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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 May 2014 06:55:46 -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/May/17/t1400324158ij0s8j6ucxfxt3k.htm/, Retrieved Sun, 19 May 2024 14:34:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234894, Retrieved Sun, 19 May 2024 14:34:10 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

166

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

-     [Mean Plot] [] [2014-05-17 10:15:07] [b1028f979da76c6c934d8a70d0d396f9]
- RMPD    [(Partial) Autocorrelation Function] [] [2014-05-17 10:55:46] [4a624b09294e96d11d180424866ab9d8] [Current]

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Dataseries X:

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Histogram

Boxplots

0.69
0.69
0.68
0.66
0.65
0.65
0.65
0.65
0.65
0.66
0.68
0.72
0.73
0.75
0.69
0.65
0.64
0.64
0.64
0.64
0.65
0.65
0.67
0.7
0.69
0.7
0.71
0.69
0.69
0.69
0.69
0.69
0.7
0.7
0.7
0.74
0.72
0.74
0.69
0.66
0.66
0.66
0.66
0.66
0.66
0.67
0.7
0.72
0.71
0.7
0.71
0.67
0.7
0.69
0.69
0.69
0.69
0.69
0.71
0.75
0.74
0.75
0.72
0.64
0.65
0.64
0.64
0.64
0.64
0.65
0.66
0.7
0.68
0.69
0.68
0.67
0.68
0.68
0.68
0.68
0.68
0.7
0.69
0.75

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=234894&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=234894&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234894&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	0.722321	6.6202	0
2	0.472617	4.3316	2e-05
3	0.153641	1.4081	0.081389
4	-0.109828	-1.0066	0.158511
5	-0.23653	-2.1678	0.0165
6	-0.311279	-2.8529	0.002726
7	-0.339402	-3.1107	0.001275
8	-0.323564	-2.9655	0.001966
9	-0.138988	-1.2738	0.103116
10	0.03582	0.3283	0.371752
11	0.158674	1.4543	0.074799
12	0.276199	2.5314	0.006612
13	0.145944	1.3376	0.092318
14	0.014802	0.1357	0.446208
15	-0.110124	-1.0093	0.157863
16	-0.257253	-2.3578	0.010355
17	-0.287596	-2.6359	0.004997
18	-0.295293	-2.7064	0.004118
19	-0.231054	-2.1176	0.018581

