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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 26 May 2012 07:54:39 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/26/t1338033343jjpzji91ejc0u0u.htm/, Retrieved Thu, 02 May 2024 17:02:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167587, Retrieved Thu, 02 May 2024 17:02:38 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

111

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

-       [(Partial) Autocorrelation Function] [Autocorrelation f...] [2012-05-26 11:54:39] [a2709f7ab86902c8a6d752383a828f6c] [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' @ 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167587&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167587&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167587&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' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.929126	7.197	0
2	0.867149	6.7169	0
3	0.808522	6.2628	0
4	0.760408	5.8901	0
5	0.719133	5.5704	0
6	0.669683	5.1873	1e-06
7	0.618676	4.7922	6e-06
8	0.56899	4.4074	2.2e-05
9	0.514017	3.9816	9.4e-05
10	0.474889	3.6785	0.000252
11	0.433869	3.3607	0.000678
12	0.39264	3.0414	0.001745
13	0.34356	2.6612	0.004988
14	0.290473	2.25	0.014065
15	0.246798	1.9117	0.030348
16	0.202118	1.5656	0.061351
17	0.169891	1.316	0.096595

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.929126 & 7.197 & 0 \tabularnewline
2 & 0.867149 & 6.7169 & 0 \tabularnewline
3 & 0.808522 & 6.2628 & 0 \tabularnewline
4 & 0.760408 & 5.8901 & 0 \tabularnewline
5 & 0.719133 & 5.5704 & 0 \tabularnewline
6 & 0.669683 & 5.1873 & 1e-06 \tabularnewline
7 & 0.618676 & 4.7922 & 6e-06 \tabularnewline
8 & 0.56899 & 4.4074 & 2.2e-05 \tabularnewline
9 & 0.514017 & 3.9816 & 9.4e-05 \tabularnewline
10 & 0.474889 & 3.6785 & 0.000252 \tabularnewline
11 & 0.433869 & 3.3607 & 0.000678 \tabularnewline
12 & 0.39264 & 3.0414 & 0.001745 \tabularnewline
13 & 0.34356 & 2.6612 & 0.004988 \tabularnewline
14 & 0.290473 & 2.25 & 0.014065 \tabularnewline
15 & 0.246798 & 1.9117 & 0.030348 \tabularnewline
16 & 0.202118 & 1.5656 & 0.061351 \tabularnewline
17 & 0.169891 & 1.316 & 0.096595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167587&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]0.929126[/C][C]7.197[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.867149[/C][C]6.7169[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.808522[/C][C]6.2628[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.760408[/C][C]5.8901[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.719133[/C][C]5.5704[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.669683[/C][C]5.1873[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.618676[/C][C]4.7922[/C][C]6e-06[/C][/ROW]
[ROW][C]8[/C][C]0.56899[/C][C]4.4074[/C][C]2.2e-05[/C][/ROW]
[ROW][C]9[/C][C]0.514017[/C][C]3.9816[/C][C]9.4e-05[/C][/ROW]
[ROW][C]10[/C][C]0.474889[/C][C]3.6785[/C][C]0.000252[/C][/ROW]
[ROW][C]11[/C][C]0.433869[/C][C]3.3607[/C][C]0.000678[/C][/ROW]
[ROW][C]12[/C][C]0.39264[/C][C]3.0414[/C][C]0.001745[/C][/ROW]
[ROW][C]13[/C][C]0.34356[/C][C]2.6612[/C][C]0.004988[/C][/ROW]
[ROW][C]14[/C][C]0.290473[/C][C]2.25[/C][C]0.014065[/C][/ROW]
[ROW][C]15[/C][C]0.246798[/C][C]1.9117[/C][C]0.030348[/C][/ROW]
[ROW][C]16[/C][C]0.202118[/C][C]1.5656[/C][C]0.061351[/C][/ROW]
[ROW][C]17[/C][C]0.169891[/C][C]1.316[/C][C]0.096595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167587&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167587&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	0.929126	7.197	0
2	0.867149	6.7169	0
3	0.808522	6.2628	0
4	0.760408	5.8901	0
5	0.719133	5.5704	0
6	0.669683	5.1873	1e-06
7	0.618676	4.7922	6e-06
8	0.56899	4.4074	2.2e-05
9	0.514017	3.9816	9.4e-05
10	0.474889	3.6785	0.000252
11	0.433869	3.3607	0.000678
12	0.39264	3.0414	0.001745
13	0.34356	2.6612	0.004988
14	0.290473	2.25	0.014065
15	0.246798	1.9117	0.030348
16	0.202118	1.5656	0.061351
17	0.169891	1.316	0.096595

