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

Fri, 23 Dec 2016 10:57:02 +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/23/t1482487077u7m9qzyom4kw64s.htm/, Retrieved Tue, 07 May 2024 05:49:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302829, Retrieved Tue, 07 May 2024 05:49:13 +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] [autocorrelation f...] [2016-12-23 09:57:02] [bd7223969ac5b08f41438741a34686d6] [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=302829&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=302829&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302829&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	-0.110017	-1.138	0.128826
2	0.044289	0.4581	0.323896
3	-0.084472	-0.8738	0.192096
4	-0.003808	-0.0394	0.484327
5	0.002322	0.024	0.490443
6	-0.047749	-0.4939	0.311189
7	-0.041561	-0.4299	0.334063
8	0.045548	0.4712	0.319245
9	-0.072468	-0.7496	0.227566
10	0.090333	0.9344	0.176099
11	-0.031487	-0.3257	0.372641
12	0.019801	0.2048	0.419049
13	-0.154522	-1.5984	0.056452
14	-0.008433	-0.0872	0.465327
15	-0.048212	-0.4987	0.309504
16	-0.062571	-0.6472	0.259432
17	-0.056914	-0.5887	0.278645
18	-0.116457	-1.2046	0.1155
19	0.135406	1.4007	0.082105
20	0.09163	0.9478	0.172676

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.110017 & -1.138 & 0.128826 \tabularnewline
2 & 0.044289 & 0.4581 & 0.323896 \tabularnewline
3 & -0.084472 & -0.8738 & 0.192096 \tabularnewline
4 & -0.003808 & -0.0394 & 0.484327 \tabularnewline
5 & 0.002322 & 0.024 & 0.490443 \tabularnewline
6 & -0.047749 & -0.4939 & 0.311189 \tabularnewline
7 & -0.041561 & -0.4299 & 0.334063 \tabularnewline
8 & 0.045548 & 0.4712 & 0.319245 \tabularnewline
9 & -0.072468 & -0.7496 & 0.227566 \tabularnewline
10 & 0.090333 & 0.9344 & 0.176099 \tabularnewline
11 & -0.031487 & -0.3257 & 0.372641 \tabularnewline
12 & 0.019801 & 0.2048 & 0.419049 \tabularnewline
13 & -0.154522 & -1.5984 & 0.056452 \tabularnewline
14 & -0.008433 & -0.0872 & 0.465327 \tabularnewline
15 & -0.048212 & -0.4987 & 0.309504 \tabularnewline
16 & -0.062571 & -0.6472 & 0.259432 \tabularnewline
17 & -0.056914 & -0.5887 & 0.278645 \tabularnewline
18 & -0.116457 & -1.2046 & 0.1155 \tabularnewline
