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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Nov 2012 11:53:29 -0500

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/2012/Nov/20/t13534304402lwofpv5ya6ldop.htm/, Retrieved Mon, 29 Apr 2024 21:54:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=191177, Retrieved Mon, 29 Apr 2024 21:54:51 +0000

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

-       [(Partial) Autocorrelation Function] [WS 9 ACF 1] [2012-11-20 16:53:29] [851af2766980873020febd248b5479af] [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	3 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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191177&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]3 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=191177&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191177&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	3 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.912257	11.3208	0
2	0.775876	9.6284	0
3	0.678677	8.4222	0
4	0.640049	7.9428	0
5	0.649166	8.0559	0
6	0.645613	8.0118	0
7	0.602421	7.4759	0
8	0.547564	6.7951	0
9	0.530247	6.5802	0
10	0.562976	6.9864	0
11	0.635186	7.8824	0
12	0.665387	8.2572	0
13	0.556056	6.9005	0
14	0.407718	5.0596	1e-06
15	0.295309	3.6647	0.00017
16	0.238012	2.9537	0.001817
17	0.226951	2.8164	0.002746
18	0.204993	2.5439	0.005974
19	0.153542	1.9054	0.029296
20	0.093493	1.1602	0.123879
21	0.074836	0.9287	0.177251

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.912257 & 11.3208 & 0 \tabularnewline
2 & 0.775876 & 9.6284 & 0 \tabularnewline
3 & 0.678677 & 8.4222 & 0 \tabularnewline
4 & 0.640049 & 7.9428 & 0 \tabularnewline
5 & 0.649166 & 8.0559 & 0 \tabularnewline
6 & 0.645613 & 8.0118 & 0 \tabularnewline
7 & 0.602421 & 7.4759 & 0 \tabularnewline
8 & 0.547564 & 6.7951 & 0 \tabularnewline
9 & 0.530247 & 6.5802 & 0 \tabularnewline
10 & 0.562976 & 6.9864 & 0 \tabularnewline
11 & 0.635186 & 7.8824 & 0 \tabularnewline
12 & 0.665387 & 8.2572 & 0 \tabularnewline
13 & 0.556056 & 6.9005 & 0 \tabularnewline
14 & 0.407718 & 5.0596 & 1e-06 \tabularnewline
15 & 0.295309 & 3.6647 & 0.00017 \tabularnewline
16 & 0.238012 & 2.9537 & 0.001817 \tabularnewline
17 & 0.226951 & 2.8164 & 0.002746 \tabularnewline
18 & 0.204993 & 2.5439 & 0.005974 \tabularnewline
19 & 0.153542 & 1.9054 & 0.029296 \tabularnewline
20 & 0.093493 & 1.1602 & 0.123879 \tabularnewline
21 & 0.074836 & 0.9287 & 0.177251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191177&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]0.912257[/C][C]11.3208[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.775876[/C][C]9.6284[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.678677[/C][C]8.4222[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.640049[/C][C]7.9428[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.649166[/C][C]8.0559[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.645613[/C][C]8.0118[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.602421[/C][C]7.4759[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.547564[/C][C]6.7951[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.530247[/C][C]6.5802[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.562976[/C][C]6.9864[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.635186[/C][C]7.8824[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.665387[/C][C]8.2572[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.556056[/C][C]6.9005[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.407718[/C][C]5.0596[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]0.295309[/C][C]3.6647[/C][C]0.00017[/C][/ROW]
[ROW][C]16[/C][C]0.238012[/C][C]2.9537[/C][C]0.001817[/C][/ROW]
[ROW][C]17[/C][C]0.226951[/C][C]2.8164[/C][C]0.002746[/C][/ROW]
[ROW][C]18[/C][C]0.204993[/C][C]2.5439[/C][C]0.005974[/C][/ROW]
[ROW][C]19[/C][C]0.153542[/C][C]1.9054[/C][C]0.029296[/C][/ROW]
[ROW][C]20[/C][C]0.093493[/C][C]1.1602[/C][C]0.123879[/C][/ROW]
[ROW][C]21[/C][C]0.074836[/C][C]0.9287[/C][C]0.177251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191177&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191177&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	0.912257	11.3208	0
2	0.775876	9.6284	0
3	0.678677	8.4222	0
4	0.640049	7.9428	0
5	0.649166	8.0559	0
6	0.645613	8.0118	0
7	0.602421	7.4759	0
8	0.547564	6.7951	0
9	0.530247	6.5802	0
10	0.562976	6.9864	0
11	0.635186	7.8824	0
12	0.665387	8.2572	0
13	0.556056	6.9005	0
14	0.407718	5.0596	1e-06
15	0.295309	3.6647	0.00017
16	0.238012	2.9537	0.001817
17	0.226951	2.8164	0.002746
18	0.204993	2.5439	0.005974
19	0.153542	1.9054	0.029296
20	0.093493	1.1602	0.123879
21	0.074836	0.9287	0.177251

