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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 18:35:32 +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/19/t1482168951ma132mrrpwykl4g.htm/, Retrieved Fri, 17 May 2024 16:19:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301432, Retrieved Fri, 17 May 2024 16:19:53 +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] [N2141 Auto d=1 D=1] [2016-12-19 17:35:32] [f8e2c3c70b883e93ecb746821352be11] [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=301432&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=301432&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301432&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	0.020667	0.2197	0.413254
2	0.129077	1.3721	0.086374
3	0.138705	1.4745	0.07157
4	-0.004117	-0.0438	0.482585
5	0.062662	0.6661	0.253351
6	0.033605	0.3572	0.360795
7	-0.011163	-0.1187	0.452878
8	0.043912	0.4668	0.320775
9	-0.019156	-0.2036	0.419503
10	-0.147471	-1.5676	0.059881
11	-0.188607	-2.0049	0.023681
12	-0.414313	-4.4042	1.2e-05
13	-0.053948	-0.5735	0.28373
14	-0.045498	-0.4836	0.314786
15	-0.051289	-0.5452	0.293342
16	-0.11756	-1.2497	0.106999
17	-0.022727	-0.2416	0.404768
18	-0.013184	-0.1402	0.444395
19	-0.046531	-0.4946	0.310911
20	0.017442	0.1854	0.426621
21	0.068812	0.7315	0.233

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.020667 & 0.2197 & 0.413254 \tabularnewline
2 & 0.129077 & 1.3721 & 0.086374 \tabularnewline
3 & 0.138705 & 1.4745 & 0.07157 \tabularnewline
4 & -0.004117 & -0.0438 & 0.482585 \tabularnewline
5 & 0.062662 & 0.6661 & 0.253351 \tabularnewline
6 & 0.033605 & 0.3572 & 0.360795 \tabularnewline
7 & -0.011163 & -0.1187 & 0.452878 \tabularnewline
8 & 0.043912 & 0.4668 & 0.320775 \tabularnewline
9 & -0.019156 & -0.2036 & 0.419503 \tabularnewline
10 & -0.147471 & -1.5676 & 0.059881 \tabularnewline
11 & -0.188607 & -2.0049 & 0.023681 \tabularnewline
12 & -0.414313 & -4.4042 & 1.2e-05 \tabularnewline
13 & -0.053948 & -0.5735 & 0.28373 \tabularnewline
14 & -0.045498 & -0.4836 & 0.314786 \tabularnewline
15 & -0.051289 & -0.5452 & 0.293342 \tabularnewline
16 & -0.11756 & -1.2497 & 0.106999 \tabularnewline
17 & -0.022727 & -0.2416 & 0.404768 \tabularnewline
18 & -0.013184 & -0.1402 & 0.444395 \tabularnewline
19 & -0.046531 & -0.4946 & 0.310911 \tabularnewline
