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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 02 Dec 2008 13:29:27 -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/t1228249819j80o5j92ru376yn.htm/, Retrieved Sun, 19 May 2024 10:45:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28384, Retrieved Sun, 19 May 2024 10:45:16 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van Dooren Leen

Estimated Impact

145

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] [NST Q8] [2008-12-02 20:29:27] [006ad2c49b6a7c2ad6ab685cfc1dae56] [Current]

Feedback Forum

2008-12-07 11:24:30 [006ad2c49b6a7c2ad6ab685cfc1dae56] [reply] 
Goede differentiaties.

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Dataseries X:

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Boxplots

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=28384&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=28384&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28384&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	0.165903	1.3781	0.086313
2	-0.220336	-1.8302	0.035766
3	-0.163532	-1.3584	0.089381
4	-0.153118	-1.2719	0.103841
5	0.19655	1.6327	0.053548
6	0.321383	2.6696	0.00473
7	0.187028	1.5536	0.062431
8	-0.132266	-1.0987	0.137862
9	-0.218876	-1.8181	0.036693
10	-0.181195	-1.5051	0.068429
11	0.223589	1.8573	0.03377
12	0.588307	4.8868	3e-06
13	0.051819	0.4304	0.334107
14	-0.160815	-1.3358	0.092998
15	-0.127744	-1.0611	0.146168
16	-0.115987	-0.9635	0.169341
17	0.11448	0.9509	0.172477
18	0.213502	1.7735	0.040281

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.165903 & 1.3781 & 0.086313 \tabularnewline
2 & -0.220336 & -1.8302 & 0.035766 \tabularnewline
3 & -0.163532 & -1.3584 & 0.089381 \tabularnewline
4 & -0.153118 & -1.2719 & 0.103841 \tabularnewline
5 & 0.19655 & 1.6327 & 0.053548 \tabularnewline
6 & 0.321383 & 2.6696 & 0.00473 \tabularnewline
7 & 0.187028 & 1.5536 & 0.062431 \tabularnewline
8 & -0.132266 & -1.0987 & 0.137862 \tabularnewline
9 & -0.218876 & -1.8181 & 0.036693 \tabularnewline
10 & -0.181195 & -1.5051 & 0.068429 \tabularnewline
11 & 0.223589 & 1.8573 & 0.03377 \tabularnewline
12 & 0.588307 & 4.8868 & 3e-06 \tabularnewline
13 & 0.051819 & 0.4304 & 0.334107 \tabularnewline
14 & -0.160815 & -1.3358 & 0.092998 \tabularnewline
15 & -0.127744 & -1.0611 & 0.146168 \tabularnewline
16 & -0.115987 & -0.9635 & 0.169341 \tabularnewline
17 & 0.11448 & 0.9509 & 0.172477 \tabularnewline
18 & 0.213502 & 1.7735 & 0.040281 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28384&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]0.165903[/C][C]1.3781[/C][C]0.086313[/C][/ROW]
[ROW][C]2[/C][C]-0.220336[/C][C]-1.8302[/C][C]0.035766[/C][/ROW]
[ROW][C]3[/C][C]-0.163532[/C][C]-1.3584[/C][C]0.089381[/C][/ROW]
[ROW][C]4[/C][C]-0.153118[/C][C]-1.2719[/C][C]0.103841[/C][/ROW]
[ROW][C]5[/C][C]0.19655[/C][C]1.6327[/C][C]0.053548[/C][/ROW]
[ROW][C]6[/C][C]0.321383[/C][C]2.6696[/C][C]0.00473[/C][/ROW]
[ROW][C]7[/C][C]0.187028[/C][C]1.5536[/C][C]0.062431[/C][/ROW]
[ROW][C]8[/C][C]-0.132266[/C][C]-1.0987[/C][C]0.137862[/C][/ROW]
[ROW][C]9[/C][C]-0.218876[/C][C]-1.8181[/C][C]0.036693[/C][/ROW]
[ROW][C]10[/C][C]-0.181195[/C][C]-1.5051[/C][C]0.068429[/C][/ROW]
[ROW][C]11[/C][C]0.223589[/C][C]1.8573[/C][C]0.03377[/C][/ROW]
[ROW][C]12[/C][C]0.588307[/C][C]4.8868[/C][C]3e-06[/C][/ROW]
[ROW][C]13[/C][C]0.051819[/C][C]0.4304[/C][C]0.334107[/C][/ROW]
[ROW][C]14[/C][C]-0.160815[/C][C]-1.3358[/C][C]0.092998[/C][/ROW]
[ROW][C]15[/C][C]-0.127744[/C][C]-1.0611[/C][C]0.146168[/C][/ROW]
[ROW][C]16[/C][C]-0.115987[/C][C]-0.9635[/C][C]0.169341[/C][/ROW]
[ROW][C]17[/C][C]0.11448[/C][C]0.9509[/C][C]0.172477[/C][/ROW]
[ROW][C]18[/C][C]0.213502[/C][C]1.7735[/C][C]0.040281[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28384&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28384&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	0.165903	1.3781	0.086313
2	-0.220336	-1.8302	0.035766
3	-0.163532	-1.3584	0.089381
4	-0.153118	-1.2719	0.103841
5	0.19655	1.6327	0.053548
6	0.321383	2.6696	0.00473
7	0.187028	1.5536	0.062431
8	-0.132266	-1.0987	0.137862
9	-0.218876	-1.8181	0.036693
10	-0.181195	-1.5051	0.068429
11	0.223589	1.8573	0.03377
12	0.588307	4.8868	3e-06
13	0.051819	0.4304	0.334107
14	-0.160815	-1.3358	0.092998
15	-0.127744	-1.0611	0.146168
16	-0.115987	-0.9635	0.169341
17	0.11448	0.9509	0.172477
18	0.213502	1.7735	0.040281

