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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 10 Dec 2015 14:29:48 +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/2015/Dec/10/t1449757838jowmcdkxp1fgf06.htm/, Retrieved Thu, 16 May 2024 11:06:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285810, Retrieved Thu, 16 May 2024 11:06:34 +0000

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Estimated Impact

114

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-       [(Partial) Autocorrelation Function] [] [2015-12-10 14:29:48] [5fd2fca6b664199b2dd86155c5786748] [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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285810&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285810&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285810&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.089192	1.0247	0.153681
2	0.292633	3.3621	0.000506
3	0.291568	3.3499	0.000527
4	-0.07178	-0.8247	0.205517
5	0.195707	2.2485	0.013101
6	-0.195394	-2.2449	0.013219
7	0.048237	0.5542	0.290188
8	0.055037	0.6323	0.264134
9	0.115262	1.3243	0.093853
10	0.12404	1.4251	0.078243
11	0.086201	0.9904	0.161901
12	0.583918	6.7087	0
13	-0.074043	-0.8507	0.19824
14	0.15187	1.7449	0.041669
15	0.00826	0.0949	0.462271
16	-0.223275	-2.5652	0.005714
17	0.047116	0.5413	0.2946
18	-0.462452	-5.3132	0
19	-0.090532	-1.0401	0.150089
20	-0.071575	-0.8223	0.206184
21	-0.134995	-1.551	0.061651

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.089192 & 1.0247 & 0.153681 \tabularnewline
2 & 0.292633 & 3.3621 & 0.000506 \tabularnewline
3 & 0.291568 & 3.3499 & 0.000527 \tabularnewline
4 & -0.07178 & -0.8247 & 0.205517 \tabularnewline
5 & 0.195707 & 2.2485 & 0.013101 \tabularnewline
6 & -0.195394 & -2.2449 & 0.013219 \tabularnewline
7 & 0.048237 & 0.5542 & 0.290188 \tabularnewline
8 & 0.055037 & 0.6323 & 0.264134 \tabularnewline
9 & 0.115262 & 1.3243 & 0.093853 \tabularnewline
10 & 0.12404 & 1.4251 & 0.078243 \tabularnewline
11 & 0.086201 & 0.9904 & 0.161901 \tabularnewline
12 & 0.583918 & 6.7087 & 0 \tabularnewline
13 & -0.074043 & -0.8507 & 0.19824 \tabularnewline
14 & 0.15187 & 1.7449 & 0.041669 \tabularnewline
15 & 0.00826 & 0.0949 & 0.462271 \tabularnewline
16 & -0.223275 & -2.5652 & 0.005714 \tabularnewline
17 & 0.047116 & 0.5413 & 0.2946 \tabularnewline
