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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 14:32:11 +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/16/t1481895191pxi1gtbuv703ezu.htm/, Retrieved Thu, 02 May 2024 19:10:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300254, Retrieved Thu, 02 May 2024 19:10:57 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-16 13:32:11] [404ac5ee4f7301873f6a96ef36861981] [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=300254&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=300254&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300254&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	-0.551328	-5.9123	0
2	0.115203	1.2354	0.109597
3	-0.031716	-0.3401	0.367194
4	0.093553	1.0032	0.158924
5	-0.062706	-0.6724	0.251323
6	-0.022362	-0.2398	0.405453
7	0.040101	0.43	0.333986
8	0.009583	0.1028	0.459163
9	-0.181038	-1.9414	0.027327
10	0.226786	2.432	0.008279
11	-0.061823	-0.663	0.254337
12	-0.127315	-1.3653	0.087412
13	0.103696	1.112	0.134225
14	0.004072	0.0437	0.482625
15	-0.048482	-0.5199	0.302063
16	0.051809	0.5556	0.289784
17	-0.063618	-0.6822	0.248235
18	0.072891	0.7817	0.218008
19	-0.113769	-1.22	0.112474
20	0.063476	0.6807	0.248713

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.551328 & -5.9123 & 0 \tabularnewline
2 & 0.115203 & 1.2354 & 0.109597 \tabularnewline
3 & -0.031716 & -0.3401 & 0.367194 \tabularnewline
4 & 0.093553 & 1.0032 & 0.158924 \tabularnewline
5 & -0.062706 & -0.6724 & 0.251323 \tabularnewline
6 & -0.022362 & -0.2398 & 0.405453 \tabularnewline
7 & 0.040101 & 0.43 & 0.333986 \tabularnewline
8 & 0.009583 & 0.1028 & 0.459163 \tabularnewline
9 & -0.181038 & -1.9414 & 0.027327 \tabularnewline
10 & 0.226786 & 2.432 & 0.008279 \tabularnewline
11 & -0.061823 & -0.663 & 0.254337 \tabularnewline
12 & -0.127315 & -1.3653 & 0.087412 \tabularnewline
13 & 0.103696 & 1.112 & 0.134225 \tabularnewline
14 & 0.004072 & 0.0437 & 0.482625 \tabularnewline
15 & -0.048482 & -0.5199 & 0.302063 \tabularnewline
16 & 0.051809 & 0.5556 & 0.289784 \tabularnewline
17 & -0.063618 & -0.6822 & 0.248235 \tabularnewline
18 & 0.072891 & 0.7817 & 0.218008 \tabularnewline
