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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 14 Dec 2009 02:23:40 -0700

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/2009/Dec/14/t1260782936g43jl4b2tek4dwk.htm/, Retrieved Sun, 05 May 2024 13:51:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67463, Retrieved Sun, 05 May 2024 13:51:42 +0000

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Estimated Impact

143

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2009-12-14 09:23:40] [6df9bd2792d60592b4a24994398a86db] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67463&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67463&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67463&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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.322163	-3.6873	0.000165
2	-0.34706	-3.9723	5.8e-05
3	0.381777	4.3696	1.3e-05
4	-0.142117	-1.6266	0.053112
5	-0.175844	-2.0126	0.023102
6	0.378515	4.3323	1.5e-05
7	-0.257863	-2.9514	0.001875
8	-0.039459	-0.4516	0.326141
9	0.294303	3.3685	0.000496
10	-0.418565	-4.7907	2e-06
11	-0.104412	-1.195	0.117114
12	0.632256	7.2365	0
13	-0.236151	-2.7029	0.003893
14	-0.27447	-3.1415	0.001039
15	0.273977	3.1358	0.001058
16	-0.146407	-1.6757	0.04809
17	-0.086184	-0.9864	0.162872
18	0.247592	2.8338	0.002664
19	-0.153951	-1.7621	0.040197
20	-0.024673	-0.2824	0.389043
21	0.165896	1.8988	0.029897

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.322163 & -3.6873 & 0.000165 \tabularnewline
2 & -0.34706 & -3.9723 & 5.8e-05 \tabularnewline
3 & 0.381777 & 4.3696 & 1.3e-05 \tabularnewline
4 & -0.142117 & -1.6266 & 0.053112 \tabularnewline
5 & -0.175844 & -2.0126 & 0.023102 \tabularnewline
6 & 0.378515 & 4.3323 & 1.5e-05 \tabularnewline
7 & -0.257863 & -2.9514 & 0.001875 \tabularnewline
8 & -0.039459 & -0.4516 & 0.326141 \tabularnewline
9 & 0.294303 & 3.3685 & 0.000496 \tabularnewline
10 & -0.418565 & -4.7907 & 2e-06 \tabularnewline
11 & -0.104412 & -1.195 & 0.117114 \tabularnewline
12 & 0.632256 & 7.2365 & 0 \tabularnewline
13 & -0.236151 & -2.7029 & 0.003893 \tabularnewline
14 & -0.27447 & -3.1415 & 0.001039 \tabularnewline
15 & 0.273977 & 3.1358 & 0.001058 \tabularnewline
16 & -0.146407 & -1.6757 & 0.04809 \tabularnewline
17 & -0.086184 & -0.9864 & 0.162872 \tabularnewline
18 & 0.247592 & 2.8338 & 0.002664 \tabularnewline
