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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 15 Mar 2014 09:56:51 -0400

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/Mar/15/t139489182246proghdfg5szdl.htm/, Retrieved Tue, 14 May 2024 23:17:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234262, Retrieved Tue, 14 May 2024 23:17:23 +0000

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Estimated Impact

167

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

-       [(Partial) Autocorrelation Function] [Niet werkende wer...] [2014-03-15 13:56:51] [778963f9ed1fb67b9d5ff0854a52552f] [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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234262&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234262&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234262&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.323843	2.9504	0.002062
2	-0.213369	-1.9439	0.027649
3	-0.395644	-3.6045	0.000266
4	-0.286149	-2.6069	0.005414
5	-0.001284	-0.0117	0.495348
6	0.188213	1.7147	0.045066
7	0.033245	0.3029	0.381373
8	-0.22577	-2.0569	0.02142
9	-0.34077	-3.1046	0.001303
10	-0.215518	-1.9635	0.026471
11	0.253297	2.3076	0.011754
12	0.816203	7.436	0
13	0.268266	2.444	0.008322
14	-0.200061	-1.8226	0.035979
15	-0.327135	-2.9803	0.001888
16	-0.236655	-2.156	0.016988
17	0.017384	0.1584	0.437274
18	0.135398	1.2335	0.110429
19	0.027436	0.2499	0.401622

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.323843 & 2.9504 & 0.002062 \tabularnewline
2 & -0.213369 & -1.9439 & 0.027649 \tabularnewline
3 & -0.395644 & -3.6045 & 0.000266 \tabularnewline
4 & -0.286149 & -2.6069 & 0.005414 \tabularnewline
5 & -0.001284 & -0.0117 & 0.495348 \tabularnewline
6 & 0.188213 & 1.7147 & 0.045066 \tabularnewline
7 & 0.033245 & 0.3029 & 0.381373 \tabularnewline
8 & -0.22577 & -2.0569 & 0.02142 \tabularnewline
9 & -0.34077 & -3.1046 & 0.001303 \tabularnewline
10 & -0.215518 & -1.9635 & 0.026471 \tabularnewline
11 & 0.253297 & 2.3076 & 0.011754 \tabularnewline
12 & 0.816203 & 7.436 & 0 \tabularnewline
13 & 0.268266 & 2.444 & 0.008322 \tabularnewline
14 & -0.200061 & -1.8226 & 0.035979 \tabularnewline
15 & -0.327135 & -2.9803 & 0.001888 \tabularnewline
16 & -0.236655 & -2.156 & 0.016988 \tabularnewline
17 & 0.017384 & 0.1584 & 0.437274 \tabularnewline
18 & 0.135398 & 1.2335 & 0.110429 \tabularnewline
19 & 0.027436 & 0.2499 & 0.401622 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234262&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]0.323843[/C][C]2.9504[/C][C]0.002062[/C][/ROW]
[ROW][C]2[/C][C]-0.213369[/C][C]-1.9439[/C][C]0.027649[/C][/ROW]
[ROW][C]3[/C][C]-0.395644[/C][C]-3.6045[/C][C]0.000266[/C][/ROW]
[ROW][C]4[/C][C]-0.286149[/C][C]-2.6069[/C][C]0.005414[/C][/ROW]
[ROW][C]5[/C][C]-0.001284[/C][C]-0.0117[/C][C]0.495348[/C][/ROW]
[ROW][C]6[/C][C]0.188213[/C][C]1.7147[/C][C]0.045066[/C][/ROW]
[ROW][C]7[/C][C]0.033245[/C][C]0.3029[/C][C]0.381373[/C][/ROW]
[ROW][C]8[/C][C]-0.22577[/C][C]-2.0569[/C][C]0.02142[/C][/ROW]
[ROW][C]9[/C][C]-0.34077[/C][C]-3.1046[/C][C]0.001303[/C][/ROW]
[ROW][C]10[/C][C]-0.215518[/C][C]-1.9635[/C][C]0.026471[/C][/ROW]
[ROW][C]11[/C][C]0.253297[/C][C]2.3076[/C][C]0.011754[/C][/ROW]
[ROW][C]12[/C][C]0.816203[/C][C]7.436[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.268266[/C][C]2.444[/C][C]0.008322[/C][/ROW]
[ROW][C]14[/C][C]-0.200061[/C][C]-1.8226[/C][C]0.035979[/C][/ROW]
[ROW][C]15[/C][C]-0.327135[/C][C]-2.9803[/C][C]0.001888[/C][/ROW]
[ROW][C]16[/C][C]-0.236655[/C][C]-2.156[/C][C]0.016988[/C][/ROW]
[ROW][C]17[/C][C]0.017384[/C][C]0.1584[/C][C]0.437274[/C][/ROW]
[ROW][C]18[/C][C]0.135398[/C][C]1.2335[/C][C]0.110429[/C][/ROW]
[ROW][C]19[/C][C]0.027436[/C][C]0.2499[/C][C]0.401622[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234262&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234262&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	0.323843	2.9504	0.002062
2	-0.213369	-1.9439	0.027649
3	-0.395644	-3.6045	0.000266
4	-0.286149	-2.6069	0.005414
5	-0.001284	-0.0117	0.495348
6	0.188213	1.7147	0.045066
7	0.033245	0.3029	0.381373
8	-0.22577	-2.0569	0.02142
9	-0.34077	-3.1046	0.001303
10	-0.215518	-1.9635	0.026471
11	0.253297	2.3076	0.011754
12	0.816203	7.436	0
13	0.268266	2.444	0.008322
14	-0.200061	-1.8226	0.035979
15	-0.327135	-2.9803	0.001888
16	-0.236655	-2.156	0.016988
17	0.017384	0.1584	0.437274
18	0.135398	1.2335	0.110429
19	0.027436	0.2499	0.401622

