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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 08 Dec 2008 13:20:51 -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/t12287676943bhyw3lkvse2v3o.htm/, Retrieved Thu, 16 May 2024 18:25:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30942, Retrieved Thu, 16 May 2024 18:25:19 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

196

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  [Cross Correlation Function] [Q7 - zonder trans...] [2008-12-01 20:04:13] [299afd6311e4c20059ea2f05c8dd029d]
F RM D    [Variance Reduction Matrix] [Q8] [2008-12-01 20:20:44] [299afd6311e4c20059ea2f05c8dd029d]
F    D      [Variance Reduction Matrix] [Q8 - 2] [2008-12-01 20:25:07] [299afd6311e4c20059ea2f05c8dd029d]
F RM D        [Standard Deviation-Mean Plot] [Deel 2: Step 1] [2008-12-08 20:09:35] [299afd6311e4c20059ea2f05c8dd029d]
- RM D            [(Partial) Autocorrelation Function] [Deel 2:  Step 2 -...] [2008-12-08 20:20:51] [5e2b1e7aa808f9f0d23fd35605d4968f] [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	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=30942&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=30942&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30942&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	0.61701	5.2355	1e-06
2	0.470548	3.9927	7.8e-05
3	0.559479	4.7473	5e-06
4	0.592954	5.0314	2e-06
5	0.539119	4.5746	1e-05
6	0.625978	5.3116	1e-06
7	0.470769	3.9946	7.7e-05
8	0.485489	4.1195	5e-05
9	0.412902	3.5036	0.000397
10	0.276122	2.343	0.010949
11	0.387267	3.2861	0.000786
12	0.607542	5.1552	1e-06
13	0.317492	2.694	0.004389
14	0.217011	1.8414	0.034841
15	0.237911	2.0187	0.02362
16	0.250924	2.1292	0.018331
17	0.254558	2.16	0.017052
18	0.295611	2.5083	0.007192

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.61701 & 5.2355 & 1e-06 \tabularnewline
2 & 0.470548 & 3.9927 & 7.8e-05 \tabularnewline
3 & 0.559479 & 4.7473 & 5e-06 \tabularnewline
4 & 0.592954 & 5.0314 & 2e-06 \tabularnewline
5 & 0.539119 & 4.5746 & 1e-05 \tabularnewline
6 & 0.625978 & 5.3116 & 1e-06 \tabularnewline
7 & 0.470769 & 3.9946 & 7.7e-05 \tabularnewline
8 & 0.485489 & 4.1195 & 5e-05 \tabularnewline
9 & 0.412902 & 3.5036 & 0.000397 \tabularnewline
10 & 0.276122 & 2.343 & 0.010949 \tabularnewline
11 & 0.387267 & 3.2861 & 0.000786 \tabularnewline
12 & 0.607542 & 5.1552 & 1e-06 \tabularnewline
13 & 0.317492 & 2.694 & 0.004389 \tabularnewline
14 & 0.217011 & 1.8414 & 0.034841 \tabularnewline
15 & 0.237911 & 2.0187 & 0.02362 \tabularnewline
16 & 0.250924 & 2.1292 & 0.018331 \tabularnewline
17 & 0.254558 & 2.16 & 0.017052 \tabularnewline
18 & 0.295611 & 2.5083 & 0.007192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30942&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]0.61701[/C][C]5.2355[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.470548[/C][C]3.9927[/C][C]7.8e-05[/C][/ROW]
[ROW][C]3[/C][C]0.559479[/C][C]4.7473[/C][C]5e-06[/C][/ROW]
[ROW][C]4[/C][C]0.592954[/C][C]5.0314[/C][C]2e-06[/C][/ROW]
[ROW][C]5[/C][C]0.539119[/C][C]4.5746[/C][C]1e-05[/C][/ROW]
[ROW][C]6[/C][C]0.625978[/C][C]5.3116[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.470769[/C][C]3.9946[/C][C]7.7e-05[/C][/ROW]
[ROW][C]8[/C][C]0.485489[/C][C]4.1195[/C][C]5e-05[/C][/ROW]
[ROW][C]9[/C][C]0.412902[/C][C]3.5036[/C][C]0.000397[/C][/ROW]
[ROW][C]10[/C][C]0.276122[/C][C]2.343[/C][C]0.010949[/C][/ROW]
[ROW][C]11[/C][C]0.387267[/C][C]3.2861[/C][C]0.000786[/C][/ROW]
[ROW][C]12[/C][C]0.607542[/C][C]5.1552[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.317492[/C][C]2.694[/C][C]0.004389[/C][/ROW]
[ROW][C]14[/C][C]0.217011[/C][C]1.8414[/C][C]0.034841[/C][/ROW]
[ROW][C]15[/C][C]0.237911[/C][C]2.0187[/C][C]0.02362[/C][/ROW]
[ROW][C]16[/C][C]0.250924[/C][C]2.1292[/C][C]0.018331[/C][/ROW]
[ROW][C]17[/C][C]0.254558[/C][C]2.16[/C][C]0.017052[/C][/ROW]
[ROW][C]18[/C][C]0.295611[/C][C]2.5083[/C][C]0.007192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30942&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30942&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	0.61701	5.2355	1e-06
2	0.470548	3.9927	7.8e-05
3	0.559479	4.7473	5e-06
4	0.592954	5.0314	2e-06
5	0.539119	4.5746	1e-05
6	0.625978	5.3116	1e-06
7	0.470769	3.9946	7.7e-05
8	0.485489	4.1195	5e-05
9	0.412902	3.5036	0.000397
10	0.276122	2.343	0.010949
11	0.387267	3.2861	0.000786
12	0.607542	5.1552	1e-06
13	0.317492	2.694	0.004389
14	0.217011	1.8414	0.034841
15	0.237911	2.0187	0.02362
16	0.250924	2.1292	0.018331
17	0.254558	2.16	0.017052
18	0.295611	2.5083	0.007192

