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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 26 Dec 2010 15:00:45 +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/26/t1293375501mkup1kpysyh7ieg.htm/, Retrieved Tue, 07 May 2024 00:45:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115637, Retrieved Tue, 07 May 2024 00:45:42 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

146

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

-     [Univariate Data Series] [tijdreeks bevolki...] [2010-12-26 10:20:42] [efd13e24149aec704f3383e33c1e842a]
-   PD  [Univariate Data Series] [tijdreeks werkloo...] [2010-12-26 13:12:25] [efd13e24149aec704f3383e33c1e842a]
- RMPD      [(Partial) Autocorrelation Function] [tijdreeks werkloo...] [2010-12-26 15:00:45] [531024149246456e4f6d79ace2e85c12] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115637&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115637&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115637&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.305932	2.7534	0.00364
2	0.451807	4.0663	5.5e-05
3	0.368052	3.3125	0.000692
4	0.384505	3.4605	0.000431
5	0.254904	2.2941	0.012186
6	0.16333	1.47	0.072722
7	0.124044	1.1164	0.133776
8	0.083216	0.7489	0.22803
9	0.017756	0.1598	0.436717
10	0.031186	0.2807	0.389839
11	-0.010623	-0.0956	0.462034
12	-0.105522	-0.9497	0.172544
13	-0.114009	-1.0261	0.153955
14	-0.025843	-0.2326	0.408336
15	-0.040362	-0.3633	0.358679
16	-0.101098	-0.9099	0.182792
17	-0.034016	-0.3061	0.380139
18	-0.033342	-0.3001	0.382442
19	0.058423	0.5258	0.300231

