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

Thu, 05 Mar 2015 18:59:48 +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/2015/Mar/05/t14255820340ewanrolalzjajt.htm/, Retrieved Sun, 19 May 2024 11:11:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277987, Retrieved Sun, 19 May 2024 11:11:27 +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] [] [2015-03-05 18:59:48] [efb69546851bccb1c0576f78d5afa44b] [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	'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277987&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277987&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277987&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.483201	4.7097	4e-06
2	0.285033	2.7782	0.003294
3	0.023765	0.2316	0.408659
4	-0.048681	-0.4745	0.318123
5	-0.181346	-1.7675	0.040174
6	-0.242246	-2.3611	0.010131
7	-0.217225	-2.1172	0.018425
8	-0.197722	-1.9272	0.028474
9	-0.183087	-1.7845	0.038766
10	-0.074525	-0.7264	0.234695
11	0.023327	0.2274	0.410313
12	2.2e-05	2e-04	0.499914
13	-0.09822	-0.9573	0.170415
14	-0.109229	-1.0646	0.14487
15	-0.017227	-0.1679	0.433507
16	-0.027996	-0.2729	0.392773
17	-0.000766	-0.0075	0.497029
18	-0.013754	-0.1341	0.44682
19	0.044353	0.4323	0.333251

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.483201 & 4.7097 & 4e-06 \tabularnewline
2 & 0.285033 & 2.7782 & 0.003294 \tabularnewline
3 & 0.023765 & 0.2316 & 0.408659 \tabularnewline
4 & -0.048681 & -0.4745 & 0.318123 \tabularnewline
5 & -0.181346 & -1.7675 & 0.040174 \tabularnewline
6 & -0.242246 & -2.3611 & 0.010131 \tabularnewline
7 & -0.217225 & -2.1172 & 0.018425 \tabularnewline
8 & -0.197722 & -1.9272 & 0.028474 \tabularnewline
9 & -0.183087 & -1.7845 & 0.038766 \tabularnewline
10 & -0.074525 & -0.7264 & 0.234695 \tabularnewline
11 & 0.023327 & 0.2274 & 0.410313 \tabularnewline
12 & 2.2e-05 & 2e-04 & 0.499914 \tabularnewline
13 & -0.09822 & -0.9573 & 0.170415 \tabularnewline
14 & -0.109229 & -1.0646 & 0.14487 \tabularnewline
15 & -0.017227 & -0.1679 & 0.433507 \tabularnewline
16 & -0.027996 & -0.2729 & 0.392773 \tabularnewline
17 & -0.000766 & -0.0075 & 0.497029 \tabularnewline
18 & -0.013754 & -0.1341 & 0.44682 \tabularnewline
19 & 0.044353 & 0.4323 & 0.333251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277987&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]0.483201[/C][C]4.7097[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]0.285033[/C][C]2.7782[/C][C]0.003294[/C][/ROW]
[ROW][C]3[/C][C]0.023765[/C][C]0.2316[/C][C]0.408659[/C][/ROW]
[ROW][C]4[/C][C]-0.048681[/C][C]-0.4745[/C][C]0.318123[/C][/ROW]
[ROW][C]5[/C][C]-0.181346[/C][C]-1.7675[/C][C]0.040174[/C][/ROW]
[ROW][C]6[/C][C]-0.242246[/C][C]-2.3611[/C][C]0.010131[/C][/ROW]
[ROW][C]7[/C][C]-0.217225[/C][C]-2.1172[/C][C]0.018425[/C][/ROW]
[ROW][C]8[/C][C]-0.197722[/C][C]-1.9272[/C][C]0.028474[/C][/ROW]
[ROW][C]9[/C][C]-0.183087[/C][C]-1.7845[/C][C]0.038766[/C][/ROW]
[ROW][C]10[/C][C]-0.074525[/C][C]-0.7264[/C][C]0.234695[/C][/ROW]
[ROW][C]11[/C][C]0.023327[/C][C]0.2274[/C][C]0.410313[/C][/ROW]
[ROW][C]12[/C][C]2.2e-05[/C][C]2e-04[/C][C]0.499914[/C][/ROW]
[ROW][C]13[/C][C]-0.09822[/C][C]-0.9573[/C][C]0.170415[/C][/ROW]
[ROW][C]14[/C][C]-0.109229[/C][C]-1.0646[/C][C]0.14487[/C][/ROW]
[ROW][C]15[/C][C]-0.017227[/C][C]-0.1679[/C][C]0.433507[/C][/ROW]
[ROW][C]16[/C][C]-0.027996[/C][C]-0.2729[/C][C]0.392773[/C][/ROW]
[ROW][C]17[/C][C]-0.000766[/C][C]-0.0075[/C][C]0.497029[/C][/ROW]
[ROW][C]18[/C][C]-0.013754[/C][C]-0.1341[/C][C]0.44682[/C][/ROW]
[ROW][C]19[/C][C]0.044353[/C][C]0.4323[/C][C]0.333251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277987&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277987&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	0.483201	4.7097	4e-06
2	0.285033	2.7782	0.003294
3	0.023765	0.2316	0.408659
4	-0.048681	-0.4745	0.318123
5	-0.181346	-1.7675	0.040174
6	-0.242246	-2.3611	0.010131
7	-0.217225	-2.1172	0.018425
8	-0.197722	-1.9272	0.028474
9	-0.183087	-1.7845	0.038766
10	-0.074525	-0.7264	0.234695
11	0.023327	0.2274	0.410313
12	2.2e-05	2e-04	0.499914
13	-0.09822	-0.9573	0.170415
14	-0.109229	-1.0646	0.14487
15	-0.017227	-0.1679	0.433507
16	-0.027996	-0.2729	0.392773
17	-0.000766	-0.0075	0.497029
18	-0.013754	-0.1341	0.44682
19	0.044353	0.4323	0.333251