19 & 0.135406 & 1.4007 & 0.082105 \tabularnewline
20 & 0.09163 & 0.9478 & 0.172676 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302829&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]-0.110017[/C][C]-1.138[/C][C]0.128826[/C][/ROW]
[ROW][C]2[/C][C]0.044289[/C][C]0.4581[/C][C]0.323896[/C][/ROW]
[ROW][C]3[/C][C]-0.084472[/C][C]-0.8738[/C][C]0.192096[/C][/ROW]
[ROW][C]4[/C][C]-0.003808[/C][C]-0.0394[/C][C]0.484327[/C][/ROW]
[ROW][C]5[/C][C]0.002322[/C][C]0.024[/C][C]0.490443[/C][/ROW]
[ROW][C]6[/C][C]-0.047749[/C][C]-0.4939[/C][C]0.311189[/C][/ROW]
[ROW][C]7[/C][C]-0.041561[/C][C]-0.4299[/C][C]0.334063[/C][/ROW]
[ROW][C]8[/C][C]0.045548[/C][C]0.4712[/C][C]0.319245[/C][/ROW]
[ROW][C]9[/C][C]-0.072468[/C][C]-0.7496[/C][C]0.227566[/C][/ROW]
[ROW][C]10[/C][C]0.090333[/C][C]0.9344[/C][C]0.176099[/C][/ROW]
[ROW][C]11[/C][C]-0.031487[/C][C]-0.3257[/C][C]0.372641[/C][/ROW]
[ROW][C]12[/C][C]0.019801[/C][C]0.2048[/C][C]0.419049[/C][/ROW]
[ROW][C]13[/C][C]-0.154522[/C][C]-1.5984[/C][C]0.056452[/C][/ROW]
[ROW][C]14[/C][C]-0.008433[/C][C]-0.0872[/C][C]0.465327[/C][/ROW]
[ROW][C]15[/C][C]-0.048212[/C][C]-0.4987[/C][C]0.309504[/C][/ROW]
[ROW][C]16[/C][C]-0.062571[/C][C]-0.6472[/C][C]0.259432[/C][/ROW]
[ROW][C]17[/C][C]-0.056914[/C][C]-0.5887[/C][C]0.278645[/C][/ROW]
[ROW][C]18[/C][C]-0.116457[/C][C]-1.2046[/C][C]0.1155[/C][/ROW]
[ROW][C]19[/C][C]0.135406[/C][C]1.4007[/C][C]0.082105[/C][/ROW]
[ROW][C]20[/C][C]0.09163[/C][C]0.9478[/C][C]0.172676[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302829&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302829&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	-0.110017	-1.138	0.128826
2	0.044289	0.4581	0.323896
3	-0.084472	-0.8738	0.192096
4	-0.003808	-0.0394	0.484327
5	0.002322	0.024	0.490443
6	-0.047749	-0.4939	0.311189
7	-0.041561	-0.4299	0.334063
8	0.045548	0.4712	0.319245
9	-0.072468	-0.7496	0.227566
10	0.090333	0.9344	0.176099
11	-0.031487	-0.3257	0.372641
12	0.019801	0.2048	0.419049
13	-0.154522	-1.5984	0.056452
14	-0.008433	-0.0872	0.465327
15	-0.048212	-0.4987	0.309504
16	-0.062571	-0.6472	0.259432
17	-0.056914	-0.5887	0.278645
18	-0.116457	-1.2046	0.1155
19	0.135406	1.4007	0.082105
20	0.09163	0.9478	0.172676

