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

Wed, 20 Nov 2013 05:41:11 -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/20/t1384944120j6j6xz0bbr1dk35.htm/, Retrieved Wed, 01 May 2024 22:19:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226587, Retrieved Wed, 01 May 2024 22:19:17 +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

105

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

-       [(Partial) Autocorrelation Function] [] [2013-11-20 10:41:11] [12e977ea58b1a83461bd6217bf886aa8] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

3.96
3.97
3.96
3.95
3.94
3.94
3.95
3.93
3.94
3.92
3.95
3.94
3.95
3.92
3.92
3.92
3.92
3.9
3.92
3.94
3.96
3.95
3.96
3.97
3.99
4
4.05
4.08
4.09
4.12
4.14
4.15
4.15
4.15
4.15
4.2
4.22
4.22
4.22
4.23
4.3
4.29
4.32
4.31
4.35
4.34
4.35
4.38
4.39
4.38
4.34
4.33
4.33
4.33
4.33
4.32
4.35
4.35
4.35
4.36
4.38
4.41
4.43
4.42
4.43
4.43
4.42
4.46
4.44
4.41
4.41
4.46
4.5
4.58
4.61
4.65
4.55
4.63
4.69
4.72
4.71
4.74
4.77
4.78

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226587&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226587&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226587&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.95877	8.7873	0
2	0.917731	8.4111	0
3	0.877073	8.0385	0
4	0.839363	7.6929	0
5	0.795929	7.2948	0
6	0.753837	6.909	0
7	0.716129	6.5634	0
8	0.683385	6.2633	0
9	0.639202	5.8584	0
10	0.597645	5.4775	0
11	0.559376	5.1268	1e-06
12	0.526918	4.8293	3e-06
13	0.497779	4.5622	9e-06
14	0.47098	4.3166	2.2e-05
15	0.443116	4.0612	5.5e-05
16	0.411914	3.7753	0.000149
17	0.377081	3.456	0.000431
18	0.34358	3.149	0.001135
19	0.3087	2.8293	0.002917

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95877 & 8.7873 & 0 \tabularnewline
2 & 0.917731 & 8.4111 & 0 \tabularnewline
3 & 0.877073 & 8.0385 & 0 \tabularnewline
4 & 0.839363 & 7.6929 & 0 \tabularnewline
5 & 0.795929 & 7.2948 & 0 \tabularnewline
6 & 0.753837 & 6.909 & 0 \tabularnewline
7 & 0.716129 & 6.5634 & 0 \tabularnewline
8 & 0.683385 & 6.2633 & 0 \tabularnewline
9 & 0.639202 & 5.8584 & 0 \tabularnewline
10 & 0.597645 & 5.4775 & 0 \tabularnewline
11 & 0.559376 & 5.1268 & 1e-06 \tabularnewline
12 & 0.526918 & 4.8293 & 3e-06 \tabularnewline
13 & 0.497779 & 4.5622 & 9e-06 \tabularnewline
14 & 0.47098 & 4.3166 & 2.2e-05 \tabularnewline
15 & 0.443116 & 4.0612 & 5.5e-05 \tabularnewline
16 & 0.411914 & 3.7753 & 0.000149 \tabularnewline
17 & 0.377081 & 3.456 & 0.000431 \tabularnewline
18 & 0.34358 & 3.149 & 0.001135 \tabularnewline
19 & 0.3087 & 2.8293 & 0.002917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226587&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]0.95877[/C][C]8.7873[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.917731[/C][C]8.4111[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.877073[/C][C]8.0385[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.839363[/C][C]7.6929[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.795929[/C][C]7.2948[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.753837[/C][C]6.909[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.716129[/C][C]6.5634[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.683385[/C][C]6.2633[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.639202[/C][C]5.8584[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.597645[/C][C]5.4775[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.559376[/C][C]5.1268[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.526918[/C][C]4.8293[/C][C]3e-06[/C][/ROW]
[ROW][C]13[/C][C]0.497779[/C][C]4.5622[/C][C]9e-06[/C][/ROW]
[ROW][C]14[/C][C]0.47098[/C][C]4.3166[/C][C]2.2e-05[/C][/ROW]
[ROW][C]15[/C][C]0.443116[/C][C]4.0612[/C][C]5.5e-05[/C][/ROW]
[ROW][C]16[/C][C]0.411914[/C][C]3.7753[/C][C]0.000149[/C][/ROW]
[ROW][C]17[/C][C]0.377081[/C][C]3.456[/C][C]0.000431[/C][/ROW]
[ROW][C]18[/C][C]0.34358[/C][C]3.149[/C][C]0.001135[/C][/ROW]
[ROW][C]19[/C][C]0.3087[/C][C]2.8293[/C][C]0.002917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226587&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226587&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	0.95877	8.7873	0
2	0.917731	8.4111	0
3	0.877073	8.0385	0
4	0.839363	7.6929	0
5	0.795929	7.2948	0
6	0.753837	6.909	0
7	0.716129	6.5634	0
8	0.683385	6.2633	0
9	0.639202	5.8584	0
10	0.597645	5.4775	0
11	0.559376	5.1268	1e-06
12	0.526918	4.8293	3e-06
13	0.497779	4.5622	9e-06
14	0.47098	4.3166	2.2e-05
15	0.443116	4.0612	5.5e-05
16	0.411914	3.7753	0.000149
17	0.377081	3.456	0.000431
18	0.34358	3.149	0.001135
19	0.3087	2.8293	0.002917