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.305932 & 2.7534 & 0.00364 \tabularnewline
2 & 0.451807 & 4.0663 & 5.5e-05 \tabularnewline
3 & 0.368052 & 3.3125 & 0.000692 \tabularnewline
4 & 0.384505 & 3.4605 & 0.000431 \tabularnewline
5 & 0.254904 & 2.2941 & 0.012186 \tabularnewline
6 & 0.16333 & 1.47 & 0.072722 \tabularnewline
7 & 0.124044 & 1.1164 & 0.133776 \tabularnewline
8 & 0.083216 & 0.7489 & 0.22803 \tabularnewline
9 & 0.017756 & 0.1598 & 0.436717 \tabularnewline
10 & 0.031186 & 0.2807 & 0.389839 \tabularnewline
11 & -0.010623 & -0.0956 & 0.462034 \tabularnewline
12 & -0.105522 & -0.9497 & 0.172544 \tabularnewline
13 & -0.114009 & -1.0261 & 0.153955 \tabularnewline
14 & -0.025843 & -0.2326 & 0.408336 \tabularnewline
15 & -0.040362 & -0.3633 & 0.358679 \tabularnewline
16 & -0.101098 & -0.9099 & 0.182792 \tabularnewline
17 & -0.034016 & -0.3061 & 0.380139 \tabularnewline
18 & -0.033342 & -0.3001 & 0.382442 \tabularnewline
19 & 0.058423 & 0.5258 & 0.300231 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115637&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]0.305932[/C][C]2.7534[/C][C]0.00364[/C][/ROW]
[ROW][C]2[/C][C]0.451807[/C][C]4.0663[/C][C]5.5e-05[/C][/ROW]
[ROW][C]3[/C][C]0.368052[/C][C]3.3125[/C][C]0.000692[/C][/ROW]
[ROW][C]4[/C][C]0.384505[/C][C]3.4605[/C][C]0.000431[/C][/ROW]
[ROW][C]5[/C][C]0.254904[/C][C]2.2941[/C][C]0.012186[/C][/ROW]
[ROW][C]6[/C][C]0.16333[/C][C]1.47[/C][C]0.072722[/C][/ROW]
[ROW][C]7[/C][C]0.124044[/C][C]1.1164[/C][C]0.133776[/C][/ROW]
[ROW][C]8[/C][C]0.083216[/C][C]0.7489[/C][C]0.22803[/C][/ROW]
[ROW][C]9[/C][C]0.017756[/C][C]0.1598[/C][C]0.436717[/C][/ROW]
[ROW][C]10[/C][C]0.031186[/C][C]0.2807[/C][C]0.389839[/C][/ROW]
[ROW][C]11[/C][C]-0.010623[/C][C]-0.0956[/C][C]0.462034[/C][/ROW]
[ROW][C]12[/C][C]-0.105522[/C][C]-0.9497[/C][C]0.172544[/C][/ROW]
[ROW][C]13[/C][C]-0.114009[/C][C]-1.0261[/C][C]0.153955[/C][/ROW]
[ROW][C]14[/C][C]-0.025843[/C][C]-0.2326[/C][C]0.408336[/C][/ROW]
[ROW][C]15[/C][C]-0.040362[/C][C]-0.3633[/C][C]0.358679[/C][/ROW]
[ROW][C]16[/C][C]-0.101098[/C][C]-0.9099[/C][C]0.182792[/C][/ROW]
[ROW][C]17[/C][C]-0.034016[/C][C]-0.3061[/C][C]0.380139[/C][/ROW]
[ROW][C]18[/C][C]-0.033342[/C][C]-0.3001[/C][C]0.382442[/C][/ROW]
[ROW][C]19[/C][C]0.058423[/C][C]0.5258[/C][C]0.300231[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115637&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115637&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	0.305932	2.7534	0.00364
2	0.451807	4.0663	5.5e-05
3	0.368052	3.3125	0.000692
4	0.384505	3.4605	0.000431
5	0.254904	2.2941	0.012186
6	0.16333	1.47	0.072722
7	0.124044	1.1164	0.133776
8	0.083216	0.7489	0.22803
9	0.017756	0.1598	0.436717
10	0.031186	0.2807	0.389839
11	-0.010623	-0.0956	0.462034
12	-0.105522	-0.9497	0.172544
13	-0.114009	-1.0261	0.153955
14	-0.025843	-0.2326	0.408336
15	-0.040362	-0.3633	0.358679
16	-0.101098	-0.9099	0.182792
17	-0.034016	-0.3061	0.380139
18	-0.033342	-0.3001	0.382442
19	0.058423	0.5258	0.300231

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.305932	2.7534	0.00364
2	0.395201	3.5568	0.000315
3	0.213837	1.9245	0.028899
4	0.166346	1.4971	0.069125
5	-0.026966	-0.2427	0.404429
6	-0.160189	-1.4417	0.076621
7	-0.123566	-1.1121	0.134693
8	-0.059313	-0.5338	0.297464
9	-0.042211	-0.3799	0.352508
10	0.06139	0.5525	0.291059
11	0.046184	0.4157	0.339381
12	-0.114634	-1.0317	0.152639
13	-0.119732	-1.0776	0.142207
14	0.077942	0.7015	0.242507
15	0.116975	1.0528	0.147787
16	0.003685	0.0332	0.486814
17	0.041719	0.3755	0.354146
18	-0.020612	-0.1855	0.426646
19	0.070491	0.6344	0.263796