20 & 0.017442 & 0.1854 & 0.426621 \tabularnewline
21 & 0.068812 & 0.7315 & 0.233 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301432&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]0.020667[/C][C]0.2197[/C][C]0.413254[/C][/ROW]
[ROW][C]2[/C][C]0.129077[/C][C]1.3721[/C][C]0.086374[/C][/ROW]
[ROW][C]3[/C][C]0.138705[/C][C]1.4745[/C][C]0.07157[/C][/ROW]
[ROW][C]4[/C][C]-0.004117[/C][C]-0.0438[/C][C]0.482585[/C][/ROW]
[ROW][C]5[/C][C]0.062662[/C][C]0.6661[/C][C]0.253351[/C][/ROW]
[ROW][C]6[/C][C]0.033605[/C][C]0.3572[/C][C]0.360795[/C][/ROW]
[ROW][C]7[/C][C]-0.011163[/C][C]-0.1187[/C][C]0.452878[/C][/ROW]
[ROW][C]8[/C][C]0.043912[/C][C]0.4668[/C][C]0.320775[/C][/ROW]
[ROW][C]9[/C][C]-0.019156[/C][C]-0.2036[/C][C]0.419503[/C][/ROW]
[ROW][C]10[/C][C]-0.147471[/C][C]-1.5676[/C][C]0.059881[/C][/ROW]
[ROW][C]11[/C][C]-0.188607[/C][C]-2.0049[/C][C]0.023681[/C][/ROW]
[ROW][C]12[/C][C]-0.414313[/C][C]-4.4042[/C][C]1.2e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.053948[/C][C]-0.5735[/C][C]0.28373[/C][/ROW]
[ROW][C]14[/C][C]-0.045498[/C][C]-0.4836[/C][C]0.314786[/C][/ROW]
[ROW][C]15[/C][C]-0.051289[/C][C]-0.5452[/C][C]0.293342[/C][/ROW]
[ROW][C]16[/C][C]-0.11756[/C][C]-1.2497[/C][C]0.106999[/C][/ROW]
[ROW][C]17[/C][C]-0.022727[/C][C]-0.2416[/C][C]0.404768[/C][/ROW]
[ROW][C]18[/C][C]-0.013184[/C][C]-0.1402[/C][C]0.444395[/C][/ROW]
[ROW][C]19[/C][C]-0.046531[/C][C]-0.4946[/C][C]0.310911[/C][/ROW]
[ROW][C]20[/C][C]0.017442[/C][C]0.1854[/C][C]0.426621[/C][/ROW]
[ROW][C]21[/C][C]0.068812[/C][C]0.7315[/C][C]0.233[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301432&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301432&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	0.020667	0.2197	0.413254
2	0.129077	1.3721	0.086374
3	0.138705	1.4745	0.07157
4	-0.004117	-0.0438	0.482585
5	0.062662	0.6661	0.253351
6	0.033605	0.3572	0.360795
7	-0.011163	-0.1187	0.452878
8	0.043912	0.4668	0.320775
9	-0.019156	-0.2036	0.419503
10	-0.147471	-1.5676	0.059881
11	-0.188607	-2.0049	0.023681
12	-0.414313	-4.4042	1.2e-05
13	-0.053948	-0.5735	0.28373
14	-0.045498	-0.4836	0.314786
15	-0.051289	-0.5452	0.293342
16	-0.11756	-1.2497	0.106999
17	-0.022727	-0.2416	0.404768
18	-0.013184	-0.1402	0.444395
19	-0.046531	-0.4946	0.310911
20	0.017442	0.1854	0.426621
21	0.068812	0.7315	0.233

