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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 08 Dec 2008 10:12:28 -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/08/t12287564909qtgo3g2qmqd18c.htm/, Retrieved Thu, 16 May 2024 12:50:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30599, Retrieved Thu, 16 May 2024 12:50:30 +0000

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User-defined keywords

Estimated Impact

148

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]
F RMPD    [(Partial) Autocorrelation Function] [Workshop 8] [2008-12-08 17:12:28] [d300b7a0882cee7d84584ad37a3d4ede] [Current]

Feedback Forum

2008-12-13 10:58:35 [Sofie Sergoynne] [reply] 
ik vind dat dit antwoord oke is.

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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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30599&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30599&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30599&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.92901	8.5145	0
2	0.869041	7.9649	0
3	0.79479	7.2844	0
4	0.723498	6.631	0
5	0.638645	5.8533	0
6	0.561168	5.1432	1e-06
7	0.483689	4.4331	1.4e-05
8	0.411106	3.7678	0.000152
9	0.348308	3.1923	0.000993
10	0.282044	2.585	0.005733
11	0.215871	1.9785	0.025575
12	0.166021	1.5216	0.065932
13	0.115367	1.0574	0.14669
14	0.066163	0.6064	0.272943
15	0.020554	0.1884	0.425515
16	-0.023584	-0.2161	0.414698
17	-0.063762	-0.5844	0.280263
18	-0.093887	-0.8605	0.195985
19	-0.124096	-1.1374	0.129311

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.92901 & 8.5145 & 0 \tabularnewline
2 & 0.869041 & 7.9649 & 0 \tabularnewline
3 & 0.79479 & 7.2844 & 0 \tabularnewline
4 & 0.723498 & 6.631 & 0 \tabularnewline
5 & 0.638645 & 5.8533 & 0 \tabularnewline
6 & 0.561168 & 5.1432 & 1e-06 \tabularnewline
7 & 0.483689 & 4.4331 & 1.4e-05 \tabularnewline
8 & 0.411106 & 3.7678 & 0.000152 \tabularnewline
9 & 0.348308 & 3.1923 & 0.000993 \tabularnewline
10 & 0.282044 & 2.585 & 0.005733 \tabularnewline
11 & 0.215871 & 1.9785 & 0.025575 \tabularnewline
12 & 0.166021 & 1.5216 & 0.065932 \tabularnewline
13 & 0.115367 & 1.0574 & 0.14669 \tabularnewline
14 & 0.066163 & 0.6064 & 0.272943 \tabularnewline
15 & 0.020554 & 0.1884 & 0.425515 \tabularnewline
16 & -0.023584 & -0.2161 & 0.414698 \tabularnewline
17 & -0.063762 & -0.5844 & 0.280263 \tabularnewline
18 & -0.093887 & -0.8605 & 0.195985 \tabularnewline
19 & -0.124096 & -1.1374 & 0.129311 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30599&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]0.92901[/C][C]8.5145[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.869041[/C][C]7.9649[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.79479[/C][C]7.2844[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.723498[/C][C]6.631[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.638645[/C][C]5.8533[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.561168[/C][C]5.1432[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.483689[/C][C]4.4331[/C][C]1.4e-05[/C][/ROW]
[ROW][C]8[/C][C]0.411106[/C][C]3.7678[/C][C]0.000152[/C][/ROW]
[ROW][C]9[/C][C]0.348308[/C][C]3.1923[/C][C]0.000993[/C][/ROW]
[ROW][C]10[/C][C]0.282044[/C][C]2.585[/C][C]0.005733[/C][/ROW]
[ROW][C]11[/C][C]0.215871[/C][C]1.9785[/C][C]0.025575[/C][/ROW]
[ROW][C]12[/C][C]0.166021[/C][C]1.5216[/C][C]0.065932[/C][/ROW]
[ROW][C]13[/C][C]0.115367[/C][C]1.0574[/C][C]0.14669[/C][/ROW]
[ROW][C]14[/C][C]0.066163[/C][C]0.6064[/C][C]0.272943[/C][/ROW]
[ROW][C]15[/C][C]0.020554[/C][C]0.1884[/C][C]0.425515[/C][/ROW]
[ROW][C]16[/C][C]-0.023584[/C][C]-0.2161[/C][C]0.414698[/C][/ROW]
[ROW][C]17[/C][C]-0.063762[/C][C]-0.5844[/C][C]0.280263[/C][/ROW]
[ROW][C]18[/C][C]-0.093887[/C][C]-0.8605[/C][C]0.195985[/C][/ROW]
[ROW][C]19[/C][C]-0.124096[/C][C]-1.1374[/C][C]0.129311[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30599&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30599&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	0.92901	8.5145	0
2	0.869041	7.9649	0
3	0.79479	7.2844	0
4	0.723498	6.631	0
5	0.638645	5.8533	0
6	0.561168	5.1432	1e-06
7	0.483689	4.4331	1.4e-05
8	0.411106	3.7678	0.000152
9	0.348308	3.1923	0.000993
10	0.282044	2.585	0.005733
11	0.215871	1.9785	0.025575
12	0.166021	1.5216	0.065932
13	0.115367	1.0574	0.14669
14	0.066163	0.6064	0.272943
15	0.020554	0.1884	0.425515
16	-0.023584	-0.2161	0.414698
17	-0.063762	-0.5844	0.280263
18	-0.093887	-0.8605	0.195985
19	-0.124096	-1.1374	0.129311

