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Author's title

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, 19 Dec 2011 10:50:30 -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/19/t1324309869a3dlvw4wsb76smg.htm/, Retrieved Wed, 15 May 2024 19:07:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157470, Retrieved Wed, 15 May 2024 19:07:09 +0000

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Original text written by user:

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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] [Paper ACF werkloo...] [2011-12-19 15:50:30] [3627de22d386f4cb93d383ef7c1ade7f] [Current]

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Dataseries X:

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Histogram

Boxplots

6,6
6,5
6,3
6,2
6,3
6,5
6,6
6,4
6,2
6,3
6,6
7,1
7,2
7,3
7,3
7,3
7,4
7,3
7,4
7,4
7,6
7,6
7,7
7,7
7,8
7,8
8
8,1
8,1
8,2
8,1
8,1
8,1
8
8,2
8,4
8,4
8,5
8,6
8,5
8,3
7,8
7,8
8
8,6
8,9
8,9
8,6
8,3
8,3
8,3
8,4
8,5
8,4
8,6
8,5
8,5
8,5
8,5
8,5
8,5
8,5
8,5
8,6
8,6
8,6
8,6
8,4
8
7,9
8
8
8
8
7,9
7,9
7,9
8
7,9
7,5
7,2
7
6,9
7,1
7,1
7,2
7,1
6,9
6,8
6,7
6,7
6,9
7,3
7,4
7,3
7,1
7
7,1
7,5
7,7
7,8
7,7
7,7
7,8
8
8,1
8,1
8
8,1
8,2
8,3
8,4
8,5
8,5
8,5
8,5
8,5
8,3
8,2
8,1
7,9
7,6
7,3
7,1
7
7
7
7
6,9
6,8
6,7
6,6

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=157470&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=157470&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157470&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	0.951839	10.9358	0
2	0.875165	10.0549	0
3	0.793229	9.1135	0
4	0.728717	8.3723	0
5	0.683284	7.8503	0
6	0.640141	7.3547	0
7	0.585629	6.7284	0
8	0.512196	5.8847	0
9	0.427164	4.9077	1e-06
10	0.344457	3.9575	6.2e-05
11	0.271787	3.1226	0.001102
12	0.213661	2.4548	0.007699
13	0.162454	1.8665	0.032098
14	0.117021	1.3445	0.090551
15	0.072892	0.8375	0.201923
16	0.030102	0.3458	0.365006
17	-0.011702	-0.1344	0.446627
18	-0.0518	-0.5951	0.276387
19	-0.086	-0.9881	0.162463
20	-0.116558	-1.3391	0.091412
21	-0.146921	-1.688	0.046887

