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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 17 Nov 2016 09:29:51 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/17/t14793714415s74q1z5r4kinlx.htm/, Retrieved Sun, 05 May 2024 20:01:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296774, Retrieved Sun, 05 May 2024 20:01:39 +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] [] [2016-11-17 08:29:51] [219800a2f11ddd28e3280d87dbde8c8d] [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=296774&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=296774&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296774&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	0.032156	0.3791	0.352593
2	-0.028995	-0.3418	0.366492
3	-0.028129	-0.3316	0.370332
4	-0.124999	-1.4737	0.07141
5	-0.003088	-0.0364	0.485505
6	-0.010871	-0.1282	0.449103
7	0.036613	0.4317	0.333327
8	-0.027174	-0.3204	0.374582
9	-0.102985	-1.2142	0.11337
10	0.020051	0.2364	0.406736
11	0.047988	0.5658	0.286232
12	-0.009788	-0.1154	0.454149
13	0.193687	2.2835	0.011958
14	-0.026478	-0.3122	0.37769
15	-0.042909	-0.5059	0.306868
16	-0.042043	-0.4957	0.310452
17	-0.020505	-0.2417	0.404666
18	0.07321	0.8631	0.194774
19	0.019197	0.2263	0.410641
20	0.060282	0.7107	0.239226
21	0.054011	0.6368	0.262657

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.032156 & 0.3791 & 0.352593 \tabularnewline
2 & -0.028995 & -0.3418 & 0.366492 \tabularnewline
3 & -0.028129 & -0.3316 & 0.370332 \tabularnewline
4 & -0.124999 & -1.4737 & 0.07141 \tabularnewline
5 & -0.003088 & -0.0364 & 0.485505 \tabularnewline
6 & -0.010871 & -0.1282 & 0.449103 \tabularnewline
7 & 0.036613 & 0.4317 & 0.333327 \tabularnewline
8 & -0.027174 & -0.3204 & 0.374582 \tabularnewline
9 & -0.102985 & -1.2142 & 0.11337 \tabularnewline
10 & 0.020051 & 0.2364 & 0.406736 \tabularnewline
11 & 0.047988 & 0.5658 & 0.286232 \tabularnewline
12 & -0.009788 & -0.1154 & 0.454149 \tabularnewline
13 & 0.193687 & 2.2835 & 0.011958 \tabularnewline
14 & -0.026478 & -0.3122 & 0.37769 \tabularnewline
15 & -0.042909 & -0.5059 & 0.306868 \tabularnewline
16 & -0.042043 & -0.4957 & 0.310452 \tabularnewline
17 & -0.020505 & -0.2417 & 0.404666 \tabularnewline
18 & 0.07321 & 0.8631 & 0.194774 \tabularnewline
19 & 0.019197 & 0.2263 & 0.410641 \tabularnewline
20 & 0.060282 & 0.7107 & 0.239226 \tabularnewline
21 & 0.054011 & 0.6368 & 0.262657 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296774&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]0.032156[/C][C]0.3791[/C][C]0.352593[/C][/ROW]
[ROW][C]2[/C][C]-0.028995[/C][C]-0.3418[/C][C]0.366492[/C][/ROW]
[ROW][C]3[/C][C]-0.028129[/C][C]-0.3316[/C][C]0.370332[/C][/ROW]
[ROW][C]4[/C][C]-0.124999[/C][C]-1.4737[/C][C]0.07141[/C][/ROW]
[ROW][C]5[/C][C]-0.003088[/C][C]-0.0364[/C][C]0.485505[/C][/ROW]
[ROW][C]6[/C][C]-0.010871[/C][C]-0.1282[/C][C]0.449103[/C][/ROW]
