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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

Tue, 02 Dec 2008 13:23:41 -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/2008/Dec/02/t1228249479zjezbz3rv3ur9ho.htm/, Retrieved Fri, 17 May 2024 01:41:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28375, Retrieved Fri, 17 May 2024 01:41:08 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

161

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD    [(Partial) Autocorrelation Function] [17.7.2] [2008-12-02 20:23:41] [0458bd763b171003ec052ce63099d477] [Current]
F    D      [(Partial) Autocorrelation Function] [17.8.2] [2008-12-02 20:39:05] [1eab65e90adf64584b8e6f0da23ff414] 

Feedback Forum

2008-12-08 18:37:46 [5faab2fc6fb120339944528a32d48a04] [reply] 
Hier werd de verkeerde calculator gebruikt het was de bedoeling de Cross Correlation Function te bereken om het verband tussen de 2 variabelen duidelijk te maken.

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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=28375&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=28375&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28375&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	0.414367	3.8203	0.000126
2	0.175065	1.614	0.055115
3	0.384837	3.548	0.000317
4	0.242256	2.2335	0.014071
5	0.244275	2.2521	0.013446
6	0.434937	4.0099	6.5e-05
7	0.207434	1.9124	0.029594
8	0.185994	1.7148	0.045014
9	0.29743	2.7422	0.00372
10	0.024236	0.2234	0.411862
11	0.275241	2.5376	0.006493
12	0.653912	6.0288	0
13	0.250565	2.3101	0.011653
14	-0.002264	-0.0209	0.491696
15	0.21537	1.9856	0.02515
16	0.050733	0.4677	0.320585
17	0.082224	0.7581	0.225252
18	0.230997	2.1297	0.018044
19	0.03449	0.318	0.37564

