/ROW]
[ROW][C]15[/C][C]0.099973[/C][C]0.9108[/C][C]0.182521[/C][/ROW]
[ROW][C]16[/C][C]0.136715[/C][C]1.2455[/C][C]0.10822[/C][/ROW]
[ROW][C]17[/C][C]0.001727[/C][C]0.0157[/C][C]0.493742[/C][/ROW]
[ROW][C]18[/C][C]-0.020076[/C][C]-0.1829[/C][C]0.427659[/C][/ROW]
[ROW][C]19[/C][C]-0.075732[/C][C]-0.69[/C][C]0.246075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280453&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280453&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	0.214661	1.9557	0.026935
2	0.038273	0.3487	0.364104
3	-0.14346	-1.307	0.097414
4	-0.11666	-1.0628	0.145472
5	-0.08827	-0.8042	0.211795
6	0.043706	0.3982	0.345761
7	0.162789	1.4831	0.070921
8	0.180508	1.6445	0.051928
9	0.072379	0.6594	0.255732
10	-0.081748	-0.7448	0.22926
11	-0.148534	-1.3532	0.089831
12	-0.428279	-3.9018	9.7e-05
13	-0.1244	-1.1333	0.130169
14	-0.041774	-0.3806	0.352244
15	0.099973	0.9108	0.182521
16	0.136715	1.2455	0.10822
17	0.001727	0.0157	0.493742
18	-0.020076	-0.1829	0.427659
19	-0.075732	-0.69	0.246075

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.214661	1.9557	0.026935
2	-0.008183	-0.0746	0.470374
3	-0.157242	-1.4325	0.077872
4	-0.057008	-0.5194	0.302443
5	-0.045849	-0.4177	0.338621
6	0.059579	0.5428	0.294364
7	0.132872	1.2105	0.114757
8	0.103095	0.9392	0.175166
9	0.010659	0.0971	0.461437
10	-0.077493	-0.706	0.241084
11	-0.072043	-0.6563	0.25671
12	-0.382758	-3.4871	0.000392
13	0.009296	0.0847	0.466356
14	-0.062432	-0.5688	0.285519
15	-0.019933	-0.1816	0.428172
16	0.080475	0.7332	0.232762
17	-0.077813	-0.7089	0.240184
18	0.075561	0.6884	0.246562
19	0.070224	0.6398	0.262041

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.214661 & 1.9557 & 0.026935 \tabularnewline
2 & -0.008183 & -0.0746 & 0.470374 \tabularnewline
3 & -0.157242 & -1.4325 & 0.077872 \tabularnewline
4 & -0.057008 & -0.5194 & 0.302443 \tabularnewline
5 & -0.045849 & -0.4177 & 0.338621 \tabularnewline
6 & 0.059579 & 0.5428 & 0.294364 \tabularnewline
7 & 0.132872 & 1.2105 & 0.114757 \tabularnewline
8 & 0.103095 & 0.9392 & 0.175166 \tabularnewline
9 & 0.010659 & 0.0971 & 0.461437 \tabularnewline
10 & -0.077493 & -0.706 & 0.241084 \tabularnewline
11 & -0.072043 & -0.6563 & 0.25671 \tabularnewline
12 & -0.382758 & -3.4871 & 0.000392 \tabularnewline
13 & 0.009296 & 0.0847 & 0.466356 \tabularnewline
14 & -0.062432 & -0.5688 & 0.285519 \tabularnewline
15 & -0.019933 & -0.1816 & 0.428172 \tabularnewline
16 & 0.080475 & 0.7332 & 0.232762 \tabularnewline
17 & -0.077813 & -0.7089 & 0.240184 \tabularnewline
18 & 0.075561 & 0.6884 & 0.246562 \tabularnewline
19 & 0.070224 & 0.6398 & 0.262041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280453&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]0.214661[/C][C]1.9557[/C][C]0.026935[/C][/ROW]
[ROW][C]2[/C][C]-0.008183[/C][C]-0.0746[/C][C]0.470374[/C][/ROW]
[ROW][C]3[/C][C]-0.157242[/C][C]-1.4325[/C][C]0.077872[/C][/ROW]
[ROW][C]4[/C][C]-0.057008[/C][C]-0.5194[/C][C]0.302443[/C][/ROW]
[ROW][C]5[/C][C]-0.045849[/C][C]-0.4177[/C][C]0.338621[/C][/ROW]
[ROW][C]6[/C][C]0.059579[/C][C]0.5428[/C][C]0.294364[/C][/ROW]
[ROW][C]7[/C][C]0.132872[/C][C]1.2105[/C][C]0.114757[/C][/ROW]
[ROW][C]8[/C][C]0.103095[/C][C]0.9392[/C][C]0.175166[/C][/ROW]
[ROW][C]9[/C][C]0.010659[/C][C]0.0971[/C][C]0.461437[/C][/ROW]
[ROW][C]10[/C][C]-0.077493[/C][C]-0.706[/C][C]0.241084[/C][/ROW]
[ROW][C]11[/C][C]-0.072043[/C][C]-0.6563[/C][C]0.25671[/C][/ROW]
[ROW][C]12[/C][C]-0.382758[/C][C]-3.4871[/C][C]0.000392[/C][/ROW]
[ROW][C]13[/C][C]0.009296[/C][C]0.0847[/C][C]0.466356[/C][/ROW]
[ROW][C]14[/C][C]-0.062432[/C][C]-0.5688[/C][C]0.285519[/C][/ROW]
[ROW][C]15[/C][C]-0.019933[/C][C]-0.1816[/C][C]0.428172[/C][/ROW]
[ROW][C]16[/C][C]0.080475[/C][C]0.7332[/C][C]0.232762[/C][/ROW]
[ROW][C]17[/C][C]-0.077813[/C][C]-0.7089[/C][C]0.240184[/C][/ROW]
[ROW][C]18[/C][C]0.075561[/C][C]0.6884[/C][C]0.246562[/C][/ROW]
[ROW][C]19[/C][C]0.070224[/C][C]0.6398[/C][C]0.262041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280453&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280453&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	0.214661	1.9557	0.026935
2	-0.008183	-0.0746	0.470374
3	-0.157242	-1.4325	0.077872
4	-0.057008	-0.5194	0.302443
5	-0.045849	-0.4177	0.338621
6	0.059579	0.5428	0.294364
7	0.132872	1.2105	0.114757
8	0.103095	0.9392	0.175166
9	0.010659	0.0971	0.461437
10	-0.077493	-0.706	0.241084
11	-0.072043	-0.6563	0.25671
12	-0.382758	-3.4871	0.000392
13	0.009296	0.0847	0.466356
14	-0.062432	-0.5688	0.285519
15	-0.019933	-0.1816	0.428172
16	0.080475	0.7332	0.232762
17	-0.077813	-0.7089	0.240184
18	0.075561	0.6884	0.246562
19	0.070224	0.6398	0.262041

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 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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