[ROW][C]7[/C][C]0.036613[/C][C]0.4317[/C][C]0.333327[/C][/ROW]
[ROW][C]8[/C][C]-0.027174[/C][C]-0.3204[/C][C]0.374582[/C][/ROW]
[ROW][C]9[/C][C]-0.102985[/C][C]-1.2142[/C][C]0.11337[/C][/ROW]
[ROW][C]10[/C][C]0.020051[/C][C]0.2364[/C][C]0.406736[/C][/ROW]
[ROW][C]11[/C][C]0.047988[/C][C]0.5658[/C][C]0.286232[/C][/ROW]
[ROW][C]12[/C][C]-0.009788[/C][C]-0.1154[/C][C]0.454149[/C][/ROW]
[ROW][C]13[/C][C]0.193687[/C][C]2.2835[/C][C]0.011958[/C][/ROW]
[ROW][C]14[/C][C]-0.026478[/C][C]-0.3122[/C][C]0.37769[/C][/ROW]
[ROW][C]15[/C][C]-0.042909[/C][C]-0.5059[/C][C]0.306868[/C][/ROW]
[ROW][C]16[/C][C]-0.042043[/C][C]-0.4957[/C][C]0.310452[/C][/ROW]
[ROW][C]17[/C][C]-0.020505[/C][C]-0.2417[/C][C]0.404666[/C][/ROW]
[ROW][C]18[/C][C]0.07321[/C][C]0.8631[/C][C]0.194774[/C][/ROW]
[ROW][C]19[/C][C]0.019197[/C][C]0.2263[/C][C]0.410641[/C][/ROW]
[ROW][C]20[/C][C]0.060282[/C][C]0.7107[/C][C]0.239226[/C][/ROW]
[ROW][C]21[/C][C]0.054011[/C][C]0.6368[/C][C]0.262657[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296774&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296774&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	0.032156	0.3791	0.352593
2	-0.028995	-0.3418	0.366492
3	-0.028129	-0.3316	0.370332
4	-0.124999	-1.4737	0.07141
5	-0.003088	-0.0364	0.485505
6	-0.010871	-0.1282	0.449103
7	0.036613	0.4317	0.333327
8	-0.027174	-0.3204	0.374582
9	-0.102985	-1.2142	0.11337
10	0.020051	0.2364	0.406736
11	0.047988	0.5658	0.286232
12	-0.009788	-0.1154	0.454149
13	0.193687	2.2835	0.011958
14	-0.026478	-0.3122	0.37769
15	-0.042909	-0.5059	0.306868
16	-0.042043	-0.4957	0.310452
17	-0.020505	-0.2417	0.404666
18	0.07321	0.8631	0.194774
19	0.019197	0.2263	0.410641
20	0.060282	0.7107	0.239226
21	0.054011	0.6368	0.262657

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.032156	0.3791	0.352593
2	-0.03006	-0.3544	0.361787
3	-0.026253	-0.3095	0.378696
4	-0.124418	-1.4669	0.072335
5	0.003033	0.0358	0.485763
6	-0.019557	-0.2306	0.40899
7	0.031805	0.375	0.354125
8	-0.046663	-0.5501	0.291551
9	-0.101262	-1.1939	0.117283
10	0.021754	0.2565	0.398981
11	0.048557	0.5725	0.28396
12	-0.025831	-0.3045	0.380586
13	0.179431	2.1155	0.018087
14	-0.03741	-0.4411	0.329929
15	-0.019739	-0.2327	0.408163
16	-0.032461	-0.3827	0.351262
17	0.017856	0.2105	0.416783
18	0.055523	0.6546	0.256901
19	0.023356	0.2754	0.391724
20	0.049426	0.5827	0.280511
21	0.066222	0.7807	0.21814

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.032156 & 0.3791 & 0.352593 \tabularnewline
2 & -0.03006 & -0.3544 & 0.361787 \tabularnewline
3 & -0.026253 & -0.3095 & 0.378696 \tabularnewline
4 & -0.124418 & -1.4669 & 0.072335 \tabularnewline
5 & 0.003033 & 0.0358 & 0.485763 \tabularnewline
6 & -0.019557 & -0.2306 & 0.40899 \tabularnewline
7 & 0.031805 & 0.375 & 0.354125 \tabularnewline
8 & -0.046663 & -0.5501 & 0.291551 \tabularnewline
9 & -0.101262 & -1.1939 & 0.117283 \tabularnewline