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.020667	0.2197	0.413254
2	0.128705	1.3682	0.08699
3	0.136031	1.446	0.075468
4	-0.024143	-0.2566	0.398959
5	0.028707	0.3052	0.380402
6	0.018706	0.1988	0.421369
7	-0.019767	-0.2101	0.416973
8	0.026151	0.278	0.390764
9	-0.021642	-0.2301	0.40923
10	-0.158964	-1.6898	0.046911
11	-0.206968	-2.2001	0.014918
12	-0.417182	-4.4347	1.1e-05
13	-0.032979	-0.3506	0.363281
14	0.100649	1.0699	0.143469
15	0.116531	1.2387	0.109005
16	-0.105841	-1.1251	0.131464
17	-0.011602	-0.1233	0.451032
18	0.056218	0.5976	0.275649
19	0.031393	0.3337	0.369606
20	0.064174	0.6822	0.248262
21	0.067679	0.7194	0.236678

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.020667 & 0.2197 & 0.413254 \tabularnewline
2 & 0.128705 & 1.3682 & 0.08699 \tabularnewline
3 & 0.136031 & 1.446 & 0.075468 \tabularnewline
4 & -0.024143 & -0.2566 & 0.398959 \tabularnewline
5 & 0.028707 & 0.3052 & 0.380402 \tabularnewline
6 & 0.018706 & 0.1988 & 0.421369 \tabularnewline
7 & -0.019767 & -0.2101 & 0.416973 \tabularnewline
8 & 0.026151 & 0.278 & 0.390764 \tabularnewline
9 & -0.021642 & -0.2301 & 0.40923 \tabularnewline
10 & -0.158964 & -1.6898 & 0.046911 \tabularnewline
11 & -0.206968 & -2.2001 & 0.014918 \tabularnewline
12 & -0.417182 & -4.4347 & 1.1e-05 \tabularnewline
13 & -0.032979 & -0.3506 & 0.363281 \tabularnewline
14 & 0.100649 & 1.0699 & 0.143469 \tabularnewline
15 & 0.116531 & 1.2387 & 0.109005 \tabularnewline
16 & -0.105841 & -1.1251 & 0.131464 \tabularnewline
17 & -0.011602 & -0.1233 & 0.451032 \tabularnewline
18 & 0.056218 & 0.5976 & 0.275649 \tabularnewline
19 & 0.031393 & 0.3337 & 0.369606 \tabularnewline
20 & 0.064174 & 0.6822 & 0.248262 \tabularnewline
21 & 0.067679 & 0.7194 & 0.236678 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301432&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]0.020667[/C][C]0.2197[/C][C]0.413254[/C][/ROW]
[ROW][C]2[/C][C]0.128705[/C][C]1.3682[/C][C]0.08699[/C][/ROW]
[ROW][C]3[/C][C]0.136031[/C][C]1.446[/C][C]0.075468[/C][/ROW]
[ROW][C]4[/C][C]-0.024143[/C][C]-0.2566[/C][C]0.398959[/C][/ROW]
[ROW][C]5[/C][C]0.028707[/C][C]0.3052[/C][C]0.380402[/C][/ROW]
[ROW][C]6[/C][C]0.018706[/C][C]0.1988[/C][C]0.421369[/C][/ROW]
[ROW][C]7[/C][C]-0.019767[/C][C]-0.2101[/C][C]0.416973[/C][/ROW]
[ROW][C]8[/C][C]0.026151[/C][C]0.278[/C][C]0.390764[/C][/ROW]
[ROW][C]9[/C][C]-0.021642[/C][C]-0.2301[/C][C]0.40923[/C][/ROW]
[ROW][C]10[/C][C]-0.158964[/C][C]-1.6898[/C][C]0.046911[/C][/ROW]
[ROW][C]11[/C][C]-0.206968[/C][C]-2.2001[/C][C]0.014918[/C][/ROW]
[ROW][C]12[/C][C]-0.417182[/C][C]-4.4347[/C][C]1.1e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.032979[/C][C]-0.3506[/C][C]0.363281[/C][/ROW]
[ROW][C]14[/C][C]0.100649[/C][C]1.0699[/C][C]0.143469[/C][/ROW]
[ROW][C]15[/C][C]0.116531[/C][C]1.2387[/C][C]0.109005[/C][/ROW]
[ROW][C]16[/C][C]-0.105841[/C][C]-1.1251[/C][C]0.131464[/C][/ROW]
[ROW][C]17[/C][C]-0.011602[/C][C]-0.1233[/C][C]0.451032[/C][/ROW]
[ROW][C]18[/C][C]0.056218[/C][C]0.5976[/C][C]0.275649[/C][/ROW]
[ROW][C]19[/C][C]0.031393[/C][C]0.3337[/C][C]0.369606[/C][/ROW]
[ROW][C]20[/C][C]0.064174[/C][C]0.6822[/C][C]0.248262[/C][/ROW]
[ROW][C]21[/C][C]0.067679[/C][C]0.7194[/C][C]0.236678[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301432&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301432&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	0.020667	0.2197	0.413254
2	0.128705	1.3682	0.08699
3	0.136031	1.446	0.075468
4	-0.024143	-0.2566	0.398959
5	0.028707	0.3052	0.380402
6	0.018706	0.1988	0.421369
7	-0.019767	-0.2101	0.416973
8	0.026151	0.278	0.390764
9	-0.021642	-0.2301	0.40923
10	-0.158964	-1.6898	0.046911
11	-0.206968	-2.2001	0.014918
12	-0.417182	-4.4347	1.1e-05
13	-0.032979	-0.3506	0.363281
14	0.100649	1.0699	0.143469
15	0.116531	1.2387	0.109005
16	-0.105841	-1.1251	0.131464
17	-0.011602	-0.1233	0.451032
18	0.056218	0.5976	0.275649
19	0.031393	0.3337	0.369606
20	0.064174	0.6822	0.248262
21	0.067679	0.7194	0.236678

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

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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 = 1 ; 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)
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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code