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Author's title

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

Wed, 29 Dec 2010 22:04:09 +0000

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/2010/Dec/29/t1293660234wwxknd0a3evdyqi.htm/, Retrieved Fri, 03 May 2024 09:25:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117158, Retrieved Fri, 03 May 2024 09:25:37 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

116

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Spectral Analysis] [Identifying Integ...] [2009-11-22 12:38:17] [b98453cac15ba1066b407e146608df68]
-    D        [Spectral Analysis] [Spectrum van Y(t)...] [2009-11-26 18:53:55] [9717cb857c153ca3061376906953b329]
-   P           [Spectral Analysis] [Spectrum van Y(t)...] [2009-11-26 20:30:28] [9717cb857c153ca3061376906953b329]
-   P             [Spectral Analysis] [Spectrum van Y(t)...] [2009-11-26 20:36:24] [9717cb857c153ca3061376906953b329]
- RMPD              [(Partial) Autocorrelation Function] [Autocorrelatie] [2010-12-27 16:02:07] [c420bdd199bcbe079f7d532ca3855317]
-                       [(Partial) Autocorrelation Function] [Autocorrelatie Op...] [2010-12-29 22:04:09] [63a115f47699ab31b1a302b9539c58a2] [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	'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117158&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117158&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117158&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	'Herman Ole Andreas Wold' @ www.yougetit.org

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.246909	2.9423	0.001903
2	0.181997	2.1687	0.015884
3	0.011496	0.137	0.445615
4	-0.153423	-1.8282	0.034806
5	-0.22142	-2.6385	0.004628
6	-0.362076	-4.3146	1.5e-05
7	-0.221079	-2.6345	0.004681
8	-0.183089	-2.1818	0.015386
9	-0.047887	-0.5706	0.284571
10	0.10277	1.2246	0.111369
11	0.298618	3.5584	0.000254
12	0.476758	5.6812	0
13	0.362707	4.3222	1.4e-05
14	0.079771	0.9506	0.171717
15	0.006254	0.0745	0.470349
16	-0.261287	-3.1136	0.001118
17	-0.286979	-3.4197	0.000409
18	-0.300217	-3.5775	0.000237
19	-0.272702	-3.2496	0.000721
20	-0.250786	-2.9885	0.001652
21	-0.001692	-0.0202	0.491971

