Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

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

Fri, 27 Nov 2009 15:22:44 -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/2009/Nov/27/t1259360597eviofeij53587tv.htm/, Retrieved Sun, 28 Apr 2024 20:15:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61312, Retrieved Sun, 28 Apr 2024 20:15:18 +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

110

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

-       [(Partial) Autocorrelation Function] [ACF 2] [2009-11-27 22:22:44] [b42c0aeada8a5fa89825c81e73c10645] [Current]

Feedback Forum

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	0 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61312&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61312&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61312&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	0 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.877622	6.0803	0
2	0.68392	4.7383	1e-05
3	0.432465	2.9962	0.002158
4	0.277842	1.9249	0.030087
5	0.186297	1.2907	0.101494
6	0.148184	1.0267	0.154865
7	0.08669	0.6006	0.275465
8	-0.00787	-0.0545	0.478372
9	-0.158075	-1.0952	0.139452
10	-0.318755	-2.2084	0.016013
11	-0.452841	-3.1374	0.001456
12	-0.518364	-3.5913	0.000386
13	-0.482102	-3.3401	0.000813
14	-0.387495	-2.6846	0.004968
15	-0.251154	-1.74	0.04413
16	-0.14548	-1.0079	0.159275
17	-0.051954	-0.3599	0.360233

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.877622 & 6.0803 & 0 \tabularnewline
2 & 0.68392 & 4.7383 & 1e-05 \tabularnewline
3 & 0.432465 & 2.9962 & 0.002158 \tabularnewline
4 & 0.277842 & 1.9249 & 0.030087 \tabularnewline
5 & 0.186297 & 1.2907 & 0.101494 \tabularnewline
6 & 0.148184 & 1.0267 & 0.154865 \tabularnewline
7 & 0.08669 & 0.6006 & 0.275465 \tabularnewline
8 & -0.00787 & -0.0545 & 0.478372 \tabularnewline
9 & -0.158075 & -1.0952 & 0.139452 \tabularnewline
10 & -0.318755 & -2.2084 & 0.016013 \tabularnewline
11 & -0.452841 & -3.1374 & 0.001456 \tabularnewline
12 & -0.518364 & -3.5913 & 0.000386 \tabularnewline
13 & -0.482102 & -3.3401 & 0.000813 \tabularnewline
14 & -0.387495 & -2.6846 & 0.004968 \tabularnewline
15 & -0.251154 & -1.74 & 0.04413 \tabularnewline
16 & -0.14548 & -1.0079 & 0.159275 \tabularnewline
17 & -0.051954 & -0.3599 & 0.360233 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61312&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]0.877622[/C][C]6.0803[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.68392[/C][C]4.7383[/C][C]1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.432465[/C][C]2.9962[/C][C]0.002158[/C][/ROW]
[ROW][C]4[/C][C]0.277842[/C][C]1.9249[/C][C]0.030087[/C][/ROW]
[ROW][C]5[/C][C]0.186297[/C][C]1.2907[/C][C]0.101494[/C][/ROW]
[ROW][C]6[/C][C]0.148184[/C][C]1.0267[/C][C]0.154865[/C][/ROW]
[ROW][C]7[/C][C]0.08669[/C][C]0.6006[/C][C]0.275465[/C][/ROW]
[ROW][C]8[/C][C]-0.00787[/C][C]-0.0545[/C][C]0.478372[/C][/ROW]
[ROW][C]9[/C][C]-0.158075[/C][C]-1.0952[/C][C]0.139452[/C][/ROW]
[ROW][C]10[/C][C]-0.318755[/C][C]-2.2084[/C][C]0.016013[/C][/ROW]
[ROW][C]11[/C][C]-0.452841[/C][C]-3.1374[/C][C]0.001456[/C][/ROW]
[ROW][C]12[/C][C]-0.518364[/C][C]-3.5913[/C][C]0.000386[/C][/ROW]
[ROW][C]13[/C][C]-0.482102[/C][C]-3.3401[/C][C]0.000813[/C][/ROW]
[ROW][C]14[/C][C]-0.387495[/C][C]-2.6846[/C][C]0.004968[/C][/ROW]
[ROW][C]15[/C][C]-0.251154[/C][C]-1.74[/C][C]0.04413[/C][/ROW]
[ROW][C]16[/C][C]-0.14548[/C][C]-1.0079[/C][C]0.159275[/C][/ROW]
[ROW][C]17[/C][C]-0.051954[/C][C]-0.3599[/C][C]0.360233[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61312&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61312&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	0.877622	6.0803	0
2	0.68392	4.7383	1e-05
3	0.432465	2.9962	0.002158
4	0.277842	1.9249	0.030087
5	0.186297	1.2907	0.101494
6	0.148184	1.0267	0.154865
7	0.08669	0.6006	0.275465
8	-0.00787	-0.0545	0.478372
9	-0.158075	-1.0952	0.139452
10	-0.318755	-2.2084	0.016013
11	-0.452841	-3.1374	0.001456
12	-0.518364	-3.5913	0.000386
13	-0.482102	-3.3401	0.000813
14	-0.387495	-2.6846	0.004968
15	-0.251154	-1.74	0.04413
16	-0.14548	-1.0079	0.159275
17	-0.051954	-0.3599	0.360233

