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

Thu, 11 Dec 2014 11:45:37 +0000

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/2014/Dec/11/t14182983567hvkh6fu4awxlhq.htm/, Retrieved Thu, 16 May 2024 05:56:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=265788, Retrieved Thu, 16 May 2024 05:56:16 +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] [stationariteit in...] [2014-12-11 11:45:37] [80d519c92fcb7b7b3d91f00690b8e112] [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	'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265788&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265788&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265788&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.50622	-5.2364	0
2	-0.053972	-0.5583	0.288907
3	0.155049	1.6038	0.055848
4	-0.226313	-2.341	0.010543
5	0.17261	1.7855	0.038507
6	0.102859	1.064	0.144865
7	-0.222252	-2.299	0.011724
8	0.004609	0.0477	0.481032
9	0.246474	2.5495	0.006102
10	-0.261181	-2.7017	0.004012
11	0.250522	2.5914	0.005446
12	-0.190701	-1.9726	0.025559
13	-0.184578	-1.9093	0.029452
14	0.337963	3.4959	0.000344
15	-0.105519	-1.0915	0.138753
16	-0.051431	-0.532	0.297912
17	0.072682	0.7518	0.226902
18	-0.02135	-0.2208	0.412817
19	-0.047386	-0.4902	0.31251
20	0.058701	0.6072	0.272499

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.50622 & -5.2364 & 0 \tabularnewline
2 & -0.053972 & -0.5583 & 0.288907 \tabularnewline
3 & 0.155049 & 1.6038 & 0.055848 \tabularnewline
4 & -0.226313 & -2.341 & 0.010543 \tabularnewline
5 & 0.17261 & 1.7855 & 0.038507 \tabularnewline
6 & 0.102859 & 1.064 & 0.144865 \tabularnewline
7 & -0.222252 & -2.299 & 0.011724 \tabularnewline
8 & 0.004609 & 0.0477 & 0.481032 \tabularnewline
9 & 0.246474 & 2.5495 & 0.006102 \tabularnewline
10 & -0.261181 & -2.7017 & 0.004012 \tabularnewline
11 & 0.250522 & 2.5914 & 0.005446 \tabularnewline
12 & -0.190701 & -1.9726 & 0.025559 \tabularnewline
13 & -0.184578 & -1.9093 & 0.029452 \tabularnewline
14 & 0.337963 & 3.4959 & 0.000344 \tabularnewline
15 & -0.105519 & -1.0915 & 0.138753 \tabularnewline
16 & -0.051431 & -0.532 & 0.297912 \tabularnewline
17 & 0.072682 & 0.7518 & 0.226902 \tabularnewline
18 & -0.02135 & -0.2208 & 0.412817 \tabularnewline
