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

Sun, 08 Mar 2015 16:17:25 +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/2015/Mar/08/t14258314667wfnvuhnh75gttx.htm/, Retrieved Sun, 19 May 2024 14:56:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278058, Retrieved Sun, 19 May 2024 14:56:51 +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

175

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

-       [(Partial) Autocorrelation Function] [] [2015-03-08 16:17:25] [567f06ca3de45fa0ce67a0a89b883c29] [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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278058&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278058&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.121078	-1.0202	0.155543
2	-0.028936	-0.2438	0.404038
3	0.060356	0.5086	0.306315
4	-0.028387	-0.2392	0.405822
5	-0.140021	-1.1798	0.121002
6	-0.131919	-1.1116	0.135037
7	-0.080264	-0.6763	0.250517
8	0.019047	0.1605	0.436476
9	0.003853	0.0325	0.487097
10	0.114787	0.9672	0.168361
11	0.042969	0.3621	0.359189
12	0.358858	3.0238	0.001736
13	-0.147351	-1.2416	0.109234
14	0.015304	0.129	0.44888
15	0.015353	0.1294	0.448718
16	-0.048564	-0.4092	0.34181
17	-0.093252	-0.7858	0.217312
18	-0.106367	-0.8963	0.18657

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.121078 & -1.0202 & 0.155543 \tabularnewline
2 & -0.028936 & -0.2438 & 0.404038 \tabularnewline
3 & 0.060356 & 0.5086 & 0.306315 \tabularnewline
4 & -0.028387 & -0.2392 & 0.405822 \tabularnewline
5 & -0.140021 & -1.1798 & 0.121002 \tabularnewline
6 & -0.131919 & -1.1116 & 0.135037 \tabularnewline
7 & -0.080264 & -0.6763 & 0.250517 \tabularnewline
8 & 0.019047 & 0.1605 & 0.436476 \tabularnewline
9 & 0.003853 & 0.0325 & 0.487097 \tabularnewline
10 & 0.114787 & 0.9672 & 0.168361 \tabularnewline
11 & 0.042969 & 0.3621 & 0.359189 \tabularnewline
12 & 0.358858 & 3.0238 & 0.001736 \tabularnewline
13 & -0.147351 & -1.2416 & 0.109234 \tabularnewline
14 & 0.015304 & 0.129 & 0.44888 \tabularnewline
15 & 0.015353 & 0.1294 & 0.448718 \tabularnewline
16 & -0.048564 & -0.4092 & 0.34181 \tabularnewline
17 & -0.093252 & -0.7858 & 0.217312 \tabularnewline
18 & -0.106367 & -0.8963 & 0.18657 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278058&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]-0.121078[/C][C]-1.0202[/C][C]0.155543[/C][/ROW]
[ROW][C]2[/C][C]-0.028936[/C][C]-0.2438[/C][C]0.404038[/C][/ROW]
[ROW][C]3[/C][C]0.060356[/C][C]0.5086[/C][C]0.306315[/C][/ROW]
[ROW][C]4[/C][C]-0.028387[/C][C]-0.2392[/C][C]0.405822[/C][/ROW]
[ROW][C]5[/C][C]-0.140021[/C][C]-1.1798[/C][C]0.121002[/C][/ROW]
[ROW][C]6[/C][C]-0.131919[/C][C]-1.1116[/C][C]0.135037[/C][/ROW]
[ROW][C]7[/C][C]-0.080264[/C][C]-0.6763[/C][C]0.250517[/C][/ROW]
[ROW][C]8[/C][C]0.019047[/C][C]0.1605[/C][C]0.436476[/C][/ROW]
[ROW][C]9[/C][C]0.003853[/C][C]0.0325[/C][C]0.487097[/C][/ROW]
[ROW][C]10[/C][C]0.114787[/C][C]0.9672[/C][C]0.168361[/C][/ROW]
[ROW][C]11[/C][C]0.042969[/C][C]0.3621[/C][C]0.359189[/C][/ROW]
[ROW][C]12[/C][C]0.358858[/C][C]3.0238[/C][C]0.001736[/C][/ROW]
[ROW][C]13[/C][C]-0.147351[/C][C]-1.2416[/C][C]0.109234[/C][/ROW]
[ROW][C]14[/C][C]0.015304[/C][C]0.129[/C][C]0.44888[/C][/ROW]
[ROW][C]15[/C][C]0.015353[/C][C]0.1294[/C][C]0.448718[/C][/ROW]
[ROW][C]16[/C][C]-0.048564[/C][C]-0.4092[/C][C]0.34181[/C][/ROW]
[ROW][C]17[/C][C]-0.093252[/C][C]-0.7858[/C][C]0.217312[/C][/ROW]
[ROW][C]18[/C][C]-0.106367[/C][C]-0.8963[/C][C]0.18657[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278058&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	-0.121078	-1.0202	0.155543
2	-0.028936	-0.2438	0.404038
3	0.060356	0.5086	0.306315
4	-0.028387	-0.2392	0.405822
5	-0.140021	-1.1798	0.121002
6	-0.131919	-1.1116	0.135037
7	-0.080264	-0.6763	0.250517
8	0.019047	0.1605	0.436476
9	0.003853	0.0325	0.487097
10	0.114787	0.9672	0.168361
11	0.042969	0.3621	0.359189
12	0.358858	3.0238	0.001736
13	-0.147351	-1.2416	0.109234
14	0.015304	0.129	0.44888
15	0.015353	0.1294	0.448718
16	-0.048564	-0.4092	0.34181
17	-0.093252	-0.7858	0.217312
18	-0.106367	-0.8963	0.18657