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.912257	11.3208	0
2	-0.335764	-4.1667	2.6e-05
3	0.265518	3.295	0.000611
4	0.157979	1.9605	0.025873
5	0.19232	2.3866	0.009109
6	-0.118315	-1.4682	0.072038
7	-0.041722	-0.5178	0.302686
8	0.062342	0.7736	0.220165
9	0.212806	2.6409	0.004561
10	0.136237	1.6907	0.046463
11	0.251853	3.1254	0.001061
12	-0.21237	-2.6354	0.004631
13	-0.695365	-8.6293	0
14	0.141091	1.7509	0.040978
15	-0.072875	-0.9044	0.183611
16	-0.139229	-1.7278	0.043016
17	-0.080476	-0.9987	0.159759
18	0.017708	0.2198	0.413178
19	0.078998	0.9803	0.164229
20	-0.070015	-0.8689	0.193137
21	0.228156	2.8313	0.002627

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.912257 & 11.3208 & 0 \tabularnewline
2 & -0.335764 & -4.1667 & 2.6e-05 \tabularnewline
3 & 0.265518 & 3.295 & 0.000611 \tabularnewline
4 & 0.157979 & 1.9605 & 0.025873 \tabularnewline
5 & 0.19232 & 2.3866 & 0.009109 \tabularnewline
6 & -0.118315 & -1.4682 & 0.072038 \tabularnewline
7 & -0.041722 & -0.5178 & 0.302686 \tabularnewline
8 & 0.062342 & 0.7736 & 0.220165 \tabularnewline
9 & 0.212806 & 2.6409 & 0.004561 \tabularnewline
10 & 0.136237 & 1.6907 & 0.046463 \tabularnewline
11 & 0.251853 & 3.1254 & 0.001061 \tabularnewline
12 & -0.21237 & -2.6354 & 0.004631 \tabularnewline
13 & -0.695365 & -8.6293 & 0 \tabularnewline
14 & 0.141091 & 1.7509 & 0.040978 \tabularnewline
15 & -0.072875 & -0.9044 & 0.183611 \tabularnewline
16 & -0.139229 & -1.7278 & 0.043016 \tabularnewline
17 & -0.080476 & -0.9987 & 0.159759 \tabularnewline
18 & 0.017708 & 0.2198 & 0.413178 \tabularnewline
19 & 0.078998 & 0.9803 & 0.164229 \tabularnewline
20 & -0.070015 & -0.8689 & 0.193137 \tabularnewline
21 & 0.228156 & 2.8313 & 0.002627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191177&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]0.912257[/C][C]11.3208[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.335764[/C][C]-4.1667[/C][C]2.6e-05[/C][/ROW]
[ROW][C]3[/C][C]0.265518[/C][C]3.295[/C][C]0.000611[/C][/ROW]
[ROW][C]4[/C][C]0.157979[/C][C]1.9605[/C][C]0.025873[/C][/ROW]
[ROW][C]5[/C][C]0.19232[/C][C]2.3866[/C][C]0.009109[/C][/ROW]
[ROW][C]6[/C][C]-0.118315[/C][C]-1.4682[/C][C]0.072038[/C][/ROW]
[ROW][C]7[/C][C]-0.041722[/C][C]-0.5178[/C][C]0.302686[/C][/ROW]
[ROW][C]8[/C][C]0.062342[/C][C]0.7736[/C][C]0.220165[/C][/ROW]
[ROW][C]9[/C][C]0.212806[/C][C]2.6409[/C][C]0.004561[/C][/ROW]
[ROW][C]10[/C][C]0.136237[/C][C]1.6907[/C][C]0.046463[/C][/ROW]
[ROW][C]11[/C][C]0.251853[/C][C]3.1254[/C][C]0.001061[/C][/ROW]
[ROW][C]12[/C][C]-0.21237[/C][C]-2.6354[/C][C]0.004631[/C][/ROW]
[ROW][C]13[/C][C]-0.695365[/C][C]-8.6293[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.141091[/C][C]1.7509[/C][C]0.040978[/C][/ROW]
[ROW][C]15[/C][C]-0.072875[/C][C]-0.9044[/C][C]0.183611[/C][/ROW]
[ROW][C]16[/C][C]-0.139229[/C][C]-1.7278[/C][C]0.043016[/C][/ROW]
[ROW][C]17[/C][C]-0.080476[/C][C]-0.9987[/C][C]0.159759[/C][/ROW]
[ROW][C]18[/C][C]0.017708[/C][C]0.2198[/C][C]0.413178[/C][/ROW]
[ROW][C]19[/C][C]0.078998[/C][C]0.9803[/C][C]0.164229[/C][/ROW]
[ROW][C]20[/C][C]-0.070015[/C][C]-0.8689[/C][C]0.193137[/C][/ROW]
[ROW][C]21[/C][C]0.228156[/C][C]2.8313[/C][C]0.002627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191177&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191177&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	0.912257	11.3208	0
2	-0.335764	-4.1667	2.6e-05
3	0.265518	3.295	0.000611
4	0.157979	1.9605	0.025873
5	0.19232	2.3866	0.009109
6	-0.118315	-1.4682	0.072038
7	-0.041722	-0.5178	0.302686
8	0.062342	0.7736	0.220165
9	0.212806	2.6409	0.004561
10	0.136237	1.6907	0.046463
11	0.251853	3.1254	0.001061
12	-0.21237	-2.6354	0.004631
13	-0.695365	-8.6293	0
14	0.141091	1.7509	0.040978
15	-0.072875	-0.9044	0.183611
16	-0.139229	-1.7278	0.043016
17	-0.080476	-0.9987	0.159759
18	0.017708	0.2198	0.413178
19	0.078998	0.9803	0.164229
20	-0.070015	-0.8689	0.193137
21	0.228156	2.8313	0.002627

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 = 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)
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