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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 12:13:50 +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/23/t1482491656tfzpxv4u38cegs1.htm/, Retrieved Wed, 08 May 2024 02:35:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302867, Retrieved Wed, 08 May 2024 02:35:19 +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] [N2071] [2016-12-23 11:13:50] [ca8d18f187365d46258cefbf7e3ea6e7] [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=302867&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=302867&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302867&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	0.482239	5.4131	0
2	0.593017	6.6566	0
3	0.588571	6.6067	0
4	0.468277	5.2564	0
5	0.638573	7.168	0
6	0.357011	4.0074	5.2e-05
7	0.593793	6.6653	0
8	0.428445	4.8093	2e-06
9	0.487772	5.4752	0
10	0.450669	5.0587	1e-06
11	0.31617	3.549	0.000272
12	0.682193	7.6576	0
13	0.283896	3.1867	0.000907
14	0.40601	4.5575	6e-06
15	0.341955	3.8384	9.7e-05
16	0.275961	3.0977	0.001203
17	0.442047	4.962	1e-06
18	0.164942	1.8515	0.033222
19	0.414532	4.6531	4e-06
20	0.272928	3.0636	0.001337
21	0.315841	3.5453	0.000276

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.482239 & 5.4131 & 0 \tabularnewline
2 & 0.593017 & 6.6566 & 0 \tabularnewline
3 & 0.588571 & 6.6067 & 0 \tabularnewline
4 & 0.468277 & 5.2564 & 0 \tabularnewline
5 & 0.638573 & 7.168 & 0 \tabularnewline
6 & 0.357011 & 4.0074 & 5.2e-05 \tabularnewline
7 & 0.593793 & 6.6653 & 0 \tabularnewline
8 & 0.428445 & 4.8093 & 2e-06 \tabularnewline
9 & 0.487772 & 5.4752 & 0 \tabularnewline
10 & 0.450669 & 5.0587 & 1e-06 \tabularnewline
11 & 0.31617 & 3.549 & 0.000272 \tabularnewline
12 & 0.682193 & 7.6576 & 0 \tabularnewline
13 & 0.283896 & 3.1867 & 0.000907 \tabularnewline
14 & 0.40601 & 4.5575 & 6e-06 \tabularnewline
15 & 0.341955 & 3.8384 & 9.7e-05 \tabularnewline
16 & 0.275961 & 3.0977 & 0.001203 \tabularnewline
17 & 0.442047 & 4.962 & 1e-06 \tabularnewline
18 & 0.164942 & 1.8515 & 0.033222 \tabularnewline
19 & 0.414532 & 4.6531 & 4e-06 \tabularnewline
20 & 0.272928 & 3.0636 & 0.001337 \tabularnewline
21 & 0.315841 & 3.5453 & 0.000276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302867&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]0.482239[/C][C]5.4131[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.593017[/C][C]6.6566[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.588571[/C][C]6.6067[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.468277[/C][C]5.2564[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.638573[/C][C]7.168[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.357011[/C][C]4.0074[/C][C]5.2e-05[/C][/ROW]
[ROW][C]7[/C][C]0.593793[/C][C]6.6653[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.428445[/C][C]4.8093[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]0.487772[/C][C]5.4752[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.450669[/C][C]5.0587[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.31617[/C][C]3.549[/C][C]0.000272[/C][/ROW]
[ROW][C]12[/C][C]0.682193[/C][C]7.6576[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.283896[/C][C]3.1867[/C][C]0.000907[/C][/ROW]
[ROW][C]14[/C][C]0.40601[/C][C]4.5575[/C][C]6e-06[/C][/ROW]
[ROW][C]15[/C][C]0.341955[/C][C]3.8384[/C][C]9.7e-05[/C][/ROW]
[ROW][C]16[/C][C]0.275961[/C][C]3.0977[/C][C]0.001203[/C][/ROW]
[ROW][C]17[/C][C]0.442047[/C][C]4.962[/C][C]1e-06[/C][/ROW]
[ROW][C]18[/C][C]0.164942[/C][C]1.8515[/C][C]0.033222[/C][/ROW]
[ROW][C]19[/C][C]0.414532[/C][C]4.6531[/C][C]4e-06[/C][/ROW]
[ROW][C]20[/C][C]0.272928[/C][C]3.0636[/C][C]0.001337[/C][/ROW]
[ROW][C]21[/C][C]0.315841[/C][C]3.5453[/C][C]0.000276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302867&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302867&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	0.482239	5.4131	0
2	0.593017	6.6566	0
3	0.588571	6.6067	0
4	0.468277	5.2564	0
5	0.638573	7.168	0
6	0.357011	4.0074	5.2e-05
7	0.593793	6.6653	0
8	0.428445	4.8093	2e-06
9	0.487772	5.4752	0
10	0.450669	5.0587	1e-06
11	0.31617	3.549	0.000272
12	0.682193	7.6576	0
13	0.283896	3.1867	0.000907
14	0.40601	4.5575	6e-06
15	0.341955	3.8384	9.7e-05
16	0.275961	3.0977	0.001203
17	0.442047	4.962	1e-06
18	0.164942	1.8515	0.033222
19	0.414532	4.6531	4e-06
20	0.272928	3.0636	0.001337
21	0.315841	3.5453	0.000276

