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

Tue, 16 Dec 2014 13:55:01 +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/16/t1418738120fbfl39qq2xci8fb.htm/, Retrieved Thu, 16 May 2024 18:38:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269566, Retrieved Thu, 16 May 2024 18:38:38 +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] [ACF ex] [2014-12-16 13:55:01] [9636d26fd774798d33054b538c301d75] [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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269566&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269566&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269566&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.005233	0.0873	0.465265
2	-0.037486	-0.625	0.266236
3	0.019009	0.3169	0.375764
4	0.102929	1.7162	0.043623
5	0.02562	0.4272	0.334796
6	0.049885	0.8317	0.203133
7	-0.03569	-0.5951	0.276139
8	0.078132	1.3027	0.096874
9	-0.047404	-0.7904	0.214989
10	-0.01406	-0.2344	0.407414
11	-0.004549	-0.0759	0.469795
12	-0.082953	-1.3831	0.08387
13	-0.065455	-1.0913	0.138033
14	-0.017774	-0.2964	0.383588
15	0.070142	1.1695	0.121603
16	-0.018042	-0.3008	0.38189
17	0.029495	0.4918	0.31163
18	0.00097	0.0162	0.493557
19	-0.071372	-1.19	0.117527
20	-0.04064	-0.6776	0.249293
21	0.085171	1.4201	0.078353
22	0.031289	0.5217	0.30115
23	-0.003715	-0.0619	0.475326
24	-0.057597	-0.9603	0.168862

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.005233 & 0.0873 & 0.465265 \tabularnewline
2 & -0.037486 & -0.625 & 0.266236 \tabularnewline
3 & 0.019009 & 0.3169 & 0.375764 \tabularnewline
4 & 0.102929 & 1.7162 & 0.043623 \tabularnewline
5 & 0.02562 & 0.4272 & 0.334796 \tabularnewline
6 & 0.049885 & 0.8317 & 0.203133 \tabularnewline
7 & -0.03569 & -0.5951 & 0.276139 \tabularnewline
8 & 0.078132 & 1.3027 & 0.096874 \tabularnewline
9 & -0.047404 & -0.7904 & 0.214989 \tabularnewline
10 & -0.01406 & -0.2344 & 0.407414 \tabularnewline
11 & -0.004549 & -0.0759 & 0.469795 \tabularnewline
12 & -0.082953 & -1.3831 & 0.08387 \tabularnewline
13 & -0.065455 & -1.0913 & 0.138033 \tabularnewline
14 & -0.017774 & -0.2964 & 0.383588 \tabularnewline
15 & 0.070142 & 1.1695 & 0.121603 \tabularnewline
16 & -0.018042 & -0.3008 & 0.38189 \tabularnewline
17 & 0.029495 & 0.4918 & 0.31163 \tabularnewline
18 & 0.00097 & 0.0162 & 0.493557 \tabularnewline
19 & -0.071372 & -1.19 & 0.117527 \tabularnewline
20 & -0.04064 & -0.6776 & 0.249293 \tabularnewline
21 & 0.085171 & 1.4201 & 0.078353 \tabularnewline
22 & 0.031289 & 0.5217 & 0.30115 \tabularnewline