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.929126	7.197	0
2	0.028336	0.2195	0.413506
3	-0.004872	-0.0377	0.48501
4	0.047621	0.3689	0.356762
5	0.032395	0.2509	0.401363
6	-0.074117	-0.5741	0.28402
7	-0.039195	-0.3036	0.38124
8	-0.01743	-0.135	0.446527
9	-0.075019	-0.5811	0.281678
10	0.070124	0.5432	0.294511
11	-0.027558	-0.2135	0.415844
12	-0.030693	-0.2377	0.406445
13	-0.078033	-0.6044	0.273914
14	-0.058657	-0.4544	0.325607
15	0.014192	0.1099	0.456414
16	-0.047335	-0.3667	0.357584
17	0.053611	0.4153	0.339714

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.929126 & 7.197 & 0 \tabularnewline
2 & 0.028336 & 0.2195 & 0.413506 \tabularnewline
3 & -0.004872 & -0.0377 & 0.48501 \tabularnewline
4 & 0.047621 & 0.3689 & 0.356762 \tabularnewline
5 & 0.032395 & 0.2509 & 0.401363 \tabularnewline
6 & -0.074117 & -0.5741 & 0.28402 \tabularnewline
7 & -0.039195 & -0.3036 & 0.38124 \tabularnewline
8 & -0.01743 & -0.135 & 0.446527 \tabularnewline
9 & -0.075019 & -0.5811 & 0.281678 \tabularnewline
10 & 0.070124 & 0.5432 & 0.294511 \tabularnewline
11 & -0.027558 & -0.2135 & 0.415844 \tabularnewline
12 & -0.030693 & -0.2377 & 0.406445 \tabularnewline
13 & -0.078033 & -0.6044 & 0.273914 \tabularnewline
14 & -0.058657 & -0.4544 & 0.325607 \tabularnewline
15 & 0.014192 & 0.1099 & 0.456414 \tabularnewline
16 & -0.047335 & -0.3667 & 0.357584 \tabularnewline
17 & 0.053611 & 0.4153 & 0.339714 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167587&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]0.929126[/C][C]7.197[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.028336[/C][C]0.2195[/C][C]0.413506[/C][/ROW]
[ROW][C]3[/C][C]-0.004872[/C][C]-0.0377[/C][C]0.48501[/C][/ROW]
[ROW][C]4[/C][C]0.047621[/C][C]0.3689[/C][C]0.356762[/C][/ROW]
[ROW][C]5[/C][C]0.032395[/C][C]0.2509[/C][C]0.401363[/C][/ROW]
[ROW][C]6[/C][C]-0.074117[/C][C]-0.5741[/C][C]0.28402[/C][/ROW]
[ROW][C]7[/C][C]-0.039195[/C][C]-0.3036[/C][C]0.38124[/C][/ROW]
[ROW][C]8[/C][C]-0.01743[/C][C]-0.135[/C][C]0.446527[/C][/ROW]
[ROW][C]9[/C][C]-0.075019[/C][C]-0.5811[/C][C]0.281678[/C][/ROW]
[ROW][C]10[/C][C]0.070124[/C][C]0.5432[/C][C]0.294511[/C][/ROW]
[ROW][C]11[/C][C]-0.027558[/C][C]-0.2135[/C][C]0.415844[/C][/ROW]
[ROW][C]12[/C][C]-0.030693[/C][C]-0.2377[/C][C]0.406445[/C][/ROW]
[ROW][C]13[/C][C]-0.078033[/C][C]-0.6044[/C][C]0.273914[/C][/ROW]
[ROW][C]14[/C][C]-0.058657[/C][C]-0.4544[/C][C]0.325607[/C][/ROW]
[ROW][C]15[/C][C]0.014192[/C][C]0.1099[/C][C]0.456414[/C][/ROW]
[ROW][C]16[/C][C]-0.047335[/C][C]-0.3667[/C][C]0.357584[/C][/ROW]
[ROW][C]17[/C][C]0.053611[/C][C]0.4153[/C][C]0.339714[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167587&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167587&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	0.929126	7.197	0
2	0.028336	0.2195	0.413506
3	-0.004872	-0.0377	0.48501
4	0.047621	0.3689	0.356762
5	0.032395	0.2509	0.401363
6	-0.074117	-0.5741	0.28402
7	-0.039195	-0.3036	0.38124
8	-0.01743	-0.135	0.446527
9	-0.075019	-0.5811	0.281678
10	0.070124	0.5432	0.294511
11	-0.027558	-0.2135	0.415844
12	-0.030693	-0.2377	0.406445
13	-0.078033	-0.6044	0.273914
14	-0.058657	-0.4544	0.325607
15	0.014192	0.1099	0.456414
16	-0.047335	-0.3667	0.357584
17	0.053611	0.4153	0.339714

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 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code