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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 05 Mar 2015 21:24:24 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Mar/05/t1425590673c1lsofxfid3uxcu.htm/, Retrieved Fri, 17 May 2024 16:34:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278025, Retrieved Fri, 17 May 2024 16:34:42 +0000

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-       [(Partial) Autocorrelation Function] [] [2015-03-05 21:24:24] [48df267a82852137cd18322add6deebf] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278025&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278025&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278025&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.947397	8.0389	0
2	0.91607	7.7731	0
3	0.874466	7.4201	0
4	0.814165	6.9084	0
5	0.787634	6.6833	0
6	0.754743	6.4042	0
7	0.72024	6.1114	0
8	0.697711	5.9203	0
9	0.668076	5.6688	0
10	0.629124	5.3383	1e-06
11	0.582875	4.9459	2e-06
12	0.530056	4.4977	1.3e-05
13	0.462796	3.927	9.8e-05
14	0.415611	3.5266	0.000368
15	0.349661	2.967	0.00204
16	0.297693	2.526	0.006868
17	0.24982	2.1198	0.018736
18	0.197927	1.6795	0.048698

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.947397 & 8.0389 & 0 \tabularnewline
2 & 0.91607 & 7.7731 & 0 \tabularnewline
3 & 0.874466 & 7.4201 & 0 \tabularnewline
4 & 0.814165 & 6.9084 & 0 \tabularnewline
5 & 0.787634 & 6.6833 & 0 \tabularnewline
6 & 0.754743 & 6.4042 & 0 \tabularnewline
7 & 0.72024 & 6.1114 & 0 \tabularnewline
8 & 0.697711 & 5.9203 & 0 \tabularnewline
9 & 0.668076 & 5.6688 & 0 \tabularnewline
10 & 0.629124 & 5.3383 & 1e-06 \tabularnewline
11 & 0.582875 & 4.9459 & 2e-06 \tabularnewline
12 & 0.530056 & 4.4977 & 1.3e-05 \tabularnewline
13 & 0.462796 & 3.927 & 9.8e-05 \tabularnewline
14 & 0.415611 & 3.5266 & 0.000368 \tabularnewline
15 & 0.349661 & 2.967 & 0.00204 \tabularnewline
16 & 0.297693 & 2.526 & 0.006868 \tabularnewline
17 & 0.24982 & 2.1198 & 0.018736 \tabularnewline
18 & 0.197927 & 1.6795 & 0.048698 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278025&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]0.947397[/C][C]8.0389[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.91607[/C][C]7.7731[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.874466[/C][C]7.4201[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.814165[/C][C]6.9084[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.787634[/C][C]6.6833[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.754743[/C][C]6.4042[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.72024[/C][C]6.1114[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.697711[/C][C]5.9203[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.668076[/C][C]5.6688[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.629124[/C][C]5.3383[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.582875[/C][C]4.9459[/C][C]2e-06[/C][/ROW]
[ROW][C]12[/C][C]0.530056[/C][C]4.4977[/C][C]1.3e-05[/C][/ROW]
[ROW][C]13[/C][C]0.462796[/C][C]3.927[/C][C]9.8e-05[/C][/ROW]
[ROW][C]14[/C][C]0.415611[/C][C]3.5266[/C][C]0.000368[/C][/ROW]
[ROW][C]15[/C][C]0.349661[/C][C]2.967[/C][C]0.00204[/C][/ROW]
[ROW][C]16[/C][C]0.297693[/C][C]2.526[/C][C]0.006868[/C][/ROW]
[ROW][C]17[/C][C]0.24982[/C][C]2.1198[/C][C]0.018736[/C][/ROW]
[ROW][C]18[/C][C]0.197927[/C][C]1.6795[/C][C]0.048698[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278025&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278025&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	0.947397	8.0389	0
2	0.91607	7.7731	0
3	0.874466	7.4201	0
4	0.814165	6.9084	0
5	0.787634	6.6833	0
6	0.754743	6.4042	0
7	0.72024	6.1114	0
8	0.697711	5.9203	0
9	0.668076	5.6688	0
10	0.629124	5.3383	1e-06
11	0.582875	4.9459	2e-06
12	0.530056	4.4977	1.3e-05
13	0.462796	3.927	9.8e-05
14	0.415611	3.5266	0.000368
15	0.349661	2.967	0.00204
16	0.297693	2.526	0.006868
17	0.24982	2.1198	0.018736
18	0.197927	1.6795	0.048698