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.110017	-1.138	0.128826
2	0.032579	0.337	0.368388
3	-0.077189	-0.7984	0.213189
4	-0.022587	-0.2336	0.407855
5	0.005162	0.0534	0.478757
6	-0.053642	-0.5549	0.290069
7	-0.055839	-0.5776	0.282373
8	0.039879	0.4125	0.340393
9	-0.070881	-0.7332	0.23252
10	0.065346	0.6759	0.250266
11	-0.005437	-0.0562	0.477627
12	-0.002212	-0.0229	0.490895
13	-0.150739	-1.5593	0.060944
14	-0.03876	-0.4009	0.344633
15	-0.052514	-0.5432	0.294057
16	-0.100788	-1.0426	0.149752
17	-0.076745	-0.7939	0.214518
18	-0.159614	-1.6511	0.050829
19	0.089577	0.9266	0.178113
20	0.088699	0.9175	0.180469

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.110017 & -1.138 & 0.128826 \tabularnewline
2 & 0.032579 & 0.337 & 0.368388 \tabularnewline
3 & -0.077189 & -0.7984 & 0.213189 \tabularnewline
4 & -0.022587 & -0.2336 & 0.407855 \tabularnewline
5 & 0.005162 & 0.0534 & 0.478757 \tabularnewline
6 & -0.053642 & -0.5549 & 0.290069 \tabularnewline
7 & -0.055839 & -0.5776 & 0.282373 \tabularnewline
8 & 0.039879 & 0.4125 & 0.340393 \tabularnewline
9 & -0.070881 & -0.7332 & 0.23252 \tabularnewline
10 & 0.065346 & 0.6759 & 0.250266 \tabularnewline
11 & -0.005437 & -0.0562 & 0.477627 \tabularnewline
12 & -0.002212 & -0.0229 & 0.490895 \tabularnewline
13 & -0.150739 & -1.5593 & 0.060944 \tabularnewline
14 & -0.03876 & -0.4009 & 0.344633 \tabularnewline
15 & -0.052514 & -0.5432 & 0.294057 \tabularnewline
16 & -0.100788 & -1.0426 & 0.149752 \tabularnewline
17 & -0.076745 & -0.7939 & 0.214518 \tabularnewline
18 & -0.159614 & -1.6511 & 0.050829 \tabularnewline
19 & 0.089577 & 0.9266 & 0.178113 \tabularnewline
20 & 0.088699 & 0.9175 & 0.180469 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302829&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]-0.110017[/C][C]-1.138[/C][C]0.128826[/C][/ROW]
[ROW][C]2[/C][C]0.032579[/C][C]0.337[/C][C]0.368388[/C][/ROW]
[ROW][C]3[/C][C]-0.077189[/C][C]-0.7984[/C][C]0.213189[/C][/ROW]
[ROW][C]4[/C][C]-0.022587[/C][C]-0.2336[/C][C]0.407855[/C][/ROW]
[ROW][C]5[/C][C]0.005162[/C][C]0.0534[/C][C]0.478757[/C][/ROW]
[ROW][C]6[/C][C]-0.053642[/C][C]-0.5549[/C][C]0.290069[/C][/ROW]
[ROW][C]7[/C][C]-0.055839[/C][C]-0.5776[/C][C]0.282373[/C][/ROW]
[ROW][C]8[/C][C]0.039879[/C][C]0.4125[/C][C]0.340393[/C][/ROW]
[ROW][C]9[/C][C]-0.070881[/C][C]-0.7332[/C][C]0.23252[/C][/ROW]
[ROW][C]10[/C][C]0.065346[/C][C]0.6759[/C][C]0.250266[/C][/ROW]
[ROW][C]11[/C][C]-0.005437[/C][C]-0.0562[/C][C]0.477627[/C][/ROW]
[ROW][C]12[/C][C]-0.002212[/C][C]-0.0229[/C][C]0.490895[/C][/ROW]
[ROW][C]13[/C][C]-0.150739[/C][C]-1.5593[/C][C]0.060944[/C][/ROW]
[ROW][C]14[/C][C]-0.03876[/C][C]-0.4009[/C][C]0.344633[/C][/ROW]
[ROW][C]15[/C][C]-0.052514[/C][C]-0.5432[/C][C]0.294057[/C][/ROW]
[ROW][C]16[/C][C]-0.100788[/C][C]-1.0426[/C][C]0.149752[/C][/ROW]
[ROW][C]17[/C][C]-0.076745[/C][C]-0.7939[/C][C]0.214518[/C][/ROW]
[ROW][C]18[/C][C]-0.159614[/C][C]-1.6511[/C][C]0.050829[/C][/ROW]
[ROW][C]19[/C][C]0.089577[/C][C]0.9266[/C][C]0.178113[/C][/ROW]
[ROW][C]20[/C][C]0.088699[/C][C]0.9175[/C][C]0.180469[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302829&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302829&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	-0.110017	-1.138	0.128826
2	0.032579	0.337	0.368388
3	-0.077189	-0.7984	0.213189
4	-0.022587	-0.2336	0.407855
5	0.005162	0.0534	0.478757
6	-0.053642	-0.5549	0.290069
7	-0.055839	-0.5776	0.282373
8	0.039879	0.4125	0.340393
9	-0.070881	-0.7332	0.23252
10	0.065346	0.6759	0.250266
11	-0.005437	-0.0562	0.477627
12	-0.002212	-0.0229	0.490895
13	-0.150739	-1.5593	0.060944
14	-0.03876	-0.4009	0.344633
15	-0.052514	-0.5432	0.294057
16	-0.100788	-1.0426	0.149752
17	-0.076745	-0.7939	0.214518
18	-0.159614	-1.6511	0.050829
19	0.089577	0.9266	0.178113
20	0.088699	0.9175	0.180469

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 = Default ; par2 = -1.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -1.0 ; 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