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.95877	8.7873	0
2	-0.018694	-0.1713	0.432185
3	-0.016673	-0.1528	0.439455
4	0.014884	0.1364	0.44591
5	-0.091306	-0.8368	0.20253
6	-0.007293	-0.0668	0.473433
7	0.03144	0.2881	0.386971
8	0.035081	0.3215	0.374307
9	-0.156688	-1.4361	0.077348
10	0.008964	0.0822	0.467359
11	0.013126	0.1203	0.452266
12	0.033261	0.3048	0.38062
13	0.044334	0.4063	0.342767
14	0.010021	0.0918	0.463519
15	-0.045189	-0.4142	0.339906
16	-0.080263	-0.7356	0.232005
17	-0.045364	-0.4158	0.339321
18	-0.008398	-0.077	0.469417
19	-0.038549	-0.3533	0.36237

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95877 & 8.7873 & 0 \tabularnewline
2 & -0.018694 & -0.1713 & 0.432185 \tabularnewline
3 & -0.016673 & -0.1528 & 0.439455 \tabularnewline
4 & 0.014884 & 0.1364 & 0.44591 \tabularnewline
5 & -0.091306 & -0.8368 & 0.20253 \tabularnewline
6 & -0.007293 & -0.0668 & 0.473433 \tabularnewline
7 & 0.03144 & 0.2881 & 0.386971 \tabularnewline
8 & 0.035081 & 0.3215 & 0.374307 \tabularnewline
9 & -0.156688 & -1.4361 & 0.077348 \tabularnewline
10 & 0.008964 & 0.0822 & 0.467359 \tabularnewline
11 & 0.013126 & 0.1203 & 0.452266 \tabularnewline
12 & 0.033261 & 0.3048 & 0.38062 \tabularnewline
13 & 0.044334 & 0.4063 & 0.342767 \tabularnewline
14 & 0.010021 & 0.0918 & 0.463519 \tabularnewline
15 & -0.045189 & -0.4142 & 0.339906 \tabularnewline
16 & -0.080263 & -0.7356 & 0.232005 \tabularnewline
17 & -0.045364 & -0.4158 & 0.339321 \tabularnewline
18 & -0.008398 & -0.077 & 0.469417 \tabularnewline
19 & -0.038549 & -0.3533 & 0.36237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226587&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]0.95877[/C][C]8.7873[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.018694[/C][C]-0.1713[/C][C]0.432185[/C][/ROW]
[ROW][C]3[/C][C]-0.016673[/C][C]-0.1528[/C][C]0.439455[/C][/ROW]
[ROW][C]4[/C][C]0.014884[/C][C]0.1364[/C][C]0.44591[/C][/ROW]
[ROW][C]5[/C][C]-0.091306[/C][C]-0.8368[/C][C]0.20253[/C][/ROW]
[ROW][C]6[/C][C]-0.007293[/C][C]-0.0668[/C][C]0.473433[/C][/ROW]
[ROW][C]7[/C][C]0.03144[/C][C]0.2881[/C][C]0.386971[/C][/ROW]
[ROW][C]8[/C][C]0.035081[/C][C]0.3215[/C][C]0.374307[/C][/ROW]
[ROW][C]9[/C][C]-0.156688[/C][C]-1.4361[/C][C]0.077348[/C][/ROW]
[ROW][C]10[/C][C]0.008964[/C][C]0.0822[/C][C]0.467359[/C][/ROW]
[ROW][C]11[/C][C]0.013126[/C][C]0.1203[/C][C]0.452266[/C][/ROW]
[ROW][C]12[/C][C]0.033261[/C][C]0.3048[/C][C]0.38062[/C][/ROW]
[ROW][C]13[/C][C]0.044334[/C][C]0.4063[/C][C]0.342767[/C][/ROW]
[ROW][C]14[/C][C]0.010021[/C][C]0.0918[/C][C]0.463519[/C][/ROW]
[ROW][C]15[/C][C]-0.045189[/C][C]-0.4142[/C][C]0.339906[/C][/ROW]
[ROW][C]16[/C][C]-0.080263[/C][C]-0.7356[/C][C]0.232005[/C][/ROW]
[ROW][C]17[/C][C]-0.045364[/C][C]-0.4158[/C][C]0.339321[/C][/ROW]
[ROW][C]18[/C][C]-0.008398[/C][C]-0.077[/C][C]0.469417[/C][/ROW]
[ROW][C]19[/C][C]-0.038549[/C][C]-0.3533[/C][C]0.36237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226587&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226587&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	0.95877	8.7873	0
2	-0.018694	-0.1713	0.432185
3	-0.016673	-0.1528	0.439455
4	0.014884	0.1364	0.44591
5	-0.091306	-0.8368	0.20253
6	-0.007293	-0.0668	0.473433
7	0.03144	0.2881	0.386971
8	0.035081	0.3215	0.374307
9	-0.156688	-1.4361	0.077348
10	0.008964	0.0822	0.467359
11	0.013126	0.1203	0.452266
12	0.033261	0.3048	0.38062
13	0.044334	0.4063	0.342767
14	0.010021	0.0918	0.463519
15	-0.045189	-0.4142	0.339906
16	-0.080263	-0.7356	0.232005
17	-0.045364	-0.4158	0.339321
18	-0.008398	-0.077	0.469417
19	-0.038549	-0.3533	0.36237

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