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, 16 Aug 2016 08:50:26 +0100

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/2016/Aug/16/t1471333858158ooeliqbwmr9v.htm/, Retrieved Sat, 04 May 2024 21:21:00 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 21:21:00 +0200

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

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' @ yule.wessa.net

\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' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.529169	-5.4738	0
2	-0.03725	-0.3853	0.350385
3	-0.012895	-0.1334	0.447069
4	0.235132	2.4322	0.008333
5	-0.357174	-3.6946	0.000174
6	0.41026	4.2438	2.3e-05
7	-0.329065	-3.4039	0.000468
8	0.166286	1.7201	0.044155
9	0.03102	0.3209	0.374465
10	-0.036273	-0.3752	0.354124
11	-0.458942	-4.7473	3e-06
12	0.837076	8.6588	0
13	-0.436838	-4.5187	8e-06
14	-0.057737	-0.5972	0.275807
15	0.012492	0.1292	0.448712
16	0.210315	2.1755	0.015896
17	-0.339211	-3.5088	0.00033
18	0.382715	3.9588	6.8e-05
19	-0.263286	-2.7235	0.003773
20	0.079116	0.8184	0.207477

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.529169 & -5.4738 & 0 \tabularnewline
2 & -0.03725 & -0.3853 & 0.350385 \tabularnewline
3 & -0.012895 & -0.1334 & 0.447069 \tabularnewline
4 & 0.235132 & 2.4322 & 0.008333 \tabularnewline
5 & -0.357174 & -3.6946 & 0.000174 \tabularnewline
6 & 0.41026 & 4.2438 & 2.3e-05 \tabularnewline
7 & -0.329065 & -3.4039 & 0.000468 \tabularnewline
8 & 0.166286 & 1.7201 & 0.044155 \tabularnewline
9 & 0.03102 & 0.3209 & 0.374465 \tabularnewline
10 & -0.036273 & -0.3752 & 0.354124 \tabularnewline
11 & -0.458942 & -4.7473 & 3e-06 \tabularnewline
12 & 0.837076 & 8.6588 & 0 \tabularnewline
13 & -0.436838 & -4.5187 & 8e-06 \tabularnewline
14 & -0.057737 & -0.5972 & 0.275807 \tabularnewline
15 & 0.012492 & 0.1292 & 0.448712 \tabularnewline
16 & 0.210315 & 2.1755 & 0.015896 \tabularnewline
17 & -0.339211 & -3.5088 & 0.00033 \tabularnewline
18 & 0.382715 & 3.9588 & 6.8e-05 \tabularnewline
19 & -0.263286 & -2.7235 & 0.003773 \tabularnewline
20 & 0.079116 & 0.8184 & 0.207477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.529169[/C][C]-5.4738[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.03725[/C][C]-0.3853[/C][C]0.350385[/C][/ROW]
[ROW][C]3[/C][C]-0.012895[/C][C]-0.1334[/C][C]0.447069[/C][/ROW]
[ROW][C]4[/C][C]0.235132[/C][C]2.4322[/C][C]0.008333[/C][/ROW]
[ROW][C]5[/C][C]-0.357174[/C][C]-3.6946[/C][C]0.000174[/C][/ROW]
[ROW][C]6[/C][C]0.41026[/C][C]4.2438[/C][C]2.3e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.329065[/C][C]-3.4039[/C][C]0.000468[/C][/ROW]
[ROW][C]8[/C][C]0.166286[/C][C]1.7201[/C][C]0.044155[/C][/ROW]
[ROW][C]9[/C][C]0.03102[/C][C]0.3209[/C][C]0.374465[/C][/ROW]
[ROW][C]10[/C][C]-0.036273[/C][C]-0.3752[/C][C]0.354124[/C][/ROW]
[ROW][C]11[/C][C]-0.458942[/C][C]-4.7473[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.837076[/C][C]8.6588[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.436838[/C][C]-4.5187[/C][C]8e-06[/C][/ROW]
[ROW][C]14[/C][C]-0.057737[/C][C]-0.5972[/C][C]0.275807[/C][/ROW]
[ROW][C]15[/C][C]0.012492[/C][C]0.1292[/C][C]0.448712[/C][/ROW]
[ROW][C]16[/C][C]0.210315[/C][C]2.1755[/C][C]0.015896[/C][/ROW]
[ROW][C]17[/C][C]-0.339211[/C][C]-3.5088[/C][C]0.00033[/C][/ROW]
[ROW][C]18[/C][C]0.382715[/C][C]3.9588[/C][C]6.8e-05[/C][/ROW]
[ROW][C]19[/C][C]-0.263286[/C][C]-2.7235[/C][C]0.003773[/C][/ROW]
[ROW][C]20[/C][C]0.079116[/C][C]0.8184[/C][C]0.207477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.529169	-5.4738	0
2	-0.03725	-0.3853	0.350385
3	-0.012895	-0.1334	0.447069
4	0.235132	2.4322	0.008333
5	-0.357174	-3.6946	0.000174
6	0.41026	4.2438	2.3e-05
7	-0.329065	-3.4039	0.000468
8	0.166286	1.7201	0.044155
9	0.03102	0.3209	0.374465
10	-0.036273	-0.3752	0.354124
11	-0.458942	-4.7473	3e-06
12	0.837076	8.6588	0
13	-0.436838	-4.5187	8e-06
14	-0.057737	-0.5972	0.275807
15	0.012492	0.1292	0.448712
16	0.210315	2.1755	0.015896
17	-0.339211	-3.5088	0.00033
18	0.382715	3.9588	6.8e-05
19	-0.263286	-2.7235	0.003773
20	0.079116	0.8184	0.207477