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.947397	8.0389	0
2	0.180684	1.5332	0.06481
3	-0.07855	-0.6665	0.253604
4	-0.243473	-2.0659	0.021217
5	0.250863	2.1286	0.018353
6	0.077169	0.6548	0.257342
7	-0.077149	-0.6546	0.257396
8	-0.024718	-0.2097	0.417233
9	0.040594	0.3444	0.365757
10	-0.124142	-1.0534	0.147844
11	-0.200768	-1.7036	0.046387
12	-0.0668	-0.5668	0.286301
13	-0.144008	-1.2219	0.112857
14	0.111918	0.9497	0.172731
15	-0.217096	-1.8421	0.034788
16	0.024848	0.2108	0.416804
17	-0.058988	-0.5005	0.309114
18	0.051926	0.4406	0.330408

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.947397 & 8.0389 & 0 \tabularnewline
2 & 0.180684 & 1.5332 & 0.06481 \tabularnewline
3 & -0.07855 & -0.6665 & 0.253604 \tabularnewline
4 & -0.243473 & -2.0659 & 0.021217 \tabularnewline
5 & 0.250863 & 2.1286 & 0.018353 \tabularnewline
6 & 0.077169 & 0.6548 & 0.257342 \tabularnewline
7 & -0.077149 & -0.6546 & 0.257396 \tabularnewline
8 & -0.024718 & -0.2097 & 0.417233 \tabularnewline
9 & 0.040594 & 0.3444 & 0.365757 \tabularnewline
10 & -0.124142 & -1.0534 & 0.147844 \tabularnewline
11 & -0.200768 & -1.7036 & 0.046387 \tabularnewline
12 & -0.0668 & -0.5668 & 0.286301 \tabularnewline
13 & -0.144008 & -1.2219 & 0.112857 \tabularnewline
14 & 0.111918 & 0.9497 & 0.172731 \tabularnewline
15 & -0.217096 & -1.8421 & 0.034788 \tabularnewline
16 & 0.024848 & 0.2108 & 0.416804 \tabularnewline
17 & -0.058988 & -0.5005 & 0.309114 \tabularnewline
18 & 0.051926 & 0.4406 & 0.330408 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278025&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]0.947397[/C][C]8.0389[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.180684[/C][C]1.5332[/C][C]0.06481[/C][/ROW]
[ROW][C]3[/C][C]-0.07855[/C][C]-0.6665[/C][C]0.253604[/C][/ROW]
[ROW][C]4[/C][C]-0.243473[/C][C]-2.0659[/C][C]0.021217[/C][/ROW]
[ROW][C]5[/C][C]0.250863[/C][C]2.1286[/C][C]0.018353[/C][/ROW]
[ROW][C]6[/C][C]0.077169[/C][C]0.6548[/C][C]0.257342[/C][/ROW]
[ROW][C]7[/C][C]-0.077149[/C][C]-0.6546[/C][C]0.257396[/C][/ROW]
[ROW][C]8[/C][C]-0.024718[/C][C]-0.2097[/C][C]0.417233[/C][/ROW]
[ROW][C]9[/C][C]0.040594[/C][C]0.3444[/C][C]0.365757[/C][/ROW]
[ROW][C]10[/C][C]-0.124142[/C][C]-1.0534[/C][C]0.147844[/C][/ROW]
[ROW][C]11[/C][C]-0.200768[/C][C]-1.7036[/C][C]0.046387[/C][/ROW]
[ROW][C]12[/C][C]-0.0668[/C][C]-0.5668[/C][C]0.286301[/C][/ROW]
[ROW][C]13[/C][C]-0.144008[/C][C]-1.2219[/C][C]0.112857[/C][/ROW]
[ROW][C]14[/C][C]0.111918[/C][C]0.9497[/C][C]0.172731[/C][/ROW]
[ROW][C]15[/C][C]-0.217096[/C][C]-1.8421[/C][C]0.034788[/C][/ROW]
[ROW][C]16[/C][C]0.024848[/C][C]0.2108[/C][C]0.416804[/C][/ROW]
[ROW][C]17[/C][C]-0.058988[/C][C]-0.5005[/C][C]0.309114[/C][/ROW]
[ROW][C]18[/C][C]0.051926[/C][C]0.4406[/C][C]0.330408[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278025&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278025&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	0.947397	8.0389	0
2	0.180684	1.5332	0.06481
3	-0.07855	-0.6665	0.253604
4	-0.243473	-2.0659	0.021217
5	0.250863	2.1286	0.018353
6	0.077169	0.6548	0.257342
7	-0.077149	-0.6546	0.257396
8	-0.024718	-0.2097	0.417233
9	0.040594	0.3444	0.365757
10	-0.124142	-1.0534	0.147844
11	-0.200768	-1.7036	0.046387
12	-0.0668	-0.5668	0.286301
13	-0.144008	-1.2219	0.112857
14	0.111918	0.9497	0.172731
15	-0.217096	-1.8421	0.034788
16	0.024848	0.2108	0.416804
17	-0.058988	-0.5005	0.309114
18	0.051926	0.4406	0.330408

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')

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