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, 21 Oct 2014 18:45:54 +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/2014/Oct/21/t1413913589dyp41ztfr0zl5jj.htm/, Retrieved Mon, 13 May 2024 13:49:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=244621, Retrieved Mon, 13 May 2024 13:49:42 +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

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

-       [(Partial) Autocorrelation Function] [] [2014-10-21 17:45:54] [77e76d07a5b02a0482982fb19d5d5436] [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	1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244621&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244621&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244621&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.84828	7.1979	0
2	0.699695	5.9371	0
3	0.574962	4.8787	3e-06
4	0.434263	3.6848	0.00022
5	0.304371	2.5827	0.005918
6	0.187149	1.588	0.058333
7	0.085853	0.7285	0.23434
8	-0.026747	-0.227	0.410549
9	-0.063918	-0.5424	0.294623
10	-0.122766	-1.0417	0.150517
11	-0.178551	-1.5151	0.067068
12	-0.192895	-1.6368	0.053022
13	-0.177623	-1.5072	0.06807
14	-0.155249	-1.3173	0.095952
15	-0.151623	-1.2866	0.101184
16	-0.131461	-1.1155	0.134177
17	-0.141342	-1.1993	0.117167
18	-0.144821	-1.2289	0.111565

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.84828 & 7.1979 & 0 \tabularnewline
2 & 0.699695 & 5.9371 & 0 \tabularnewline
3 & 0.574962 & 4.8787 & 3e-06 \tabularnewline
4 & 0.434263 & 3.6848 & 0.00022 \tabularnewline
5 & 0.304371 & 2.5827 & 0.005918 \tabularnewline
6 & 0.187149 & 1.588 & 0.058333 \tabularnewline
7 & 0.085853 & 0.7285 & 0.23434 \tabularnewline
8 & -0.026747 & -0.227 & 0.410549 \tabularnewline
9 & -0.063918 & -0.5424 & 0.294623 \tabularnewline
10 & -0.122766 & -1.0417 & 0.150517 \tabularnewline
11 & -0.178551 & -1.5151 & 0.067068 \tabularnewline
12 & -0.192895 & -1.6368 & 0.053022 \tabularnewline
13 & -0.177623 & -1.5072 & 0.06807 \tabularnewline
14 & -0.155249 & -1.3173 & 0.095952 \tabularnewline
15 & -0.151623 & -1.2866 & 0.101184 \tabularnewline
16 & -0.131461 & -1.1155 & 0.134177 \tabularnewline
17 & -0.141342 & -1.1993 & 0.117167 \tabularnewline
18 & -0.144821 & -1.2289 & 0.111565 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244621&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]0.84828[/C][C]7.1979[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.699695[/C][C]5.9371[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.574962[/C][C]4.8787[/C][C]3e-06[/C][/ROW]
[ROW][C]4[/C][C]0.434263[/C][C]3.6848[/C][C]0.00022[/C][/ROW]
[ROW][C]5[/C][C]0.304371[/C][C]2.5827[/C][C]0.005918[/C][/ROW]
[ROW][C]6[/C][C]0.187149[/C][C]1.588[/C][C]0.058333[/C][/ROW]
[ROW][C]7[/C][C]0.085853[/C][C]0.7285[/C][C]0.23434[/C][/ROW]
[ROW][C]8[/C][C]-0.026747[/C][C]-0.227[/C][C]0.410549[/C][/ROW]
[ROW][C]9[/C][C]-0.063918[/C][C]-0.5424[/C][C]0.294623[/C][/ROW]
[ROW][C]10[/C][C]-0.122766[/C][C]-1.0417[/C][C]0.150517[/C][/ROW]
[ROW][C]11[/C][C]-0.178551[/C][C]-1.5151[/C][C]0.067068[/C][/ROW]
[ROW][C]12[/C][C]-0.192895[/C][C]-1.6368[/C][C]0.053022[/C][/ROW]
[ROW][C]13[/C][C]-0.177623[/C][C]-1.5072[/C][C]0.06807[/C][/ROW]
[ROW][C]14[/C][C]-0.155249[/C][C]-1.3173[/C][C]0.095952[/C][/ROW]
[ROW][C]15[/C][C]-0.151623[/C][C]-1.2866[/C][C]0.101184[/C][/ROW]
[ROW][C]16[/C][C]-0.131461[/C][C]-1.1155[/C][C]0.134177[/C][/ROW]
[ROW][C]17[/C][C]-0.141342[/C][C]-1.1993[/C][C]0.117167[/C][/ROW]
[ROW][C]18[/C][C]-0.144821[/C][C]-1.2289[/C][C]0.111565[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244621&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244621&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	0.84828	7.1979	0
2	0.699695	5.9371	0
3	0.574962	4.8787	3e-06
4	0.434263	3.6848	0.00022
5	0.304371	2.5827	0.005918
6	0.187149	1.588	0.058333
7	0.085853	0.7285	0.23434
8	-0.026747	-0.227	0.410549
9	-0.063918	-0.5424	0.294623
10	-0.122766	-1.0417	0.150517
11	-0.178551	-1.5151	0.067068
12	-0.192895	-1.6368	0.053022
13	-0.177623	-1.5072	0.06807
14	-0.155249	-1.3173	0.095952
15	-0.151623	-1.2866	0.101184
16	-0.131461	-1.1155	0.134177
17	-0.141342	-1.1993	0.117167
18	-0.144821	-1.2289	0.111565