19 & -0.047386 & -0.4902 & 0.31251 \tabularnewline
20 & 0.058701 & 0.6072 & 0.272499 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265788&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]-0.50622[/C][C]-5.2364[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.053972[/C][C]-0.5583[/C][C]0.288907[/C][/ROW]
[ROW][C]3[/C][C]0.155049[/C][C]1.6038[/C][C]0.055848[/C][/ROW]
[ROW][C]4[/C][C]-0.226313[/C][C]-2.341[/C][C]0.010543[/C][/ROW]
[ROW][C]5[/C][C]0.17261[/C][C]1.7855[/C][C]0.038507[/C][/ROW]
[ROW][C]6[/C][C]0.102859[/C][C]1.064[/C][C]0.144865[/C][/ROW]
[ROW][C]7[/C][C]-0.222252[/C][C]-2.299[/C][C]0.011724[/C][/ROW]
[ROW][C]8[/C][C]0.004609[/C][C]0.0477[/C][C]0.481032[/C][/ROW]
[ROW][C]9[/C][C]0.246474[/C][C]2.5495[/C][C]0.006102[/C][/ROW]
[ROW][C]10[/C][C]-0.261181[/C][C]-2.7017[/C][C]0.004012[/C][/ROW]
[ROW][C]11[/C][C]0.250522[/C][C]2.5914[/C][C]0.005446[/C][/ROW]
[ROW][C]12[/C][C]-0.190701[/C][C]-1.9726[/C][C]0.025559[/C][/ROW]
[ROW][C]13[/C][C]-0.184578[/C][C]-1.9093[/C][C]0.029452[/C][/ROW]
[ROW][C]14[/C][C]0.337963[/C][C]3.4959[/C][C]0.000344[/C][/ROW]
[ROW][C]15[/C][C]-0.105519[/C][C]-1.0915[/C][C]0.138753[/C][/ROW]
[ROW][C]16[/C][C]-0.051431[/C][C]-0.532[/C][C]0.297912[/C][/ROW]
[ROW][C]17[/C][C]0.072682[/C][C]0.7518[/C][C]0.226902[/C][/ROW]
[ROW][C]18[/C][C]-0.02135[/C][C]-0.2208[/C][C]0.412817[/C][/ROW]
[ROW][C]19[/C][C]-0.047386[/C][C]-0.4902[/C][C]0.31251[/C][/ROW]
[ROW][C]20[/C][C]0.058701[/C][C]0.6072[/C][C]0.272499[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265788&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265788&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	-0.50622	-5.2364	0
2	-0.053972	-0.5583	0.288907
3	0.155049	1.6038	0.055848
4	-0.226313	-2.341	0.010543
5	0.17261	1.7855	0.038507
6	0.102859	1.064	0.144865
7	-0.222252	-2.299	0.011724
8	0.004609	0.0477	0.481032
9	0.246474	2.5495	0.006102
10	-0.261181	-2.7017	0.004012
11	0.250522	2.5914	0.005446
12	-0.190701	-1.9726	0.025559
13	-0.184578	-1.9093	0.029452
14	0.337963	3.4959	0.000344
15	-0.105519	-1.0915	0.138753
16	-0.051431	-0.532	0.297912
17	0.072682	0.7518	0.226902
18	-0.02135	-0.2208	0.412817
19	-0.047386	-0.4902	0.31251
20	0.058701	0.6072	0.272499