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.121078	-1.0202	0.155543
2	-0.044244	-0.3728	0.355201
3	0.052207	0.4399	0.330672
4	-0.015971	-0.1346	0.446664
5	-0.144514	-1.2177	0.113686
6	-0.178705	-1.5058	0.068277
7	-0.137757	-1.1608	0.124814
8	-0.010269	-0.0865	0.465644
9	0.006194	0.0522	0.479263
10	0.104711	0.8823	0.190293
11	0.025802	0.2174	0.414257
12	0.355773	2.9978	0.001873
13	-0.080541	-0.6787	0.249783
14	0.01999	0.1684	0.433359
15	-0.00491	-0.0414	0.483557
16	0.039479	0.3327	0.370188
17	0.026999	0.2275	0.410345
18	-0.056569	-0.4767	0.317534

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.121078 & -1.0202 & 0.155543 \tabularnewline
2 & -0.044244 & -0.3728 & 0.355201 \tabularnewline
3 & 0.052207 & 0.4399 & 0.330672 \tabularnewline
4 & -0.015971 & -0.1346 & 0.446664 \tabularnewline
5 & -0.144514 & -1.2177 & 0.113686 \tabularnewline
6 & -0.178705 & -1.5058 & 0.068277 \tabularnewline
7 & -0.137757 & -1.1608 & 0.124814 \tabularnewline
8 & -0.010269 & -0.0865 & 0.465644 \tabularnewline
9 & 0.006194 & 0.0522 & 0.479263 \tabularnewline
10 & 0.104711 & 0.8823 & 0.190293 \tabularnewline
11 & 0.025802 & 0.2174 & 0.414257 \tabularnewline
12 & 0.355773 & 2.9978 & 0.001873 \tabularnewline
13 & -0.080541 & -0.6787 & 0.249783 \tabularnewline
14 & 0.01999 & 0.1684 & 0.433359 \tabularnewline
15 & -0.00491 & -0.0414 & 0.483557 \tabularnewline
16 & 0.039479 & 0.3327 & 0.370188 \tabularnewline
17 & 0.026999 & 0.2275 & 0.410345 \tabularnewline
18 & -0.056569 & -0.4767 & 0.317534 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278058&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]-0.121078[/C][C]-1.0202[/C][C]0.155543[/C][/ROW]
[ROW][C]2[/C][C]-0.044244[/C][C]-0.3728[/C][C]0.355201[/C][/ROW]
[ROW][C]3[/C][C]0.052207[/C][C]0.4399[/C][C]0.330672[/C][/ROW]
[ROW][C]4[/C][C]-0.015971[/C][C]-0.1346[/C][C]0.446664[/C][/ROW]
[ROW][C]5[/C][C]-0.144514[/C][C]-1.2177[/C][C]0.113686[/C][/ROW]
[ROW][C]6[/C][C]-0.178705[/C][C]-1.5058[/C][C]0.068277[/C][/ROW]
[ROW][C]7[/C][C]-0.137757[/C][C]-1.1608[/C][C]0.124814[/C][/ROW]
[ROW][C]8[/C][C]-0.010269[/C][C]-0.0865[/C][C]0.465644[/C][/ROW]
[ROW][C]9[/C][C]0.006194[/C][C]0.0522[/C][C]0.479263[/C][/ROW]
[ROW][C]10[/C][C]0.104711[/C][C]0.8823[/C][C]0.190293[/C][/ROW]
[ROW][C]11[/C][C]0.025802[/C][C]0.2174[/C][C]0.414257[/C][/ROW]
[ROW][C]12[/C][C]0.355773[/C][C]2.9978[/C][C]0.001873[/C][/ROW]
[ROW][C]13[/C][C]-0.080541[/C][C]-0.6787[/C][C]0.249783[/C][/ROW]
[ROW][C]14[/C][C]0.01999[/C][C]0.1684[/C][C]0.433359[/C][/ROW]
[ROW][C]15[/C][C]-0.00491[/C][C]-0.0414[/C][C]0.483557[/C][/ROW]
[ROW][C]16[/C][C]0.039479[/C][C]0.3327[/C][C]0.370188[/C][/ROW]
[ROW][C]17[/C][C]0.026999[/C][C]0.2275[/C][C]0.410345[/C][/ROW]
[ROW][C]18[/C][C]-0.056569[/C][C]-0.4767[/C][C]0.317534[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278058&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278058&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	-0.121078	-1.0202	0.155543
2	-0.044244	-0.3728	0.355201
3	0.052207	0.4399	0.330672
4	-0.015971	-0.1346	0.446664
5	-0.144514	-1.2177	0.113686
6	-0.178705	-1.5058	0.068277
7	-0.137757	-1.1608	0.124814
8	-0.010269	-0.0865	0.465644
9	0.006194	0.0522	0.479263
10	0.104711	0.8823	0.190293
11	0.025802	0.2174	0.414257
12	0.355773	2.9978	0.001873
13	-0.080541	-0.6787	0.249783
14	0.01999	0.1684	0.433359
15	-0.00491	-0.0414	0.483557
16	0.039479	0.3327	0.370188
17	0.026999	0.2275	0.410345
18	-0.056569	-0.4767	0.317534

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)
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