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.529169	-5.4738	0
2	-0.440663	-4.5583	7e-06
3	-0.473098	-4.8938	2e-06
4	-0.127877	-1.3228	0.094366
5	-0.488191	-5.0499	1e-06
6	0.016075	0.1663	0.434126
7	-0.247722	-2.5625	0.005892
8	-0.068507	-0.7086	0.240044
9	0.311878	3.2261	0.000833
10	0.249858	2.5845	0.005549
11	-0.648319	-6.7063	0
12	0.170422	1.7629	0.04039
13	0.066743	0.6904	0.245721
14	-0.034733	-0.3593	0.360045
15	0.161048	1.6659	0.04933
16	-0.030316	-0.3136	0.37722
17	0.007232	0.0748	0.470255
18	-0.021167	-0.219	0.41355
19	0.100254	1.037	0.15103
20	0.057497	0.5948	0.276631

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.529169 & -5.4738 & 0 \tabularnewline
2 & -0.440663 & -4.5583 & 7e-06 \tabularnewline
3 & -0.473098 & -4.8938 & 2e-06 \tabularnewline
4 & -0.127877 & -1.3228 & 0.094366 \tabularnewline
5 & -0.488191 & -5.0499 & 1e-06 \tabularnewline
6 & 0.016075 & 0.1663 & 0.434126 \tabularnewline
7 & -0.247722 & -2.5625 & 0.005892 \tabularnewline
8 & -0.068507 & -0.7086 & 0.240044 \tabularnewline
9 & 0.311878 & 3.2261 & 0.000833 \tabularnewline
10 & 0.249858 & 2.5845 & 0.005549 \tabularnewline
11 & -0.648319 & -6.7063 & 0 \tabularnewline
12 & 0.170422 & 1.7629 & 0.04039 \tabularnewline
13 & 0.066743 & 0.6904 & 0.245721 \tabularnewline
14 & -0.034733 & -0.3593 & 0.360045 \tabularnewline
15 & 0.161048 & 1.6659 & 0.04933 \tabularnewline
16 & -0.030316 & -0.3136 & 0.37722 \tabularnewline
17 & 0.007232 & 0.0748 & 0.470255 \tabularnewline
18 & -0.021167 & -0.219 & 0.41355 \tabularnewline
19 & 0.100254 & 1.037 & 0.15103 \tabularnewline
20 & 0.057497 & 0.5948 & 0.276631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.529169[/C][C]-5.4738[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.440663[/C][C]-4.5583[/C][C]7e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.473098[/C][C]-4.8938[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.127877[/C][C]-1.3228[/C][C]0.094366[/C][/ROW]
[ROW][C]5[/C][C]-0.488191[/C][C]-5.0499[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.016075[/C][C]0.1663[/C][C]0.434126[/C][/ROW]
[ROW][C]7[/C][C]-0.247722[/C][C]-2.5625[/C][C]0.005892[/C][/ROW]
[ROW][C]8[/C][C]-0.068507[/C][C]-0.7086[/C][C]0.240044[/C][/ROW]
[ROW][C]9[/C][C]0.311878[/C][C]3.2261[/C][C]0.000833[/C][/ROW]
[ROW][C]10[/C][C]0.249858[/C][C]2.5845[/C][C]0.005549[/C][/ROW]
[ROW][C]11[/C][C]-0.648319[/C][C]-6.7063[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.170422[/C][C]1.7629[/C][C]0.04039[/C][/ROW]
[ROW][C]13[/C][C]0.066743[/C][C]0.6904[/C][C]0.245721[/C][/ROW]
[ROW][C]14[/C][C]-0.034733[/C][C]-0.3593[/C][C]0.360045[/C][/ROW]
[ROW][C]15[/C][C]0.161048[/C][C]1.6659[/C][C]0.04933[/C][/ROW]
[ROW][C]16[/C][C]-0.030316[/C][C]-0.3136[/C][C]0.37722[/C][/ROW]
[ROW][C]17[/C][C]0.007232[/C][C]0.0748[/C][C]0.470255[/C][/ROW]
[ROW][C]18[/C][C]-0.021167[/C][C]-0.219[/C][C]0.41355[/C][/ROW]
[ROW][C]19[/C][C]0.100254[/C][C]1.037[/C][C]0.15103[/C][/ROW]
[ROW][C]20[/C][C]0.057497[/C][C]0.5948[/C][C]0.276631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.529169	-5.4738	0
2	-0.440663	-4.5583	7e-06
3	-0.473098	-4.8938	2e-06
4	-0.127877	-1.3228	0.094366
5	-0.488191	-5.0499	1e-06
6	0.016075	0.1663	0.434126
7	-0.247722	-2.5625	0.005892
8	-0.068507	-0.7086	0.240044
9	0.311878	3.2261	0.000833
10	0.249858	2.5845	0.005549
11	-0.648319	-6.7063	0
12	0.170422	1.7629	0.04039
13	0.066743	0.6904	0.245721
14	-0.034733	-0.3593	0.360045
15	0.161048	1.6659	0.04933
16	-0.030316	-0.3136	0.37722
17	0.007232	0.0748	0.470255
18	-0.021167	-0.219	0.41355
19	0.100254	1.037	0.15103
20	0.057497	0.5948	0.276631

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 = ;

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)
x <- na.omit(x)
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