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.482239	5.4131	0
2	0.46969	5.2723	0
3	0.351777	3.9487	6.5e-05
4	0.038501	0.4322	0.333178
5	0.310559	3.486	0.000338
6	-0.21465	-2.4094	0.008712
7	0.259626	2.9143	0.00211
8	-0.102478	-1.1503	0.126096
9	0.220584	2.476	0.007306
10	-0.22551	-2.5313	0.006296
11	0.035574	0.3993	0.345169
12	0.413744	4.6443	4e-06
13	-0.268702	-3.0162	0.001549
14	-0.13459	-1.5108	0.066676
15	-0.201778	-2.265	0.012612
16	0.073566	0.8258	0.205247
17	0.021109	0.2369	0.406542
18	0.013437	0.1508	0.440176
19	0.076515	0.8589	0.19602
20	0.067022	0.7523	0.22663
21	-0.015054	-0.169	0.433043

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.482239 & 5.4131 & 0 \tabularnewline
2 & 0.46969 & 5.2723 & 0 \tabularnewline
3 & 0.351777 & 3.9487 & 6.5e-05 \tabularnewline
4 & 0.038501 & 0.4322 & 0.333178 \tabularnewline
5 & 0.310559 & 3.486 & 0.000338 \tabularnewline
6 & -0.21465 & -2.4094 & 0.008712 \tabularnewline
7 & 0.259626 & 2.9143 & 0.00211 \tabularnewline
8 & -0.102478 & -1.1503 & 0.126096 \tabularnewline
9 & 0.220584 & 2.476 & 0.007306 \tabularnewline
10 & -0.22551 & -2.5313 & 0.006296 \tabularnewline
11 & 0.035574 & 0.3993 & 0.345169 \tabularnewline
12 & 0.413744 & 4.6443 & 4e-06 \tabularnewline
13 & -0.268702 & -3.0162 & 0.001549 \tabularnewline
14 & -0.13459 & -1.5108 & 0.066676 \tabularnewline
15 & -0.201778 & -2.265 & 0.012612 \tabularnewline
16 & 0.073566 & 0.8258 & 0.205247 \tabularnewline
17 & 0.021109 & 0.2369 & 0.406542 \tabularnewline
18 & 0.013437 & 0.1508 & 0.440176 \tabularnewline
19 & 0.076515 & 0.8589 & 0.19602 \tabularnewline
20 & 0.067022 & 0.7523 & 0.22663 \tabularnewline
21 & -0.015054 & -0.169 & 0.433043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302867&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]0.482239[/C][C]5.4131[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.46969[/C][C]5.2723[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.351777[/C][C]3.9487[/C][C]6.5e-05[/C][/ROW]
[ROW][C]4[/C][C]0.038501[/C][C]0.4322[/C][C]0.333178[/C][/ROW]
[ROW][C]5[/C][C]0.310559[/C][C]3.486[/C][C]0.000338[/C][/ROW]
[ROW][C]6[/C][C]-0.21465[/C][C]-2.4094[/C][C]0.008712[/C][/ROW]
[ROW][C]7[/C][C]0.259626[/C][C]2.9143[/C][C]0.00211[/C][/ROW]
[ROW][C]8[/C][C]-0.102478[/C][C]-1.1503[/C][C]0.126096[/C][/ROW]
[ROW][C]9[/C][C]0.220584[/C][C]2.476[/C][C]0.007306[/C][/ROW]
[ROW][C]10[/C][C]-0.22551[/C][C]-2.5313[/C][C]0.006296[/C][/ROW]
[ROW][C]11[/C][C]0.035574[/C][C]0.3993[/C][C]0.345169[/C][/ROW]
[ROW][C]12[/C][C]0.413744[/C][C]4.6443[/C][C]4e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.268702[/C][C]-3.0162[/C][C]0.001549[/C][/ROW]
[ROW][C]14[/C][C]-0.13459[/C][C]-1.5108[/C][C]0.066676[/C][/ROW]
[ROW][C]15[/C][C]-0.201778[/C][C]-2.265[/C][C]0.012612[/C][/ROW]
[ROW][C]16[/C][C]0.073566[/C][C]0.8258[/C][C]0.205247[/C][/ROW]
[ROW][C]17[/C][C]0.021109[/C][C]0.2369[/C][C]0.406542[/C][/ROW]
[ROW][C]18[/C][C]0.013437[/C][C]0.1508[/C][C]0.440176[/C][/ROW]
[ROW][C]19[/C][C]0.076515[/C][C]0.8589[/C][C]0.19602[/C][/ROW]
[ROW][C]20[/C][C]0.067022[/C][C]0.7523[/C][C]0.22663[/C][/ROW]
[ROW][C]21[/C][C]-0.015054[/C][C]-0.169[/C][C]0.433043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302867&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302867&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	0.482239	5.4131	0
2	0.46969	5.2723	0
3	0.351777	3.9487	6.5e-05
4	0.038501	0.4322	0.333178
5	0.310559	3.486	0.000338
6	-0.21465	-2.4094	0.008712
7	0.259626	2.9143	0.00211
8	-0.102478	-1.1503	0.126096
9	0.220584	2.476	0.007306
10	-0.22551	-2.5313	0.006296
11	0.035574	0.3993	0.345169
12	0.413744	4.6443	4e-06
13	-0.268702	-3.0162	0.001549
14	-0.13459	-1.5108	0.066676
15	-0.201778	-2.265	0.012612
16	0.073566	0.8258	0.205247
17	0.021109	0.2369	0.406542
18	0.013437	0.1508	0.440176
19	0.076515	0.8589	0.19602
20	0.067022	0.7523	0.22663
21	-0.015054	-0.169	0.433043

Figure 1

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Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

par1 = 12 ;

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,'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