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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 23 Dec 2008 07:38:06 -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/23/t1230043215yl9ubr4djvjgavx.htm/, Retrieved Fri, 17 May 2024 04:42:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36305, Retrieved Fri, 17 May 2024 04:42:34 +0000

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User-defined keywords

Estimated Impact

172

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 RMP   [Standard Deviation-Mean Plot] [Q1 ] [2008-12-07 13:13:15] [74be16979710d4c4e7c6647856088456]
-    D    [Standard Deviation-Mean Plot] [SMP eigen tijdreeks] [2008-12-15 19:50:53] [74be16979710d4c4e7c6647856088456]
- RMPD      [(Partial) Autocorrelation Function] [paper] [2008-12-23 14:27:57] [5262baed313b307078ce11eb68e9efe6]
-   P           [(Partial) Autocorrelation Function] [paper] [2008-12-23 14:38:06] [5bd06487453d0eec7a1bf04bf9f25085] [Current]
-   P             [(Partial) Autocorrelation Function] [Paper] [2008-12-23 15:13:44] [5262baed313b307078ce11eb68e9efe6] 
-   P               [(Partial) Autocorrelation Function] [paper] [2008-12-23 15:16:02] [5262baed313b307078ce11eb68e9efe6] 

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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	'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36305&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36305&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36305&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.928959	9.5642	0
2	0.820549	8.4481	0
3	0.738355	7.6018	0
4	0.696009	7.1659	0
5	0.686315	7.066	0
6	0.671491	6.9134	0
7	0.638973	6.5786	0
8	0.604692	6.2257	0
9	0.604312	6.2218	0
10	0.637382	6.5622	0
11	0.690451	7.1086	0
12	0.705429	7.2628	0
13	0.613949	6.321	0
14	0.496009	5.1067	1e-06
15	0.39847	4.1025	4e-05
16	0.336307	3.4625	0.000386
17	0.303495	3.1247	0.001148
18	0.268154	2.7608	0.003398
19	0.221225	2.2776	0.012377
20	0.174761	1.7993	0.03741

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.928959 & 9.5642 & 0 \tabularnewline
2 & 0.820549 & 8.4481 & 0 \tabularnewline
3 & 0.738355 & 7.6018 & 0 \tabularnewline
4 & 0.696009 & 7.1659 & 0 \tabularnewline
5 & 0.686315 & 7.066 & 0 \tabularnewline
6 & 0.671491 & 6.9134 & 0 \tabularnewline
7 & 0.638973 & 6.5786 & 0 \tabularnewline
8 & 0.604692 & 6.2257 & 0 \tabularnewline
9 & 0.604312 & 6.2218 & 0 \tabularnewline
10 & 0.637382 & 6.5622 & 0 \tabularnewline
11 & 0.690451 & 7.1086 & 0 \tabularnewline
12 & 0.705429 & 7.2628 & 0 \tabularnewline
13 & 0.613949 & 6.321 & 0 \tabularnewline
14 & 0.496009 & 5.1067 & 1e-06 \tabularnewline
15 & 0.39847 & 4.1025 & 4e-05 \tabularnewline
16 & 0.336307 & 3.4625 & 0.000386 \tabularnewline
17 & 0.303495 & 3.1247 & 0.001148 \tabularnewline
18 & 0.268154 & 2.7608 & 0.003398 \tabularnewline
19 & 0.221225 & 2.2776 & 0.012377 \tabularnewline
20 & 0.174761 & 1.7993 & 0.03741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36305&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]0.928959[/C][C]9.5642[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.820549[/C][C]8.4481[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.738355[/C][C]7.6018[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.696009[/C][C]7.1659[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.686315[/C][C]7.066[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.671491[/C][C]6.9134[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.638973[/C][C]6.5786[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.604692[/C][C]6.2257[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.604312[/C][C]6.2218[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.637382[/C][C]6.5622[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.690451[/C][C]7.1086[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.705429[/C][C]7.2628[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.613949[/C][C]6.321[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.496009[/C][C]5.1067[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]0.39847[/C][C]4.1025[/C][C]4e-05[/C][/ROW]
[ROW][C]16[/C][C]0.336307[/C][C]3.4625[/C][C]0.000386[/C][/ROW]
[ROW][C]17[/C][C]0.303495[/C][C]3.1247[/C][C]0.001148[/C][/ROW]
[ROW][C]18[/C][C]0.268154[/C][C]2.7608[/C][C]0.003398[/C][/ROW]
[ROW][C]19[/C][C]0.221225[/C][C]2.2776[/C][C]0.012377[/C][/ROW]
[ROW][C]20[/C][C]0.174761[/C][C]1.7993[/C][C]0.03741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36305&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36305&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	0.928959	9.5642	0
2	0.820549	8.4481	0
3	0.738355	7.6018	0
4	0.696009	7.1659	0
5	0.686315	7.066	0
6	0.671491	6.9134	0
7	0.638973	6.5786	0
8	0.604692	6.2257	0
9	0.604312	6.2218	0
10	0.637382	6.5622	0
11	0.690451	7.1086	0
12	0.705429	7.2628	0
13	0.613949	6.321	0
14	0.496009	5.1067	1e-06
15	0.39847	4.1025	4e-05
16	0.336307	3.4625	0.000386
17	0.303495	3.1247	0.001148
18	0.268154	2.7608	0.003398
19	0.221225	2.2776	0.012377
20	0.174761	1.7993	0.03741

