Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 02 Dec 2008 11:18:54 -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/02/t1228242023dct4eb5afraeffb.htm/, Retrieved Thu, 23 May 2024 09:16:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28207, Retrieved Thu, 23 May 2024 09:16:13 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

153

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

F       [(Partial) Autocorrelation Function] [Q8 autocorr non s...] [2008-12-02 18:18:54] [441cddd6b019c6452f1399cb0038dc92] [Current]

Feedback Forum

2008-12-08 19:50:09 [94a54c888ac7f7d6874c3108eb0e1808] [reply] 
Zeer goed uitgewerkt en de juiste waarden gevonden. Ook de conclusie is juist. 
2008-12-10 08:14:18 [Peter Van Doninck] [reply] 
Juiste conclusie.

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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	'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28207&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28207&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.144591	1.3013	0.098419
2	-0.055279	-0.4975	0.310089
3	-0.188207	-1.6939	0.047067
4	0.028143	0.2533	0.400343
5	-0.000686	-0.0062	0.497543
6	0.001371	0.0123	0.495092
7	0.10357	0.9321	0.17702
8	0.002032	0.0183	0.492728
9	-0.186543	-1.6789	0.048514
10	0.013803	0.1242	0.450723
11	0.155571	1.4001	0.082645
12	0.050878	0.4579	0.324123
13	-0.143097	-1.2879	0.100728
14	-0.055466	-0.4992	0.309499
15	0.104022	0.9362	0.175978
16	-0.128836	-1.1595	0.124825
17	-0.159001	-1.431	0.078138
18	-0.141011	-1.2691	0.10402
19	-7.8e-05	-7e-04	0.49972