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.50622	-5.2364	0
2	-0.417121	-4.3147	1.8e-05
3	-0.154351	-1.5966	0.05665
4	-0.353053	-3.652	0.000202
5	-0.205459	-2.1253	0.017932
6	0.070056	0.7247	0.235121
7	-0.038057	-0.3937	0.347306
8	-0.240263	-2.4853	0.007246
9	0.140547	1.4538	0.07446
10	-0.007279	-0.0753	0.47006
11	0.225168	2.3292	0.010864
12	0.014261	0.1475	0.441501
13	-0.272091	-2.8145	0.002908
14	-0.172372	-1.783	0.038709
15	-0.104889	-1.085	0.140185
16	-0.130994	-1.355	0.089134
17	-0.116008	-1.2	0.116396
18	0.136469	1.4116	0.080478
19	0.174464	1.8047	0.036969
20	-0.101805	-1.0531	0.147338

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.50622 & -5.2364 & 0 \tabularnewline
2 & -0.417121 & -4.3147 & 1.8e-05 \tabularnewline
3 & -0.154351 & -1.5966 & 0.05665 \tabularnewline
4 & -0.353053 & -3.652 & 0.000202 \tabularnewline
5 & -0.205459 & -2.1253 & 0.017932 \tabularnewline
6 & 0.070056 & 0.7247 & 0.235121 \tabularnewline
7 & -0.038057 & -0.3937 & 0.347306 \tabularnewline
8 & -0.240263 & -2.4853 & 0.007246 \tabularnewline
9 & 0.140547 & 1.4538 & 0.07446 \tabularnewline
10 & -0.007279 & -0.0753 & 0.47006 \tabularnewline
11 & 0.225168 & 2.3292 & 0.010864 \tabularnewline
12 & 0.014261 & 0.1475 & 0.441501 \tabularnewline
13 & -0.272091 & -2.8145 & 0.002908 \tabularnewline
14 & -0.172372 & -1.783 & 0.038709 \tabularnewline
15 & -0.104889 & -1.085 & 0.140185 \tabularnewline
16 & -0.130994 & -1.355 & 0.089134 \tabularnewline
17 & -0.116008 & -1.2 & 0.116396 \tabularnewline
18 & 0.136469 & 1.4116 & 0.080478 \tabularnewline
19 & 0.174464 & 1.8047 & 0.036969 \tabularnewline
20 & -0.101805 & -1.0531 & 0.147338 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265788&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]-0.50622[/C][C]-5.2364[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.417121[/C][C]-4.3147[/C][C]1.8e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.154351[/C][C]-1.5966[/C][C]0.05665[/C][/ROW]
[ROW][C]4[/C][C]-0.353053[/C][C]-3.652[/C][C]0.000202[/C][/ROW]
[ROW][C]5[/C][C]-0.205459[/C][C]-2.1253[/C][C]0.017932[/C][/ROW]
[ROW][C]6[/C][C]0.070056[/C][C]0.7247[/C][C]0.235121[/C][/ROW]
[ROW][C]7[/C][C]-0.038057[/C][C]-0.3937[/C][C]0.347306[/C][/ROW]
[ROW][C]8[/C][C]-0.240263[/C][C]-2.4853[/C][C]0.007246[/C][/ROW]
[ROW][C]9[/C][C]0.140547[/C][C]1.4538[/C][C]0.07446[/C][/ROW]
[ROW][C]10[/C][C]-0.007279[/C][C]-0.0753[/C][C]0.47006[/C][/ROW]
[ROW][C]11[/C][C]0.225168[/C][C]2.3292[/C][C]0.010864[/C][/ROW]
[ROW][C]12[/C][C]0.014261[/C][C]0.1475[/C][C]0.441501[/C][/ROW]
[ROW][C]13[/C][C]-0.272091[/C][C]-2.8145[/C][C]0.002908[/C][/ROW]
[ROW][C]14[/C][C]-0.172372[/C][C]-1.783[/C][C]0.038709[/C][/ROW]
[ROW][C]15[/C][C]-0.104889[/C][C]-1.085[/C][C]0.140185[/C][/ROW]
[ROW][C]16[/C][C]-0.130994[/C][C]-1.355[/C][C]0.089134[/C][/ROW]
[ROW][C]17[/C][C]-0.116008[/C][C]-1.2[/C][C]0.116396[/C][/ROW]
[ROW][C]18[/C][C]0.136469[/C][C]1.4116[/C][C]0.080478[/C][/ROW]
[ROW][C]19[/C][C]0.174464[/C][C]1.8047[/C][C]0.036969[/C][/ROW]
[ROW][C]20[/C][C]-0.101805[/C][C]-1.0531[/C][C]0.147338[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265788&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265788&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	-0.50622	-5.2364	0
2	-0.417121	-4.3147	1.8e-05
3	-0.154351	-1.5966	0.05665
4	-0.353053	-3.652	0.000202
5	-0.205459	-2.1253	0.017932
6	0.070056	0.7247	0.235121
7	-0.038057	-0.3937	0.347306
8	-0.240263	-2.4853	0.007246
9	0.140547	1.4538	0.07446
10	-0.007279	-0.0753	0.47006
11	0.225168	2.3292	0.010864
12	0.014261	0.1475	0.441501
13	-0.272091	-2.8145	0.002908
14	-0.172372	-1.783	0.038709
15	-0.104889	-1.085	0.140185
16	-0.130994	-1.355	0.089134
17	-0.116008	-1.2	0.116396
18	0.136469	1.4116	0.080478
19	0.174464	1.8047	0.036969
20	-0.101805	-1.0531	0.147338

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 = -0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -0.3 ; par3 = 1 ; par4 = 1 ; 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