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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 14 Mar 2016 18:09:04 +0000

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/Mar/14/t1457978974i80241hga0yo6ke.htm/, Retrieved Mon, 29 Apr 2024 05:33:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294021, Retrieved Mon, 29 Apr 2024 05:33:00 +0000

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User-defined keywords

Estimated Impact

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

-     [Mean Plot] [] [2016-03-14 17:50:31] [588a76e56dbe7fb46b0fa630eb6cb6b1]
- RMPD    [(Partial) Autocorrelation Function] [] [2016-03-14 18:09:04] [383002b29a4d7fe40259202a4bc884b2] [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	2 seconds
R Server	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294021&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294021&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294021&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.019086	-0.2082	0.417713
2	-0.019245	-0.2099	0.417037
3	-0.006998	-0.0763	0.469639
4	-0.007119	-0.0777	0.469113
5	-0.007278	-0.0794	0.468425
6	-0.007437	-0.0811	0.467736
7	-0.007596	-0.0829	0.467048
8	-0.007756	-0.0846	0.46636
9	-0.007067	-0.0771	0.469338
10	-0.007197	-0.0785	0.468775
11	-0.007356	-0.0802	0.468087
12	0.050362	0.5494	0.291885
13	-0.007675	-0.0837	0.46671
14	-0.007834	-0.0855	0.466022
15	-0.007455	-0.0813	0.46766
16	-0.007604	-0.083	0.467015
17	-0.007763	-0.0847	0.466327
18	-0.007922	-0.0864	0.465639
19	-0.008081	-0.0882	0.46495
20	-0.00824	-0.0899	0.464263

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.019086 & -0.2082 & 0.417713 \tabularnewline
2 & -0.019245 & -0.2099 & 0.417037 \tabularnewline
3 & -0.006998 & -0.0763 & 0.469639 \tabularnewline
4 & -0.007119 & -0.0777 & 0.469113 \tabularnewline
5 & -0.007278 & -0.0794 & 0.468425 \tabularnewline
6 & -0.007437 & -0.0811 & 0.467736 \tabularnewline
7 & -0.007596 & -0.0829 & 0.467048 \tabularnewline
8 & -0.007756 & -0.0846 & 0.46636 \tabularnewline
9 & -0.007067 & -0.0771 & 0.469338 \tabularnewline
10 & -0.007197 & -0.0785 & 0.468775 \tabularnewline
11 & -0.007356 & -0.0802 & 0.468087 \tabularnewline
12 & 0.050362 & 0.5494 & 0.291885 \tabularnewline
13 & -0.007675 & -0.0837 & 0.46671 \tabularnewline
14 & -0.007834 & -0.0855 & 0.466022 \tabularnewline
15 & -0.007455 & -0.0813 & 0.46766 \tabularnewline
