Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 15:37:13 +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/18/t1482071946n6x33u50kuk0g0k.htm/, Retrieved Wed, 08 May 2024 21:23:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301111, Retrieved Wed, 08 May 2024 21:23:33 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [Partial Autocorre...] [2016-12-18 14:37:13] [3b055ff671ad33431c4331443bac114d] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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=301111&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=301111&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301111&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	-0.265608	-1.8968	0.031761
2	-0.20082	-1.4341	0.078818
3	0.130705	0.9334	0.177501
4	0.079073	0.5647	0.287378
5	-0.056563	-0.4039	0.343972
6	-0.017634	-0.1259	0.450141
7	0.204451	1.4601	0.075201
8	-0.146892	-1.049	0.149558
9	-0.042908	-0.3064	0.380263
10	-0.01074	-0.0767	0.469582
11	0.015179	0.1084	0.457051
12	-0.044227	-0.3158	0.376706

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.265608 & -1.8968 & 0.031761 \tabularnewline
2 & -0.20082 & -1.4341 & 0.078818 \tabularnewline
3 & 0.130705 & 0.9334 & 0.177501 \tabularnewline
4 & 0.079073 & 0.5647 & 0.287378 \tabularnewline
5 & -0.056563 & -0.4039 & 0.343972 \tabularnewline
6 & -0.017634 & -0.1259 & 0.450141 \tabularnewline
7 & 0.204451 & 1.4601 & 0.075201 \tabularnewline
8 & -0.146892 & -1.049 & 0.149558 \tabularnewline
9 & -0.042908 & -0.3064 & 0.380263 \tabularnewline
10 & -0.01074 & -0.0767 & 0.469582 \tabularnewline
11 & 0.015179 & 0.1084 & 0.457051 \tabularnewline
12 & -0.044227 & -0.3158 & 0.376706 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301111&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]-0.265608[/C][C]-1.8968[/C][C]0.031761[/C][/ROW]
[ROW][C]2[/C][C]-0.20082[/C][C]-1.4341[/C][C]0.078818[/C][/ROW]
[ROW][C]3[/C][C]0.130705[/C][C]0.9334[/C][C]0.177501[/C][/ROW]
[ROW][C]4[/C][C]0.079073[/C][C]0.5647[/C][C]0.287378[/C][/ROW]
[ROW][C]5[/C][C]-0.056563[/C][C]-0.4039[/C][C]0.343972[/C][/ROW]
[ROW][C]6[/C][C]-0.017634[/C][C]-0.1259[/C][C]0.450141[/C][/ROW]
[ROW][C]7[/C][C]0.204451[/C][C]1.4601[/C][C]0.075201[/C][/ROW]
[ROW][C]8[/C][C]-0.146892[/C][C]-1.049[/C][C]0.149558[/C][/ROW]
[ROW][C]9[/C][C]-0.042908[/C][C]-0.3064[/C][C]0.380263[/C][/ROW]
[ROW][C]10[/C][C]-0.01074[/C][C]-0.0767[/C][C]0.469582[/C][/ROW]
[ROW][C]11[/C][C]0.015179[/C][C]0.1084[/C][C]0.457051[/C][/ROW]
[ROW][C]12[/C][C]-0.044227[/C][C]-0.3158[/C][C]0.376706[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301111&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301111&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	-0.265608	-1.8968	0.031761
2	-0.20082	-1.4341	0.078818
3	0.130705	0.9334	0.177501
4	0.079073	0.5647	0.287378
5	-0.056563	-0.4039	0.343972
6	-0.017634	-0.1259	0.450141
7	0.204451	1.4601	0.075201
8	-0.146892	-1.049	0.149558
9	-0.042908	-0.3064	0.380263
10	-0.01074	-0.0767	0.469582
11	0.015179	0.1084	0.457051
12	-0.044227	-0.3158	0.376706

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.265608	-1.8968	0.031761
2	-0.291965	-2.085	0.021045
3	-0.018531	-0.1323	0.447618
4	0.07036	0.5025	0.30875
5	0.031969	0.2283	0.410163
6	0.008817	0.063	0.475019
7	0.212826	1.5199	0.067358
8	-0.031824	-0.2273	0.410562
9	-0.019969	-0.1426	0.443581
10	-0.129706	-0.9263	0.179329
11	-0.07913	-0.5651	0.28724
12	-0.089672	-0.6404	0.262394

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.265608 & -1.8968 & 0.031761 \tabularnewline
2 & -0.291965 & -2.085 & 0.021045 \tabularnewline
3 & -0.018531 & -0.1323 & 0.447618 \tabularnewline
4 & 0.07036 & 0.5025 & 0.30875 \tabularnewline
5 & 0.031969 & 0.2283 & 0.410163 \tabularnewline
6 & 0.008817 & 0.063 & 0.475019 \tabularnewline
7 & 0.212826 & 1.5199 & 0.067358 \tabularnewline
8 & -0.031824 & -0.2273 & 0.410562 \tabularnewline
9 & -0.019969 & -0.1426 & 0.443581 \tabularnewline
10 & -0.129706 & -0.9263 & 0.179329 \tabularnewline
11 & -0.07913 & -0.5651 & 0.28724 \tabularnewline
12 & -0.089672 & -0.6404 & 0.262394 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301111&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]-0.265608[/C][C]-1.8968[/C][C]0.031761[/C][/ROW]
[ROW][C]2[/C][C]-0.291965[/C][C]-2.085[/C][C]0.021045[/C][/ROW]
[ROW][C]3[/C][C]-0.018531[/C][C]-0.1323[/C][C]0.447618[/C][/ROW]
[ROW][C]4[/C][C]0.07036[/C][C]0.5025[/C][C]0.30875[/C][/ROW]
[ROW][C]5[/C][C]0.031969[/C][C]0.2283[/C][C]0.410163[/C][/ROW]
[ROW][C]6[/C][C]0.008817[/C][C]0.063[/C][C]0.475019[/C][/ROW]
[ROW][C]7[/C][C]0.212826[/C][C]1.5199[/C][C]0.067358[/C][/ROW]
[ROW][C]8[/C][C]-0.031824[/C][C]-0.2273[/C][C]0.410562[/C][/ROW]
[ROW][C]9[/C][C]-0.019969[/C][C]-0.1426[/C][C]0.443581[/C][/ROW]
[ROW][C]10[/C][C]-0.129706[/C][C]-0.9263[/C][C]0.179329[/C][/ROW]
[ROW][C]11[/C][C]-0.07913[/C][C]-0.5651[/C][C]0.28724[/C][/ROW]
[ROW][C]12[/C][C]-0.089672[/C][C]-0.6404[/C][C]0.262394[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301111&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301111&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	-0.265608	-1.8968	0.031761
2	-0.291965	-2.085	0.021045
3	-0.018531	-0.1323	0.447618
4	0.07036	0.5025	0.30875
5	0.031969	0.2283	0.410163
6	0.008817	0.063	0.475019
7	0.212826	1.5199	0.067358
8	-0.031824	-0.2273	0.410562
9	-0.019969	-0.1426	0.443581
10	-0.129706	-0.9263	0.179329
11	-0.07913	-0.5651	0.28724
12	-0.089672	-0.6404	0.262394

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; 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