18 & -0.462452 & -5.3132 & 0 \tabularnewline
19 & -0.090532 & -1.0401 & 0.150089 \tabularnewline
20 & -0.071575 & -0.8223 & 0.206184 \tabularnewline
21 & -0.134995 & -1.551 & 0.061651 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285810&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]0.089192[/C][C]1.0247[/C][C]0.153681[/C][/ROW]
[ROW][C]2[/C][C]0.292633[/C][C]3.3621[/C][C]0.000506[/C][/ROW]
[ROW][C]3[/C][C]0.291568[/C][C]3.3499[/C][C]0.000527[/C][/ROW]
[ROW][C]4[/C][C]-0.07178[/C][C]-0.8247[/C][C]0.205517[/C][/ROW]
[ROW][C]5[/C][C]0.195707[/C][C]2.2485[/C][C]0.013101[/C][/ROW]
[ROW][C]6[/C][C]-0.195394[/C][C]-2.2449[/C][C]0.013219[/C][/ROW]
[ROW][C]7[/C][C]0.048237[/C][C]0.5542[/C][C]0.290188[/C][/ROW]
[ROW][C]8[/C][C]0.055037[/C][C]0.6323[/C][C]0.264134[/C][/ROW]
[ROW][C]9[/C][C]0.115262[/C][C]1.3243[/C][C]0.093853[/C][/ROW]
[ROW][C]10[/C][C]0.12404[/C][C]1.4251[/C][C]0.078243[/C][/ROW]
[ROW][C]11[/C][C]0.086201[/C][C]0.9904[/C][C]0.161901[/C][/ROW]
[ROW][C]12[/C][C]0.583918[/C][C]6.7087[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.074043[/C][C]-0.8507[/C][C]0.19824[/C][/ROW]
[ROW][C]14[/C][C]0.15187[/C][C]1.7449[/C][C]0.041669[/C][/ROW]
[ROW][C]15[/C][C]0.00826[/C][C]0.0949[/C][C]0.462271[/C][/ROW]
[ROW][C]16[/C][C]-0.223275[/C][C]-2.5652[/C][C]0.005714[/C][/ROW]
[ROW][C]17[/C][C]0.047116[/C][C]0.5413[/C][C]0.2946[/C][/ROW]
[ROW][C]18[/C][C]-0.462452[/C][C]-5.3132[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.090532[/C][C]-1.0401[/C][C]0.150089[/C][/ROW]
[ROW][C]20[/C][C]-0.071575[/C][C]-0.8223[/C][C]0.206184[/C][/ROW]
[ROW][C]21[/C][C]-0.134995[/C][C]-1.551[/C][C]0.061651[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285810&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285810&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	0.089192	1.0247	0.153681
2	0.292633	3.3621	0.000506
3	0.291568	3.3499	0.000527
4	-0.07178	-0.8247	0.205517
5	0.195707	2.2485	0.013101
6	-0.195394	-2.2449	0.013219
7	0.048237	0.5542	0.290188
8	0.055037	0.6323	0.264134
9	0.115262	1.3243	0.093853
10	0.12404	1.4251	0.078243
11	0.086201	0.9904	0.161901
12	0.583918	6.7087	0
13	-0.074043	-0.8507	0.19824
14	0.15187	1.7449	0.041669
15	0.00826	0.0949	0.462271
16	-0.223275	-2.5652	0.005714
17	0.047116	0.5413	0.2946
18	-0.462452	-5.3132	0
19	-0.090532	-1.0401	0.150089
20	-0.071575	-0.8223	0.206184
21	-0.134995	-1.551	0.061651