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.144591 & 1.3013 & 0.098419 \tabularnewline
2 & -0.055279 & -0.4975 & 0.310089 \tabularnewline
3 & -0.188207 & -1.6939 & 0.047067 \tabularnewline
4 & 0.028143 & 0.2533 & 0.400343 \tabularnewline
5 & -0.000686 & -0.0062 & 0.497543 \tabularnewline
6 & 0.001371 & 0.0123 & 0.495092 \tabularnewline
7 & 0.10357 & 0.9321 & 0.17702 \tabularnewline
8 & 0.002032 & 0.0183 & 0.492728 \tabularnewline
9 & -0.186543 & -1.6789 & 0.048514 \tabularnewline
10 & 0.013803 & 0.1242 & 0.450723 \tabularnewline
11 & 0.155571 & 1.4001 & 0.082645 \tabularnewline
12 & 0.050878 & 0.4579 & 0.324123 \tabularnewline
13 & -0.143097 & -1.2879 & 0.100728 \tabularnewline
14 & -0.055466 & -0.4992 & 0.309499 \tabularnewline
15 & 0.104022 & 0.9362 & 0.175978 \tabularnewline
16 & -0.128836 & -1.1595 & 0.124825 \tabularnewline
17 & -0.159001 & -1.431 & 0.078138 \tabularnewline
18 & -0.141011 & -1.2691 & 0.10402 \tabularnewline
19 & -7.8e-05 & -7e-04 & 0.49972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28207&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]0.144591[/C][C]1.3013[/C][C]0.098419[/C][/ROW]
[ROW][C]2[/C][C]-0.055279[/C][C]-0.4975[/C][C]0.310089[/C][/ROW]
[ROW][C]3[/C][C]-0.188207[/C][C]-1.6939[/C][C]0.047067[/C][/ROW]
[ROW][C]4[/C][C]0.028143[/C][C]0.2533[/C][C]0.400343[/C][/ROW]
[ROW][C]5[/C][C]-0.000686[/C][C]-0.0062[/C][C]0.497543[/C][/ROW]
[ROW][C]6[/C][C]0.001371[/C][C]0.0123[/C][C]0.495092[/C][/ROW]
[ROW][C]7[/C][C]0.10357[/C][C]0.9321[/C][C]0.17702[/C][/ROW]
[ROW][C]8[/C][C]0.002032[/C][C]0.0183[/C][C]0.492728[/C][/ROW]
[ROW][C]9[/C][C]-0.186543[/C][C]-1.6789[/C][C]0.048514[/C][/ROW]
[ROW][C]10[/C][C]0.013803[/C][C]0.1242[/C][C]0.450723[/C][/ROW]
[ROW][C]11[/C][C]0.155571[/C][C]1.4001[/C][C]0.082645[/C][/ROW]
[ROW][C]12[/C][C]0.050878[/C][C]0.4579[/C][C]0.324123[/C][/ROW]
[ROW][C]13[/C][C]-0.143097[/C][C]-1.2879[/C][C]0.100728[/C][/ROW]
[ROW][C]14[/C][C]-0.055466[/C][C]-0.4992[/C][C]0.309499[/C][/ROW]
[ROW][C]15[/C][C]0.104022[/C][C]0.9362[/C][C]0.175978[/C][/ROW]
[ROW][C]16[/C][C]-0.128836[/C][C]-1.1595[/C][C]0.124825[/C][/ROW]
[ROW][C]17[/C][C]-0.159001[/C][C]-1.431[/C][C]0.078138[/C][/ROW]
[ROW][C]18[/C][C]-0.141011[/C][C]-1.2691[/C][C]0.10402[/C][/ROW]
[ROW][C]19[/C][C]-7.8e-05[/C][C]-7e-04[/C][C]0.49972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28207&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	0.144591	1.3013	0.098419
2	-0.055279	-0.4975	0.310089
3	-0.188207	-1.6939	0.047067
4	0.028143	0.2533	0.400343
5	-0.000686	-0.0062	0.497543
6	0.001371	0.0123	0.495092
7	0.10357	0.9321	0.17702
8	0.002032	0.0183	0.492728
9	-0.186543	-1.6789	0.048514
10	0.013803	0.1242	0.450723
11	0.155571	1.4001	0.082645
12	0.050878	0.4579	0.324123
13	-0.143097	-1.2879	0.100728
14	-0.055466	-0.4992	0.309499
15	0.104022	0.9362	0.175978
16	-0.128836	-1.1595	0.124825
17	-0.159001	-1.431	0.078138
18	-0.141011	-1.2691	0.10402
19	-7.8e-05	-7e-04	0.49972

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.144591	1.3013	0.098419
2	-0.077812	-0.7003	0.24287
3	-0.172984	-1.5569	0.061702
4	0.081714	0.7354	0.232103
5	-0.038284	-0.3446	0.365659
6	-0.02318	-0.2086	0.417634
7	0.135059	1.2155	0.113848
8	-0.049148	-0.4423	0.329715
9	-0.190043	-1.7104	0.045511
10	0.135268	1.2174	0.113491
11	0.113697	1.0233	0.154612
12	-0.079384	-0.7145	0.238499
13	-0.086979	-0.7828	0.21801
14	0.025775	0.232	0.40857
15	0.085071	0.7656	0.223059
16	-0.195492	-1.7594	0.04114
17	-0.124449	-1.12	0.133003
18	-0.131061	-1.1796	0.120815
19	-0.025823	-0.2324	0.408403