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.414367 & 3.8203 & 0.000126 \tabularnewline
2 & 0.175065 & 1.614 & 0.055115 \tabularnewline
3 & 0.384837 & 3.548 & 0.000317 \tabularnewline
4 & 0.242256 & 2.2335 & 0.014071 \tabularnewline
5 & 0.244275 & 2.2521 & 0.013446 \tabularnewline
6 & 0.434937 & 4.0099 & 6.5e-05 \tabularnewline
7 & 0.207434 & 1.9124 & 0.029594 \tabularnewline
8 & 0.185994 & 1.7148 & 0.045014 \tabularnewline
9 & 0.29743 & 2.7422 & 0.00372 \tabularnewline
10 & 0.024236 & 0.2234 & 0.411862 \tabularnewline
11 & 0.275241 & 2.5376 & 0.006493 \tabularnewline
12 & 0.653912 & 6.0288 & 0 \tabularnewline
13 & 0.250565 & 2.3101 & 0.011653 \tabularnewline
14 & -0.002264 & -0.0209 & 0.491696 \tabularnewline
15 & 0.21537 & 1.9856 & 0.02515 \tabularnewline
16 & 0.050733 & 0.4677 & 0.320585 \tabularnewline
17 & 0.082224 & 0.7581 & 0.225252 \tabularnewline
18 & 0.230997 & 2.1297 & 0.018044 \tabularnewline
19 & 0.03449 & 0.318 & 0.37564 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28375&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]0.414367[/C][C]3.8203[/C][C]0.000126[/C][/ROW]
[ROW][C]2[/C][C]0.175065[/C][C]1.614[/C][C]0.055115[/C][/ROW]
[ROW][C]3[/C][C]0.384837[/C][C]3.548[/C][C]0.000317[/C][/ROW]
[ROW][C]4[/C][C]0.242256[/C][C]2.2335[/C][C]0.014071[/C][/ROW]
[ROW][C]5[/C][C]0.244275[/C][C]2.2521[/C][C]0.013446[/C][/ROW]
[ROW][C]6[/C][C]0.434937[/C][C]4.0099[/C][C]6.5e-05[/C][/ROW]
[ROW][C]7[/C][C]0.207434[/C][C]1.9124[/C][C]0.029594[/C][/ROW]
[ROW][C]8[/C][C]0.185994[/C][C]1.7148[/C][C]0.045014[/C][/ROW]
[ROW][C]9[/C][C]0.29743[/C][C]2.7422[/C][C]0.00372[/C][/ROW]
[ROW][C]10[/C][C]0.024236[/C][C]0.2234[/C][C]0.411862[/C][/ROW]
[ROW][C]11[/C][C]0.275241[/C][C]2.5376[/C][C]0.006493[/C][/ROW]
[ROW][C]12[/C][C]0.653912[/C][C]6.0288[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.250565[/C][C]2.3101[/C][C]0.011653[/C][/ROW]
[ROW][C]14[/C][C]-0.002264[/C][C]-0.0209[/C][C]0.491696[/C][/ROW]
[ROW][C]15[/C][C]0.21537[/C][C]1.9856[/C][C]0.02515[/C][/ROW]
[ROW][C]16[/C][C]0.050733[/C][C]0.4677[/C][C]0.320585[/C][/ROW]
[ROW][C]17[/C][C]0.082224[/C][C]0.7581[/C][C]0.225252[/C][/ROW]
[ROW][C]18[/C][C]0.230997[/C][C]2.1297[/C][C]0.018044[/C][/ROW]
[ROW][C]19[/C][C]0.03449[/C][C]0.318[/C][C]0.37564[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28375&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28375&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	0.414367	3.8203	0.000126
2	0.175065	1.614	0.055115
3	0.384837	3.548	0.000317
4	0.242256	2.2335	0.014071
5	0.244275	2.2521	0.013446
6	0.434937	4.0099	6.5e-05
7	0.207434	1.9124	0.029594
8	0.185994	1.7148	0.045014
9	0.29743	2.7422	0.00372
10	0.024236	0.2234	0.411862
11	0.275241	2.5376	0.006493
12	0.653912	6.0288	0
13	0.250565	2.3101	0.011653
14	-0.002264	-0.0209	0.491696
15	0.21537	1.9856	0.02515
16	0.050733	0.4677	0.320585
17	0.082224	0.7581	0.225252
18	0.230997	2.1297	0.018044
19	0.03449	0.318	0.37564

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.414367	3.8203	0.000126
2	0.004062	0.0374	0.485108
3	0.375362	3.4607	0.000423
4	-0.063384	-0.5844	0.280259
5	0.220995	2.0375	0.022356
6	0.228218	2.1041	0.019164
7	-0.111787	-1.0306	0.15282
8	0.131647	1.2137	0.114107
9	-0.017182	-0.1584	0.437255
10	-0.228878	-2.1102	0.018892
11	0.415816	3.8336	0.000121
12	0.400482	3.6923	0.000196
13	-0.175114	-1.6145	0.055066
14	-0.345832	-3.1884	0.001002
15	-0.015268	-0.1408	0.444196
16	-0.12763	-1.1767	0.121302
17	-0.015795	-0.1456	0.442281
18	-0.07267	-0.67	0.252342
19	0.018952	0.1747	0.430853