19 & -0.153951 & -1.7621 & 0.040197 \tabularnewline
20 & -0.024673 & -0.2824 & 0.389043 \tabularnewline
21 & 0.165896 & 1.8988 & 0.029897 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67463&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]-0.322163[/C][C]-3.6873[/C][C]0.000165[/C][/ROW]
[ROW][C]2[/C][C]-0.34706[/C][C]-3.9723[/C][C]5.8e-05[/C][/ROW]
[ROW][C]3[/C][C]0.381777[/C][C]4.3696[/C][C]1.3e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.142117[/C][C]-1.6266[/C][C]0.053112[/C][/ROW]
[ROW][C]5[/C][C]-0.175844[/C][C]-2.0126[/C][C]0.023102[/C][/ROW]
[ROW][C]6[/C][C]0.378515[/C][C]4.3323[/C][C]1.5e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.257863[/C][C]-2.9514[/C][C]0.001875[/C][/ROW]
[ROW][C]8[/C][C]-0.039459[/C][C]-0.4516[/C][C]0.326141[/C][/ROW]
[ROW][C]9[/C][C]0.294303[/C][C]3.3685[/C][C]0.000496[/C][/ROW]
[ROW][C]10[/C][C]-0.418565[/C][C]-4.7907[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]-0.104412[/C][C]-1.195[/C][C]0.117114[/C][/ROW]
[ROW][C]12[/C][C]0.632256[/C][C]7.2365[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.236151[/C][C]-2.7029[/C][C]0.003893[/C][/ROW]
[ROW][C]14[/C][C]-0.27447[/C][C]-3.1415[/C][C]0.001039[/C][/ROW]
[ROW][C]15[/C][C]0.273977[/C][C]3.1358[/C][C]0.001058[/C][/ROW]
[ROW][C]16[/C][C]-0.146407[/C][C]-1.6757[/C][C]0.04809[/C][/ROW]
[ROW][C]17[/C][C]-0.086184[/C][C]-0.9864[/C][C]0.162872[/C][/ROW]
[ROW][C]18[/C][C]0.247592[/C][C]2.8338[/C][C]0.002664[/C][/ROW]
[ROW][C]19[/C][C]-0.153951[/C][C]-1.7621[/C][C]0.040197[/C][/ROW]
[ROW][C]20[/C][C]-0.024673[/C][C]-0.2824[/C][C]0.389043[/C][/ROW]
[ROW][C]21[/C][C]0.165896[/C][C]1.8988[/C][C]0.029897[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67463&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67463&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	-0.322163	-3.6873	0.000165
2	-0.34706	-3.9723	5.8e-05
3	0.381777	4.3696	1.3e-05
4	-0.142117	-1.6266	0.053112
5	-0.175844	-2.0126	0.023102
6	0.378515	4.3323	1.5e-05
7	-0.257863	-2.9514	0.001875
8	-0.039459	-0.4516	0.326141
9	0.294303	3.3685	0.000496
10	-0.418565	-4.7907	2e-06
11	-0.104412	-1.195	0.117114
12	0.632256	7.2365	0
13	-0.236151	-2.7029	0.003893
14	-0.27447	-3.1415	0.001039
15	0.273977	3.1358	0.001058
16	-0.146407	-1.6757	0.04809
17	-0.086184	-0.9864	0.162872
18	0.247592	2.8338	0.002664
19	-0.153951	-1.7621	0.040197
20	-0.024673	-0.2824	0.389043
21	0.165896	1.8988	0.029897

