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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 12 Dec 2016 14:59:05 +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/12/t1481551532y7pnrw5sy5m8yj2.htm/, Retrieved Fri, 03 May 2024 17:43:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298908, Retrieved Fri, 03 May 2024 17:43:56 +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] [(Partial) Autocor...] [2016-12-12 13:59:05] [2a4be59ea15844c348dc523b08af79fc] [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=298908&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=298908&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298908&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	0.941457	10.4413	0
2	0.845113	9.3728	0
3	0.737345	8.1776	0
4	0.631341	7.0019	0
5	0.534127	5.9238	0
6	0.448138	4.9701	1e-06
7	0.385531	4.2757	1.9e-05
8	0.339711	3.7676	0.000127
9	0.299786	3.3248	0.000583
10	0.254742	2.8252	0.002757
11	0.211392	2.3444	0.010329
12	0.169606	1.881	0.031167
13	0.13044	1.4466	0.07527
14	0.09237	1.0244	0.15382
15	0.046772	0.5187	0.302444
16	0.023415	0.2597	0.397772
17	0.016507	0.1831	0.427521
18	0.01954	0.2167	0.414396
19	0.028121	0.3119	0.377829
20	0.040371	0.4477	0.327566

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.941457 & 10.4413 & 0 \tabularnewline
2 & 0.845113 & 9.3728 & 0 \tabularnewline
3 & 0.737345 & 8.1776 & 0 \tabularnewline
4 & 0.631341 & 7.0019 & 0 \tabularnewline
5 & 0.534127 & 5.9238 & 0 \tabularnewline
6 & 0.448138 & 4.9701 & 1e-06 \tabularnewline
7 & 0.385531 & 4.2757 & 1.9e-05 \tabularnewline
8 & 0.339711 & 3.7676 & 0.000127 \tabularnewline
9 & 0.299786 & 3.3248 & 0.000583 \tabularnewline
10 & 0.254742 & 2.8252 & 0.002757 \tabularnewline
11 & 0.211392 & 2.3444 & 0.010329 \tabularnewline
12 & 0.169606 & 1.881 & 0.031167 \tabularnewline
13 & 0.13044 & 1.4466 & 0.07527 \tabularnewline
14 & 0.09237 & 1.0244 & 0.15382 \tabularnewline
15 & 0.046772 & 0.5187 & 0.302444 \tabularnewline
16 & 0.023415 & 0.2597 & 0.397772 \tabularnewline
17 & 0.016507 & 0.1831 & 0.427521 \tabularnewline
18 & 0.01954 & 0.2167 & 0.414396 \tabularnewline
19 & 0.028121 & 0.3119 & 0.377829 \tabularnewline
20 & 0.040371 & 0.4477 & 0.327566 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298908&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]0.941457[/C][C]10.4413[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.845113[/C][C]9.3728[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.737345[/C][C]8.1776[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.631341[/C][C]7.0019[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.534127[/C][C]5.9238[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.448138[/C][C]4.9701[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.385531[/C][C]4.2757[/C][C]1.9e-05[/C][/ROW]
[ROW][C]8[/C][C]0.339711[/C][C]3.7676[/C][C]0.000127[/C][/ROW]
[ROW][C]9[/C][C]0.299786[/C][C]3.3248[/C][C]0.000583[/C][/ROW]
[ROW][C]10[/C][C]0.254742[/C][C]2.8252[/C][C]0.002757[/C][/ROW]
[ROW][C]11[/C][C]0.211392[/C][C]2.3444[/C][C]0.010329[/C][/ROW]
[ROW][C]12[/C][C]0.169606[/C][C]1.881[/C][C]0.031167[/C][/ROW]
[ROW][C]13[/C][C]0.13044[/C][C]1.4466[/C][C]0.07527[/C][/ROW]
[ROW][C]14[/C][C]0.09237[/C][C]1.0244[/C][C]0.15382[/C][/ROW]
[ROW][C]15[/C][C]0.046772[/C][C]0.5187[/C][C]0.302444[/C][/ROW]
[ROW][C]16[/C][C]0.023415[/C][C]0.2597[/C][C]0.397772[/C][/ROW]
[ROW][C]17[/C][C]0.016507[/C][C]0.1831[/C][C]0.427521[/C][/ROW]
[ROW][C]18[/C][C]0.01954[/C][C]0.2167[/C][C]0.414396[/C][/ROW]
[ROW][C]19[/C][C]0.028121[/C][C]0.3119[/C][C]0.377829[/C][/ROW]
[ROW][C]20[/C][C]0.040371[/C][C]0.4477[/C][C]0.327566[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298908&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298908&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	0.941457	10.4413	0
2	0.845113	9.3728	0
3	0.737345	8.1776	0
4	0.631341	7.0019	0
5	0.534127	5.9238	0
6	0.448138	4.9701	1e-06
7	0.385531	4.2757	1.9e-05
8	0.339711	3.7676	0.000127
9	0.299786	3.3248	0.000583
10	0.254742	2.8252	0.002757
11	0.211392	2.3444	0.010329
12	0.169606	1.881	0.031167
13	0.13044	1.4466	0.07527
14	0.09237	1.0244	0.15382
15	0.046772	0.5187	0.302444
16	0.023415	0.2597	0.397772
17	0.016507	0.1831	0.427521
18	0.01954	0.2167	0.414396
19	0.028121	0.3119	0.377829
20	0.040371	0.4477	0.327566

