Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 18 Nov 2013 15:54:29 -0500

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/2013/Nov/18/t1384808091uw0cran50l92jbc.htm/, Retrieved Sat, 27 Apr 2024 10:58:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226286, Retrieved Sat, 27 Apr 2024 10:58:35 +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] [] [2013-11-18 20:54:29] [23be8e4142dc0b2e5f6a7ba847207dc8] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

1,65
1,66
1,66
1,67
1,68
1,68
1,68
1,68
1,69
1,7
1,7
1,71
1,72
1,73
1,74
1,74
1,75
1,75
1,75
1,76
1,79
1,83
1,84
1,85
1,87
1,87
1,87
1,88
1,88
1,88
1,88
1,89
1,89
1,89
1,9
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,9
1,9
1,92
1,93
1,92
1,95
1,96
1,96
1,96
1,96
1,96
1,97
1,97
1,97
1,97
1,97
1,97
1,98
1,98
1,98
1,98
1,98
1,98
1,97
1,98
1,98
1,99
2
2

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226286&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226286&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226286&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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.958275	8.7827	0
2	0.915937	8.3947	0
3	0.8727	7.9984	0
4	0.830161	7.6086	0
5	0.788404	7.2258	0
6	0.746214	6.8392	0
7	0.700735	6.4223	0
8	0.653161	5.9863	0
9	0.606137	5.5553	0
10	0.559895	5.1315	1e-06
11	0.511443	4.6875	5e-06
12	0.463773	4.2506	2.7e-05
13	0.418431	3.835	0.000121
14	0.374103	3.4287	0.000471
15	0.331955	3.0424	0.001566
16	0.288876	2.6476	0.00484
17	0.24751	2.2685	0.012933
18	0.205213	1.8808	0.031731
19	0.163646	1.4998	0.068702

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.958275 & 8.7827 & 0 \tabularnewline
2 & 0.915937 & 8.3947 & 0 \tabularnewline
3 & 0.8727 & 7.9984 & 0 \tabularnewline
4 & 0.830161 & 7.6086 & 0 \tabularnewline
5 & 0.788404 & 7.2258 & 0 \tabularnewline
6 & 0.746214 & 6.8392 & 0 \tabularnewline
7 & 0.700735 & 6.4223 & 0 \tabularnewline
8 & 0.653161 & 5.9863 & 0 \tabularnewline
9 & 0.606137 & 5.5553 & 0 \tabularnewline
10 & 0.559895 & 5.1315 & 1e-06 \tabularnewline
11 & 0.511443 & 4.6875 & 5e-06 \tabularnewline
12 & 0.463773 & 4.2506 & 2.7e-05 \tabularnewline
13 & 0.418431 & 3.835 & 0.000121 \tabularnewline
14 & 0.374103 & 3.4287 & 0.000471 \tabularnewline
15 & 0.331955 & 3.0424 & 0.001566 \tabularnewline
16 & 0.288876 & 2.6476 & 0.00484 \tabularnewline
17 & 0.24751 & 2.2685 & 0.012933 \tabularnewline
18 & 0.205213 & 1.8808 & 0.031731 \tabularnewline
19 & 0.163646 & 1.4998 & 0.068702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226286&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]0.958275[/C][C]8.7827[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.915937[/C][C]8.3947[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.8727[/C][C]7.9984[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.830161[/C][C]7.6086[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.788404[/C][C]7.2258[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.746214[/C][C]6.8392[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.700735[/C][C]6.4223[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.653161[/C][C]5.9863[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.606137[/C][C]5.5553[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.559895[/C][C]5.1315[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.511443[/C][C]4.6875[/C][C]5e-06[/C][/ROW]
[ROW][C]12[/C][C]0.463773[/C][C]4.2506[/C][C]2.7e-05[/C][/ROW]
[ROW][C]13[/C][C]0.418431[/C][C]3.835[/C][C]0.000121[/C][/ROW]
[ROW][C]14[/C][C]0.374103[/C][C]3.4287[/C][C]0.000471[/C][/ROW]
[ROW][C]15[/C][C]0.331955[/C][C]3.0424[/C][C]0.001566[/C][/ROW]
[ROW][C]16[/C][C]0.288876[/C][C]2.6476[/C][C]0.00484[/C][/ROW]
[ROW][C]17[/C][C]0.24751[/C][C]2.2685[/C][C]0.012933[/C][/ROW]
[ROW][C]18[/C][C]0.205213[/C][C]1.8808[/C][C]0.031731[/C][/ROW]
[ROW][C]19[/C][C]0.163646[/C][C]1.4998[/C][C]0.068702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226286&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226286&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	0.958275	8.7827	0
2	0.915937	8.3947	0
3	0.8727	7.9984	0
4	0.830161	7.6086	0
5	0.788404	7.2258	0
6	0.746214	6.8392	0
7	0.700735	6.4223	0
8	0.653161	5.9863	0
9	0.606137	5.5553	0
10	0.559895	5.1315	1e-06
11	0.511443	4.6875	5e-06
12	0.463773	4.2506	2.7e-05
13	0.418431	3.835	0.000121
14	0.374103	3.4287	0.000471
15	0.331955	3.0424	0.001566
16	0.288876	2.6476	0.00484
17	0.24751	2.2685	0.012933
18	0.205213	1.8808	0.031731
19	0.163646	1.4998	0.068702