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.877622	6.0803	0
2	-0.375578	-2.6021	0.006143
3	-0.322105	-2.2316	0.015173
4	0.461736	3.199	0.001222
5	-0.013155	-0.0911	0.46388
6	-0.295973	-2.0506	0.022896
7	-0.113934	-0.7894	0.216892
8	-0.020192	-0.1399	0.444663
9	-0.278515	-1.9296	0.029789
10	-0.197222	-1.3664	0.089091
11	0.084577	0.586	0.280322
12	-0.012738	-0.0883	0.465023
13	0.167411	1.1599	0.125921
14	0.008152	0.0565	0.477597
15	0.096781	0.6705	0.252869
16	0.062281	0.4315	0.33402
17	0.157501	1.0912	0.140317

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.877622 & 6.0803 & 0 \tabularnewline
2 & -0.375578 & -2.6021 & 0.006143 \tabularnewline
3 & -0.322105 & -2.2316 & 0.015173 \tabularnewline
4 & 0.461736 & 3.199 & 0.001222 \tabularnewline
5 & -0.013155 & -0.0911 & 0.46388 \tabularnewline
6 & -0.295973 & -2.0506 & 0.022896 \tabularnewline
7 & -0.113934 & -0.7894 & 0.216892 \tabularnewline
8 & -0.020192 & -0.1399 & 0.444663 \tabularnewline
9 & -0.278515 & -1.9296 & 0.029789 \tabularnewline
10 & -0.197222 & -1.3664 & 0.089091 \tabularnewline
11 & 0.084577 & 0.586 & 0.280322 \tabularnewline
12 & -0.012738 & -0.0883 & 0.465023 \tabularnewline
13 & 0.167411 & 1.1599 & 0.125921 \tabularnewline
14 & 0.008152 & 0.0565 & 0.477597 \tabularnewline
15 & 0.096781 & 0.6705 & 0.252869 \tabularnewline
16 & 0.062281 & 0.4315 & 0.33402 \tabularnewline
17 & 0.157501 & 1.0912 & 0.140317 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61312&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]0.877622[/C][C]6.0803[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.375578[/C][C]-2.6021[/C][C]0.006143[/C][/ROW]
[ROW][C]3[/C][C]-0.322105[/C][C]-2.2316[/C][C]0.015173[/C][/ROW]
[ROW][C]4[/C][C]0.461736[/C][C]3.199[/C][C]0.001222[/C][/ROW]
[ROW][C]5[/C][C]-0.013155[/C][C]-0.0911[/C][C]0.46388[/C][/ROW]
[ROW][C]6[/C][C]-0.295973[/C][C]-2.0506[/C][C]0.022896[/C][/ROW]
[ROW][C]7[/C][C]-0.113934[/C][C]-0.7894[/C][C]0.216892[/C][/ROW]
[ROW][C]8[/C][C]-0.020192[/C][C]-0.1399[/C][C]0.444663[/C][/ROW]
[ROW][C]9[/C][C]-0.278515[/C][C]-1.9296[/C][C]0.029789[/C][/ROW]
[ROW][C]10[/C][C]-0.197222[/C][C]-1.3664[/C][C]0.089091[/C][/ROW]
[ROW][C]11[/C][C]0.084577[/C][C]0.586[/C][C]0.280322[/C][/ROW]
[ROW][C]12[/C][C]-0.012738[/C][C]-0.0883[/C][C]0.465023[/C][/ROW]
[ROW][C]13[/C][C]0.167411[/C][C]1.1599[/C][C]0.125921[/C][/ROW]
[ROW][C]14[/C][C]0.008152[/C][C]0.0565[/C][C]0.477597[/C][/ROW]
[ROW][C]15[/C][C]0.096781[/C][C]0.6705[/C][C]0.252869[/C][/ROW]
[ROW][C]16[/C][C]0.062281[/C][C]0.4315[/C][C]0.33402[/C][/ROW]
[ROW][C]17[/C][C]0.157501[/C][C]1.0912[/C][C]0.140317[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61312&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61312&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	0.877622	6.0803	0
2	-0.375578	-2.6021	0.006143
3	-0.322105	-2.2316	0.015173
4	0.461736	3.199	0.001222
5	-0.013155	-0.0911	0.46388
6	-0.295973	-2.0506	0.022896
7	-0.113934	-0.7894	0.216892
8	-0.020192	-0.1399	0.444663
9	-0.278515	-1.9296	0.029789
10	-0.197222	-1.3664	0.089091
11	0.084577	0.586	0.280322
12	-0.012738	-0.0883	0.465023
13	0.167411	1.1599	0.125921
14	0.008152	0.0565	0.477597
15	0.096781	0.6705	0.252869
16	0.062281	0.4315	0.33402
17	0.157501	1.0912	0.140317

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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