19 & -0.113769 & -1.22 & 0.112474 \tabularnewline
20 & 0.063476 & 0.6807 & 0.248713 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300254&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]-0.551328[/C][C]-5.9123[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.115203[/C][C]1.2354[/C][C]0.109597[/C][/ROW]
[ROW][C]3[/C][C]-0.031716[/C][C]-0.3401[/C][C]0.367194[/C][/ROW]
[ROW][C]4[/C][C]0.093553[/C][C]1.0032[/C][C]0.158924[/C][/ROW]
[ROW][C]5[/C][C]-0.062706[/C][C]-0.6724[/C][C]0.251323[/C][/ROW]
[ROW][C]6[/C][C]-0.022362[/C][C]-0.2398[/C][C]0.405453[/C][/ROW]
[ROW][C]7[/C][C]0.040101[/C][C]0.43[/C][C]0.333986[/C][/ROW]
[ROW][C]8[/C][C]0.009583[/C][C]0.1028[/C][C]0.459163[/C][/ROW]
[ROW][C]9[/C][C]-0.181038[/C][C]-1.9414[/C][C]0.027327[/C][/ROW]
[ROW][C]10[/C][C]0.226786[/C][C]2.432[/C][C]0.008279[/C][/ROW]
[ROW][C]11[/C][C]-0.061823[/C][C]-0.663[/C][C]0.254337[/C][/ROW]
[ROW][C]12[/C][C]-0.127315[/C][C]-1.3653[/C][C]0.087412[/C][/ROW]
[ROW][C]13[/C][C]0.103696[/C][C]1.112[/C][C]0.134225[/C][/ROW]
[ROW][C]14[/C][C]0.004072[/C][C]0.0437[/C][C]0.482625[/C][/ROW]
[ROW][C]15[/C][C]-0.048482[/C][C]-0.5199[/C][C]0.302063[/C][/ROW]
[ROW][C]16[/C][C]0.051809[/C][C]0.5556[/C][C]0.289784[/C][/ROW]
[ROW][C]17[/C][C]-0.063618[/C][C]-0.6822[/C][C]0.248235[/C][/ROW]
[ROW][C]18[/C][C]0.072891[/C][C]0.7817[/C][C]0.218008[/C][/ROW]
[ROW][C]19[/C][C]-0.113769[/C][C]-1.22[/C][C]0.112474[/C][/ROW]
[ROW][C]20[/C][C]0.063476[/C][C]0.6807[/C][C]0.248713[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300254&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300254&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	-0.551328	-5.9123	0
2	0.115203	1.2354	0.109597
3	-0.031716	-0.3401	0.367194
4	0.093553	1.0032	0.158924
5	-0.062706	-0.6724	0.251323
6	-0.022362	-0.2398	0.405453
7	0.040101	0.43	0.333986
8	0.009583	0.1028	0.459163
9	-0.181038	-1.9414	0.027327
10	0.226786	2.432	0.008279
11	-0.061823	-0.663	0.254337
12	-0.127315	-1.3653	0.087412
13	0.103696	1.112	0.134225
14	0.004072	0.0437	0.482625
15	-0.048482	-0.5199	0.302063
16	0.051809	0.5556	0.289784
17	-0.063618	-0.6822	0.248235
18	0.072891	0.7817	0.218008
19	-0.113769	-1.22	0.112474
20	0.063476	0.6807	0.248713

