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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

Fri, 18 Dec 2015 17:46:58 +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/2015/Dec/18/t1450460927by5lm2o3umiysl4.htm/, Retrieved Thu, 16 May 2024 16:48:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286925, Retrieved Thu, 16 May 2024 16:48:56 +0000

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

-       [(Partial) Autocorrelation Function] [] [2015-12-18 17:46:58] [bed289d0f16a0909ee61cbc85c11d541] [Current]

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6.5
6.8
6.8
6.5
6.2
6.2
6.6
6.7
6.5
6.4
6.5
6.8
7.1
7.2
7.1
7
6.9
6.9
7.4
7.3
7
6.8
6.5
6.4
6.3
6
5.9
5.7
5.7
5.7
6.2
6.4
6.2
6.2
6.1
6.1
6.2
6.1
6.1
6.2
6.2
6.2
6.4
6.4
6.4
6.7
6.9
7.1
7.3
7.2
7.1
6.9
6.8
6.7
7.2
7.2
7.1
7.1
7
7.1
7.3
7.2
7.1
7
6.9
7
7.5
7.6
7.5
7.3
7.3
7.4
7.7
7.8
7.7
7.5
7.3
7.3
7.6
7.6

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	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286925&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286925&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286925&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.915485	8.1883	0
2	0.794099	7.1026	0
3	0.710033	6.3507	0
4	0.661941	5.9206	0
5	0.630931	5.6432	0
6	0.570698	5.1045	1e-06
7	0.465035	4.1594	4e-05
8	0.358025	3.2023	0.000979
9	0.286561	2.5631	0.006125
10	0.251957	2.2536	0.01348
11	0.249688	2.2333	0.014162
12	0.237929	2.1281	0.018203
13	0.164578	1.472	0.072468
14	0.091676	0.82	0.207333
15	0.066911	0.5985	0.275608
16	0.068225	0.6102	0.271722
17	0.079422	0.7104	0.23977
18	0.07129	0.6376	0.262764
19	0.030746	0.275	0.392014

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.915485 & 8.1883 & 0 \tabularnewline
2 & 0.794099 & 7.1026 & 0 \tabularnewline
3 & 0.710033 & 6.3507 & 0 \tabularnewline
4 & 0.661941 & 5.9206 & 0 \tabularnewline
5 & 0.630931 & 5.6432 & 0 \tabularnewline
6 & 0.570698 & 5.1045 & 1e-06 \tabularnewline
7 & 0.465035 & 4.1594 & 4e-05 \tabularnewline
8 & 0.358025 & 3.2023 & 0.000979 \tabularnewline
9 & 0.286561 & 2.5631 & 0.006125 \tabularnewline
10 & 0.251957 & 2.2536 & 0.01348 \tabularnewline
11 & 0.249688 & 2.2333 & 0.014162 \tabularnewline
12 & 0.237929 & 2.1281 & 0.018203 \tabularnewline
13 & 0.164578 & 1.472 & 0.072468 \tabularnewline
14 & 0.091676 & 0.82 & 0.207333 \tabularnewline
15 & 0.066911 & 0.5985 & 0.275608 \tabularnewline
16 & 0.068225 & 0.6102 & 0.271722 \tabularnewline
17 & 0.079422 & 0.7104 & 0.23977 \tabularnewline
18 & 0.07129 & 0.6376 & 0.262764 \tabularnewline
19 & 0.030746 & 0.275 & 0.392014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286925&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]0.915485[/C][C]8.1883[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.794099[/C][C]7.1026[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.710033[/C][C]6.3507[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.661941[/C][C]5.9206[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.630931[/C][C]5.6432[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.570698[/C][C]5.1045[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.465035[/C][C]4.1594[/C][C]4e-05[/C][/ROW]
[ROW][C]8[/C][C]0.358025[/C][C]3.2023[/C][C]0.000979[/C][/ROW]
[ROW][C]9[/C][C]0.286561[/C][C]2.5631[/C][C]0.006125[/C][/ROW]
[ROW][C]10[/C][C]0.251957[/C][C]2.2536[/C][C]0.01348[/C][/ROW]
[ROW][C]11[/C][C]0.249688[/C][C]2.2333[/C][C]0.014162[/C][/ROW]
[ROW][C]12[/C][C]0.237929[/C][C]2.1281[/C][C]0.018203[/C][/ROW]
[ROW][C]13[/C][C]0.164578[/C][C]1.472[/C][C]0.072468[/C][/ROW]
[ROW][C]14[/C][C]0.091676[/C][C]0.82[/C][C]0.207333[/C][/ROW]
[ROW][C]15[/C][C]0.066911[/C][C]0.5985[/C][C]0.275608[/C][/ROW]
[ROW][C]16[/C][C]0.068225[/C][C]0.6102[/C][C]0.271722[/C][/ROW]
[ROW][C]17[/C][C]0.079422[/C][C]0.7104[/C][C]0.23977[/C][/ROW]
[ROW][C]18[/C][C]0.07129[/C][C]0.6376[/C][C]0.262764[/C][/ROW]
[ROW][C]19[/C][C]0.030746[/C][C]0.275[/C][C]0.392014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286925&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286925&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	0.915485	8.1883	0
2	0.794099	7.1026	0
3	0.710033	6.3507	0
4	0.661941	5.9206	0
5	0.630931	5.6432	0
6	0.570698	5.1045	1e-06
7	0.465035	4.1594	4e-05
8	0.358025	3.2023	0.000979
9	0.286561	2.5631	0.006125
10	0.251957	2.2536	0.01348
11	0.249688	2.2333	0.014162
12	0.237929	2.1281	0.018203
13	0.164578	1.472	0.072468
14	0.091676	0.82	0.207333
15	0.066911	0.5985	0.275608
16	0.068225	0.6102	0.271722
17	0.079422	0.7104	0.23977
18	0.07129	0.6376	0.262764
19	0.030746	0.275	0.392014