10 & 0.021754 & 0.2565 & 0.398981 \tabularnewline
11 & 0.048557 & 0.5725 & 0.28396 \tabularnewline
12 & -0.025831 & -0.3045 & 0.380586 \tabularnewline
13 & 0.179431 & 2.1155 & 0.018087 \tabularnewline
14 & -0.03741 & -0.4411 & 0.329929 \tabularnewline
15 & -0.019739 & -0.2327 & 0.408163 \tabularnewline
16 & -0.032461 & -0.3827 & 0.351262 \tabularnewline
17 & 0.017856 & 0.2105 & 0.416783 \tabularnewline
18 & 0.055523 & 0.6546 & 0.256901 \tabularnewline
19 & 0.023356 & 0.2754 & 0.391724 \tabularnewline
20 & 0.049426 & 0.5827 & 0.280511 \tabularnewline
21 & 0.066222 & 0.7807 & 0.21814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296774&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]0.032156[/C][C]0.3791[/C][C]0.352593[/C][/ROW]
[ROW][C]2[/C][C]-0.03006[/C][C]-0.3544[/C][C]0.361787[/C][/ROW]
[ROW][C]3[/C][C]-0.026253[/C][C]-0.3095[/C][C]0.378696[/C][/ROW]
[ROW][C]4[/C][C]-0.124418[/C][C]-1.4669[/C][C]0.072335[/C][/ROW]
[ROW][C]5[/C][C]0.003033[/C][C]0.0358[/C][C]0.485763[/C][/ROW]
[ROW][C]6[/C][C]-0.019557[/C][C]-0.2306[/C][C]0.40899[/C][/ROW]
[ROW][C]7[/C][C]0.031805[/C][C]0.375[/C][C]0.354125[/C][/ROW]
[ROW][C]8[/C][C]-0.046663[/C][C]-0.5501[/C][C]0.291551[/C][/ROW]
[ROW][C]9[/C][C]-0.101262[/C][C]-1.1939[/C][C]0.117283[/C][/ROW]
[ROW][C]10[/C][C]0.021754[/C][C]0.2565[/C][C]0.398981[/C][/ROW]
[ROW][C]11[/C][C]0.048557[/C][C]0.5725[/C][C]0.28396[/C][/ROW]
[ROW][C]12[/C][C]-0.025831[/C][C]-0.3045[/C][C]0.380586[/C][/ROW]
[ROW][C]13[/C][C]0.179431[/C][C]2.1155[/C][C]0.018087[/C][/ROW]
[ROW][C]14[/C][C]-0.03741[/C][C]-0.4411[/C][C]0.329929[/C][/ROW]
[ROW][C]15[/C][C]-0.019739[/C][C]-0.2327[/C][C]0.408163[/C][/ROW]
[ROW][C]16[/C][C]-0.032461[/C][C]-0.3827[/C][C]0.351262[/C][/ROW]
[ROW][C]17[/C][C]0.017856[/C][C]0.2105[/C][C]0.416783[/C][/ROW]
[ROW][C]18[/C][C]0.055523[/C][C]0.6546[/C][C]0.256901[/C][/ROW]
[ROW][C]19[/C][C]0.023356[/C][C]0.2754[/C][C]0.391724[/C][/ROW]
[ROW][C]20[/C][C]0.049426[/C][C]0.5827[/C][C]0.280511[/C][/ROW]
[ROW][C]21[/C][C]0.066222[/C][C]0.7807[/C][C]0.21814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296774&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296774&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	0.032156	0.3791	0.352593
2	-0.03006	-0.3544	0.361787
3	-0.026253	-0.3095	0.378696
4	-0.124418	-1.4669	0.072335
5	0.003033	0.0358	0.485763
6	-0.019557	-0.2306	0.40899
7	0.031805	0.375	0.354125
8	-0.046663	-0.5501	0.291551
9	-0.101262	-1.1939	0.117283
10	0.021754	0.2565	0.398981
11	0.048557	0.5725	0.28396
12	-0.025831	-0.3045	0.380586
13	0.179431	2.1155	0.018087
14	-0.03741	-0.4411	0.329929
15	-0.019739	-0.2327	0.408163
16	-0.032461	-0.3827	0.351262
17	0.017856	0.2105	0.416783
18	0.055523	0.6546	0.256901
19	0.023356	0.2754	0.391724
20	0.049426	0.5827	0.280511
21	0.066222	0.7807	0.21814

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 = 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