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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 13:05:31 +0100

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/2016/Dec/18/t1482062769sybx0ieojwip881.htm/, Retrieved Wed, 08 May 2024 13:40:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301024, Retrieved Wed, 08 May 2024 13:40:55 +0000

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User-defined keywords

Estimated Impact

116

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

-     [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2015-11-15 16:35:00] [32b17a345b130fdf5cc88718ed94a974]
- RMPD    [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2016-12-18 12:05:31] [2ea868439aa9f960cb5a0f1a9b97f873] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301024&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301024&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301024&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.130493	-1.3994	0.082194
2	0.00848	0.0909	0.463852
3	-0.015119	-0.1621	0.435743
4	0.040591	0.4353	0.332084
5	0.153546	1.6466	0.051185
6	-0.043277	-0.4641	0.321728
7	0.022058	0.2365	0.406714
8	0.035125	0.3767	0.353554
9	-0.081235	-0.8711	0.192744
10	-0.031254	-0.3352	0.369059
11	-0.147043	-1.5769	0.058787
12	0.080697	0.8654	0.194316
13	-0.142239	-1.5253	0.064959
14	0.065499	0.7024	0.241926
15	-0.040167	-0.4307	0.333729
16	0.026971	0.2892	0.386463
17	0.059434	0.6374	0.262577
18	-0.0865	-0.9276	0.177776
19	0.089139	0.9559	0.170561
20	0.015414	0.1653	0.434501

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.130493 & -1.3994 & 0.082194 \tabularnewline
2 & 0.00848 & 0.0909 & 0.463852 \tabularnewline
3 & -0.015119 & -0.1621 & 0.435743 \tabularnewline
4 & 0.040591 & 0.4353 & 0.332084 \tabularnewline
5 & 0.153546 & 1.6466 & 0.051185 \tabularnewline
6 & -0.043277 & -0.4641 & 0.321728 \tabularnewline
7 & 0.022058 & 0.2365 & 0.406714 \tabularnewline
8 & 0.035125 & 0.3767 & 0.353554 \tabularnewline
9 & -0.081235 & -0.8711 & 0.192744 \tabularnewline
10 & -0.031254 & -0.3352 & 0.369059 \tabularnewline
11 & -0.147043 & -1.5769 & 0.058787 \tabularnewline
12 & 0.080697 & 0.8654 & 0.194316 \tabularnewline
13 & -0.142239 & -1.5253 & 0.064959 \tabularnewline
14 & 0.065499 & 0.7024 & 0.241926 \tabularnewline
15 & -0.040167 & -0.4307 & 0.333729 \tabularnewline