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.483201	4.7097	4e-06
2	0.067252	0.6555	0.256869
3	-0.1798	-1.7525	0.04146
4	-0.020405	-0.1989	0.421389
5	-0.141144	-1.3757	0.086075
6	-0.130257	-1.2696	0.103666
7	-0.014684	-0.1431	0.443248
8	-0.076414	-0.7448	0.229118
9	-0.10095	-0.9839	0.163823
10	0.051913	0.506	0.307018
11	0.033864	0.3301	0.371037
12	-0.128737	-1.2548	0.10632
13	-0.178517	-1.74	0.042551
14	-0.060157	-0.5863	0.279518
15	0.067834	0.6612	0.255053
16	-0.073993	-0.7212	0.236279
17	-0.026343	-0.2568	0.398958
18	-0.06123	-0.5968	0.27603
19	0.001781	0.0174	0.493094

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.483201 & 4.7097 & 4e-06 \tabularnewline
2 & 0.067252 & 0.6555 & 0.256869 \tabularnewline
3 & -0.1798 & -1.7525 & 0.04146 \tabularnewline
4 & -0.020405 & -0.1989 & 0.421389 \tabularnewline
5 & -0.141144 & -1.3757 & 0.086075 \tabularnewline
6 & -0.130257 & -1.2696 & 0.103666 \tabularnewline
7 & -0.014684 & -0.1431 & 0.443248 \tabularnewline
8 & -0.076414 & -0.7448 & 0.229118 \tabularnewline
9 & -0.10095 & -0.9839 & 0.163823 \tabularnewline
10 & 0.051913 & 0.506 & 0.307018 \tabularnewline
11 & 0.033864 & 0.3301 & 0.371037 \tabularnewline
12 & -0.128737 & -1.2548 & 0.10632 \tabularnewline
13 & -0.178517 & -1.74 & 0.042551 \tabularnewline
14 & -0.060157 & -0.5863 & 0.279518 \tabularnewline
15 & 0.067834 & 0.6612 & 0.255053 \tabularnewline
16 & -0.073993 & -0.7212 & 0.236279 \tabularnewline
17 & -0.026343 & -0.2568 & 0.398958 \tabularnewline
18 & -0.06123 & -0.5968 & 0.27603 \tabularnewline
19 & 0.001781 & 0.0174 & 0.493094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277987&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]0.483201[/C][C]4.7097[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]0.067252[/C][C]0.6555[/C][C]0.256869[/C][/ROW]
[ROW][C]3[/C][C]-0.1798[/C][C]-1.7525[/C][C]0.04146[/C][/ROW]
[ROW][C]4[/C][C]-0.020405[/C][C]-0.1989[/C][C]0.421389[/C][/ROW]
[ROW][C]5[/C][C]-0.141144[/C][C]-1.3757[/C][C]0.086075[/C][/ROW]
[ROW][C]6[/C][C]-0.130257[/C][C]-1.2696[/C][C]0.103666[/C][/ROW]
[ROW][C]7[/C][C]-0.014684[/C][C]-0.1431[/C][C]0.443248[/C][/ROW]
[ROW][C]8[/C][C]-0.076414[/C][C]-0.7448[/C][C]0.229118[/C][/ROW]
[ROW][C]9[/C][C]-0.10095[/C][C]-0.9839[/C][C]0.163823[/C][/ROW]
[ROW][C]10[/C][C]0.051913[/C][C]0.506[/C][C]0.307018[/C][/ROW]
[ROW][C]11[/C][C]0.033864[/C][C]0.3301[/C][C]0.371037[/C][/ROW]
[ROW][C]12[/C][C]-0.128737[/C][C]-1.2548[/C][C]0.10632[/C][/ROW]
[ROW][C]13[/C][C]-0.178517[/C][C]-1.74[/C][C]0.042551[/C][/ROW]
[ROW][C]14[/C][C]-0.060157[/C][C]-0.5863[/C][C]0.279518[/C][/ROW]
[ROW][C]15[/C][C]0.067834[/C][C]0.6612[/C][C]0.255053[/C][/ROW]
[ROW][C]16[/C][C]-0.073993[/C][C]-0.7212[/C][C]0.236279[/C][/ROW]
[ROW][C]17[/C][C]-0.026343[/C][C]-0.2568[/C][C]0.398958[/C][/ROW]
[ROW][C]18[/C][C]-0.06123[/C][C]-0.5968[/C][C]0.27603[/C][/ROW]
[ROW][C]19[/C][C]0.001781[/C][C]0.0174[/C][C]0.493094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277987&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277987&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	0.483201	4.7097	4e-06
2	0.067252	0.6555	0.256869
3	-0.1798	-1.7525	0.04146
4	-0.020405	-0.1989	0.421389
5	-0.141144	-1.3757	0.086075
6	-0.130257	-1.2696	0.103666
7	-0.014684	-0.1431	0.443248
8	-0.076414	-0.7448	0.229118
9	-0.10095	-0.9839	0.163823
10	0.051913	0.506	0.307018
11	0.033864	0.3301	0.371037
12	-0.128737	-1.2548	0.10632
13	-0.178517	-1.74	0.042551
14	-0.060157	-0.5863	0.279518
15	0.067834	0.6612	0.255053
16	-0.073993	-0.7212	0.236279
17	-0.026343	-0.2568	0.398958
18	-0.06123	-0.5968	0.27603
19	0.001781	0.0174	0.493094

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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