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.165903	1.3781	0.086313
2	-0.254875	-2.1171	0.018927
3	-0.082895	-0.6886	0.246699
4	-0.178428	-1.4821	0.071428
5	0.22398	1.8605	0.033537
6	0.187461	1.5572	0.062003
7	0.201004	1.6697	0.049759
8	-0.088824	-0.7378	0.23156
9	-0.023493	-0.1951	0.422926
10	-0.187367	-1.5564	0.062096
11	0.234191	1.9453	0.027905
12	0.421194	3.4987	0.000412
13	-0.078704	-0.6538	0.25772
14	0.032632	0.2711	0.393577
15	0.048359	0.4017	0.344573
16	0.015029	0.1248	0.450508
17	-0.108835	-0.904	0.184557
18	-0.091491	-0.76	0.224928

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.165903 & 1.3781 & 0.086313 \tabularnewline
2 & -0.254875 & -2.1171 & 0.018927 \tabularnewline
3 & -0.082895 & -0.6886 & 0.246699 \tabularnewline
4 & -0.178428 & -1.4821 & 0.071428 \tabularnewline
5 & 0.22398 & 1.8605 & 0.033537 \tabularnewline
6 & 0.187461 & 1.5572 & 0.062003 \tabularnewline
7 & 0.201004 & 1.6697 & 0.049759 \tabularnewline
8 & -0.088824 & -0.7378 & 0.23156 \tabularnewline
9 & -0.023493 & -0.1951 & 0.422926 \tabularnewline
10 & -0.187367 & -1.5564 & 0.062096 \tabularnewline
11 & 0.234191 & 1.9453 & 0.027905 \tabularnewline
12 & 0.421194 & 3.4987 & 0.000412 \tabularnewline
13 & -0.078704 & -0.6538 & 0.25772 \tabularnewline
14 & 0.032632 & 0.2711 & 0.393577 \tabularnewline
15 & 0.048359 & 0.4017 & 0.344573 \tabularnewline
16 & 0.015029 & 0.1248 & 0.450508 \tabularnewline
17 & -0.108835 & -0.904 & 0.184557 \tabularnewline
18 & -0.091491 & -0.76 & 0.224928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28384&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]0.165903[/C][C]1.3781[/C][C]0.086313[/C][/ROW]
[ROW][C]2[/C][C]-0.254875[/C][C]-2.1171[/C][C]0.018927[/C][/ROW]
[ROW][C]3[/C][C]-0.082895[/C][C]-0.6886[/C][C]0.246699[/C][/ROW]
[ROW][C]4[/C][C]-0.178428[/C][C]-1.4821[/C][C]0.071428[/C][/ROW]
[ROW][C]5[/C][C]0.22398[/C][C]1.8605[/C][C]0.033537[/C][/ROW]
[ROW][C]6[/C][C]0.187461[/C][C]1.5572[/C][C]0.062003[/C][/ROW]
[ROW][C]7[/C][C]0.201004[/C][C]1.6697[/C][C]0.049759[/C][/ROW]
[ROW][C]8[/C][C]-0.088824[/C][C]-0.7378[/C][C]0.23156[/C][/ROW]
[ROW][C]9[/C][C]-0.023493[/C][C]-0.1951[/C][C]0.422926[/C][/ROW]
[ROW][C]10[/C][C]-0.187367[/C][C]-1.5564[/C][C]0.062096[/C][/ROW]
[ROW][C]11[/C][C]0.234191[/C][C]1.9453[/C][C]0.027905[/C][/ROW]
[ROW][C]12[/C][C]0.421194[/C][C]3.4987[/C][C]0.000412[/C][/ROW]
[ROW][C]13[/C][C]-0.078704[/C][C]-0.6538[/C][C]0.25772[/C][/ROW]
[ROW][C]14[/C][C]0.032632[/C][C]0.2711[/C][C]0.393577[/C][/ROW]
[ROW][C]15[/C][C]0.048359[/C][C]0.4017[/C][C]0.344573[/C][/ROW]
[ROW][C]16[/C][C]0.015029[/C][C]0.1248[/C][C]0.450508[/C][/ROW]
[ROW][C]17[/C][C]-0.108835[/C][C]-0.904[/C][C]0.184557[/C][/ROW]
[ROW][C]18[/C][C]-0.091491[/C][C]-0.76[/C][C]0.224928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28384&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28384&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	0.165903	1.3781	0.086313
2	-0.254875	-2.1171	0.018927
3	-0.082895	-0.6886	0.246699
4	-0.178428	-1.4821	0.071428
5	0.22398	1.8605	0.033537
6	0.187461	1.5572	0.062003
7	0.201004	1.6697	0.049759
8	-0.088824	-0.7378	0.23156
9	-0.023493	-0.1951	0.422926
10	-0.187367	-1.5564	0.062096
11	0.234191	1.9453	0.027905
12	0.421194	3.4987	0.000412
13	-0.078704	-0.6538	0.25772
14	0.032632	0.2711	0.393577
15	0.048359	0.4017	0.344573
16	0.015029	0.1248	0.450508
17	-0.108835	-0.904	0.184557
18	-0.091491	-0.76	0.224928

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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