16 & 0.026971 & 0.2892 & 0.386463 \tabularnewline
17 & 0.059434 & 0.6374 & 0.262577 \tabularnewline
18 & -0.0865 & -0.9276 & 0.177776 \tabularnewline
19 & 0.089139 & 0.9559 & 0.170561 \tabularnewline
20 & 0.015414 & 0.1653 & 0.434501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301024&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]-0.130493[/C][C]-1.3994[/C][C]0.082194[/C][/ROW]
[ROW][C]2[/C][C]0.00848[/C][C]0.0909[/C][C]0.463852[/C][/ROW]
[ROW][C]3[/C][C]-0.015119[/C][C]-0.1621[/C][C]0.435743[/C][/ROW]
[ROW][C]4[/C][C]0.040591[/C][C]0.4353[/C][C]0.332084[/C][/ROW]
[ROW][C]5[/C][C]0.153546[/C][C]1.6466[/C][C]0.051185[/C][/ROW]
[ROW][C]6[/C][C]-0.043277[/C][C]-0.4641[/C][C]0.321728[/C][/ROW]
[ROW][C]7[/C][C]0.022058[/C][C]0.2365[/C][C]0.406714[/C][/ROW]
[ROW][C]8[/C][C]0.035125[/C][C]0.3767[/C][C]0.353554[/C][/ROW]
[ROW][C]9[/C][C]-0.081235[/C][C]-0.8711[/C][C]0.192744[/C][/ROW]
[ROW][C]10[/C][C]-0.031254[/C][C]-0.3352[/C][C]0.369059[/C][/ROW]
[ROW][C]11[/C][C]-0.147043[/C][C]-1.5769[/C][C]0.058787[/C][/ROW]
[ROW][C]12[/C][C]0.080697[/C][C]0.8654[/C][C]0.194316[/C][/ROW]
[ROW][C]13[/C][C]-0.142239[/C][C]-1.5253[/C][C]0.064959[/C][/ROW]
[ROW][C]14[/C][C]0.065499[/C][C]0.7024[/C][C]0.241926[/C][/ROW]
[ROW][C]15[/C][C]-0.040167[/C][C]-0.4307[/C][C]0.333729[/C][/ROW]
[ROW][C]16[/C][C]0.026971[/C][C]0.2892[/C][C]0.386463[/C][/ROW]
[ROW][C]17[/C][C]0.059434[/C][C]0.6374[/C][C]0.262577[/C][/ROW]
[ROW][C]18[/C][C]-0.0865[/C][C]-0.9276[/C][C]0.177776[/C][/ROW]
[ROW][C]19[/C][C]0.089139[/C][C]0.9559[/C][C]0.170561[/C][/ROW]
[ROW][C]20[/C][C]0.015414[/C][C]0.1653[/C][C]0.434501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301024&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301024&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	-0.130493	-1.3994	0.082194
2	0.00848	0.0909	0.463852
3	-0.015119	-0.1621	0.435743
4	0.040591	0.4353	0.332084
5	0.153546	1.6466	0.051185
6	-0.043277	-0.4641	0.321728
7	0.022058	0.2365	0.406714
8	0.035125	0.3767	0.353554
9	-0.081235	-0.8711	0.192744
10	-0.031254	-0.3352	0.369059
11	-0.147043	-1.5769	0.058787
12	0.080697	0.8654	0.194316
13	-0.142239	-1.5253	0.064959
14	0.065499	0.7024	0.241926
15	-0.040167	-0.4307	0.333729
16	0.026971	0.2892	0.386463
17	0.059434	0.6374	0.262577
18	-0.0865	-0.9276	0.177776
19	0.089139	0.9559	0.170561
20	0.015414	0.1653	0.434501