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.089192	1.0247	0.153681
2	0.286961	3.2969	0.000628
3	0.271722	3.1218	0.001104
4	-0.202506	-2.3266	0.010754
5	0.053762	0.6177	0.268925
6	-0.24984	-2.8704	0.002388
7	0.096241	1.1057	0.135429
8	0.105534	1.2125	0.113744
9	0.318775	3.6624	0.00018
10	-0.048225	-0.5541	0.290235
11	0.009787	0.1124	0.455319
12	0.531032	6.1011	0
13	-0.308619	-3.5458	0.000271
14	-0.258366	-2.9684	0.001778
15	-0.287582	-3.3041	0.000613
16	0.011075	0.1272	0.449472
17	-0.074882	-0.8603	0.195585
18	-0.197053	-2.264	0.012604
19	-0.024985	-0.2871	0.387262
20	0.017134	0.1969	0.422122
21	0.042767	0.4914	0.311995

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.089192 & 1.0247 & 0.153681 \tabularnewline
2 & 0.286961 & 3.2969 & 0.000628 \tabularnewline
3 & 0.271722 & 3.1218 & 0.001104 \tabularnewline
4 & -0.202506 & -2.3266 & 0.010754 \tabularnewline
5 & 0.053762 & 0.6177 & 0.268925 \tabularnewline
6 & -0.24984 & -2.8704 & 0.002388 \tabularnewline
7 & 0.096241 & 1.1057 & 0.135429 \tabularnewline
8 & 0.105534 & 1.2125 & 0.113744 \tabularnewline
9 & 0.318775 & 3.6624 & 0.00018 \tabularnewline
10 & -0.048225 & -0.5541 & 0.290235 \tabularnewline
11 & 0.009787 & 0.1124 & 0.455319 \tabularnewline
12 & 0.531032 & 6.1011 & 0 \tabularnewline
13 & -0.308619 & -3.5458 & 0.000271 \tabularnewline
14 & -0.258366 & -2.9684 & 0.001778 \tabularnewline
15 & -0.287582 & -3.3041 & 0.000613 \tabularnewline
16 & 0.011075 & 0.1272 & 0.449472 \tabularnewline
17 & -0.074882 & -0.8603 & 0.195585 \tabularnewline
18 & -0.197053 & -2.264 & 0.012604 \tabularnewline
19 & -0.024985 & -0.2871 & 0.387262 \tabularnewline
20 & 0.017134 & 0.1969 & 0.422122 \tabularnewline
21 & 0.042767 & 0.4914 & 0.311995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285810&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]0.089192[/C][C]1.0247[/C][C]0.153681[/C][/ROW]
[ROW][C]2[/C][C]0.286961[/C][C]3.2969[/C][C]0.000628[/C][/ROW]
[ROW][C]3[/C][C]0.271722[/C][C]3.1218[/C][C]0.001104[/C][/ROW]
[ROW][C]4[/C][C]-0.202506[/C][C]-2.3266[/C][C]0.010754[/C][/ROW]
[ROW][C]5[/C][C]0.053762[/C][C]0.6177[/C][C]0.268925[/C][/ROW]
[ROW][C]6[/C][C]-0.24984[/C][C]-2.8704[/C][C]0.002388[/C][/ROW]
[ROW][C]7[/C][C]0.096241[/C][C]1.1057[/C][C]0.135429[/C][/ROW]
[ROW][C]8[/C][C]0.105534[/C][C]1.2125[/C][C]0.113744[/C][/ROW]
[ROW][C]9[/C][C]0.318775[/C][C]3.6624[/C][C]0.00018[/C][/ROW]
[ROW][C]10[/C][C]-0.048225[/C][C]-0.5541[/C][C]0.290235[/C][/ROW]
[ROW][C]11[/C][C]0.009787[/C][C]0.1124[/C][C]0.455319[/C][/ROW]
[ROW][C]12[/C][C]0.531032[/C][C]6.1011[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.308619[/C][C]-3.5458[/C][C]0.000271[/C][/ROW]
[ROW][C]14[/C][C]-0.258366[/C][C]-2.9684[/C][C]0.001778[/C][/ROW]
[ROW][C]15[/C][C]-0.287582[/C][C]-3.3041[/C][C]0.000613[/C][/ROW]
[ROW][C]16[/C][C]0.011075[/C][C]0.1272[/C][C]0.449472[/C][/ROW]
[ROW][C]17[/C][C]-0.074882[/C][C]-0.8603[/C][C]0.195585[/C][/ROW]
[ROW][C]18[/C][C]-0.197053[/C][C]-2.264[/C][C]0.012604[/C][/ROW]
[ROW][C]19[/C][C]-0.024985[/C][C]-0.2871[/C][C]0.387262[/C][/ROW]
[ROW][C]20[/C][C]0.017134[/C][C]0.1969[/C][C]0.422122[/C][/ROW]
[ROW][C]21[/C][C]0.042767[/C][C]0.4914[/C][C]0.311995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285810&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285810&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	0.089192	1.0247	0.153681
2	0.286961	3.2969	0.000628
3	0.271722	3.1218	0.001104
4	-0.202506	-2.3266	0.010754
5	0.053762	0.6177	0.268925
6	-0.24984	-2.8704	0.002388
7	0.096241	1.1057	0.135429
8	0.105534	1.2125	0.113744
9	0.318775	3.6624	0.00018
10	-0.048225	-0.5541	0.290235
11	0.009787	0.1124	0.455319
12	0.531032	6.1011	0
13	-0.308619	-3.5458	0.000271
14	-0.258366	-2.9684	0.001778
15	-0.287582	-3.3041	0.000613
16	0.011075	0.1272	0.449472
17	-0.074882	-0.8603	0.195585
18	-0.197053	-2.264	0.012604
19	-0.024985	-0.2871	0.387262
20	0.017134	0.1969	0.422122
21	0.042767	0.4914	0.311995

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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)
x <- na.omit(x)
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