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.414367 & 3.8203 & 0.000126 \tabularnewline
2 & 0.004062 & 0.0374 & 0.485108 \tabularnewline
3 & 0.375362 & 3.4607 & 0.000423 \tabularnewline
4 & -0.063384 & -0.5844 & 0.280259 \tabularnewline
5 & 0.220995 & 2.0375 & 0.022356 \tabularnewline
6 & 0.228218 & 2.1041 & 0.019164 \tabularnewline
7 & -0.111787 & -1.0306 & 0.15282 \tabularnewline
8 & 0.131647 & 1.2137 & 0.114107 \tabularnewline
9 & -0.017182 & -0.1584 & 0.437255 \tabularnewline
10 & -0.228878 & -2.1102 & 0.018892 \tabularnewline
11 & 0.415816 & 3.8336 & 0.000121 \tabularnewline
12 & 0.400482 & 3.6923 & 0.000196 \tabularnewline
13 & -0.175114 & -1.6145 & 0.055066 \tabularnewline
14 & -0.345832 & -3.1884 & 0.001002 \tabularnewline
15 & -0.015268 & -0.1408 & 0.444196 \tabularnewline
16 & -0.12763 & -1.1767 & 0.121302 \tabularnewline
17 & -0.015795 & -0.1456 & 0.442281 \tabularnewline
18 & -0.07267 & -0.67 & 0.252342 \tabularnewline
19 & 0.018952 & 0.1747 & 0.430853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28375&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]0.414367[/C][C]3.8203[/C][C]0.000126[/C][/ROW]
[ROW][C]2[/C][C]0.004062[/C][C]0.0374[/C][C]0.485108[/C][/ROW]
[ROW][C]3[/C][C]0.375362[/C][C]3.4607[/C][C]0.000423[/C][/ROW]
[ROW][C]4[/C][C]-0.063384[/C][C]-0.5844[/C][C]0.280259[/C][/ROW]
[ROW][C]5[/C][C]0.220995[/C][C]2.0375[/C][C]0.022356[/C][/ROW]
[ROW][C]6[/C][C]0.228218[/C][C]2.1041[/C][C]0.019164[/C][/ROW]
[ROW][C]7[/C][C]-0.111787[/C][C]-1.0306[/C][C]0.15282[/C][/ROW]
[ROW][C]8[/C][C]0.131647[/C][C]1.2137[/C][C]0.114107[/C][/ROW]
[ROW][C]9[/C][C]-0.017182[/C][C]-0.1584[/C][C]0.437255[/C][/ROW]
[ROW][C]10[/C][C]-0.228878[/C][C]-2.1102[/C][C]0.018892[/C][/ROW]
[ROW][C]11[/C][C]0.415816[/C][C]3.8336[/C][C]0.000121[/C][/ROW]
[ROW][C]12[/C][C]0.400482[/C][C]3.6923[/C][C]0.000196[/C][/ROW]
[ROW][C]13[/C][C]-0.175114[/C][C]-1.6145[/C][C]0.055066[/C][/ROW]
[ROW][C]14[/C][C]-0.345832[/C][C]-3.1884[/C][C]0.001002[/C][/ROW]
[ROW][C]15[/C][C]-0.015268[/C][C]-0.1408[/C][C]0.444196[/C][/ROW]
[ROW][C]16[/C][C]-0.12763[/C][C]-1.1767[/C][C]0.121302[/C][/ROW]
[ROW][C]17[/C][C]-0.015795[/C][C]-0.1456[/C][C]0.442281[/C][/ROW]
[ROW][C]18[/C][C]-0.07267[/C][C]-0.67[/C][C]0.252342[/C][/ROW]
[ROW][C]19[/C][C]0.018952[/C][C]0.1747[/C][C]0.430853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28375&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28375&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	0.414367	3.8203	0.000126
2	0.004062	0.0374	0.485108
3	0.375362	3.4607	0.000423
4	-0.063384	-0.5844	0.280259
5	0.220995	2.0375	0.022356
6	0.228218	2.1041	0.019164
7	-0.111787	-1.0306	0.15282
8	0.131647	1.2137	0.114107
9	-0.017182	-0.1584	0.437255
10	-0.228878	-2.1102	0.018892
11	0.415816	3.8336	0.000121
12	0.400482	3.6923	0.000196
13	-0.175114	-1.6145	0.055066
14	-0.345832	-3.1884	0.001002
15	-0.015268	-0.1408	0.444196
16	-0.12763	-1.1767	0.121302
17	-0.015795	-0.1456	0.442281
18	-0.07267	-0.67	0.252342
19	0.018952	0.1747	0.430853

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code