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.551328	-5.9123	0
2	-0.271192	-2.9082	0.002182
3	-0.155839	-1.6712	0.048702
4	0.044329	0.4754	0.317712
5	0.052926	0.5676	0.285717
6	-0.030301	-0.3249	0.372907
7	-0.01046	-0.1122	0.455442
8	0.027761	0.2977	0.383234
9	-0.235782	-2.5285	0.006406
10	-0.00583	-0.0625	0.475128
11	0.106553	1.1427	0.127778
12	-0.118117	-1.2667	0.103917
13	-0.036862	-0.3953	0.346676
14	0.010556	0.1132	0.455033
15	-0.067942	-0.7286	0.233866
16	0.06204	0.6653	0.253592
17	-0.039131	-0.4196	0.337768
18	-0.038495	-0.4128	0.340257
19	-0.050367	-0.5401	0.295077
20	-0.094327	-1.0115	0.156939

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.551328 & -5.9123 & 0 \tabularnewline
2 & -0.271192 & -2.9082 & 0.002182 \tabularnewline
3 & -0.155839 & -1.6712 & 0.048702 \tabularnewline
4 & 0.044329 & 0.4754 & 0.317712 \tabularnewline
5 & 0.052926 & 0.5676 & 0.285717 \tabularnewline
6 & -0.030301 & -0.3249 & 0.372907 \tabularnewline
7 & -0.01046 & -0.1122 & 0.455442 \tabularnewline
8 & 0.027761 & 0.2977 & 0.383234 \tabularnewline
9 & -0.235782 & -2.5285 & 0.006406 \tabularnewline
10 & -0.00583 & -0.0625 & 0.475128 \tabularnewline
11 & 0.106553 & 1.1427 & 0.127778 \tabularnewline
12 & -0.118117 & -1.2667 & 0.103917 \tabularnewline
13 & -0.036862 & -0.3953 & 0.346676 \tabularnewline
14 & 0.010556 & 0.1132 & 0.455033 \tabularnewline
15 & -0.067942 & -0.7286 & 0.233866 \tabularnewline
16 & 0.06204 & 0.6653 & 0.253592 \tabularnewline
17 & -0.039131 & -0.4196 & 0.337768 \tabularnewline
18 & -0.038495 & -0.4128 & 0.340257 \tabularnewline
19 & -0.050367 & -0.5401 & 0.295077 \tabularnewline
20 & -0.094327 & -1.0115 & 0.156939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300254&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]-0.551328[/C][C]-5.9123[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.271192[/C][C]-2.9082[/C][C]0.002182[/C][/ROW]
[ROW][C]3[/C][C]-0.155839[/C][C]-1.6712[/C][C]0.048702[/C][/ROW]
[ROW][C]4[/C][C]0.044329[/C][C]0.4754[/C][C]0.317712[/C][/ROW]
[ROW][C]5[/C][C]0.052926[/C][C]0.5676[/C][C]0.285717[/C][/ROW]
[ROW][C]6[/C][C]-0.030301[/C][C]-0.3249[/C][C]0.372907[/C][/ROW]
[ROW][C]7[/C][C]-0.01046[/C][C]-0.1122[/C][C]0.455442[/C][/ROW]
[ROW][C]8[/C][C]0.027761[/C][C]0.2977[/C][C]0.383234[/C][/ROW]
[ROW][C]9[/C][C]-0.235782[/C][C]-2.5285[/C][C]0.006406[/C][/ROW]
[ROW][C]10[/C][C]-0.00583[/C][C]-0.0625[/C][C]0.475128[/C][/ROW]
[ROW][C]11[/C][C]0.106553[/C][C]1.1427[/C][C]0.127778[/C][/ROW]
[ROW][C]12[/C][C]-0.118117[/C][C]-1.2667[/C][C]0.103917[/C][/ROW]
[ROW][C]13[/C][C]-0.036862[/C][C]-0.3953[/C][C]0.346676[/C][/ROW]
[ROW][C]14[/C][C]0.010556[/C][C]0.1132[/C][C]0.455033[/C][/ROW]
[ROW][C]15[/C][C]-0.067942[/C][C]-0.7286[/C][C]0.233866[/C][/ROW]
[ROW][C]16[/C][C]0.06204[/C][C]0.6653[/C][C]0.253592[/C][/ROW]
[ROW][C]17[/C][C]-0.039131[/C][C]-0.4196[/C][C]0.337768[/C][/ROW]
[ROW][C]18[/C][C]-0.038495[/C][C]-0.4128[/C][C]0.340257[/C][/ROW]
[ROW][C]19[/C][C]-0.050367[/C][C]-0.5401[/C][C]0.295077[/C][/ROW]
[ROW][C]20[/C][C]-0.094327[/C][C]-1.0115[/C][C]0.156939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300254&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300254&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	-0.551328	-5.9123	0
2	-0.271192	-2.9082	0.002182
3	-0.155839	-1.6712	0.048702
4	0.044329	0.4754	0.317712
5	0.052926	0.5676	0.285717
6	-0.030301	-0.3249	0.372907
7	-0.01046	-0.1122	0.455442
8	0.027761	0.2977	0.383234
9	-0.235782	-2.5285	0.006406
10	-0.00583	-0.0625	0.475128
11	0.106553	1.1427	0.127778
12	-0.118117	-1.2667	0.103917
13	-0.036862	-0.3953	0.346676
14	0.010556	0.1132	0.455033
15	-0.067942	-0.7286	0.233866
16	0.06204	0.6653	0.253592
17	-0.039131	-0.4196	0.337768
18	-0.038495	-0.4128	0.340257
19	-0.050367	-0.5401	0.295077
20	-0.094327	-1.0115	0.156939

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

Postscript link

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Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code