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.130493	-1.3994	0.082194
2	-0.008697	-0.0933	0.462928
3	-0.015401	-0.1652	0.434555
4	0.037327	0.4003	0.344843
5	0.166795	1.7887	0.03815
6	-0.000732	-0.0079	0.496874
7	0.017997	0.193	0.423653
8	0.043632	0.4679	0.320372
9	-0.091244	-0.9785	0.164944
10	-0.081208	-0.8709	0.192824
11	-0.166541	-1.7859	0.038371
12	0.024667	0.2645	0.395926
13	-0.142921	-1.5327	0.064053
14	0.066722	0.7155	0.23787
15	0.010215	0.1095	0.456481
16	0.078209	0.8387	0.201691
17	0.091441	0.9806	0.164424
18	-0.022775	-0.2442	0.403743
19	0.063785	0.684	0.247669
20	0.002305	0.0247	0.490162

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.130493 & -1.3994 & 0.082194 \tabularnewline
2 & -0.008697 & -0.0933 & 0.462928 \tabularnewline
3 & -0.015401 & -0.1652 & 0.434555 \tabularnewline
4 & 0.037327 & 0.4003 & 0.344843 \tabularnewline
5 & 0.166795 & 1.7887 & 0.03815 \tabularnewline
6 & -0.000732 & -0.0079 & 0.496874 \tabularnewline
7 & 0.017997 & 0.193 & 0.423653 \tabularnewline
8 & 0.043632 & 0.4679 & 0.320372 \tabularnewline
9 & -0.091244 & -0.9785 & 0.164944 \tabularnewline
10 & -0.081208 & -0.8709 & 0.192824 \tabularnewline
11 & -0.166541 & -1.7859 & 0.038371 \tabularnewline
12 & 0.024667 & 0.2645 & 0.395926 \tabularnewline
13 & -0.142921 & -1.5327 & 0.064053 \tabularnewline
14 & 0.066722 & 0.7155 & 0.23787 \tabularnewline
15 & 0.010215 & 0.1095 & 0.456481 \tabularnewline
16 & 0.078209 & 0.8387 & 0.201691 \tabularnewline
17 & 0.091441 & 0.9806 & 0.164424 \tabularnewline
18 & -0.022775 & -0.2442 & 0.403743 \tabularnewline
19 & 0.063785 & 0.684 & 0.247669 \tabularnewline
20 & 0.002305 & 0.0247 & 0.490162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301024&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]-0.130493[/C][C]-1.3994[/C][C]0.082194[/C][/ROW]
[ROW][C]2[/C][C]-0.008697[/C][C]-0.0933[/C][C]0.462928[/C][/ROW]
[ROW][C]3[/C][C]-0.015401[/C][C]-0.1652[/C][C]0.434555[/C][/ROW]
[ROW][C]4[/C][C]0.037327[/C][C]0.4003[/C][C]0.344843[/C][/ROW]
[ROW][C]5[/C][C]0.166795[/C][C]1.7887[/C][C]0.03815[/C][/ROW]
[ROW][C]6[/C][C]-0.000732[/C][C]-0.0079[/C][C]0.496874[/C][/ROW]
[ROW][C]7[/C][C]0.017997[/C][C]0.193[/C][C]0.423653[/C][/ROW]
[ROW][C]8[/C][C]0.043632[/C][C]0.4679[/C][C]0.320372[/C][/ROW]
[ROW][C]9[/C][C]-0.091244[/C][C]-0.9785[/C][C]0.164944[/C][/ROW]
[ROW][C]10[/C][C]-0.081208[/C][C]-0.8709[/C][C]0.192824[/C][/ROW]
[ROW][C]11[/C][C]-0.166541[/C][C]-1.7859[/C][C]0.038371[/C][/ROW]
[ROW][C]12[/C][C]0.024667[/C][C]0.2645[/C][C]0.395926[/C][/ROW]
[ROW][C]13[/C][C]-0.142921[/C][C]-1.5327[/C][C]0.064053[/C][/ROW]
[ROW][C]14[/C][C]0.066722[/C][C]0.7155[/C][C]0.23787[/C][/ROW]
[ROW][C]15[/C][C]0.010215[/C][C]0.1095[/C][C]0.456481[/C][/ROW]
[ROW][C]16[/C][C]0.078209[/C][C]0.8387[/C][C]0.201691[/C][/ROW]
[ROW][C]17[/C][C]0.091441[/C][C]0.9806[/C][C]0.164424[/C][/ROW]
[ROW][C]18[/C][C]-0.022775[/C][C]-0.2442[/C][C]0.403743[/C][/ROW]
[ROW][C]19[/C][C]0.063785[/C][C]0.684[/C][C]0.247669[/C][/ROW]
[ROW][C]20[/C][C]0.002305[/C][C]0.0247[/C][C]0.490162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301024&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301024&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	-0.130493	-1.3994	0.082194
2	-0.008697	-0.0933	0.462928
3	-0.015401	-0.1652	0.434555
4	0.037327	0.4003	0.344843
5	0.166795	1.7887	0.03815
6	-0.000732	-0.0079	0.496874
7	0.017997	0.193	0.423653
8	0.043632	0.4679	0.320372
9	-0.091244	-0.9785	0.164944
10	-0.081208	-0.8709	0.192824
11	-0.166541	-1.7859	0.038371
12	0.024667	0.2645	0.395926
13	-0.142921	-1.5327	0.064053
14	0.066722	0.7155	0.23787
15	0.010215	0.1095	0.456481
16	0.078209	0.8387	0.201691
17	0.091441	0.9806	0.164424
18	-0.022775	-0.2442	0.403743
19	0.063785	0.684	0.247669
20	0.002305	0.0247	0.490162

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):

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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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