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

Wed, 13 Dec 2017 17:14:52 +0100

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/2017/Dec/13/t1513181708jp52ozfbtmiixst.htm/, Retrieved Wed, 15 May 2024 17:19:32 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 17:19:32 +0200

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

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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.909439	13.2416	0
2	0.883546	12.8646	0
3	0.87639	12.7604	0
4	0.824832	12.0097	0
5	0.847539	12.3404	0
6	0.845764	12.3145	0
7	0.805305	11.7254	0
8	0.786527	11.452	0
9	0.792818	11.5436	0
10	0.77373	11.2657	0
11	0.797325	11.6092	0
12	0.82278	11.9799	0
13	0.757407	11.028	0
14	0.743764	10.8294	0
15	0.713172	10.3839	0
16	0.672344	9.7895	0
17	0.700168	10.1946	0
18	0.684929	9.9727	0
19	0.651513	9.4862	0
20	0.645429	9.3976	0
21	0.633531	9.2243	0
22	0.627934	9.1429	0
23	0.656584	9.56	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.909439 & 13.2416 & 0 \tabularnewline
2 & 0.883546 & 12.8646 & 0 \tabularnewline
3 & 0.87639 & 12.7604 & 0 \tabularnewline
4 & 0.824832 & 12.0097 & 0 \tabularnewline
5 & 0.847539 & 12.3404 & 0 \tabularnewline
6 & 0.845764 & 12.3145 & 0 \tabularnewline
7 & 0.805305 & 11.7254 & 0 \tabularnewline
8 & 0.786527 & 11.452 & 0 \tabularnewline
9 & 0.792818 & 11.5436 & 0 \tabularnewline
10 & 0.77373 & 11.2657 & 0 \tabularnewline
11 & 0.797325 & 11.6092 & 0 \tabularnewline
12 & 0.82278 & 11.9799 & 0 \tabularnewline
13 & 0.757407 & 11.028 & 0 \tabularnewline
14 & 0.743764 & 10.8294 & 0 \tabularnewline
15 & 0.713172 & 10.3839 & 0 \tabularnewline
16 & 0.672344 & 9.7895 & 0 \tabularnewline
17 & 0.700168 & 10.1946 & 0 \tabularnewline
18 & 0.684929 & 9.9727 & 0 \tabularnewline
19 & 0.651513 & 9.4862 & 0 \tabularnewline
20 & 0.645429 & 9.3976 & 0 \tabularnewline
21 & 0.633531 & 9.2243 & 0 \tabularnewline
22 & 0.627934 & 9.1429 & 0 \tabularnewline
23 & 0.656584 & 9.56 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.909439[/C][C]13.2416[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.883546[/C][C]12.8646[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.87639[/C][C]12.7604[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.824832[/C][C]12.0097[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.847539[/C][C]12.3404[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.845764[/C][C]12.3145[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.805305[/C][C]11.7254[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.786527[/C][C]11.452[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.792818[/C][C]11.5436[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.77373[/C][C]11.2657[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.797325[/C][C]11.6092[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.82278[/C][C]11.9799[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.757407[/C][C]11.028[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.743764[/C][C]10.8294[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.713172[/C][C]10.3839[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.672344[/C][C]9.7895[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.700168[/C][C]10.1946[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.684929[/C][C]9.9727[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.651513[/C][C]9.4862[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.645429[/C][C]9.3976[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.633531[/C][C]9.2243[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.627934[/C][C]9.1429[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.656584[/C][C]9.56[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.909439	13.2416	0
2	0.883546	12.8646	0
3	0.87639	12.7604	0
4	0.824832	12.0097	0
5	0.847539	12.3404	0
6	0.845764	12.3145	0
7	0.805305	11.7254	0
8	0.786527	11.452	0
9	0.792818	11.5436	0
10	0.77373	11.2657	0
11	0.797325	11.6092	0
12	0.82278	11.9799	0
13	0.757407	11.028	0
14	0.743764	10.8294	0
15	0.713172	10.3839	0
16	0.672344	9.7895	0
17	0.700168	10.1946	0
18	0.684929	9.9727	0
19	0.651513	9.4862	0
20	0.645429	9.3976	0
21	0.633531	9.2243	0
22	0.627934	9.1429	0
23	0.656584	9.56	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.909439	13.2416	0
2	0.326549	4.7546	2e-06
3	0.247763	3.6075	0.000193
4	-0.14338	-2.0876	0.019013
5	0.343464	5.0009	1e-06
6	0.103576	1.5081	0.066511
7	-0.131535	-1.9152	0.028408
8	-0.16502	-2.4027	0.008568
9	0.304066	4.4273	8e-06
10	0.017874	0.2603	0.39746
11	0.16383	2.3854	0.00897
12	0.15681	2.2832	0.011705
13	-0.340992	-4.9649	1e-06
14	-0.169351	-2.4658	0.007233
15	-0.139558	-2.032	0.021701
16	0.010913	0.1589	0.436953
17	0.099565	1.4497	0.074311
18	0.061879	0.901	0.184312
19	-0.007093	-0.1033	0.458918
20	0.02283	0.3324	0.369953
21	0.05559	0.8094	0.209597
22	0.052875	0.7699	0.221117
23	0.016697	0.2431	0.404079