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.84828	7.1979	0
2	-0.070907	-0.6017	0.274643
3	-0.001836	-0.0156	0.493808
4	-0.136094	-1.1548	0.125996
5	-0.052929	-0.4491	0.327348
6	-0.061566	-0.5224	0.301497
7	-0.033433	-0.2837	0.388733
8	-0.137467	-1.1664	0.123642
9	0.171146	1.4522	0.075392
10	-0.16811	-1.4265	0.079029
11	-0.017348	-0.1472	0.441693
12	0.021295	0.1807	0.428559
13	0.081489	0.6915	0.24575
14	-0.010976	-0.0931	0.463028
15	-0.070306	-0.5966	0.276334
16	-0.015166	-0.1287	0.448983
17	-0.076397	-0.6483	0.259442
18	-0.036644	-0.3109	0.378375

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.84828 & 7.1979 & 0 \tabularnewline
2 & -0.070907 & -0.6017 & 0.274643 \tabularnewline
3 & -0.001836 & -0.0156 & 0.493808 \tabularnewline
4 & -0.136094 & -1.1548 & 0.125996 \tabularnewline
5 & -0.052929 & -0.4491 & 0.327348 \tabularnewline
6 & -0.061566 & -0.5224 & 0.301497 \tabularnewline
7 & -0.033433 & -0.2837 & 0.388733 \tabularnewline
8 & -0.137467 & -1.1664 & 0.123642 \tabularnewline
9 & 0.171146 & 1.4522 & 0.075392 \tabularnewline
10 & -0.16811 & -1.4265 & 0.079029 \tabularnewline
11 & -0.017348 & -0.1472 & 0.441693 \tabularnewline
12 & 0.021295 & 0.1807 & 0.428559 \tabularnewline
13 & 0.081489 & 0.6915 & 0.24575 \tabularnewline
14 & -0.010976 & -0.0931 & 0.463028 \tabularnewline
15 & -0.070306 & -0.5966 & 0.276334 \tabularnewline
16 & -0.015166 & -0.1287 & 0.448983 \tabularnewline
17 & -0.076397 & -0.6483 & 0.259442 \tabularnewline
18 & -0.036644 & -0.3109 & 0.378375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244621&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]0.84828[/C][C]7.1979[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.070907[/C][C]-0.6017[/C][C]0.274643[/C][/ROW]
[ROW][C]3[/C][C]-0.001836[/C][C]-0.0156[/C][C]0.493808[/C][/ROW]
[ROW][C]4[/C][C]-0.136094[/C][C]-1.1548[/C][C]0.125996[/C][/ROW]
[ROW][C]5[/C][C]-0.052929[/C][C]-0.4491[/C][C]0.327348[/C][/ROW]
[ROW][C]6[/C][C]-0.061566[/C][C]-0.5224[/C][C]0.301497[/C][/ROW]
[ROW][C]7[/C][C]-0.033433[/C][C]-0.2837[/C][C]0.388733[/C][/ROW]
[ROW][C]8[/C][C]-0.137467[/C][C]-1.1664[/C][C]0.123642[/C][/ROW]
[ROW][C]9[/C][C]0.171146[/C][C]1.4522[/C][C]0.075392[/C][/ROW]
[ROW][C]10[/C][C]-0.16811[/C][C]-1.4265[/C][C]0.079029[/C][/ROW]
[ROW][C]11[/C][C]-0.017348[/C][C]-0.1472[/C][C]0.441693[/C][/ROW]
[ROW][C]12[/C][C]0.021295[/C][C]0.1807[/C][C]0.428559[/C][/ROW]
[ROW][C]13[/C][C]0.081489[/C][C]0.6915[/C][C]0.24575[/C][/ROW]
[ROW][C]14[/C][C]-0.010976[/C][C]-0.0931[/C][C]0.463028[/C][/ROW]
[ROW][C]15[/C][C]-0.070306[/C][C]-0.5966[/C][C]0.276334[/C][/ROW]
[ROW][C]16[/C][C]-0.015166[/C][C]-0.1287[/C][C]0.448983[/C][/ROW]
[ROW][C]17[/C][C]-0.076397[/C][C]-0.6483[/C][C]0.259442[/C][/ROW]
[ROW][C]18[/C][C]-0.036644[/C][C]-0.3109[/C][C]0.378375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244621&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244621&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	0.84828	7.1979	0
2	-0.070907	-0.6017	0.274643
3	-0.001836	-0.0156	0.493808
4	-0.136094	-1.1548	0.125996
5	-0.052929	-0.4491	0.327348
6	-0.061566	-0.5224	0.301497
7	-0.033433	-0.2837	0.388733
8	-0.137467	-1.1664	0.123642
9	0.171146	1.4522	0.075392
10	-0.16811	-1.4265	0.079029
11	-0.017348	-0.1472	0.441693
12	0.021295	0.1807	0.428559
13	0.081489	0.6915	0.24575
14	-0.010976	-0.0931	0.463028
15	-0.070306	-0.5966	0.276334
16	-0.015166	-0.1287	0.448983
17	-0.076397	-0.6483	0.259442
18	-0.036644	-0.3109	0.378375

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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)
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