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.951839 & 10.9358 & 0 \tabularnewline
2 & 0.875165 & 10.0549 & 0 \tabularnewline
3 & 0.793229 & 9.1135 & 0 \tabularnewline
4 & 0.728717 & 8.3723 & 0 \tabularnewline
5 & 0.683284 & 7.8503 & 0 \tabularnewline
6 & 0.640141 & 7.3547 & 0 \tabularnewline
7 & 0.585629 & 6.7284 & 0 \tabularnewline
8 & 0.512196 & 5.8847 & 0 \tabularnewline
9 & 0.427164 & 4.9077 & 1e-06 \tabularnewline
10 & 0.344457 & 3.9575 & 6.2e-05 \tabularnewline
11 & 0.271787 & 3.1226 & 0.001102 \tabularnewline
12 & 0.213661 & 2.4548 & 0.007699 \tabularnewline
13 & 0.162454 & 1.8665 & 0.032098 \tabularnewline
14 & 0.117021 & 1.3445 & 0.090551 \tabularnewline
15 & 0.072892 & 0.8375 & 0.201923 \tabularnewline
16 & 0.030102 & 0.3458 & 0.365006 \tabularnewline
17 & -0.011702 & -0.1344 & 0.446627 \tabularnewline
18 & -0.0518 & -0.5951 & 0.276387 \tabularnewline
19 & -0.086 & -0.9881 & 0.162463 \tabularnewline
20 & -0.116558 & -1.3391 & 0.091412 \tabularnewline
21 & -0.146921 & -1.688 & 0.046887 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157470&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]0.951839[/C][C]10.9358[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.875165[/C][C]10.0549[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.793229[/C][C]9.1135[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.728717[/C][C]8.3723[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.683284[/C][C]7.8503[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.640141[/C][C]7.3547[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.585629[/C][C]6.7284[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.512196[/C][C]5.8847[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.427164[/C][C]4.9077[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.344457[/C][C]3.9575[/C][C]6.2e-05[/C][/ROW]
[ROW][C]11[/C][C]0.271787[/C][C]3.1226[/C][C]0.001102[/C][/ROW]
[ROW][C]12[/C][C]0.213661[/C][C]2.4548[/C][C]0.007699[/C][/ROW]
[ROW][C]13[/C][C]0.162454[/C][C]1.8665[/C][C]0.032098[/C][/ROW]
[ROW][C]14[/C][C]0.117021[/C][C]1.3445[/C][C]0.090551[/C][/ROW]
[ROW][C]15[/C][C]0.072892[/C][C]0.8375[/C][C]0.201923[/C][/ROW]
[ROW][C]16[/C][C]0.030102[/C][C]0.3458[/C][C]0.365006[/C][/ROW]
[ROW][C]17[/C][C]-0.011702[/C][C]-0.1344[/C][C]0.446627[/C][/ROW]
[ROW][C]18[/C][C]-0.0518[/C][C]-0.5951[/C][C]0.276387[/C][/ROW]
[ROW][C]19[/C][C]-0.086[/C][C]-0.9881[/C][C]0.162463[/C][/ROW]
[ROW][C]20[/C][C]-0.116558[/C][C]-1.3391[/C][C]0.091412[/C][/ROW]
[ROW][C]21[/C][C]-0.146921[/C][C]-1.688[/C][C]0.046887[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157470&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157470&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	0.951839	10.9358	0
2	0.875165	10.0549	0
3	0.793229	9.1135	0
4	0.728717	8.3723	0
5	0.683284	7.8503	0
6	0.640141	7.3547	0
7	0.585629	6.7284	0
8	0.512196	5.8847	0
9	0.427164	4.9077	1e-06
10	0.344457	3.9575	6.2e-05
11	0.271787	3.1226	0.001102
12	0.213661	2.4548	0.007699
13	0.162454	1.8665	0.032098
14	0.117021	1.3445	0.090551
15	0.072892	0.8375	0.201923
16	0.030102	0.3458	0.365006
17	-0.011702	-0.1344	0.446627
18	-0.0518	-0.5951	0.276387
19	-0.086	-0.9881	0.162463
20	-0.116558	-1.3391	0.091412
21	-0.146921	-1.688	0.046887

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.951839	10.9358	0
2	-0.327981	-3.7682	0.000123
3	-0.009723	-0.1117	0.455613
4	0.168358	1.9343	0.027609
5	0.068562	0.7877	0.216139
6	-0.115948	-1.3321	0.092555
7	-0.131763	-1.5138	0.066229
8	-0.137398	-1.5786	0.058413
9	-0.070336	-0.8081	0.210245
10	-0.010628	-0.1221	0.451501
11	-0.028718	-0.3299	0.370982
12	0.015326	0.1761	0.430249
13	-0.030525	-0.3507	0.363184
14	0.04708	0.5409	0.294743
15	0.007988	0.0918	0.463509
16	-0.004382	-0.0503	0.479962
17	-0.041001	-0.4711	0.319185
18	-0.040875	-0.4696	0.319703
19	0.000543	0.0062	0.497514
20	-0.049284	-0.5662	0.286098
21	-0.079817	-0.917	0.180401