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.323843	2.9504	0.002062
2	-0.355529	-3.239	0.000863
3	-0.238938	-2.1768	0.016167
4	-0.165704	-1.5096	0.067467
5	-0.016326	-0.1487	0.441061
6	0.002763	0.0252	0.489988
7	-0.204195	-1.8603	0.033192
8	-0.272361	-2.4813	0.007554
9	-0.331911	-3.0239	0.00166
10	-0.372116	-3.3901	0.000536
11	-0.041188	-0.3752	0.35422
12	0.640331	5.8337	0
13	-0.347289	-3.164	0.001088
14	0.014148	0.1289	0.448878
15	0.201027	1.8314	0.035311
16	0.020732	0.1889	0.425325
17	0.00283	0.0258	0.489748
18	-0.188073	-1.7134	0.045183
19	0.072741	0.6627	0.254678

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.323843 & 2.9504 & 0.002062 \tabularnewline
2 & -0.355529 & -3.239 & 0.000863 \tabularnewline
3 & -0.238938 & -2.1768 & 0.016167 \tabularnewline
4 & -0.165704 & -1.5096 & 0.067467 \tabularnewline
5 & -0.016326 & -0.1487 & 0.441061 \tabularnewline
6 & 0.002763 & 0.0252 & 0.489988 \tabularnewline
7 & -0.204195 & -1.8603 & 0.033192 \tabularnewline
8 & -0.272361 & -2.4813 & 0.007554 \tabularnewline
9 & -0.331911 & -3.0239 & 0.00166 \tabularnewline
10 & -0.372116 & -3.3901 & 0.000536 \tabularnewline
11 & -0.041188 & -0.3752 & 0.35422 \tabularnewline
12 & 0.640331 & 5.8337 & 0 \tabularnewline
13 & -0.347289 & -3.164 & 0.001088 \tabularnewline
14 & 0.014148 & 0.1289 & 0.448878 \tabularnewline
15 & 0.201027 & 1.8314 & 0.035311 \tabularnewline
16 & 0.020732 & 0.1889 & 0.425325 \tabularnewline
17 & 0.00283 & 0.0258 & 0.489748 \tabularnewline
18 & -0.188073 & -1.7134 & 0.045183 \tabularnewline
19 & 0.072741 & 0.6627 & 0.254678 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234262&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]0.323843[/C][C]2.9504[/C][C]0.002062[/C][/ROW]
[ROW][C]2[/C][C]-0.355529[/C][C]-3.239[/C][C]0.000863[/C][/ROW]
[ROW][C]3[/C][C]-0.238938[/C][C]-2.1768[/C][C]0.016167[/C][/ROW]
[ROW][C]4[/C][C]-0.165704[/C][C]-1.5096[/C][C]0.067467[/C][/ROW]
[ROW][C]5[/C][C]-0.016326[/C][C]-0.1487[/C][C]0.441061[/C][/ROW]
[ROW][C]6[/C][C]0.002763[/C][C]0.0252[/C][C]0.489988[/C][/ROW]
[ROW][C]7[/C][C]-0.204195[/C][C]-1.8603[/C][C]0.033192[/C][/ROW]
[ROW][C]8[/C][C]-0.272361[/C][C]-2.4813[/C][C]0.007554[/C][/ROW]
[ROW][C]9[/C][C]-0.331911[/C][C]-3.0239[/C][C]0.00166[/C][/ROW]
[ROW][C]10[/C][C]-0.372116[/C][C]-3.3901[/C][C]0.000536[/C][/ROW]
[ROW][C]11[/C][C]-0.041188[/C][C]-0.3752[/C][C]0.35422[/C][/ROW]
[ROW][C]12[/C][C]0.640331[/C][C]5.8337[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.347289[/C][C]-3.164[/C][C]0.001088[/C][/ROW]
[ROW][C]14[/C][C]0.014148[/C][C]0.1289[/C][C]0.448878[/C][/ROW]
[ROW][C]15[/C][C]0.201027[/C][C]1.8314[/C][C]0.035311[/C][/ROW]
[ROW][C]16[/C][C]0.020732[/C][C]0.1889[/C][C]0.425325[/C][/ROW]
[ROW][C]17[/C][C]0.00283[/C][C]0.0258[/C][C]0.489748[/C][/ROW]
[ROW][C]18[/C][C]-0.188073[/C][C]-1.7134[/C][C]0.045183[/C][/ROW]
[ROW][C]19[/C][C]0.072741[/C][C]0.6627[/C][C]0.254678[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234262&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234262&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	0.323843	2.9504	0.002062
2	-0.355529	-3.239	0.000863
3	-0.238938	-2.1768	0.016167
4	-0.165704	-1.5096	0.067467
5	-0.016326	-0.1487	0.441061
6	0.002763	0.0252	0.489988
7	-0.204195	-1.8603	0.033192
8	-0.272361	-2.4813	0.007554
9	-0.331911	-3.0239	0.00166
10	-0.372116	-3.3901	0.000536
11	-0.041188	-0.3752	0.35422
12	0.640331	5.8337	0
13	-0.347289	-3.164	0.001088
14	0.014148	0.1289	0.448878
15	0.201027	1.8314	0.035311
16	0.020732	0.1889	0.425325
17	0.00283	0.0258	0.489748
18	-0.188073	-1.7134	0.045183
19	0.072741	0.6627	0.254678

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code