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.92901	8.5145	0
2	0.043677	0.4003	0.344972
3	-0.130762	-1.1985	0.117055
4	-0.034217	-0.3136	0.3773
5	-0.131073	-1.2013	0.116506
6	-0.012953	-0.1187	0.452893
7	-0.026706	-0.2448	0.403618
8	-0.023216	-0.2128	0.416007
9	0.034296	0.3143	0.377024
10	-0.075113	-0.6884	0.246542
11	-0.068253	-0.6256	0.266653
12	0.069878	0.6404	0.261815
13	-0.045811	-0.4199	0.337827
14	-0.046607	-0.4272	0.335176
15	-0.016981	-0.1556	0.438348
16	-0.055041	-0.5045	0.307628
17	-0.010327	-0.0947	0.462408
18	0.02871	0.2631	0.396546
19	-0.040076	-0.3673	0.35716

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.92901 & 8.5145 & 0 \tabularnewline
2 & 0.043677 & 0.4003 & 0.344972 \tabularnewline
3 & -0.130762 & -1.1985 & 0.117055 \tabularnewline
4 & -0.034217 & -0.3136 & 0.3773 \tabularnewline
5 & -0.131073 & -1.2013 & 0.116506 \tabularnewline
6 & -0.012953 & -0.1187 & 0.452893 \tabularnewline
7 & -0.026706 & -0.2448 & 0.403618 \tabularnewline
8 & -0.023216 & -0.2128 & 0.416007 \tabularnewline
9 & 0.034296 & 0.3143 & 0.377024 \tabularnewline
10 & -0.075113 & -0.6884 & 0.246542 \tabularnewline
11 & -0.068253 & -0.6256 & 0.266653 \tabularnewline
12 & 0.069878 & 0.6404 & 0.261815 \tabularnewline
13 & -0.045811 & -0.4199 & 0.337827 \tabularnewline
14 & -0.046607 & -0.4272 & 0.335176 \tabularnewline
15 & -0.016981 & -0.1556 & 0.438348 \tabularnewline
16 & -0.055041 & -0.5045 & 0.307628 \tabularnewline
17 & -0.010327 & -0.0947 & 0.462408 \tabularnewline
18 & 0.02871 & 0.2631 & 0.396546 \tabularnewline
19 & -0.040076 & -0.3673 & 0.35716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30599&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]0.92901[/C][C]8.5145[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.043677[/C][C]0.4003[/C][C]0.344972[/C][/ROW]
[ROW][C]3[/C][C]-0.130762[/C][C]-1.1985[/C][C]0.117055[/C][/ROW]
[ROW][C]4[/C][C]-0.034217[/C][C]-0.3136[/C][C]0.3773[/C][/ROW]
[ROW][C]5[/C][C]-0.131073[/C][C]-1.2013[/C][C]0.116506[/C][/ROW]
[ROW][C]6[/C][C]-0.012953[/C][C]-0.1187[/C][C]0.452893[/C][/ROW]
[ROW][C]7[/C][C]-0.026706[/C][C]-0.2448[/C][C]0.403618[/C][/ROW]
[ROW][C]8[/C][C]-0.023216[/C][C]-0.2128[/C][C]0.416007[/C][/ROW]
[ROW][C]9[/C][C]0.034296[/C][C]0.3143[/C][C]0.377024[/C][/ROW]
[ROW][C]10[/C][C]-0.075113[/C][C]-0.6884[/C][C]0.246542[/C][/ROW]
[ROW][C]11[/C][C]-0.068253[/C][C]-0.6256[/C][C]0.266653[/C][/ROW]
[ROW][C]12[/C][C]0.069878[/C][C]0.6404[/C][C]0.261815[/C][/ROW]
[ROW][C]13[/C][C]-0.045811[/C][C]-0.4199[/C][C]0.337827[/C][/ROW]
[ROW][C]14[/C][C]-0.046607[/C][C]-0.4272[/C][C]0.335176[/C][/ROW]
[ROW][C]15[/C][C]-0.016981[/C][C]-0.1556[/C][C]0.438348[/C][/ROW]
[ROW][C]16[/C][C]-0.055041[/C][C]-0.5045[/C][C]0.307628[/C][/ROW]
[ROW][C]17[/C][C]-0.010327[/C][C]-0.0947[/C][C]0.462408[/C][/ROW]
[ROW][C]18[/C][C]0.02871[/C][C]0.2631[/C][C]0.396546[/C][/ROW]
[ROW][C]19[/C][C]-0.040076[/C][C]-0.3673[/C][C]0.35716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30599&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30599&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	0.92901	8.5145	0
2	0.043677	0.4003	0.344972
3	-0.130762	-1.1985	0.117055
4	-0.034217	-0.3136	0.3773
5	-0.131073	-1.2013	0.116506
6	-0.012953	-0.1187	0.452893
7	-0.026706	-0.2448	0.403618
8	-0.023216	-0.2128	0.416007
9	0.034296	0.3143	0.377024
10	-0.075113	-0.6884	0.246542
11	-0.068253	-0.6256	0.266653
12	0.069878	0.6404	0.261815
13	-0.045811	-0.4199	0.337827
14	-0.046607	-0.4272	0.335176
15	-0.016981	-0.1556	0.438348
16	-0.055041	-0.5045	0.307628
17	-0.010327	-0.0947	0.462408
18	0.02871	0.2631	0.396546
19	-0.040076	-0.3673	0.35716

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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Dataset

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Figures (Output of Computation)

Input Parameters & R Code