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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

Mon, 05 Dec 2011 09:10:10 -0500

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/2011/Dec/05/t1323094226rdgbt03zs9x1h2y.htm/, Retrieved Wed, 24 Apr 2024 14:23:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150924, Retrieved Wed, 24 Apr 2024 14:23:31 +0000

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User-defined keywords

Estimated Impact

111

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

F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Univariate Data Series] [] [2011-11-25 14:57:13] [493236dcc414c5f9e1823f06b33a5ad6]
- RMPD      [(Partial) Autocorrelation Function] [] [2011-12-05 14:10:10] [75a32e1bc492240bc1028714aca23077] [Current]

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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	'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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150924&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150924&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150924&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.26737	1.833	0.036571
2	-0.256588	-1.7591	0.042537
3	-0.123197	-0.8446	0.201308
4	0.219351	1.5038	0.069662
5	0.152744	1.0472	0.150191
6	-0.18232	-1.2499	0.108759
7	-0.164122	-1.1252	0.133117
8	-0.026741	-0.1833	0.427666
9	0.133263	0.9136	0.182794
10	0.100747	0.6907	0.246581
11	-0.126103	-0.8645	0.195846
12	-0.352306	-2.4153	0.009832
13	0.009512	0.0652	0.474141
14	0.235153	1.6121	0.056815
15	-0.005037	-0.0345	0.4863
16	-0.148724	-1.0196	0.156569
17	0.004441	0.0304	0.48792

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.26737 & 1.833 & 0.036571 \tabularnewline
2 & -0.256588 & -1.7591 & 0.042537 \tabularnewline
3 & -0.123197 & -0.8446 & 0.201308 \tabularnewline
4 & 0.219351 & 1.5038 & 0.069662 \tabularnewline
5 & 0.152744 & 1.0472 & 0.150191 \tabularnewline
6 & -0.18232 & -1.2499 & 0.108759 \tabularnewline
7 & -0.164122 & -1.1252 & 0.133117 \tabularnewline
8 & -0.026741 & -0.1833 & 0.427666 \tabularnewline
9 & 0.133263 & 0.9136 & 0.182794 \tabularnewline
10 & 0.100747 & 0.6907 & 0.246581 \tabularnewline
11 & -0.126103 & -0.8645 & 0.195846 \tabularnewline
12 & -0.352306 & -2.4153 & 0.009832 \tabularnewline
13 & 0.009512 & 0.0652 & 0.474141 \tabularnewline
14 & 0.235153 & 1.6121 & 0.056815 \tabularnewline
15 & -0.005037 & -0.0345 & 0.4863 \tabularnewline
16 & -0.148724 & -1.0196 & 0.156569 \tabularnewline
17 & 0.004441 & 0.0304 & 0.48792 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150924&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]0.26737[/C][C]1.833[/C][C]0.036571[/C][/ROW]
[ROW][C]2[/C][C]-0.256588[/C][C]-1.7591[/C][C]0.042537[/C][/ROW]
[ROW][C]3[/C][C]-0.123197[/C][C]-0.8446[/C][C]0.201308[/C][/ROW]
[ROW][C]4[/C][C]0.219351[/C][C]1.5038[/C][C]0.069662[/C][/ROW]
[ROW][C]5[/C][C]0.152744[/C][C]1.0472[/C][C]0.150191[/C][/ROW]
[ROW][C]6[/C][C]-0.18232[/C][C]-1.2499[/C][C]0.108759[/C][/ROW]
[ROW][C]7[/C][C]-0.164122[/C][C]-1.1252[/C][C]0.133117[/C][/ROW]
[ROW][C]8[/C][C]-0.026741[/C][C]-0.1833[/C][C]0.427666[/C][/ROW]
[ROW][C]9[/C][C]0.133263[/C][C]0.9136[/C][C]0.182794[/C][/ROW]
[ROW][C]10[/C][C]0.100747[/C][C]0.6907[/C][C]0.246581[/C][/ROW]
[ROW][C]11[/C][C]-0.126103[/C][C]-0.8645[/C][C]0.195846[/C][/ROW]
[ROW][C]12[/C][C]-0.352306[/C][C]-2.4153[/C][C]0.009832[/C][/ROW]
[ROW][C]13[/C][C]0.009512[/C][C]0.0652[/C][C]0.474141[/C][/ROW]
[ROW][C]14[/C][C]0.235153[/C][C]1.6121[/C][C]0.056815[/C][/ROW]
[ROW][C]15[/C][C]-0.005037[/C][C]-0.0345[/C][C]0.4863[/C][/ROW]
[ROW][C]16[/C][C]-0.148724[/C][C]-1.0196[/C][C]0.156569[/C][/ROW]
[ROW][C]17[/C][C]0.004441[/C][C]0.0304[/C][C]0.48792[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150924&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150924&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	0.26737	1.833	0.036571
2	-0.256588	-1.7591	0.042537
3	-0.123197	-0.8446	0.201308
4	0.219351	1.5038	0.069662
5	0.152744	1.0472	0.150191
6	-0.18232	-1.2499	0.108759
7	-0.164122	-1.1252	0.133117
8	-0.026741	-0.1833	0.427666
9	0.133263	0.9136	0.182794
10	0.100747	0.6907	0.246581
11	-0.126103	-0.8645	0.195846
12	-0.352306	-2.4153	0.009832
13	0.009512	0.0652	0.474141
14	0.235153	1.6121	0.056815
15	-0.005037	-0.0345	0.4863
16	-0.148724	-1.0196	0.156569
17	0.004441	0.0304	0.48792