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.61701	5.2355	1e-06
2	0.145078	1.231	0.111159
3	0.365768	3.1036	0.001366
4	0.236805	2.0094	0.024124
5	0.129597	1.0997	0.137571
6	0.333223	2.8275	0.003035
7	-0.195712	-1.6607	0.050565
8	0.173612	1.4731	0.072535
9	-0.308032	-2.6137	0.005449
10	-0.334456	-2.8379	0.002947
11	0.199039	1.6889	0.047783
12	0.338124	2.8691	0.0027
13	-0.212703	-1.8048	0.03764
14	-0.021401	-0.1816	0.428206
15	-0.200054	-1.6975	0.046959
16	-0.002523	-0.0214	0.491488
17	0.033262	0.2822	0.389284
18	-0.030304	-0.2571	0.398904

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.61701 & 5.2355 & 1e-06 \tabularnewline
2 & 0.145078 & 1.231 & 0.111159 \tabularnewline
3 & 0.365768 & 3.1036 & 0.001366 \tabularnewline
4 & 0.236805 & 2.0094 & 0.024124 \tabularnewline
5 & 0.129597 & 1.0997 & 0.137571 \tabularnewline
6 & 0.333223 & 2.8275 & 0.003035 \tabularnewline
7 & -0.195712 & -1.6607 & 0.050565 \tabularnewline
8 & 0.173612 & 1.4731 & 0.072535 \tabularnewline
9 & -0.308032 & -2.6137 & 0.005449 \tabularnewline
10 & -0.334456 & -2.8379 & 0.002947 \tabularnewline
11 & 0.199039 & 1.6889 & 0.047783 \tabularnewline
12 & 0.338124 & 2.8691 & 0.0027 \tabularnewline
13 & -0.212703 & -1.8048 & 0.03764 \tabularnewline
14 & -0.021401 & -0.1816 & 0.428206 \tabularnewline
15 & -0.200054 & -1.6975 & 0.046959 \tabularnewline
16 & -0.002523 & -0.0214 & 0.491488 \tabularnewline
17 & 0.033262 & 0.2822 & 0.389284 \tabularnewline
18 & -0.030304 & -0.2571 & 0.398904 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30942&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]0.61701[/C][C]5.2355[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.145078[/C][C]1.231[/C][C]0.111159[/C][/ROW]
[ROW][C]3[/C][C]0.365768[/C][C]3.1036[/C][C]0.001366[/C][/ROW]
[ROW][C]4[/C][C]0.236805[/C][C]2.0094[/C][C]0.024124[/C][/ROW]
[ROW][C]5[/C][C]0.129597[/C][C]1.0997[/C][C]0.137571[/C][/ROW]
[ROW][C]6[/C][C]0.333223[/C][C]2.8275[/C][C]0.003035[/C][/ROW]
[ROW][C]7[/C][C]-0.195712[/C][C]-1.6607[/C][C]0.050565[/C][/ROW]
[ROW][C]8[/C][C]0.173612[/C][C]1.4731[/C][C]0.072535[/C][/ROW]
[ROW][C]9[/C][C]-0.308032[/C][C]-2.6137[/C][C]0.005449[/C][/ROW]
[ROW][C]10[/C][C]-0.334456[/C][C]-2.8379[/C][C]0.002947[/C][/ROW]
[ROW][C]11[/C][C]0.199039[/C][C]1.6889[/C][C]0.047783[/C][/ROW]
[ROW][C]12[/C][C]0.338124[/C][C]2.8691[/C][C]0.0027[/C][/ROW]
[ROW][C]13[/C][C]-0.212703[/C][C]-1.8048[/C][C]0.03764[/C][/ROW]
[ROW][C]14[/C][C]-0.021401[/C][C]-0.1816[/C][C]0.428206[/C][/ROW]
[ROW][C]15[/C][C]-0.200054[/C][C]-1.6975[/C][C]0.046959[/C][/ROW]
[ROW][C]16[/C][C]-0.002523[/C][C]-0.0214[/C][C]0.491488[/C][/ROW]
[ROW][C]17[/C][C]0.033262[/C][C]0.2822[/C][C]0.389284[/C][/ROW]
[ROW][C]18[/C][C]-0.030304[/C][C]-0.2571[/C][C]0.398904[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30942&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30942&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	0.61701	5.2355	1e-06
2	0.145078	1.231	0.111159
3	0.365768	3.1036	0.001366
4	0.236805	2.0094	0.024124
5	0.129597	1.0997	0.137571
6	0.333223	2.8275	0.003035
7	-0.195712	-1.6607	0.050565
8	0.173612	1.4731	0.072535
9	-0.308032	-2.6137	0.005449
10	-0.334456	-2.8379	0.002947
11	0.199039	1.6889	0.047783
12	0.338124	2.8691	0.0027
13	-0.212703	-1.8048	0.03764
14	-0.021401	-0.1816	0.428206
15	-0.200054	-1.6975	0.046959
16	-0.002523	-0.0214	0.491488
17	0.033262	0.2822	0.389284
18	-0.030304	-0.2571	0.398904

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code