16 & -0.007604 & -0.083 & 0.467015 \tabularnewline
17 & -0.007763 & -0.0847 & 0.466327 \tabularnewline
18 & -0.007922 & -0.0864 & 0.465639 \tabularnewline
19 & -0.008081 & -0.0882 & 0.46495 \tabularnewline
20 & -0.00824 & -0.0899 & 0.464263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294021&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]-0.019086[/C][C]-0.2082[/C][C]0.417713[/C][/ROW]
[ROW][C]2[/C][C]-0.019245[/C][C]-0.2099[/C][C]0.417037[/C][/ROW]
[ROW][C]3[/C][C]-0.006998[/C][C]-0.0763[/C][C]0.469639[/C][/ROW]
[ROW][C]4[/C][C]-0.007119[/C][C]-0.0777[/C][C]0.469113[/C][/ROW]
[ROW][C]5[/C][C]-0.007278[/C][C]-0.0794[/C][C]0.468425[/C][/ROW]
[ROW][C]6[/C][C]-0.007437[/C][C]-0.0811[/C][C]0.467736[/C][/ROW]
[ROW][C]7[/C][C]-0.007596[/C][C]-0.0829[/C][C]0.467048[/C][/ROW]
[ROW][C]8[/C][C]-0.007756[/C][C]-0.0846[/C][C]0.46636[/C][/ROW]
[ROW][C]9[/C][C]-0.007067[/C][C]-0.0771[/C][C]0.469338[/C][/ROW]
[ROW][C]10[/C][C]-0.007197[/C][C]-0.0785[/C][C]0.468775[/C][/ROW]
[ROW][C]11[/C][C]-0.007356[/C][C]-0.0802[/C][C]0.468087[/C][/ROW]
[ROW][C]12[/C][C]0.050362[/C][C]0.5494[/C][C]0.291885[/C][/ROW]
[ROW][C]13[/C][C]-0.007675[/C][C]-0.0837[/C][C]0.46671[/C][/ROW]
[ROW][C]14[/C][C]-0.007834[/C][C]-0.0855[/C][C]0.466022[/C][/ROW]
[ROW][C]15[/C][C]-0.007455[/C][C]-0.0813[/C][C]0.46766[/C][/ROW]
[ROW][C]16[/C][C]-0.007604[/C][C]-0.083[/C][C]0.467015[/C][/ROW]
[ROW][C]17[/C][C]-0.007763[/C][C]-0.0847[/C][C]0.466327[/C][/ROW]
[ROW][C]18[/C][C]-0.007922[/C][C]-0.0864[/C][C]0.465639[/C][/ROW]
[ROW][C]19[/C][C]-0.008081[/C][C]-0.0882[/C][C]0.46495[/C][/ROW]
[ROW][C]20[/C][C]-0.00824[/C][C]-0.0899[/C][C]0.464263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294021&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294021&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	-0.019086	-0.2082	0.417713
2	-0.019245	-0.2099	0.417037
3	-0.006998	-0.0763	0.469639
4	-0.007119	-0.0777	0.469113
5	-0.007278	-0.0794	0.468425
6	-0.007437	-0.0811	0.467736
7	-0.007596	-0.0829	0.467048
8	-0.007756	-0.0846	0.46636
9	-0.007067	-0.0771	0.469338
10	-0.007197	-0.0785	0.468775
11	-0.007356	-0.0802	0.468087
12	0.050362	0.5494	0.291885
13	-0.007675	-0.0837	0.46671
14	-0.007834	-0.0855	0.466022
15	-0.007455	-0.0813	0.46766
16	-0.007604	-0.083	0.467015
17	-0.007763	-0.0847	0.466327
18	-0.007922	-0.0864	0.465639
19	-0.008081	-0.0882	0.46495
20	-0.00824	-0.0899	0.464263