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.246909 & 2.9423 & 0.001903 \tabularnewline
2 & 0.181997 & 2.1687 & 0.015884 \tabularnewline
3 & 0.011496 & 0.137 & 0.445615 \tabularnewline
4 & -0.153423 & -1.8282 & 0.034806 \tabularnewline
5 & -0.22142 & -2.6385 & 0.004628 \tabularnewline
6 & -0.362076 & -4.3146 & 1.5e-05 \tabularnewline
7 & -0.221079 & -2.6345 & 0.004681 \tabularnewline
8 & -0.183089 & -2.1818 & 0.015386 \tabularnewline
9 & -0.047887 & -0.5706 & 0.284571 \tabularnewline
10 & 0.10277 & 1.2246 & 0.111369 \tabularnewline
11 & 0.298618 & 3.5584 & 0.000254 \tabularnewline
12 & 0.476758 & 5.6812 & 0 \tabularnewline
13 & 0.362707 & 4.3222 & 1.4e-05 \tabularnewline
14 & 0.079771 & 0.9506 & 0.171717 \tabularnewline
15 & 0.006254 & 0.0745 & 0.470349 \tabularnewline
16 & -0.261287 & -3.1136 & 0.001118 \tabularnewline
17 & -0.286979 & -3.4197 & 0.000409 \tabularnewline
18 & -0.300217 & -3.5775 & 0.000237 \tabularnewline
19 & -0.272702 & -3.2496 & 0.000721 \tabularnewline
20 & -0.250786 & -2.9885 & 0.001652 \tabularnewline
21 & -0.001692 & -0.0202 & 0.491971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117158&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]0.246909[/C][C]2.9423[/C][C]0.001903[/C][/ROW]
[ROW][C]2[/C][C]0.181997[/C][C]2.1687[/C][C]0.015884[/C][/ROW]
[ROW][C]3[/C][C]0.011496[/C][C]0.137[/C][C]0.445615[/C][/ROW]
[ROW][C]4[/C][C]-0.153423[/C][C]-1.8282[/C][C]0.034806[/C][/ROW]
[ROW][C]5[/C][C]-0.22142[/C][C]-2.6385[/C][C]0.004628[/C][/ROW]
[ROW][C]6[/C][C]-0.362076[/C][C]-4.3146[/C][C]1.5e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.221079[/C][C]-2.6345[/C][C]0.004681[/C][/ROW]
[ROW][C]8[/C][C]-0.183089[/C][C]-2.1818[/C][C]0.015386[/C][/ROW]
[ROW][C]9[/C][C]-0.047887[/C][C]-0.5706[/C][C]0.284571[/C][/ROW]
[ROW][C]10[/C][C]0.10277[/C][C]1.2246[/C][C]0.111369[/C][/ROW]
[ROW][C]11[/C][C]0.298618[/C][C]3.5584[/C][C]0.000254[/C][/ROW]
[ROW][C]12[/C][C]0.476758[/C][C]5.6812[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.362707[/C][C]4.3222[/C][C]1.4e-05[/C][/ROW]
[ROW][C]14[/C][C]0.079771[/C][C]0.9506[/C][C]0.171717[/C][/ROW]
[ROW][C]15[/C][C]0.006254[/C][C]0.0745[/C][C]0.470349[/C][/ROW]
[ROW][C]16[/C][C]-0.261287[/C][C]-3.1136[/C][C]0.001118[/C][/ROW]
[ROW][C]17[/C][C]-0.286979[/C][C]-3.4197[/C][C]0.000409[/C][/ROW]
[ROW][C]18[/C][C]-0.300217[/C][C]-3.5775[/C][C]0.000237[/C][/ROW]
[ROW][C]19[/C][C]-0.272702[/C][C]-3.2496[/C][C]0.000721[/C][/ROW]
[ROW][C]20[/C][C]-0.250786[/C][C]-2.9885[/C][C]0.001652[/C][/ROW]
[ROW][C]21[/C][C]-0.001692[/C][C]-0.0202[/C][C]0.491971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117158&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117158&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	0.246909	2.9423	0.001903
2	0.181997	2.1687	0.015884
3	0.011496	0.137	0.445615
4	-0.153423	-1.8282	0.034806
5	-0.22142	-2.6385	0.004628
6	-0.362076	-4.3146	1.5e-05
7	-0.221079	-2.6345	0.004681
8	-0.183089	-2.1818	0.015386
9	-0.047887	-0.5706	0.284571
10	0.10277	1.2246	0.111369
11	0.298618	3.5584	0.000254
12	0.476758	5.6812	0
13	0.362707	4.3222	1.4e-05
14	0.079771	0.9506	0.171717
15	0.006254	0.0745	0.470349
16	-0.261287	-3.1136	0.001118
17	-0.286979	-3.4197	0.000409
18	-0.300217	-3.5775	0.000237
19	-0.272702	-3.2496	0.000721
20	-0.250786	-2.9885	0.001652
21	-0.001692	-0.0202	0.491971

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.246909	2.9423	0.001903
2	0.128891	1.5359	0.063393
3	-0.064404	-0.7675	0.222042
4	-0.180586	-2.1519	0.016547
5	-0.159509	-1.9008	0.029679
6	-0.265554	-3.1644	0.000951
7	-0.068071	-0.8112	0.209317
8	-0.08128	-0.9686	0.167206
9	-0.02021	-0.2408	0.405016
10	0.05037	0.6002	0.274654
11	0.203883	2.4296	0.008183
12	0.331202	3.9467	6.2e-05
13	0.196565	2.3423	0.010276
14	-0.155357	-1.8513	0.033103
15	-0.080702	-0.9617	0.168925
16	-0.238872	-2.8465	0.002538
17	-0.107054	-1.2757	0.102072
18	0.007391	0.0881	0.46497
19	0.013636	0.1625	0.435574
20	-0.155575	-1.8539	0.032915
21	0.107309	1.2787	0.101538