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.951839 & 10.9358 & 0 \tabularnewline
2 & -0.327981 & -3.7682 & 0.000123 \tabularnewline
3 & -0.009723 & -0.1117 & 0.455613 \tabularnewline
4 & 0.168358 & 1.9343 & 0.027609 \tabularnewline
5 & 0.068562 & 0.7877 & 0.216139 \tabularnewline
6 & -0.115948 & -1.3321 & 0.092555 \tabularnewline
7 & -0.131763 & -1.5138 & 0.066229 \tabularnewline
8 & -0.137398 & -1.5786 & 0.058413 \tabularnewline
9 & -0.070336 & -0.8081 & 0.210245 \tabularnewline
10 & -0.010628 & -0.1221 & 0.451501 \tabularnewline
11 & -0.028718 & -0.3299 & 0.370982 \tabularnewline
12 & 0.015326 & 0.1761 & 0.430249 \tabularnewline
13 & -0.030525 & -0.3507 & 0.363184 \tabularnewline
14 & 0.04708 & 0.5409 & 0.294743 \tabularnewline
15 & 0.007988 & 0.0918 & 0.463509 \tabularnewline
16 & -0.004382 & -0.0503 & 0.479962 \tabularnewline
17 & -0.041001 & -0.4711 & 0.319185 \tabularnewline
18 & -0.040875 & -0.4696 & 0.319703 \tabularnewline
19 & 0.000543 & 0.0062 & 0.497514 \tabularnewline
20 & -0.049284 & -0.5662 & 0.286098 \tabularnewline
21 & -0.079817 & -0.917 & 0.180401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157470&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]0.951839[/C][C]10.9358[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.327981[/C][C]-3.7682[/C][C]0.000123[/C][/ROW]
[ROW][C]3[/C][C]-0.009723[/C][C]-0.1117[/C][C]0.455613[/C][/ROW]
[ROW][C]4[/C][C]0.168358[/C][C]1.9343[/C][C]0.027609[/C][/ROW]
[ROW][C]5[/C][C]0.068562[/C][C]0.7877[/C][C]0.216139[/C][/ROW]
[ROW][C]6[/C][C]-0.115948[/C][C]-1.3321[/C][C]0.092555[/C][/ROW]
[ROW][C]7[/C][C]-0.131763[/C][C]-1.5138[/C][C]0.066229[/C][/ROW]
[ROW][C]8[/C][C]-0.137398[/C][C]-1.5786[/C][C]0.058413[/C][/ROW]
[ROW][C]9[/C][C]-0.070336[/C][C]-0.8081[/C][C]0.210245[/C][/ROW]
[ROW][C]10[/C][C]-0.010628[/C][C]-0.1221[/C][C]0.451501[/C][/ROW]
[ROW][C]11[/C][C]-0.028718[/C][C]-0.3299[/C][C]0.370982[/C][/ROW]
[ROW][C]12[/C][C]0.015326[/C][C]0.1761[/C][C]0.430249[/C][/ROW]
[ROW][C]13[/C][C]-0.030525[/C][C]-0.3507[/C][C]0.363184[/C][/ROW]
[ROW][C]14[/C][C]0.04708[/C][C]0.5409[/C][C]0.294743[/C][/ROW]
[ROW][C]15[/C][C]0.007988[/C][C]0.0918[/C][C]0.463509[/C][/ROW]
[ROW][C]16[/C][C]-0.004382[/C][C]-0.0503[/C][C]0.479962[/C][/ROW]
[ROW][C]17[/C][C]-0.041001[/C][C]-0.4711[/C][C]0.319185[/C][/ROW]
[ROW][C]18[/C][C]-0.040875[/C][C]-0.4696[/C][C]0.319703[/C][/ROW]
[ROW][C]19[/C][C]0.000543[/C][C]0.0062[/C][C]0.497514[/C][/ROW]
[ROW][C]20[/C][C]-0.049284[/C][C]-0.5662[/C][C]0.286098[/C][/ROW]
[ROW][C]21[/C][C]-0.079817[/C][C]-0.917[/C][C]0.180401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157470&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157470&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	0.951839	10.9358	0
2	-0.327981	-3.7682	0.000123
3	-0.009723	-0.1117	0.455613
4	0.168358	1.9343	0.027609
5	0.068562	0.7877	0.216139
6	-0.115948	-1.3321	0.092555
7	-0.131763	-1.5138	0.066229
8	-0.137398	-1.5786	0.058413
9	-0.070336	-0.8081	0.210245
10	-0.010628	-0.1221	0.451501
11	-0.028718	-0.3299	0.370982
12	0.015326	0.1761	0.430249
13	-0.030525	-0.3507	0.363184
14	0.04708	0.5409	0.294743
15	0.007988	0.0918	0.463509
16	-0.004382	-0.0503	0.479962
17	-0.041001	-0.4711	0.319185
18	-0.040875	-0.4696	0.319703
19	0.000543	0.0062	0.497514
20	-0.049284	-0.5662	0.286098
21	-0.079817	-0.917	0.180401

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