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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 20:08:03 +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/Dec/18/t148208811467cw8s4qwnqomxb.htm/, Retrieved Wed, 08 May 2024 21:08:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301224, Retrieved Wed, 08 May 2024 21:08:28 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [ARIMA Forecasting] [ ARIMA FORECAST] [2016-12-15 19:00:32] [d1d385d9b7e195437bdc484ddbefdda4]
- RMP     [(Partial) Autocorrelation Function] [AUtocorrelation ] [2016-12-18 19:08:03] [b95f76f605693b3a3343a287ab24f42a] [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=301224&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=301224&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301224&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	0.911754	10.2344	0
2	0.856979	9.6196	0
3	0.823164	9.24	0
4	0.790718	8.8758	0
5	0.793758	8.9099	0
6	0.758742	8.5169	0
7	0.751086	8.4309	0
8	0.703618	7.8981	0
9	0.672291	7.5464	0
10	0.667568	7.4934	0
11	0.668355	7.5023	0
12	0.687215	7.714	0
13	0.607155	6.8153	0
14	0.557691	6.2601	0
15	0.530476	5.9546	0
16	0.506733	5.6881	0
17	0.521563	5.8545	0
18	0.497002	5.5788	0
19	0.496592	5.5742	0
20	0.464555	5.2146	0
21	0.437945	4.9159	1e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.911754 & 10.2344 & 0 \tabularnewline
2 & 0.856979 & 9.6196 & 0 \tabularnewline
3 & 0.823164 & 9.24 & 0 \tabularnewline
4 & 0.790718 & 8.8758 & 0 \tabularnewline
5 & 0.793758 & 8.9099 & 0 \tabularnewline
6 & 0.758742 & 8.5169 & 0 \tabularnewline
7 & 0.751086 & 8.4309 & 0 \tabularnewline
8 & 0.703618 & 7.8981 & 0 \tabularnewline
9 & 0.672291 & 7.5464 & 0 \tabularnewline
10 & 0.667568 & 7.4934 & 0 \tabularnewline
11 & 0.668355 & 7.5023 & 0 \tabularnewline
12 & 0.687215 & 7.714 & 0 \tabularnewline
13 & 0.607155 & 6.8153 & 0 \tabularnewline
14 & 0.557691 & 6.2601 & 0 \tabularnewline
15 & 0.530476 & 5.9546 & 0 \tabularnewline
16 & 0.506733 & 5.6881 & 0 \tabularnewline
17 & 0.521563 & 5.8545 & 0 \tabularnewline
18 & 0.497002 & 5.5788 & 0 \tabularnewline
19 & 0.496592 & 5.5742 & 0 \tabularnewline
20 & 0.464555 & 5.2146 & 0 \tabularnewline
21 & 0.437945 & 4.9159 & 1e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301224&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]0.911754[/C][C]10.2344[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.856979[/C][C]9.6196[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.823164[/C][C]9.24[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.790718[/C][C]8.8758[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.793758[/C][C]8.9099[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.758742[/C][C]8.5169[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.751086[/C][C]8.4309[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.703618[/C][C]7.8981[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.672291[/C][C]7.5464[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.667568[/C][C]7.4934[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.668355[/C][C]7.5023[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.687215[/C][C]7.714[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.607155[/C][C]6.8153[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.557691[/C][C]6.2601[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.530476[/C][C]5.9546[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.506733[/C][C]5.6881[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.521563[/C][C]5.8545[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.497002[/C][C]5.5788[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.496592[/C][C]5.5742[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.464555[/C][C]5.2146[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.437945[/C][C]4.9159[/C][C]1e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301224&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301224&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	0.911754	10.2344	0
2	0.856979	9.6196	0
3	0.823164	9.24	0
4	0.790718	8.8758	0
5	0.793758	8.9099	0
6	0.758742	8.5169	0
7	0.751086	8.4309	0
8	0.703618	7.8981	0
9	0.672291	7.5464	0
10	0.667568	7.4934	0
11	0.668355	7.5023	0
12	0.687215	7.714	0
13	0.607155	6.8153	0
14	0.557691	6.2601	0