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.941457	10.4413	0
2	-0.362739	-4.023	5e-05
3	-0.054683	-0.6065	0.272662
4	-0.012914	-0.1432	0.443176
5	0.002209	0.0245	0.490247
6	-0.001187	-0.0132	0.494759
7	0.118917	1.3188	0.094835
8	-0.004324	-0.048	0.480916
9	-0.056391	-0.6254	0.266431
10	-0.097764	-1.0843	0.140187
11	0.033257	0.3688	0.35644
12	-0.022872	-0.2537	0.400091
13	0.004093	0.0454	0.481934
14	-0.027247	-0.3022	0.38151
15	-0.118363	-1.3127	0.095863
16	0.21705	2.4072	0.008781
17	0.005176	0.0574	0.477158
18	0.001093	0.0121	0.495174
19	0.01146	0.1271	0.449534
20	0.019507	0.2163	0.414539

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.941457 & 10.4413 & 0 \tabularnewline
2 & -0.362739 & -4.023 & 5e-05 \tabularnewline
3 & -0.054683 & -0.6065 & 0.272662 \tabularnewline
4 & -0.012914 & -0.1432 & 0.443176 \tabularnewline
5 & 0.002209 & 0.0245 & 0.490247 \tabularnewline
6 & -0.001187 & -0.0132 & 0.494759 \tabularnewline
7 & 0.118917 & 1.3188 & 0.094835 \tabularnewline
8 & -0.004324 & -0.048 & 0.480916 \tabularnewline
9 & -0.056391 & -0.6254 & 0.266431 \tabularnewline
10 & -0.097764 & -1.0843 & 0.140187 \tabularnewline
11 & 0.033257 & 0.3688 & 0.35644 \tabularnewline
12 & -0.022872 & -0.2537 & 0.400091 \tabularnewline
13 & 0.004093 & 0.0454 & 0.481934 \tabularnewline
14 & -0.027247 & -0.3022 & 0.38151 \tabularnewline
15 & -0.118363 & -1.3127 & 0.095863 \tabularnewline
16 & 0.21705 & 2.4072 & 0.008781 \tabularnewline
17 & 0.005176 & 0.0574 & 0.477158 \tabularnewline
18 & 0.001093 & 0.0121 & 0.495174 \tabularnewline
19 & 0.01146 & 0.1271 & 0.449534 \tabularnewline
20 & 0.019507 & 0.2163 & 0.414539 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298908&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]0.941457[/C][C]10.4413[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.362739[/C][C]-4.023[/C][C]5e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.054683[/C][C]-0.6065[/C][C]0.272662[/C][/ROW]
[ROW][C]4[/C][C]-0.012914[/C][C]-0.1432[/C][C]0.443176[/C][/ROW]
[ROW][C]5[/C][C]0.002209[/C][C]0.0245[/C][C]0.490247[/C][/ROW]
[ROW][C]6[/C][C]-0.001187[/C][C]-0.0132[/C][C]0.494759[/C][/ROW]
[ROW][C]7[/C][C]0.118917[/C][C]1.3188[/C][C]0.094835[/C][/ROW]
[ROW][C]8[/C][C]-0.004324[/C][C]-0.048[/C][C]0.480916[/C][/ROW]
[ROW][C]9[/C][C]-0.056391[/C][C]-0.6254[/C][C]0.266431[/C][/ROW]
[ROW][C]10[/C][C]-0.097764[/C][C]-1.0843[/C][C]0.140187[/C][/ROW]
[ROW][C]11[/C][C]0.033257[/C][C]0.3688[/C][C]0.35644[/C][/ROW]
[ROW][C]12[/C][C]-0.022872[/C][C]-0.2537[/C][C]0.400091[/C][/ROW]
[ROW][C]13[/C][C]0.004093[/C][C]0.0454[/C][C]0.481934[/C][/ROW]
[ROW][C]14[/C][C]-0.027247[/C][C]-0.3022[/C][C]0.38151[/C][/ROW]
[ROW][C]15[/C][C]-0.118363[/C][C]-1.3127[/C][C]0.095863[/C][/ROW]
[ROW][C]16[/C][C]0.21705[/C][C]2.4072[/C][C]0.008781[/C][/ROW]
[ROW][C]17[/C][C]0.005176[/C][C]0.0574[/C][C]0.477158[/C][/ROW]
[ROW][C]18[/C][C]0.001093[/C][C]0.0121[/C][C]0.495174[/C][/ROW]
[ROW][C]19[/C][C]0.01146[/C][C]0.1271[/C][C]0.449534[/C][/ROW]
[ROW][C]20[/C][C]0.019507[/C][C]0.2163[/C][C]0.414539[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298908&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298908&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	0.941457	10.4413	0
2	-0.362739	-4.023	5e-05
3	-0.054683	-0.6065	0.272662
4	-0.012914	-0.1432	0.443176
5	0.002209	0.0245	0.490247
6	-0.001187	-0.0132	0.494759
7	0.118917	1.3188	0.094835
8	-0.004324	-0.048	0.480916
9	-0.056391	-0.6254	0.266431
10	-0.097764	-1.0843	0.140187
11	0.033257	0.3688	0.35644
12	-0.022872	-0.2537	0.400091
13	0.004093	0.0454	0.481934
14	-0.027247	-0.3022	0.38151
15	-0.118363	-1.3127	0.095863
16	0.21705	2.4072	0.008781
17	0.005176	0.0574	0.477158
18	0.001093	0.0121	0.495174
19	0.01146	0.1271	0.449534
20	0.019507	0.2163	0.414539

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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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,'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