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.915485	8.1883	0
2	-0.271885	-2.4318	0.008629
3	0.228775	2.0462	0.02201
4	0.063476	0.5677	0.285899
5	0.06069	0.5428	0.294377
6	-0.200644	-1.7946	0.038246
7	-0.201928	-1.8061	0.037332
8	-0.01338	-0.1197	0.45252
9	0.043502	0.3891	0.349119
10	0.058412	0.5224	0.301401
11	0.179203	1.6028	0.056455
12	-0.015937	-0.1425	0.443505
13	-0.296262	-2.6498	0.004851
14	0.113088	1.0115	0.157415
15	0.078801	0.7048	0.241486
16	-0.07765	-0.6945	0.244685
17	0.037727	0.3374	0.368336
18	0.020855	0.1865	0.426248
19	-0.037336	-0.3339	0.369649

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.915485 & 8.1883 & 0 \tabularnewline
2 & -0.271885 & -2.4318 & 0.008629 \tabularnewline
3 & 0.228775 & 2.0462 & 0.02201 \tabularnewline
4 & 0.063476 & 0.5677 & 0.285899 \tabularnewline
5 & 0.06069 & 0.5428 & 0.294377 \tabularnewline
6 & -0.200644 & -1.7946 & 0.038246 \tabularnewline
7 & -0.201928 & -1.8061 & 0.037332 \tabularnewline
8 & -0.01338 & -0.1197 & 0.45252 \tabularnewline
9 & 0.043502 & 0.3891 & 0.349119 \tabularnewline
10 & 0.058412 & 0.5224 & 0.301401 \tabularnewline
11 & 0.179203 & 1.6028 & 0.056455 \tabularnewline
12 & -0.015937 & -0.1425 & 0.443505 \tabularnewline
13 & -0.296262 & -2.6498 & 0.004851 \tabularnewline
14 & 0.113088 & 1.0115 & 0.157415 \tabularnewline
15 & 0.078801 & 0.7048 & 0.241486 \tabularnewline
16 & -0.07765 & -0.6945 & 0.244685 \tabularnewline
17 & 0.037727 & 0.3374 & 0.368336 \tabularnewline
18 & 0.020855 & 0.1865 & 0.426248 \tabularnewline
19 & -0.037336 & -0.3339 & 0.369649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286925&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]0.915485[/C][C]8.1883[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.271885[/C][C]-2.4318[/C][C]0.008629[/C][/ROW]
[ROW][C]3[/C][C]0.228775[/C][C]2.0462[/C][C]0.02201[/C][/ROW]
[ROW][C]4[/C][C]0.063476[/C][C]0.5677[/C][C]0.285899[/C][/ROW]
[ROW][C]5[/C][C]0.06069[/C][C]0.5428[/C][C]0.294377[/C][/ROW]
[ROW][C]6[/C][C]-0.200644[/C][C]-1.7946[/C][C]0.038246[/C][/ROW]
[ROW][C]7[/C][C]-0.201928[/C][C]-1.8061[/C][C]0.037332[/C][/ROW]
[ROW][C]8[/C][C]-0.01338[/C][C]-0.1197[/C][C]0.45252[/C][/ROW]
[ROW][C]9[/C][C]0.043502[/C][C]0.3891[/C][C]0.349119[/C][/ROW]
[ROW][C]10[/C][C]0.058412[/C][C]0.5224[/C][C]0.301401[/C][/ROW]
[ROW][C]11[/C][C]0.179203[/C][C]1.6028[/C][C]0.056455[/C][/ROW]
[ROW][C]12[/C][C]-0.015937[/C][C]-0.1425[/C][C]0.443505[/C][/ROW]
[ROW][C]13[/C][C]-0.296262[/C][C]-2.6498[/C][C]0.004851[/C][/ROW]
[ROW][C]14[/C][C]0.113088[/C][C]1.0115[/C][C]0.157415[/C][/ROW]
[ROW][C]15[/C][C]0.078801[/C][C]0.7048[/C][C]0.241486[/C][/ROW]
[ROW][C]16[/C][C]-0.07765[/C][C]-0.6945[/C][C]0.244685[/C][/ROW]
[ROW][C]17[/C][C]0.037727[/C][C]0.3374[/C][C]0.368336[/C][/ROW]
[ROW][C]18[/C][C]0.020855[/C][C]0.1865[/C][C]0.426248[/C][/ROW]
[ROW][C]19[/C][C]-0.037336[/C][C]-0.3339[/C][C]0.369649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286925&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286925&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	0.915485	8.1883	0
2	-0.271885	-2.4318	0.008629
3	0.228775	2.0462	0.02201
4	0.063476	0.5677	0.285899
5	0.06069	0.5428	0.294377
6	-0.200644	-1.7946	0.038246
7	-0.201928	-1.8061	0.037332
8	-0.01338	-0.1197	0.45252
9	0.043502	0.3891	0.349119
10	0.058412	0.5224	0.301401
11	0.179203	1.6028	0.056455
12	-0.015937	-0.1425	0.443505
13	-0.296262	-2.6498	0.004851
14	0.113088	1.0115	0.157415
15	0.078801	0.7048	0.241486
16	-0.07765	-0.6945	0.244685
17	0.037727	0.3374	0.368336
18	0.020855	0.1865	0.426248
19	-0.037336	-0.3339	0.369649

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)
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