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.909439 & 13.2416 & 0 \tabularnewline
2 & 0.326549 & 4.7546 & 2e-06 \tabularnewline
3 & 0.247763 & 3.6075 & 0.000193 \tabularnewline
4 & -0.14338 & -2.0876 & 0.019013 \tabularnewline
5 & 0.343464 & 5.0009 & 1e-06 \tabularnewline
6 & 0.103576 & 1.5081 & 0.066511 \tabularnewline
7 & -0.131535 & -1.9152 & 0.028408 \tabularnewline
8 & -0.16502 & -2.4027 & 0.008568 \tabularnewline
9 & 0.304066 & 4.4273 & 8e-06 \tabularnewline
10 & 0.017874 & 0.2603 & 0.39746 \tabularnewline
11 & 0.16383 & 2.3854 & 0.00897 \tabularnewline
12 & 0.15681 & 2.2832 & 0.011705 \tabularnewline
13 & -0.340992 & -4.9649 & 1e-06 \tabularnewline
14 & -0.169351 & -2.4658 & 0.007233 \tabularnewline
15 & -0.139558 & -2.032 & 0.021701 \tabularnewline
16 & 0.010913 & 0.1589 & 0.436953 \tabularnewline
17 & 0.099565 & 1.4497 & 0.074311 \tabularnewline
18 & 0.061879 & 0.901 & 0.184312 \tabularnewline
19 & -0.007093 & -0.1033 & 0.458918 \tabularnewline
20 & 0.02283 & 0.3324 & 0.369953 \tabularnewline
21 & 0.05559 & 0.8094 & 0.209597 \tabularnewline
22 & 0.052875 & 0.7699 & 0.221117 \tabularnewline
23 & 0.016697 & 0.2431 & 0.404079 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.909439[/C][C]13.2416[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.326549[/C][C]4.7546[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.247763[/C][C]3.6075[/C][C]0.000193[/C][/ROW]
[ROW][C]4[/C][C]-0.14338[/C][C]-2.0876[/C][C]0.019013[/C][/ROW]
[ROW][C]5[/C][C]0.343464[/C][C]5.0009[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.103576[/C][C]1.5081[/C][C]0.066511[/C][/ROW]
[ROW][C]7[/C][C]-0.131535[/C][C]-1.9152[/C][C]0.028408[/C][/ROW]
[ROW][C]8[/C][C]-0.16502[/C][C]-2.4027[/C][C]0.008568[/C][/ROW]
[ROW][C]9[/C][C]0.304066[/C][C]4.4273[/C][C]8e-06[/C][/ROW]
[ROW][C]10[/C][C]0.017874[/C][C]0.2603[/C][C]0.39746[/C][/ROW]
[ROW][C]11[/C][C]0.16383[/C][C]2.3854[/C][C]0.00897[/C][/ROW]
[ROW][C]12[/C][C]0.15681[/C][C]2.2832[/C][C]0.011705[/C][/ROW]
[ROW][C]13[/C][C]-0.340992[/C][C]-4.9649[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]-0.169351[/C][C]-2.4658[/C][C]0.007233[/C][/ROW]
[ROW][C]15[/C][C]-0.139558[/C][C]-2.032[/C][C]0.021701[/C][/ROW]
[ROW][C]16[/C][C]0.010913[/C][C]0.1589[/C][C]0.436953[/C][/ROW]
[ROW][C]17[/C][C]0.099565[/C][C]1.4497[/C][C]0.074311[/C][/ROW]
[ROW][C]18[/C][C]0.061879[/C][C]0.901[/C][C]0.184312[/C][/ROW]
[ROW][C]19[/C][C]-0.007093[/C][C]-0.1033[/C][C]0.458918[/C][/ROW]
[ROW][C]20[/C][C]0.02283[/C][C]0.3324[/C][C]0.369953[/C][/ROW]
[ROW][C]21[/C][C]0.05559[/C][C]0.8094[/C][C]0.209597[/C][/ROW]
[ROW][C]22[/C][C]0.052875[/C][C]0.7699[/C][C]0.221117[/C][/ROW]
[ROW][C]23[/C][C]0.016697[/C][C]0.2431[/C][C]0.404079[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.909439	13.2416	0
2	0.326549	4.7546	2e-06
3	0.247763	3.6075	0.000193
4	-0.14338	-2.0876	0.019013
5	0.343464	5.0009	1e-06
6	0.103576	1.5081	0.066511
7	-0.131535	-1.9152	0.028408
8	-0.16502	-2.4027	0.008568
9	0.304066	4.4273	8e-06
10	0.017874	0.2603	0.39746
11	0.16383	2.3854	0.00897
12	0.15681	2.2832	0.011705
13	-0.340992	-4.9649	1e-06
14	-0.169351	-2.4658	0.007233
15	-0.139558	-2.032	0.021701
16	0.010913	0.1589	0.436953
17	0.099565	1.4497	0.074311
18	0.061879	0.901	0.184312
19	-0.007093	-0.1033	0.458918
20	0.02283	0.3324	0.369953
21	0.05559	0.8094	0.209597
22	0.052875	0.7699	0.221117
23	0.016697	0.2431	0.404079

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 = 1Full Box-Cox transformDefault1Default112DefaultDefault111111111111111111Default111Default ; par2 = 1-211111111111111110101111111101 ; par3 = 1211111011001101101000010010000 ; par4 = 10112012010011001001121212121212121201212120 ; par5 = No12121212121212121212121212121212 ; par6 = White NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite NoiseWhite Noise ; par7 = 0.950.950.950.950,950.950.950.950.500.950.950.95 ;

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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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