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.322163	-3.6873	0.000165
2	-0.503061	-5.7578	0
3	0.077161	0.8831	0.189388
4	-0.163558	-1.872	0.031718
5	-0.126118	-1.4435	0.075636
6	0.203915	2.3339	0.010561
7	-0.156231	-1.7881	0.038032
8	0.100487	1.1501	0.126093
9	0.093096	1.0655	0.144298
10	-0.330441	-3.7821	0.000118
11	-0.335745	-3.8428	9.4e-05
12	0.285105	3.2632	0.000703
13	0.279288	3.1966	0.000872
14	-0.001935	-0.0221	0.491184
15	-0.159225	-1.8224	0.035337
16	-0.112296	-1.2853	0.100479
17	-0.069379	-0.7941	0.214294
18	-0.097447	-1.1153	0.133374
19	0.057745	0.6609	0.254912
20	-0.006419	-0.0735	0.470772
21	-0.114423	-1.3096	0.096307

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.322163 & -3.6873 & 0.000165 \tabularnewline
2 & -0.503061 & -5.7578 & 0 \tabularnewline
3 & 0.077161 & 0.8831 & 0.189388 \tabularnewline
4 & -0.163558 & -1.872 & 0.031718 \tabularnewline
5 & -0.126118 & -1.4435 & 0.075636 \tabularnewline
6 & 0.203915 & 2.3339 & 0.010561 \tabularnewline
7 & -0.156231 & -1.7881 & 0.038032 \tabularnewline
8 & 0.100487 & 1.1501 & 0.126093 \tabularnewline
9 & 0.093096 & 1.0655 & 0.144298 \tabularnewline
10 & -0.330441 & -3.7821 & 0.000118 \tabularnewline
11 & -0.335745 & -3.8428 & 9.4e-05 \tabularnewline
12 & 0.285105 & 3.2632 & 0.000703 \tabularnewline
13 & 0.279288 & 3.1966 & 0.000872 \tabularnewline
14 & -0.001935 & -0.0221 & 0.491184 \tabularnewline
15 & -0.159225 & -1.8224 & 0.035337 \tabularnewline
16 & -0.112296 & -1.2853 & 0.100479 \tabularnewline
17 & -0.069379 & -0.7941 & 0.214294 \tabularnewline
18 & -0.097447 & -1.1153 & 0.133374 \tabularnewline
19 & 0.057745 & 0.6609 & 0.254912 \tabularnewline
20 & -0.006419 & -0.0735 & 0.470772 \tabularnewline
21 & -0.114423 & -1.3096 & 0.096307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67463&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]-0.322163[/C][C]-3.6873[/C][C]0.000165[/C][/ROW]
[ROW][C]2[/C][C]-0.503061[/C][C]-5.7578[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.077161[/C][C]0.8831[/C][C]0.189388[/C][/ROW]
[ROW][C]4[/C][C]-0.163558[/C][C]-1.872[/C][C]0.031718[/C][/ROW]
[ROW][C]5[/C][C]-0.126118[/C][C]-1.4435[/C][C]0.075636[/C][/ROW]
[ROW][C]6[/C][C]0.203915[/C][C]2.3339[/C][C]0.010561[/C][/ROW]
[ROW][C]7[/C][C]-0.156231[/C][C]-1.7881[/C][C]0.038032[/C][/ROW]
[ROW][C]8[/C][C]0.100487[/C][C]1.1501[/C][C]0.126093[/C][/ROW]
[ROW][C]9[/C][C]0.093096[/C][C]1.0655[/C][C]0.144298[/C][/ROW]
[ROW][C]10[/C][C]-0.330441[/C][C]-3.7821[/C][C]0.000118[/C][/ROW]
[ROW][C]11[/C][C]-0.335745[/C][C]-3.8428[/C][C]9.4e-05[/C][/ROW]
[ROW][C]12[/C][C]0.285105[/C][C]3.2632[/C][C]0.000703[/C][/ROW]
[ROW][C]13[/C][C]0.279288[/C][C]3.1966[/C][C]0.000872[/C][/ROW]
[ROW][C]14[/C][C]-0.001935[/C][C]-0.0221[/C][C]0.491184[/C][/ROW]
[ROW][C]15[/C][C]-0.159225[/C][C]-1.8224[/C][C]0.035337[/C][/ROW]
[ROW][C]16[/C][C]-0.112296[/C][C]-1.2853[/C][C]0.100479[/C][/ROW]
[ROW][C]17[/C][C]-0.069379[/C][C]-0.7941[/C][C]0.214294[/C][/ROW]
[ROW][C]18[/C][C]-0.097447[/C][C]-1.1153[/C][C]0.133374[/C][/ROW]
[ROW][C]19[/C][C]0.057745[/C][C]0.6609[/C][C]0.254912[/C][/ROW]
[ROW][C]20[/C][C]-0.006419[/C][C]-0.0735[/C][C]0.470772[/C][/ROW]
[ROW][C]21[/C][C]-0.114423[/C][C]-1.3096[/C][C]0.096307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67463&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67463&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	-0.322163	-3.6873	0.000165
2	-0.503061	-5.7578	0
3	0.077161	0.8831	0.189388
4	-0.163558	-1.872	0.031718
5	-0.126118	-1.4435	0.075636
6	0.203915	2.3339	0.010561
7	-0.156231	-1.7881	0.038032
8	0.100487	1.1501	0.126093
9	0.093096	1.0655	0.144298
10	-0.330441	-3.7821	0.000118
11	-0.335745	-3.8428	9.4e-05
12	0.285105	3.2632	0.000703
13	0.279288	3.1966	0.000872
14	-0.001935	-0.0221	0.491184
15	-0.159225	-1.8224	0.035337
16	-0.112296	-1.2853	0.100479
17	-0.069379	-0.7941	0.214294
18	-0.097447	-1.1153	0.133374
19	0.057745	0.6609	0.254912
20	-0.006419	-0.0735	0.470772
21	-0.114423	-1.3096	0.096307

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Invoer (België 1998-2008) ; par2 = Belgostat ; par3 = u ;

Parameters (R input):

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

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code