23 & -0.003715 & -0.0619 & 0.475326 \tabularnewline
24 & -0.057597 & -0.9603 & 0.168862 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269566&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]0.005233[/C][C]0.0873[/C][C]0.465265[/C][/ROW]
[ROW][C]2[/C][C]-0.037486[/C][C]-0.625[/C][C]0.266236[/C][/ROW]
[ROW][C]3[/C][C]0.019009[/C][C]0.3169[/C][C]0.375764[/C][/ROW]
[ROW][C]4[/C][C]0.102929[/C][C]1.7162[/C][C]0.043623[/C][/ROW]
[ROW][C]5[/C][C]0.02562[/C][C]0.4272[/C][C]0.334796[/C][/ROW]
[ROW][C]6[/C][C]0.049885[/C][C]0.8317[/C][C]0.203133[/C][/ROW]
[ROW][C]7[/C][C]-0.03569[/C][C]-0.5951[/C][C]0.276139[/C][/ROW]
[ROW][C]8[/C][C]0.078132[/C][C]1.3027[/C][C]0.096874[/C][/ROW]
[ROW][C]9[/C][C]-0.047404[/C][C]-0.7904[/C][C]0.214989[/C][/ROW]
[ROW][C]10[/C][C]-0.01406[/C][C]-0.2344[/C][C]0.407414[/C][/ROW]
[ROW][C]11[/C][C]-0.004549[/C][C]-0.0759[/C][C]0.469795[/C][/ROW]
[ROW][C]12[/C][C]-0.082953[/C][C]-1.3831[/C][C]0.08387[/C][/ROW]
[ROW][C]13[/C][C]-0.065455[/C][C]-1.0913[/C][C]0.138033[/C][/ROW]
[ROW][C]14[/C][C]-0.017774[/C][C]-0.2964[/C][C]0.383588[/C][/ROW]
[ROW][C]15[/C][C]0.070142[/C][C]1.1695[/C][C]0.121603[/C][/ROW]
[ROW][C]16[/C][C]-0.018042[/C][C]-0.3008[/C][C]0.38189[/C][/ROW]
[ROW][C]17[/C][C]0.029495[/C][C]0.4918[/C][C]0.31163[/C][/ROW]
[ROW][C]18[/C][C]0.00097[/C][C]0.0162[/C][C]0.493557[/C][/ROW]
[ROW][C]19[/C][C]-0.071372[/C][C]-1.19[/C][C]0.117527[/C][/ROW]
[ROW][C]20[/C][C]-0.04064[/C][C]-0.6776[/C][C]0.249293[/C][/ROW]
[ROW][C]21[/C][C]0.085171[/C][C]1.4201[/C][C]0.078353[/C][/ROW]
[ROW][C]22[/C][C]0.031289[/C][C]0.5217[/C][C]0.30115[/C][/ROW]
[ROW][C]23[/C][C]-0.003715[/C][C]-0.0619[/C][C]0.475326[/C][/ROW]
[ROW][C]24[/C][C]-0.057597[/C][C]-0.9603[/C][C]0.168862[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269566&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269566&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	0.005233	0.0873	0.465265
2	-0.037486	-0.625	0.266236
3	0.019009	0.3169	0.375764
4	0.102929	1.7162	0.043623
5	0.02562	0.4272	0.334796
6	0.049885	0.8317	0.203133
7	-0.03569	-0.5951	0.276139
8	0.078132	1.3027	0.096874
9	-0.047404	-0.7904	0.214989
10	-0.01406	-0.2344	0.407414
11	-0.004549	-0.0759	0.469795
12	-0.082953	-1.3831	0.08387
13	-0.065455	-1.0913	0.138033
14	-0.017774	-0.2964	0.383588
15	0.070142	1.1695	0.121603
16	-0.018042	-0.3008	0.38189
17	0.029495	0.4918	0.31163
18	0.00097	0.0162	0.493557
19	-0.071372	-1.19	0.117527
20	-0.04064	-0.6776	0.249293
21	0.085171	1.4201	0.078353
22	0.031289	0.5217	0.30115
23	-0.003715	-0.0619	0.475326
24	-0.057597	-0.9603	0.168862