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.722321 & 6.6202 & 0 \tabularnewline
2 & 0.472617 & 4.3316 & 2e-05 \tabularnewline
3 & 0.153641 & 1.4081 & 0.081389 \tabularnewline
4 & -0.109828 & -1.0066 & 0.158511 \tabularnewline
5 & -0.23653 & -2.1678 & 0.0165 \tabularnewline
6 & -0.311279 & -2.8529 & 0.002726 \tabularnewline
7 & -0.339402 & -3.1107 & 0.001275 \tabularnewline
8 & -0.323564 & -2.9655 & 0.001966 \tabularnewline
9 & -0.138988 & -1.2738 & 0.103116 \tabularnewline
10 & 0.03582 & 0.3283 & 0.371752 \tabularnewline
11 & 0.158674 & 1.4543 & 0.074799 \tabularnewline
12 & 0.276199 & 2.5314 & 0.006612 \tabularnewline
13 & 0.145944 & 1.3376 & 0.092318 \tabularnewline
14 & 0.014802 & 0.1357 & 0.446208 \tabularnewline
15 & -0.110124 & -1.0093 & 0.157863 \tabularnewline
16 & -0.257253 & -2.3578 & 0.010355 \tabularnewline
17 & -0.287596 & -2.6359 & 0.004997 \tabularnewline
18 & -0.295293 & -2.7064 & 0.004118 \tabularnewline
19 & -0.231054 & -2.1176 & 0.018581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234894&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]0.722321[/C][C]6.6202[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.472617[/C][C]4.3316[/C][C]2e-05[/C][/ROW]
[ROW][C]3[/C][C]0.153641[/C][C]1.4081[/C][C]0.081389[/C][/ROW]
[ROW][C]4[/C][C]-0.109828[/C][C]-1.0066[/C][C]0.158511[/C][/ROW]
[ROW][C]5[/C][C]-0.23653[/C][C]-2.1678[/C][C]0.0165[/C][/ROW]
[ROW][C]6[/C][C]-0.311279[/C][C]-2.8529[/C][C]0.002726[/C][/ROW]
[ROW][C]7[/C][C]-0.339402[/C][C]-3.1107[/C][C]0.001275[/C][/ROW]
[ROW][C]8[/C][C]-0.323564[/C][C]-2.9655[/C][C]0.001966[/C][/ROW]
[ROW][C]9[/C][C]-0.138988[/C][C]-1.2738[/C][C]0.103116[/C][/ROW]
[ROW][C]10[/C][C]0.03582[/C][C]0.3283[/C][C]0.371752[/C][/ROW]
[ROW][C]11[/C][C]0.158674[/C][C]1.4543[/C][C]0.074799[/C][/ROW]
[ROW][C]12[/C][C]0.276199[/C][C]2.5314[/C][C]0.006612[/C][/ROW]
[ROW][C]13[/C][C]0.145944[/C][C]1.3376[/C][C]0.092318[/C][/ROW]
[ROW][C]14[/C][C]0.014802[/C][C]0.1357[/C][C]0.446208[/C][/ROW]
[ROW][C]15[/C][C]-0.110124[/C][C]-1.0093[/C][C]0.157863[/C][/ROW]
[ROW][C]16[/C][C]-0.257253[/C][C]-2.3578[/C][C]0.010355[/C][/ROW]
[ROW][C]17[/C][C]-0.287596[/C][C]-2.6359[/C][C]0.004997[/C][/ROW]
[ROW][C]18[/C][C]-0.295293[/C][C]-2.7064[/C][C]0.004118[/C][/ROW]
[ROW][C]19[/C][C]-0.231054[/C][C]-2.1176[/C][C]0.018581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234894&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234894&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	0.722321	6.6202	0
2	0.472617	4.3316	2e-05
3	0.153641	1.4081	0.081389
4	-0.109828	-1.0066	0.158511
5	-0.23653	-2.1678	0.0165
6	-0.311279	-2.8529	0.002726
7	-0.339402	-3.1107	0.001275
8	-0.323564	-2.9655	0.001966
9	-0.138988	-1.2738	0.103116
10	0.03582	0.3283	0.371752
11	0.158674	1.4543	0.074799
12	0.276199	2.5314	0.006612
13	0.145944	1.3376	0.092318
14	0.014802	0.1357	0.446208
15	-0.110124	-1.0093	0.157863
16	-0.257253	-2.3578	0.010355
17	-0.287596	-2.6359	0.004997
18	-0.295293	-2.7064	0.004118
19	-0.231054	-2.1176	0.018581

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.722321	6.6202	0
2	-0.102729	-0.9415	0.174567
3	-0.314042	-2.8782	0.002535
4	-0.164303	-1.5059	0.067927
5	0.055719	0.5107	0.30546
6	-0.082043	-0.7519	0.227095
7	-0.155047	-1.421	0.079505
8	-0.075803	-0.6947	0.244567
9	0.328687	3.0125	0.001712
10	0.083639	0.7666	0.222744
11	-0.191346	-1.7537	0.041564
12	0.106579	0.9768	0.165732
13	-0.256307	-2.3491	0.010583
14	-0.131825	-1.2082	0.115181
15	0.027301	0.2502	0.401513
16	-0.155437	-1.4246	0.078989
17	0.075515	0.6921	0.245389
18	-0.024155	-0.2214	0.412665
19	0.000135	0.0012	0.499507