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.246909 & 2.9423 & 0.001903 \tabularnewline
2 & 0.128891 & 1.5359 & 0.063393 \tabularnewline
3 & -0.064404 & -0.7675 & 0.222042 \tabularnewline
4 & -0.180586 & -2.1519 & 0.016547 \tabularnewline
5 & -0.159509 & -1.9008 & 0.029679 \tabularnewline
6 & -0.265554 & -3.1644 & 0.000951 \tabularnewline
7 & -0.068071 & -0.8112 & 0.209317 \tabularnewline
8 & -0.08128 & -0.9686 & 0.167206 \tabularnewline
9 & -0.02021 & -0.2408 & 0.405016 \tabularnewline
10 & 0.05037 & 0.6002 & 0.274654 \tabularnewline
11 & 0.203883 & 2.4296 & 0.008183 \tabularnewline
12 & 0.331202 & 3.9467 & 6.2e-05 \tabularnewline
13 & 0.196565 & 2.3423 & 0.010276 \tabularnewline
14 & -0.155357 & -1.8513 & 0.033103 \tabularnewline
15 & -0.080702 & -0.9617 & 0.168925 \tabularnewline
16 & -0.238872 & -2.8465 & 0.002538 \tabularnewline
17 & -0.107054 & -1.2757 & 0.102072 \tabularnewline
18 & 0.007391 & 0.0881 & 0.46497 \tabularnewline
19 & 0.013636 & 0.1625 & 0.435574 \tabularnewline
20 & -0.155575 & -1.8539 & 0.032915 \tabularnewline
21 & 0.107309 & 1.2787 & 0.101538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117158&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]0.246909[/C][C]2.9423[/C][C]0.001903[/C][/ROW]
[ROW][C]2[/C][C]0.128891[/C][C]1.5359[/C][C]0.063393[/C][/ROW]
[ROW][C]3[/C][C]-0.064404[/C][C]-0.7675[/C][C]0.222042[/C][/ROW]
[ROW][C]4[/C][C]-0.180586[/C][C]-2.1519[/C][C]0.016547[/C][/ROW]
[ROW][C]5[/C][C]-0.159509[/C][C]-1.9008[/C][C]0.029679[/C][/ROW]
[ROW][C]6[/C][C]-0.265554[/C][C]-3.1644[/C][C]0.000951[/C][/ROW]
[ROW][C]7[/C][C]-0.068071[/C][C]-0.8112[/C][C]0.209317[/C][/ROW]
[ROW][C]8[/C][C]-0.08128[/C][C]-0.9686[/C][C]0.167206[/C][/ROW]
[ROW][C]9[/C][C]-0.02021[/C][C]-0.2408[/C][C]0.405016[/C][/ROW]
[ROW][C]10[/C][C]0.05037[/C][C]0.6002[/C][C]0.274654[/C][/ROW]
[ROW][C]11[/C][C]0.203883[/C][C]2.4296[/C][C]0.008183[/C][/ROW]
[ROW][C]12[/C][C]0.331202[/C][C]3.9467[/C][C]6.2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.196565[/C][C]2.3423[/C][C]0.010276[/C][/ROW]
[ROW][C]14[/C][C]-0.155357[/C][C]-1.8513[/C][C]0.033103[/C][/ROW]
[ROW][C]15[/C][C]-0.080702[/C][C]-0.9617[/C][C]0.168925[/C][/ROW]
[ROW][C]16[/C][C]-0.238872[/C][C]-2.8465[/C][C]0.002538[/C][/ROW]
[ROW][C]17[/C][C]-0.107054[/C][C]-1.2757[/C][C]0.102072[/C][/ROW]
[ROW][C]18[/C][C]0.007391[/C][C]0.0881[/C][C]0.46497[/C][/ROW]
[ROW][C]19[/C][C]0.013636[/C][C]0.1625[/C][C]0.435574[/C][/ROW]
[ROW][C]20[/C][C]-0.155575[/C][C]-1.8539[/C][C]0.032915[/C][/ROW]
[ROW][C]21[/C][C]0.107309[/C][C]1.2787[/C][C]0.101538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117158&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117158&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	0.246909	2.9423	0.001903
2	0.128891	1.5359	0.063393
3	-0.064404	-0.7675	0.222042
4	-0.180586	-2.1519	0.016547
5	-0.159509	-1.9008	0.029679
6	-0.265554	-3.1644	0.000951
7	-0.068071	-0.8112	0.209317
8	-0.08128	-0.9686	0.167206
9	-0.02021	-0.2408	0.405016
10	0.05037	0.6002	0.274654
11	0.203883	2.4296	0.008183
12	0.331202	3.9467	6.2e-05
13	0.196565	2.3423	0.010276
14	-0.155357	-1.8513	0.033103
15	-0.080702	-0.9617	0.168925
16	-0.238872	-2.8465	0.002538
17	-0.107054	-1.2757	0.102072
18	0.007391	0.0881	0.46497
19	0.013636	0.1625	0.435574
20	-0.155575	-1.8539	0.032915
21	0.107309	1.2787	0.101538

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code