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.144591 & 1.3013 & 0.098419 \tabularnewline
2 & -0.077812 & -0.7003 & 0.24287 \tabularnewline
3 & -0.172984 & -1.5569 & 0.061702 \tabularnewline
4 & 0.081714 & 0.7354 & 0.232103 \tabularnewline
5 & -0.038284 & -0.3446 & 0.365659 \tabularnewline
6 & -0.02318 & -0.2086 & 0.417634 \tabularnewline
7 & 0.135059 & 1.2155 & 0.113848 \tabularnewline
8 & -0.049148 & -0.4423 & 0.329715 \tabularnewline
9 & -0.190043 & -1.7104 & 0.045511 \tabularnewline
10 & 0.135268 & 1.2174 & 0.113491 \tabularnewline
11 & 0.113697 & 1.0233 & 0.154612 \tabularnewline
12 & -0.079384 & -0.7145 & 0.238499 \tabularnewline
13 & -0.086979 & -0.7828 & 0.21801 \tabularnewline
14 & 0.025775 & 0.232 & 0.40857 \tabularnewline
15 & 0.085071 & 0.7656 & 0.223059 \tabularnewline
16 & -0.195492 & -1.7594 & 0.04114 \tabularnewline
17 & -0.124449 & -1.12 & 0.133003 \tabularnewline
18 & -0.131061 & -1.1796 & 0.120815 \tabularnewline
19 & -0.025823 & -0.2324 & 0.408403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28207&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]0.144591[/C][C]1.3013[/C][C]0.098419[/C][/ROW]
[ROW][C]2[/C][C]-0.077812[/C][C]-0.7003[/C][C]0.24287[/C][/ROW]
[ROW][C]3[/C][C]-0.172984[/C][C]-1.5569[/C][C]0.061702[/C][/ROW]
[ROW][C]4[/C][C]0.081714[/C][C]0.7354[/C][C]0.232103[/C][/ROW]
[ROW][C]5[/C][C]-0.038284[/C][C]-0.3446[/C][C]0.365659[/C][/ROW]
[ROW][C]6[/C][C]-0.02318[/C][C]-0.2086[/C][C]0.417634[/C][/ROW]
[ROW][C]7[/C][C]0.135059[/C][C]1.2155[/C][C]0.113848[/C][/ROW]
[ROW][C]8[/C][C]-0.049148[/C][C]-0.4423[/C][C]0.329715[/C][/ROW]
[ROW][C]9[/C][C]-0.190043[/C][C]-1.7104[/C][C]0.045511[/C][/ROW]
[ROW][C]10[/C][C]0.135268[/C][C]1.2174[/C][C]0.113491[/C][/ROW]
[ROW][C]11[/C][C]0.113697[/C][C]1.0233[/C][C]0.154612[/C][/ROW]
[ROW][C]12[/C][C]-0.079384[/C][C]-0.7145[/C][C]0.238499[/C][/ROW]
[ROW][C]13[/C][C]-0.086979[/C][C]-0.7828[/C][C]0.21801[/C][/ROW]
[ROW][C]14[/C][C]0.025775[/C][C]0.232[/C][C]0.40857[/C][/ROW]
[ROW][C]15[/C][C]0.085071[/C][C]0.7656[/C][C]0.223059[/C][/ROW]
[ROW][C]16[/C][C]-0.195492[/C][C]-1.7594[/C][C]0.04114[/C][/ROW]
[ROW][C]17[/C][C]-0.124449[/C][C]-1.12[/C][C]0.133003[/C][/ROW]
[ROW][C]18[/C][C]-0.131061[/C][C]-1.1796[/C][C]0.120815[/C][/ROW]
[ROW][C]19[/C][C]-0.025823[/C][C]-0.2324[/C][C]0.408403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28207&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28207&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	0.144591	1.3013	0.098419
2	-0.077812	-0.7003	0.24287
3	-0.172984	-1.5569	0.061702
4	0.081714	0.7354	0.232103
5	-0.038284	-0.3446	0.365659
6	-0.02318	-0.2086	0.417634
7	0.135059	1.2155	0.113848
8	-0.049148	-0.4423	0.329715
9	-0.190043	-1.7104	0.045511
10	0.135268	1.2174	0.113491
11	0.113697	1.0233	0.154612
12	-0.079384	-0.7145	0.238499
13	-0.086979	-0.7828	0.21801
14	0.025775	0.232	0.40857
15	0.085071	0.7656	0.223059
16	-0.195492	-1.7594	0.04114
17	-0.124449	-1.12	0.133003
18	-0.131061	-1.1796	0.120815
19	-0.025823	-0.2324	0.408403

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code