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.305932 & 2.7534 & 0.00364 \tabularnewline
2 & 0.395201 & 3.5568 & 0.000315 \tabularnewline
3 & 0.213837 & 1.9245 & 0.028899 \tabularnewline
4 & 0.166346 & 1.4971 & 0.069125 \tabularnewline
5 & -0.026966 & -0.2427 & 0.404429 \tabularnewline
6 & -0.160189 & -1.4417 & 0.076621 \tabularnewline
7 & -0.123566 & -1.1121 & 0.134693 \tabularnewline
8 & -0.059313 & -0.5338 & 0.297464 \tabularnewline
9 & -0.042211 & -0.3799 & 0.352508 \tabularnewline
10 & 0.06139 & 0.5525 & 0.291059 \tabularnewline
11 & 0.046184 & 0.4157 & 0.339381 \tabularnewline
12 & -0.114634 & -1.0317 & 0.152639 \tabularnewline
13 & -0.119732 & -1.0776 & 0.142207 \tabularnewline
14 & 0.077942 & 0.7015 & 0.242507 \tabularnewline
15 & 0.116975 & 1.0528 & 0.147787 \tabularnewline
16 & 0.003685 & 0.0332 & 0.486814 \tabularnewline
17 & 0.041719 & 0.3755 & 0.354146 \tabularnewline
18 & -0.020612 & -0.1855 & 0.426646 \tabularnewline
19 & 0.070491 & 0.6344 & 0.263796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115637&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]0.305932[/C][C]2.7534[/C][C]0.00364[/C][/ROW]
[ROW][C]2[/C][C]0.395201[/C][C]3.5568[/C][C]0.000315[/C][/ROW]
[ROW][C]3[/C][C]0.213837[/C][C]1.9245[/C][C]0.028899[/C][/ROW]
[ROW][C]4[/C][C]0.166346[/C][C]1.4971[/C][C]0.069125[/C][/ROW]
[ROW][C]5[/C][C]-0.026966[/C][C]-0.2427[/C][C]0.404429[/C][/ROW]
[ROW][C]6[/C][C]-0.160189[/C][C]-1.4417[/C][C]0.076621[/C][/ROW]
[ROW][C]7[/C][C]-0.123566[/C][C]-1.1121[/C][C]0.134693[/C][/ROW]
[ROW][C]8[/C][C]-0.059313[/C][C]-0.5338[/C][C]0.297464[/C][/ROW]
[ROW][C]9[/C][C]-0.042211[/C][C]-0.3799[/C][C]0.352508[/C][/ROW]
[ROW][C]10[/C][C]0.06139[/C][C]0.5525[/C][C]0.291059[/C][/ROW]
[ROW][C]11[/C][C]0.046184[/C][C]0.4157[/C][C]0.339381[/C][/ROW]
[ROW][C]12[/C][C]-0.114634[/C][C]-1.0317[/C][C]0.152639[/C][/ROW]
[ROW][C]13[/C][C]-0.119732[/C][C]-1.0776[/C][C]0.142207[/C][/ROW]
[ROW][C]14[/C][C]0.077942[/C][C]0.7015[/C][C]0.242507[/C][/ROW]
[ROW][C]15[/C][C]0.116975[/C][C]1.0528[/C][C]0.147787[/C][/ROW]
[ROW][C]16[/C][C]0.003685[/C][C]0.0332[/C][C]0.486814[/C][/ROW]
[ROW][C]17[/C][C]0.041719[/C][C]0.3755[/C][C]0.354146[/C][/ROW]
[ROW][C]18[/C][C]-0.020612[/C][C]-0.1855[/C][C]0.426646[/C][/ROW]
[ROW][C]19[/C][C]0.070491[/C][C]0.6344[/C][C]0.263796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115637&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115637&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	0.305932	2.7534	0.00364
2	0.395201	3.5568	0.000315
3	0.213837	1.9245	0.028899
4	0.166346	1.4971	0.069125
5	-0.026966	-0.2427	0.404429
6	-0.160189	-1.4417	0.076621
7	-0.123566	-1.1121	0.134693
8	-0.059313	-0.5338	0.297464
9	-0.042211	-0.3799	0.352508
10	0.06139	0.5525	0.291059
11	0.046184	0.4157	0.339381
12	-0.114634	-1.0317	0.152639
13	-0.119732	-1.0776	0.142207
14	0.077942	0.7015	0.242507
15	0.116975	1.0528	0.147787
16	0.003685	0.0332	0.486814
17	0.041719	0.3755	0.354146
18	-0.020612	-0.1855	0.426646
19	0.070491	0.6344	0.263796

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):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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