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.928959	9.5642	0
2	-0.309535	-3.1869	0.000945
3	0.223547	2.3016	0.011658
4	0.137399	1.4146	0.080057
5	0.14777	1.5214	0.065571
6	-0.081024	-0.8342	0.203025
7	0.002745	0.0283	0.488752
8	0.06824	0.7026	0.24193
9	0.257595	2.6521	0.004614
10	0.123664	1.2732	0.102866
11	0.210467	2.1669	0.016241
12	-0.214213	-2.2055	0.014791
13	-0.642938	-6.6195	0
14	0.069022	0.7106	0.23944
15	-0.185379	-1.9086	0.02951
16	-0.089609	-0.9226	0.179161
17	-0.036958	-0.3805	0.352167
18	-0.001882	-0.0194	0.492289
19	0.022354	0.2302	0.409208
20	-0.052809	-0.5437	0.293893

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.928959 & 9.5642 & 0 \tabularnewline
2 & -0.309535 & -3.1869 & 0.000945 \tabularnewline
3 & 0.223547 & 2.3016 & 0.011658 \tabularnewline
4 & 0.137399 & 1.4146 & 0.080057 \tabularnewline
5 & 0.14777 & 1.5214 & 0.065571 \tabularnewline
6 & -0.081024 & -0.8342 & 0.203025 \tabularnewline
7 & 0.002745 & 0.0283 & 0.488752 \tabularnewline
8 & 0.06824 & 0.7026 & 0.24193 \tabularnewline
9 & 0.257595 & 2.6521 & 0.004614 \tabularnewline
10 & 0.123664 & 1.2732 & 0.102866 \tabularnewline
11 & 0.210467 & 2.1669 & 0.016241 \tabularnewline
12 & -0.214213 & -2.2055 & 0.014791 \tabularnewline
13 & -0.642938 & -6.6195 & 0 \tabularnewline
14 & 0.069022 & 0.7106 & 0.23944 \tabularnewline
15 & -0.185379 & -1.9086 & 0.02951 \tabularnewline
16 & -0.089609 & -0.9226 & 0.179161 \tabularnewline
17 & -0.036958 & -0.3805 & 0.352167 \tabularnewline
18 & -0.001882 & -0.0194 & 0.492289 \tabularnewline
19 & 0.022354 & 0.2302 & 0.409208 \tabularnewline
20 & -0.052809 & -0.5437 & 0.293893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36305&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]0.928959[/C][C]9.5642[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.309535[/C][C]-3.1869[/C][C]0.000945[/C][/ROW]
[ROW][C]3[/C][C]0.223547[/C][C]2.3016[/C][C]0.011658[/C][/ROW]
[ROW][C]4[/C][C]0.137399[/C][C]1.4146[/C][C]0.080057[/C][/ROW]
[ROW][C]5[/C][C]0.14777[/C][C]1.5214[/C][C]0.065571[/C][/ROW]
[ROW][C]6[/C][C]-0.081024[/C][C]-0.8342[/C][C]0.203025[/C][/ROW]
[ROW][C]7[/C][C]0.002745[/C][C]0.0283[/C][C]0.488752[/C][/ROW]
[ROW][C]8[/C][C]0.06824[/C][C]0.7026[/C][C]0.24193[/C][/ROW]
[ROW][C]9[/C][C]0.257595[/C][C]2.6521[/C][C]0.004614[/C][/ROW]
[ROW][C]10[/C][C]0.123664[/C][C]1.2732[/C][C]0.102866[/C][/ROW]
[ROW][C]11[/C][C]0.210467[/C][C]2.1669[/C][C]0.016241[/C][/ROW]
[ROW][C]12[/C][C]-0.214213[/C][C]-2.2055[/C][C]0.014791[/C][/ROW]
[ROW][C]13[/C][C]-0.642938[/C][C]-6.6195[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.069022[/C][C]0.7106[/C][C]0.23944[/C][/ROW]
[ROW][C]15[/C][C]-0.185379[/C][C]-1.9086[/C][C]0.02951[/C][/ROW]
[ROW][C]16[/C][C]-0.089609[/C][C]-0.9226[/C][C]0.179161[/C][/ROW]
[ROW][C]17[/C][C]-0.036958[/C][C]-0.3805[/C][C]0.352167[/C][/ROW]
[ROW][C]18[/C][C]-0.001882[/C][C]-0.0194[/C][C]0.492289[/C][/ROW]
[ROW][C]19[/C][C]0.022354[/C][C]0.2302[/C][C]0.409208[/C][/ROW]
[ROW][C]20[/C][C]-0.052809[/C][C]-0.5437[/C][C]0.293893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36305&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36305&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	0.928959	9.5642	0
2	-0.309535	-3.1869	0.000945
3	0.223547	2.3016	0.011658
4	0.137399	1.4146	0.080057
5	0.14777	1.5214	0.065571
6	-0.081024	-0.8342	0.203025
7	0.002745	0.0283	0.488752
8	0.06824	0.7026	0.24193
9	0.257595	2.6521	0.004614
10	0.123664	1.2732	0.102866
11	0.210467	2.1669	0.016241
12	-0.214213	-2.2055	0.014791
13	-0.642938	-6.6195	0
14	0.069022	0.7106	0.23944
15	-0.185379	-1.9086	0.02951
16	-0.089609	-0.9226	0.179161
17	-0.036958	-0.3805	0.352167
18	-0.001882	-0.0194	0.492289
19	0.022354	0.2302	0.409208
20	-0.052809	-0.5437	0.293893

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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