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.958275	8.7827	0
2	-0.028817	-0.2641	0.396172
3	-0.033056	-0.303	0.381333
4	-0.01438	-0.1318	0.447732
5	-0.013648	-0.1251	0.450377
6	-0.028984	-0.2656	0.395582
7	-0.064612	-0.5922	0.277661
8	-0.051809	-0.4748	0.318068
9	-0.020973	-0.1922	0.424018
10	-0.02002	-0.1835	0.427428
11	-0.058533	-0.5365	0.296527
12	-0.022563	-0.2068	0.418334
13	-0.001295	-0.0119	0.495279
14	-0.018264	-0.1674	0.43373
15	-0.006391	-0.0586	0.476715
16	-0.043857	-0.402	0.344368
17	-0.009924	-0.091	0.463871
18	-0.043312	-0.397	0.346201
19	-0.029064	-0.2664	0.3953

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.958275 & 8.7827 & 0 \tabularnewline
2 & -0.028817 & -0.2641 & 0.396172 \tabularnewline
3 & -0.033056 & -0.303 & 0.381333 \tabularnewline
4 & -0.01438 & -0.1318 & 0.447732 \tabularnewline
5 & -0.013648 & -0.1251 & 0.450377 \tabularnewline
6 & -0.028984 & -0.2656 & 0.395582 \tabularnewline
7 & -0.064612 & -0.5922 & 0.277661 \tabularnewline
8 & -0.051809 & -0.4748 & 0.318068 \tabularnewline
9 & -0.020973 & -0.1922 & 0.424018 \tabularnewline
10 & -0.02002 & -0.1835 & 0.427428 \tabularnewline
11 & -0.058533 & -0.5365 & 0.296527 \tabularnewline
12 & -0.022563 & -0.2068 & 0.418334 \tabularnewline
13 & -0.001295 & -0.0119 & 0.495279 \tabularnewline
14 & -0.018264 & -0.1674 & 0.43373 \tabularnewline
15 & -0.006391 & -0.0586 & 0.476715 \tabularnewline
16 & -0.043857 & -0.402 & 0.344368 \tabularnewline
17 & -0.009924 & -0.091 & 0.463871 \tabularnewline
18 & -0.043312 & -0.397 & 0.346201 \tabularnewline
19 & -0.029064 & -0.2664 & 0.3953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226286&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]0.958275[/C][C]8.7827[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.028817[/C][C]-0.2641[/C][C]0.396172[/C][/ROW]
[ROW][C]3[/C][C]-0.033056[/C][C]-0.303[/C][C]0.381333[/C][/ROW]
[ROW][C]4[/C][C]-0.01438[/C][C]-0.1318[/C][C]0.447732[/C][/ROW]
[ROW][C]5[/C][C]-0.013648[/C][C]-0.1251[/C][C]0.450377[/C][/ROW]
[ROW][C]6[/C][C]-0.028984[/C][C]-0.2656[/C][C]0.395582[/C][/ROW]
[ROW][C]7[/C][C]-0.064612[/C][C]-0.5922[/C][C]0.277661[/C][/ROW]
[ROW][C]8[/C][C]-0.051809[/C][C]-0.4748[/C][C]0.318068[/C][/ROW]
[ROW][C]9[/C][C]-0.020973[/C][C]-0.1922[/C][C]0.424018[/C][/ROW]
[ROW][C]10[/C][C]-0.02002[/C][C]-0.1835[/C][C]0.427428[/C][/ROW]
[ROW][C]11[/C][C]-0.058533[/C][C]-0.5365[/C][C]0.296527[/C][/ROW]
[ROW][C]12[/C][C]-0.022563[/C][C]-0.2068[/C][C]0.418334[/C][/ROW]
[ROW][C]13[/C][C]-0.001295[/C][C]-0.0119[/C][C]0.495279[/C][/ROW]
[ROW][C]14[/C][C]-0.018264[/C][C]-0.1674[/C][C]0.43373[/C][/ROW]
[ROW][C]15[/C][C]-0.006391[/C][C]-0.0586[/C][C]0.476715[/C][/ROW]
[ROW][C]16[/C][C]-0.043857[/C][C]-0.402[/C][C]0.344368[/C][/ROW]
[ROW][C]17[/C][C]-0.009924[/C][C]-0.091[/C][C]0.463871[/C][/ROW]
[ROW][C]18[/C][C]-0.043312[/C][C]-0.397[/C][C]0.346201[/C][/ROW]
[ROW][C]19[/C][C]-0.029064[/C][C]-0.2664[/C][C]0.3953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226286&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226286&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	0.958275	8.7827	0
2	-0.028817	-0.2641	0.396172
3	-0.033056	-0.303	0.381333
4	-0.01438	-0.1318	0.447732
5	-0.013648	-0.1251	0.450377
6	-0.028984	-0.2656	0.395582
7	-0.064612	-0.5922	0.277661
8	-0.051809	-0.4748	0.318068
9	-0.020973	-0.1922	0.424018
10	-0.02002	-0.1835	0.427428
11	-0.058533	-0.5365	0.296527
12	-0.022563	-0.2068	0.418334
13	-0.001295	-0.0119	0.495279
14	-0.018264	-0.1674	0.43373
15	-0.006391	-0.0586	0.476715
16	-0.043857	-0.402	0.344368
17	-0.009924	-0.091	0.463871
18	-0.043312	-0.397	0.346201
19	-0.029064	-0.2664	0.3953

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 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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)
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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