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.722321 & 6.6202 & 0 \tabularnewline
2 & -0.102729 & -0.9415 & 0.174567 \tabularnewline
3 & -0.314042 & -2.8782 & 0.002535 \tabularnewline
4 & -0.164303 & -1.5059 & 0.067927 \tabularnewline
5 & 0.055719 & 0.5107 & 0.30546 \tabularnewline
6 & -0.082043 & -0.7519 & 0.227095 \tabularnewline
7 & -0.155047 & -1.421 & 0.079505 \tabularnewline
8 & -0.075803 & -0.6947 & 0.244567 \tabularnewline
9 & 0.328687 & 3.0125 & 0.001712 \tabularnewline
10 & 0.083639 & 0.7666 & 0.222744 \tabularnewline
11 & -0.191346 & -1.7537 & 0.041564 \tabularnewline
12 & 0.106579 & 0.9768 & 0.165732 \tabularnewline
13 & -0.256307 & -2.3491 & 0.010583 \tabularnewline
14 & -0.131825 & -1.2082 & 0.115181 \tabularnewline
15 & 0.027301 & 0.2502 & 0.401513 \tabularnewline
16 & -0.155437 & -1.4246 & 0.078989 \tabularnewline
17 & 0.075515 & 0.6921 & 0.245389 \tabularnewline
18 & -0.024155 & -0.2214 & 0.412665 \tabularnewline
19 & 0.000135 & 0.0012 & 0.499507 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234894&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]0.722321[/C][C]6.6202[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.102729[/C][C]-0.9415[/C][C]0.174567[/C][/ROW]
[ROW][C]3[/C][C]-0.314042[/C][C]-2.8782[/C][C]0.002535[/C][/ROW]
[ROW][C]4[/C][C]-0.164303[/C][C]-1.5059[/C][C]0.067927[/C][/ROW]
[ROW][C]5[/C][C]0.055719[/C][C]0.5107[/C][C]0.30546[/C][/ROW]
[ROW][C]6[/C][C]-0.082043[/C][C]-0.7519[/C][C]0.227095[/C][/ROW]
[ROW][C]7[/C][C]-0.155047[/C][C]-1.421[/C][C]0.079505[/C][/ROW]
[ROW][C]8[/C][C]-0.075803[/C][C]-0.6947[/C][C]0.244567[/C][/ROW]
[ROW][C]9[/C][C]0.328687[/C][C]3.0125[/C][C]0.001712[/C][/ROW]
[ROW][C]10[/C][C]0.083639[/C][C]0.7666[/C][C]0.222744[/C][/ROW]
[ROW][C]11[/C][C]-0.191346[/C][C]-1.7537[/C][C]0.041564[/C][/ROW]
[ROW][C]12[/C][C]0.106579[/C][C]0.9768[/C][C]0.165732[/C][/ROW]
[ROW][C]13[/C][C]-0.256307[/C][C]-2.3491[/C][C]0.010583[/C][/ROW]
[ROW][C]14[/C][C]-0.131825[/C][C]-1.2082[/C][C]0.115181[/C][/ROW]
[ROW][C]15[/C][C]0.027301[/C][C]0.2502[/C][C]0.401513[/C][/ROW]
[ROW][C]16[/C][C]-0.155437[/C][C]-1.4246[/C][C]0.078989[/C][/ROW]
[ROW][C]17[/C][C]0.075515[/C][C]0.6921[/C][C]0.245389[/C][/ROW]
[ROW][C]18[/C][C]-0.024155[/C][C]-0.2214[/C][C]0.412665[/C][/ROW]
[ROW][C]19[/C][C]0.000135[/C][C]0.0012[/C][C]0.499507[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234894&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234894&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	0.722321	6.6202	0
2	-0.102729	-0.9415	0.174567
3	-0.314042	-2.8782	0.002535
4	-0.164303	-1.5059	0.067927
5	0.055719	0.5107	0.30546
6	-0.082043	-0.7519	0.227095
7	-0.155047	-1.421	0.079505
8	-0.075803	-0.6947	0.244567
9	0.328687	3.0125	0.001712
10	0.083639	0.7666	0.222744
11	-0.191346	-1.7537	0.041564
12	0.106579	0.9768	0.165732
13	-0.256307	-2.3491	0.010583
14	-0.131825	-1.2082	0.115181
15	0.027301	0.2502	0.401513
16	-0.155437	-1.4246	0.078989
17	0.075515	0.6921	0.245389
18	-0.024155	-0.2214	0.412665
19	0.000135	0.0012	0.499507

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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