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.005233	0.0873	0.465265
2	-0.037514	-0.6255	0.266081
3	0.019436	0.3241	0.373064
4	0.101484	1.6921	0.045877
5	0.026324	0.4389	0.330537
6	0.057397	0.957	0.169698
7	-0.038472	-0.6415	0.260877
8	0.072017	1.2008	0.115434
9	-0.059535	-0.9926	0.160873
10	-0.0178	-0.2968	0.383426
11	-0.007415	-0.1236	0.450846
12	-0.100717	-1.6793	0.04711
13	-0.054943	-0.9161	0.180208
14	-0.030185	-0.5033	0.307581
15	0.085504	1.4256	0.077548
16	-0.007391	-0.1232	0.451008
17	0.065636	1.0944	0.137371
18	0.015786	0.2632	0.396294
19	-0.085082	-1.4186	0.078568
20	-0.032937	-0.5492	0.291666
21	0.060674	1.0116	0.156295
22	0.030974	0.5164	0.30298
23	-0.006617	-0.1103	0.456116
24	-0.046245	-0.7711	0.220664

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.005233 & 0.0873 & 0.465265 \tabularnewline
2 & -0.037514 & -0.6255 & 0.266081 \tabularnewline
3 & 0.019436 & 0.3241 & 0.373064 \tabularnewline
4 & 0.101484 & 1.6921 & 0.045877 \tabularnewline
5 & 0.026324 & 0.4389 & 0.330537 \tabularnewline
6 & 0.057397 & 0.957 & 0.169698 \tabularnewline
7 & -0.038472 & -0.6415 & 0.260877 \tabularnewline
8 & 0.072017 & 1.2008 & 0.115434 \tabularnewline
9 & -0.059535 & -0.9926 & 0.160873 \tabularnewline
10 & -0.0178 & -0.2968 & 0.383426 \tabularnewline
11 & -0.007415 & -0.1236 & 0.450846 \tabularnewline
12 & -0.100717 & -1.6793 & 0.04711 \tabularnewline
13 & -0.054943 & -0.9161 & 0.180208 \tabularnewline
14 & -0.030185 & -0.5033 & 0.307581 \tabularnewline
15 & 0.085504 & 1.4256 & 0.077548 \tabularnewline
16 & -0.007391 & -0.1232 & 0.451008 \tabularnewline
17 & 0.065636 & 1.0944 & 0.137371 \tabularnewline
18 & 0.015786 & 0.2632 & 0.396294 \tabularnewline
19 & -0.085082 & -1.4186 & 0.078568 \tabularnewline
20 & -0.032937 & -0.5492 & 0.291666 \tabularnewline
21 & 0.060674 & 1.0116 & 0.156295 \tabularnewline
22 & 0.030974 & 0.5164 & 0.30298 \tabularnewline
23 & -0.006617 & -0.1103 & 0.456116 \tabularnewline
24 & -0.046245 & -0.7711 & 0.220664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269566&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]0.005233[/C][C]0.0873[/C][C]0.465265[/C][/ROW]
[ROW][C]2[/C][C]-0.037514[/C][C]-0.6255[/C][C]0.266081[/C][/ROW]
[ROW][C]3[/C][C]0.019436[/C][C]0.3241[/C][C]0.373064[/C][/ROW]
[ROW][C]4[/C][C]0.101484[/C][C]1.6921[/C][C]0.045877[/C][/ROW]
[ROW][C]5[/C][C]0.026324[/C][C]0.4389[/C][C]0.330537[/C][/ROW]
[ROW][C]6[/C][C]0.057397[/C][C]0.957[/C][C]0.169698[/C][/ROW]
[ROW][C]7[/C][C]-0.038472[/C][C]-0.6415[/C][C]0.260877[/C][/ROW]
[ROW][C]8[/C][C]0.072017[/C][C]1.2008[/C][C]0.115434[/C][/ROW]
[ROW][C]9[/C][C]-0.059535[/C][C]-0.9926[/C][C]0.160873[/C][/ROW]
[ROW][C]10[/C][C]-0.0178[/C][C]-0.2968[/C][C]0.383426[/C][/ROW]
[ROW][C]11[/C][C]-0.007415[/C][C]-0.1236[/C][C]0.450846[/C][/ROW]
[ROW][C]12[/C][C]-0.100717[/C][C]-1.6793[/C][C]0.04711[/C][/ROW]
[ROW][C]13[/C][C]-0.054943[/C][C]-0.9161[/C][C]0.180208[/C][/ROW]
[ROW][C]14[/C][C]-0.030185[/C][C]-0.5033[/C][C]0.307581[/C][/ROW]
[ROW][C]15[/C][C]0.085504[/C][C]1.4256[/C][C]0.077548[/C][/ROW]
[ROW][C]16[/C][C]-0.007391[/C][C]-0.1232[/C][C]0.451008[/C][/ROW]
[ROW][C]17[/C][C]0.065636[/C][C]1.0944[/C][C]0.137371[/C][/ROW]
[ROW][C]18[/C][C]0.015786[/C][C]0.2632[/C][C]0.396294[/C][/ROW]
[ROW][C]19[/C][C]-0.085082[/C][C]-1.4186[/C][C]0.078568[/C][/ROW]
[ROW][C]20[/C][C]-0.032937[/C][C]-0.5492[/C][C]0.291666[/C][/ROW]
[ROW][C]21[/C][C]0.060674[/C][C]1.0116[/C][C]0.156295[/C][/ROW]
[ROW][C]22[/C][C]0.030974[/C][C]0.5164[/C][C]0.30298[/C][/ROW]
[ROW][C]23[/C][C]-0.006617[/C][C]-0.1103[/C][C]0.456116[/C][/ROW]
[ROW][C]24[/C][C]-0.046245[/C][C]-0.7711[/C][C]0.220664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269566&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269566&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	0.005233	0.0873	0.465265
2	-0.037514	-0.6255	0.266081
3	0.019436	0.3241	0.373064
4	0.101484	1.6921	0.045877
5	0.026324	0.4389	0.330537
6	0.057397	0.957	0.169698
7	-0.038472	-0.6415	0.260877
8	0.072017	1.2008	0.115434
9	-0.059535	-0.9926	0.160873
10	-0.0178	-0.2968	0.383426
11	-0.007415	-0.1236	0.450846
12	-0.100717	-1.6793	0.04711
13	-0.054943	-0.9161	0.180208
14	-0.030185	-0.5033	0.307581
15	0.085504	1.4256	0.077548
16	-0.007391	-0.1232	0.451008
17	0.065636	1.0944	0.137371
18	0.015786	0.2632	0.396294
19	-0.085082	-1.4186	0.078568
20	-0.032937	-0.5492	0.291666
21	0.060674	1.0116	0.156295
22	0.030974	0.5164	0.30298
23	-0.006617	-0.1103	0.456116
24	-0.046245	-0.7711	0.220664

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.99 ; 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