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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Dec 2010 15:56:02 +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/2010/Dec/19/t1292774086z8ym4mufr78y4k4.htm/, Retrieved Sun, 05 May 2024 08:11:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112530, Retrieved Sun, 05 May 2024 08:11:12 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

139

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D    [(Partial) Autocorrelation Function] [Autocorrelation WS9] [2010-12-06 11:15:00] [f4dc4aa51d65be851b8508203d9f6001]
-    D        [(Partial) Autocorrelation Function] [Autocorrelation B...] [2010-12-19 15:56:02] [7a87ed98a7b21a29d6a45388a9b7b229] [Current]
-   P           [(Partial) Autocorrelation Function] [Autocorrelation B...] [2010-12-19 16:00:59] [f4dc4aa51d65be851b8508203d9f6001] 
-   P             [(Partial) Autocorrelation Function] [Autocorrelation B...] [2010-12-19 16:15:04] [f4dc4aa51d65be851b8508203d9f6001] 
- R  D          [(Partial) Autocorrelation Function] [WS 9 Partial Auto...] [2011-12-06 20:23:10] [f5fdea4413921432bb019d1f20c4f2ec] 
- RM              [(Partial) Autocorrelation Function] [WS 9 Partial Auto...] [2011-12-06 20:49:10] [f5fdea4413921432bb019d1f20c4f2ec] 

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112530&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112530&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112530&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.794648	6.1553	0
2	0.440253	3.4102	0.000583
3	0.029361	0.2274	0.410432
4	-0.367608	-2.8475	0.003013
5	-0.630699	-4.8854	4e-06
6	-0.707177	-5.4778	0
7	-0.599109	-4.6407	1e-05
8	-0.32809	-2.5414	0.006822
9	0.061985	0.4801	0.31644
10	0.417964	3.2375	0.000983
11	0.647241	5.0135	3e-06
12	0.736282	5.7032	0
13	0.568748	4.4055	2.2e-05
14	0.28274	2.1901	0.016208
15	-0.038634	-0.2993	0.382888
16	-0.334366	-2.59	0.006015
17	-0.529658	-4.1027	6.2e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.794648 & 6.1553 & 0 \tabularnewline
2 & 0.440253 & 3.4102 & 0.000583 \tabularnewline
3 & 0.029361 & 0.2274 & 0.410432 \tabularnewline
4 & -0.367608 & -2.8475 & 0.003013 \tabularnewline
5 & -0.630699 & -4.8854 & 4e-06 \tabularnewline
6 & -0.707177 & -5.4778 & 0 \tabularnewline
7 & -0.599109 & -4.6407 & 1e-05 \tabularnewline
8 & -0.32809 & -2.5414 & 0.006822 \tabularnewline
9 & 0.061985 & 0.4801 & 0.31644 \tabularnewline
10 & 0.417964 & 3.2375 & 0.000983 \tabularnewline
11 & 0.647241 & 5.0135 & 3e-06 \tabularnewline
12 & 0.736282 & 5.7032 & 0 \tabularnewline
13 & 0.568748 & 4.4055 & 2.2e-05 \tabularnewline
14 & 0.28274 & 2.1901 & 0.016208 \tabularnewline
15 & -0.038634 & -0.2993 & 0.382888 \tabularnewline
16 & -0.334366 & -2.59 & 0.006015 \tabularnewline
17 & -0.529658 & -4.1027 & 6.2e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112530&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]0.794648[/C][C]6.1553[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.440253[/C][C]3.4102[/C][C]0.000583[/C][/ROW]
[ROW][C]3[/C][C]0.029361[/C][C]0.2274[/C][C]0.410432[/C][/ROW]
[ROW][C]4[/C][C]-0.367608[/C][C]-2.8475[/C][C]0.003013[/C][/ROW]
[ROW][C]5[/C][C]-0.630699[/C][C]-4.8854[/C][C]4e-06[/C][/ROW]
[ROW][C]6[/C][C]-0.707177[/C][C]-5.4778[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.599109[/C][C]-4.6407[/C][C]1e-05[/C][/ROW]
[ROW][C]8[/C][C]-0.32809[/C][C]-2.5414[/C][C]0.006822[/C][/ROW]
[ROW][C]9[/C][C]0.061985[/C][C]0.4801[/C][C]0.31644[/C][/ROW]
[ROW][C]10[/C][C]0.417964[/C][C]3.2375[/C][C]0.000983[/C][/ROW]
[ROW][C]11[/C][C]0.647241[/C][C]5.0135[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.736282[/C][C]5.7032[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.568748[/C][C]4.4055[/C][C]2.2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.28274[/C][C]2.1901[/C][C]0.016208[/C][/ROW]
[ROW][C]15[/C][C]-0.038634[/C][C]-0.2993[/C][C]0.382888[/C][/ROW]
[ROW][C]16[/C][C]-0.334366[/C][C]-2.59[/C][C]0.006015[/C][/ROW]
[ROW][C]17[/C][C]-0.529658[/C][C]-4.1027[/C][C]6.2e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112530&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112530&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	0.794648	6.1553	0
2	0.440253	3.4102	0.000583
3	0.029361	0.2274	0.410432
4	-0.367608	-2.8475	0.003013
5	-0.630699	-4.8854	4e-06
6	-0.707177	-5.4778	0
7	-0.599109	-4.6407	1e-05
8	-0.32809	-2.5414	0.006822
9	0.061985	0.4801	0.31644
10	0.417964	3.2375	0.000983
11	0.647241	5.0135	3e-06
12	0.736282	5.7032	0
13	0.568748	4.4055	2.2e-05
14	0.28274	2.1901	0.016208
15	-0.038634	-0.2993	0.382888
16	-0.334366	-2.59	0.006015
17	-0.529658	-4.1027	6.2e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.794648	6.1553	0
2	-0.518846	-4.019	8.3e-05
3	-0.333064	-2.5799	0.006175
4	-0.341858	-2.648	0.005165
5	-0.118913	-0.9211	0.180344
6	-0.059375	-0.4599	0.323618
7	-0.018154	-0.1406	0.444322
8	0.094074	0.7287	0.234512
9	0.286259	2.2174	0.015199
10	0.07934	0.6146	0.270584
11	0.056113	0.4346	0.332688
12	0.210745	1.6324	0.053914
13	-0.280806	-2.1751	0.016787
14	0.157661	1.2212	0.113387
15	0.06121	0.4741	0.318565
16	0.067865	0.5257	0.300525
17	-0.01028	-0.0796	0.468397