15	0.530476	5.9546	0
16	0.506733	5.6881	0
17	0.521563	5.8545	0
18	0.497002	5.5788	0
19	0.496592	5.5742	0
20	0.464555	5.2146	0
21	0.437945	4.9159	1e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.911754	10.2344	0
2	0.152238	1.7089	0.044969
3	0.133248	1.4957	0.068615
4	0.046087	0.5173	0.302918
5	0.237219	2.6628	0.004381
6	-0.129717	-1.4561	0.07393
7	0.165549	1.8583	0.032731
8	-0.249825	-2.8043	0.002921
9	0.11171	1.2539	0.106092
10	0.015418	0.1731	0.431439
11	0.227208	2.5504	0.005979
12	0.028771	0.323	0.373634
13	-0.459295	-5.1556	0
14	-0.00232	-0.026	0.489631
15	0.04021	0.4514	0.326254
16	0.125412	1.4077	0.080835
17	0.064103	0.7196	0.236565
18	-0.044112	-0.4952	0.310676
19	0.064175	0.7204	0.23632
20	0.006823	0.0766	0.469535
21	0.030998	0.348	0.364228

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.911754 & 10.2344 & 0 \tabularnewline
2 & 0.152238 & 1.7089 & 0.044969 \tabularnewline
3 & 0.133248 & 1.4957 & 0.068615 \tabularnewline
4 & 0.046087 & 0.5173 & 0.302918 \tabularnewline
5 & 0.237219 & 2.6628 & 0.004381 \tabularnewline
6 & -0.129717 & -1.4561 & 0.07393 \tabularnewline
7 & 0.165549 & 1.8583 & 0.032731 \tabularnewline
8 & -0.249825 & -2.8043 & 0.002921 \tabularnewline
9 & 0.11171 & 1.2539 & 0.106092 \tabularnewline
10 & 0.015418 & 0.1731 & 0.431439 \tabularnewline
11 & 0.227208 & 2.5504 & 0.005979 \tabularnewline
12 & 0.028771 & 0.323 & 0.373634 \tabularnewline
13 & -0.459295 & -5.1556 & 0 \tabularnewline
14 & -0.00232 & -0.026 & 0.489631 \tabularnewline
15 & 0.04021 & 0.4514 & 0.326254 \tabularnewline
16 & 0.125412 & 1.4077 & 0.080835 \tabularnewline
17 & 0.064103 & 0.7196 & 0.236565 \tabularnewline
18 & -0.044112 & -0.4952 & 0.310676 \tabularnewline
19 & 0.064175 & 0.7204 & 0.23632 \tabularnewline
20 & 0.006823 & 0.0766 & 0.469535 \tabularnewline
21 & 0.030998 & 0.348 & 0.364228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301224&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]0.911754[/C][C]10.2344[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.152238[/C][C]1.7089[/C][C]0.044969[/C][/ROW]
[ROW][C]3[/C][C]0.133248[/C][C]1.4957[/C][C]0.068615[/C][/ROW]
[ROW][C]4[/C][C]0.046087[/C][C]0.5173[/C][C]0.302918[/C][/ROW]
[ROW][C]5[/C][C]0.237219[/C][C]2.6628[/C][C]0.004381[/C][/ROW]
[ROW][C]6[/C][C]-0.129717[/C][C]-1.4561[/C][C]0.07393[/C][/ROW]
[ROW][C]7[/C][C]0.165549[/C][C]1.8583[/C][C]0.032731[/C][/ROW]
[ROW][C]8[/C][C]-0.249825[/C][C]-2.8043[/C][C]0.002921[/C][/ROW]
[ROW][C]9[/C][C]0.11171[/C][C]1.2539[/C][C]0.106092[/C][/ROW]
[ROW][C]10[/C][C]0.015418[/C][C]0.1731[/C][C]0.431439[/C][/ROW]
[ROW][C]11[/C][C]0.227208[/C][C]2.5504[/C][C]0.005979[/C][/ROW]
[ROW][C]12[/C][C]0.028771[/C][C]0.323[/C][C]0.373634[/C][/ROW]
[ROW][C]13[/C][C]-0.459295[/C][C]-5.1556[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.00232[/C][C]-0.026[/C][C]0.489631[/C][/ROW]
[ROW][C]15[/C][C]0.04021[/C][C]0.4514[/C][C]0.326254[/C][/ROW]
[ROW][C]16[/C][C]0.125412[/C][C]1.4077[/C][C]0.080835[/C][/ROW]
[ROW][C]17[/C][C]0.064103[/C][C]0.7196[/C][C]0.236565[/C][/ROW]
[ROW][C]18[/C][C]-0.044112[/C][C]-0.4952[/C][C]0.310676[/C][/ROW]
[ROW][C]19[/C][C]0.064175[/C][C]0.7204[/C][C]0.23632[/C][/ROW]
[ROW][C]20[/C][C]0.006823[/C][C]0.0766[/C][C]0.469535[/C][/ROW]
[ROW][C]21[/C][C]0.030998[/C][C]0.348[/C][C]0.364228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301224&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301224&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	0.911754	10.2344	0
2	0.152238	1.7089	0.044969
3	0.133248	1.4957	0.068615
4	0.046087	0.5173	0.302918
5	0.237219	2.6628	0.004381
6	-0.129717	-1.4561	0.07393
7	0.165549	1.8583	0.032731
8	-0.249825	-2.8043	0.002921
9	0.11171	1.2539	0.106092
10	0.015418	0.1731	0.431439
11	0.227208	2.5504	0.005979
12	0.028771	0.323	0.373634
13	-0.459295	-5.1556	0
14	-0.00232	-0.026	0.489631
15	0.04021	0.4514	0.326254
16	0.125412	1.4077	0.080835
17	0.064103	0.7196	0.236565
18	-0.044112	-0.4952	0.310676
19	0.064175	0.7204	0.23632
20	0.006823	0.0766	0.469535
21	0.030998	0.348	0.364228

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 ; par2 = -0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; 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 <- '0'
par2 <- '0.0'
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