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.019086	-0.2082	0.417713
2	-0.019617	-0.214	0.41546
3	-0.007753	-0.0846	0.466372
4	-0.007791	-0.085	0.466205
5	-0.007866	-0.0858	0.465884
6	-0.00809	-0.0883	0.464911
7	-0.008321	-0.0908	0.463912
8	-0.008558	-0.0934	0.462888
9	-0.00795	-0.0867	0.465516
10	-0.008132	-0.0887	0.464731
11	-0.008344	-0.091	0.463813
12	0.049375	0.5386	0.29558
13	-0.006523	-0.0712	0.471698
14	-0.006705	-0.0731	0.470907
15	-0.007765	-0.0847	0.466319
16	-0.007983	-0.0871	0.465377
17	-0.008207	-0.0895	0.464408
18	-0.008422	-0.0919	0.463476
19	-0.008642	-0.0943	0.462527
20	-0.008865	-0.0967	0.461561

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.019086 & -0.2082 & 0.417713 \tabularnewline
2 & -0.019617 & -0.214 & 0.41546 \tabularnewline
3 & -0.007753 & -0.0846 & 0.466372 \tabularnewline
4 & -0.007791 & -0.085 & 0.466205 \tabularnewline
5 & -0.007866 & -0.0858 & 0.465884 \tabularnewline
6 & -0.00809 & -0.0883 & 0.464911 \tabularnewline
7 & -0.008321 & -0.0908 & 0.463912 \tabularnewline
8 & -0.008558 & -0.0934 & 0.462888 \tabularnewline
9 & -0.00795 & -0.0867 & 0.465516 \tabularnewline
10 & -0.008132 & -0.0887 & 0.464731 \tabularnewline
11 & -0.008344 & -0.091 & 0.463813 \tabularnewline
12 & 0.049375 & 0.5386 & 0.29558 \tabularnewline
13 & -0.006523 & -0.0712 & 0.471698 \tabularnewline
14 & -0.006705 & -0.0731 & 0.470907 \tabularnewline
15 & -0.007765 & -0.0847 & 0.466319 \tabularnewline
16 & -0.007983 & -0.0871 & 0.465377 \tabularnewline
17 & -0.008207 & -0.0895 & 0.464408 \tabularnewline
18 & -0.008422 & -0.0919 & 0.463476 \tabularnewline
19 & -0.008642 & -0.0943 & 0.462527 \tabularnewline
20 & -0.008865 & -0.0967 & 0.461561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294021&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]-0.019086[/C][C]-0.2082[/C][C]0.417713[/C][/ROW]
[ROW][C]2[/C][C]-0.019617[/C][C]-0.214[/C][C]0.41546[/C][/ROW]
[ROW][C]3[/C][C]-0.007753[/C][C]-0.0846[/C][C]0.466372[/C][/ROW]
[ROW][C]4[/C][C]-0.007791[/C][C]-0.085[/C][C]0.466205[/C][/ROW]
[ROW][C]5[/C][C]-0.007866[/C][C]-0.0858[/C][C]0.465884[/C][/ROW]
[ROW][C]6[/C][C]-0.00809[/C][C]-0.0883[/C][C]0.464911[/C][/ROW]
[ROW][C]7[/C][C]-0.008321[/C][C]-0.0908[/C][C]0.463912[/C][/ROW]
[ROW][C]8[/C][C]-0.008558[/C][C]-0.0934[/C][C]0.462888[/C][/ROW]
[ROW][C]9[/C][C]-0.00795[/C][C]-0.0867[/C][C]0.465516[/C][/ROW]
[ROW][C]10[/C][C]-0.008132[/C][C]-0.0887[/C][C]0.464731[/C][/ROW]
[ROW][C]11[/C][C]-0.008344[/C][C]-0.091[/C][C]0.463813[/C][/ROW]
[ROW][C]12[/C][C]0.049375[/C][C]0.5386[/C][C]0.29558[/C][/ROW]
[ROW][C]13[/C][C]-0.006523[/C][C]-0.0712[/C][C]0.471698[/C][/ROW]
[ROW][C]14[/C][C]-0.006705[/C][C]-0.0731[/C][C]0.470907[/C][/ROW]
[ROW][C]15[/C][C]-0.007765[/C][C]-0.0847[/C][C]0.466319[/C][/ROW]
[ROW][C]16[/C][C]-0.007983[/C][C]-0.0871[/C][C]0.465377[/C][/ROW]
[ROW][C]17[/C][C]-0.008207[/C][C]-0.0895[/C][C]0.464408[/C][/ROW]
[ROW][C]18[/C][C]-0.008422[/C][C]-0.0919[/C][C]0.463476[/C][/ROW]
[ROW][C]19[/C][C]-0.008642[/C][C]-0.0943[/C][C]0.462527[/C][/ROW]
[ROW][C]20[/C][C]-0.008865[/C][C]-0.0967[/C][C]0.461561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294021&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294021&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	-0.019086	-0.2082	0.417713
2	-0.019617	-0.214	0.41546
3	-0.007753	-0.0846	0.466372
4	-0.007791	-0.085	0.466205
5	-0.007866	-0.0858	0.465884
6	-0.00809	-0.0883	0.464911
7	-0.008321	-0.0908	0.463912
8	-0.008558	-0.0934	0.462888
9	-0.00795	-0.0867	0.465516
10	-0.008132	-0.0887	0.464731
11	-0.008344	-0.091	0.463813
12	0.049375	0.5386	0.29558
13	-0.006523	-0.0712	0.471698
14	-0.006705	-0.0731	0.470907
15	-0.007765	-0.0847	0.466319
16	-0.007983	-0.0871	0.465377
17	-0.008207	-0.0895	0.464408
18	-0.008422	-0.0919	0.463476
19	-0.008642	-0.0943	0.462527
20	-0.008865	-0.0967	0.461561

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)
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,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