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.794648 & 6.1553 & 0 \tabularnewline
2 & -0.518846 & -4.019 & 8.3e-05 \tabularnewline
3 & -0.333064 & -2.5799 & 0.006175 \tabularnewline
4 & -0.341858 & -2.648 & 0.005165 \tabularnewline
5 & -0.118913 & -0.9211 & 0.180344 \tabularnewline
6 & -0.059375 & -0.4599 & 0.323618 \tabularnewline
7 & -0.018154 & -0.1406 & 0.444322 \tabularnewline
8 & 0.094074 & 0.7287 & 0.234512 \tabularnewline
9 & 0.286259 & 2.2174 & 0.015199 \tabularnewline
10 & 0.07934 & 0.6146 & 0.270584 \tabularnewline
11 & 0.056113 & 0.4346 & 0.332688 \tabularnewline
12 & 0.210745 & 1.6324 & 0.053914 \tabularnewline
13 & -0.280806 & -2.1751 & 0.016787 \tabularnewline
14 & 0.157661 & 1.2212 & 0.113387 \tabularnewline
15 & 0.06121 & 0.4741 & 0.318565 \tabularnewline
16 & 0.067865 & 0.5257 & 0.300525 \tabularnewline
17 & -0.01028 & -0.0796 & 0.468397 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112530&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]0.794648[/C][C]6.1553[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.518846[/C][C]-4.019[/C][C]8.3e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.333064[/C][C]-2.5799[/C][C]0.006175[/C][/ROW]
[ROW][C]4[/C][C]-0.341858[/C][C]-2.648[/C][C]0.005165[/C][/ROW]
[ROW][C]5[/C][C]-0.118913[/C][C]-0.9211[/C][C]0.180344[/C][/ROW]
[ROW][C]6[/C][C]-0.059375[/C][C]-0.4599[/C][C]0.323618[/C][/ROW]
[ROW][C]7[/C][C]-0.018154[/C][C]-0.1406[/C][C]0.444322[/C][/ROW]
[ROW][C]8[/C][C]0.094074[/C][C]0.7287[/C][C]0.234512[/C][/ROW]
[ROW][C]9[/C][C]0.286259[/C][C]2.2174[/C][C]0.015199[/C][/ROW]
[ROW][C]10[/C][C]0.07934[/C][C]0.6146[/C][C]0.270584[/C][/ROW]
[ROW][C]11[/C][C]0.056113[/C][C]0.4346[/C][C]0.332688[/C][/ROW]
[ROW][C]12[/C][C]0.210745[/C][C]1.6324[/C][C]0.053914[/C][/ROW]
[ROW][C]13[/C][C]-0.280806[/C][C]-2.1751[/C][C]0.016787[/C][/ROW]
[ROW][C]14[/C][C]0.157661[/C][C]1.2212[/C][C]0.113387[/C][/ROW]
[ROW][C]15[/C][C]0.06121[/C][C]0.4741[/C][C]0.318565[/C][/ROW]
[ROW][C]16[/C][C]0.067865[/C][C]0.5257[/C][C]0.300525[/C][/ROW]
[ROW][C]17[/C][C]-0.01028[/C][C]-0.0796[/C][C]0.468397[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112530&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112530&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	0.794648	6.1553	0
2	-0.518846	-4.019	8.3e-05
3	-0.333064	-2.5799	0.006175
4	-0.341858	-2.648	0.005165
5	-0.118913	-0.9211	0.180344
6	-0.059375	-0.4599	0.323618
7	-0.018154	-0.1406	0.444322
8	0.094074	0.7287	0.234512
9	0.286259	2.2174	0.015199
10	0.07934	0.6146	0.270584
11	0.056113	0.4346	0.332688
12	0.210745	1.6324	0.053914
13	-0.280806	-2.1751	0.016787
14	0.157661	1.2212	0.113387
15	0.06121	0.4741	0.318565
16	0.067865	0.5257	0.300525
17	-0.01028	-0.0796	0.468397

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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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Figures (Output of Computation)

Input Parameters & R Code