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.26737	1.833	0.036571
2	-0.353333	-2.4223	0.009665
3	0.078905	0.5409	0.29555
4	0.183621	1.2588	0.107153
5	-0.019457	-0.1334	0.447228
6	-0.15061	-1.0325	0.153554
7	0.019604	0.1344	0.446831
8	-0.115621	-0.7927	0.21598
9	0.112117	0.7686	0.222978
10	0.07001	0.48	0.316739
11	-0.131007	-0.8981	0.186845
12	-0.306421	-2.1007	0.020529
13	0.22482	1.5413	0.064977
14	-0.050979	-0.3495	0.36414
15	-0.077179	-0.5291	0.299608
16	0.159716	1.095	0.139557
17	0.016033	0.1099	0.456473

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.26737 & 1.833 & 0.036571 \tabularnewline
2 & -0.353333 & -2.4223 & 0.009665 \tabularnewline
3 & 0.078905 & 0.5409 & 0.29555 \tabularnewline
4 & 0.183621 & 1.2588 & 0.107153 \tabularnewline
5 & -0.019457 & -0.1334 & 0.447228 \tabularnewline
6 & -0.15061 & -1.0325 & 0.153554 \tabularnewline
7 & 0.019604 & 0.1344 & 0.446831 \tabularnewline
8 & -0.115621 & -0.7927 & 0.21598 \tabularnewline
9 & 0.112117 & 0.7686 & 0.222978 \tabularnewline
10 & 0.07001 & 0.48 & 0.316739 \tabularnewline
11 & -0.131007 & -0.8981 & 0.186845 \tabularnewline
12 & -0.306421 & -2.1007 & 0.020529 \tabularnewline
13 & 0.22482 & 1.5413 & 0.064977 \tabularnewline
14 & -0.050979 & -0.3495 & 0.36414 \tabularnewline
15 & -0.077179 & -0.5291 & 0.299608 \tabularnewline
16 & 0.159716 & 1.095 & 0.139557 \tabularnewline
17 & 0.016033 & 0.1099 & 0.456473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150924&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]0.26737[/C][C]1.833[/C][C]0.036571[/C][/ROW]
[ROW][C]2[/C][C]-0.353333[/C][C]-2.4223[/C][C]0.009665[/C][/ROW]
[ROW][C]3[/C][C]0.078905[/C][C]0.5409[/C][C]0.29555[/C][/ROW]
[ROW][C]4[/C][C]0.183621[/C][C]1.2588[/C][C]0.107153[/C][/ROW]
[ROW][C]5[/C][C]-0.019457[/C][C]-0.1334[/C][C]0.447228[/C][/ROW]
[ROW][C]6[/C][C]-0.15061[/C][C]-1.0325[/C][C]0.153554[/C][/ROW]
[ROW][C]7[/C][C]0.019604[/C][C]0.1344[/C][C]0.446831[/C][/ROW]
[ROW][C]8[/C][C]-0.115621[/C][C]-0.7927[/C][C]0.21598[/C][/ROW]
[ROW][C]9[/C][C]0.112117[/C][C]0.7686[/C][C]0.222978[/C][/ROW]
[ROW][C]10[/C][C]0.07001[/C][C]0.48[/C][C]0.316739[/C][/ROW]
[ROW][C]11[/C][C]-0.131007[/C][C]-0.8981[/C][C]0.186845[/C][/ROW]
[ROW][C]12[/C][C]-0.306421[/C][C]-2.1007[/C][C]0.020529[/C][/ROW]
[ROW][C]13[/C][C]0.22482[/C][C]1.5413[/C][C]0.064977[/C][/ROW]
[ROW][C]14[/C][C]-0.050979[/C][C]-0.3495[/C][C]0.36414[/C][/ROW]
[ROW][C]15[/C][C]-0.077179[/C][C]-0.5291[/C][C]0.299608[/C][/ROW]
[ROW][C]16[/C][C]0.159716[/C][C]1.095[/C][C]0.139557[/C][/ROW]
[ROW][C]17[/C][C]0.016033[/C][C]0.1099[/C][C]0.456473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150924&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150924&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	0.26737	1.833	0.036571
2	-0.353333	-2.4223	0.009665
3	0.078905	0.5409	0.29555
4	0.183621	1.2588	0.107153
5	-0.019457	-0.1334	0.447228
6	-0.15061	-1.0325	0.153554
7	0.019604	0.1344	0.446831
8	-0.115621	-0.7927	0.21598
9	0.112117	0.7686	0.222978
10	0.07001	0.48	0.316739
11	-0.131007	-0.8981	0.186845
12	-0.306421	-2.1007	0.020529
13	0.22482	1.5413	0.064977
14	-0.050979	-0.3495	0.36414
15	-0.077179	-0.5291	0.299608
16	0.159716	1.095	0.139557
17	0.016033	0.1099	0.456473

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 = additive ; par2 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code