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, 20 Dec 2017 16:33:48 +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/20/t1513784140cfca3750vf1ns1c.htm/, Retrieved Tue, 14 May 2024 14:26:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310532, Retrieved Tue, 14 May 2024 14:26:36 +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

112

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

-       [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2017-12-20 15:33:48] [265bf64618ae5fabb4f8135a65428bee] [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	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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310532&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]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310532&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310532&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.812942	11.8366	0
2	0.749845	10.9179	0
3	0.782707	11.3964	0
4	0.755884	11.0058	0
5	0.74463	10.842	0
6	0.747929	10.89	0
7	0.71404	10.3966	0
8	0.69945	10.1841	0
9	0.697157	10.1508	0
10	0.650787	9.4756	0
11	0.678221	9.8751	0
12	0.757998	11.0366	0
13	0.656294	9.5558	0
14	0.62881	9.1556	0
15	0.659577	9.6036	0
16	0.627827	9.1413	0
17	0.624652	9.0951	0
18	0.622916	9.0698	0
19	0.581259	8.4633	0
20	0.569849	8.2971	0
21	0.541555	7.8852	0
22	0.495064	7.2082	0
23	0.522837	7.6126	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.812942 & 11.8366 & 0 \tabularnewline
2 & 0.749845 & 10.9179 & 0 \tabularnewline
3 & 0.782707 & 11.3964 & 0 \tabularnewline
4 & 0.755884 & 11.0058 & 0 \tabularnewline
5 & 0.74463 & 10.842 & 0 \tabularnewline
6 & 0.747929 & 10.89 & 0 \tabularnewline
7 & 0.71404 & 10.3966 & 0 \tabularnewline
8 & 0.69945 & 10.1841 & 0 \tabularnewline
9 & 0.697157 & 10.1508 & 0 \tabularnewline
10 & 0.650787 & 9.4756 & 0 \tabularnewline
11 & 0.678221 & 9.8751 & 0 \tabularnewline
12 & 0.757998 & 11.0366 & 0 \tabularnewline
13 & 0.656294 & 9.5558 & 0 \tabularnewline
14 & 0.62881 & 9.1556 & 0 \tabularnewline
15 & 0.659577 & 9.6036 & 0 \tabularnewline
16 & 0.627827 & 9.1413 & 0 \tabularnewline
17 & 0.624652 & 9.0951 & 0 \tabularnewline
18 & 0.622916 & 9.0698 & 0 \tabularnewline
19 & 0.581259 & 8.4633 & 0 \tabularnewline
20 & 0.569849 & 8.2971 & 0 \tabularnewline
21 & 0.541555 & 7.8852 & 0 \tabularnewline
22 & 0.495064 & 7.2082 & 0 \tabularnewline
23 & 0.522837 & 7.6126 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310532&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]0.812942[/C][C]11.8366[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.749845[/C][C]10.9179[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.782707[/C][C]11.3964[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.755884[/C][C]11.0058[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.74463[/C][C]10.842[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.747929[/C][C]10.89[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.71404[/C][C]10.3966[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.69945[/C][C]10.1841[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.697157[/C][C]10.1508[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.650787[/C][C]9.4756[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.678221[/C][C]9.8751[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.757998[/C][C]11.0366[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.656294[/C][C]9.5558[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.62881[/C][C]9.1556[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.659577[/C][C]9.6036[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.627827[/C][C]9.1413[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.624652[/C][C]9.0951[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.622916[/C][C]9.0698[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.581259[/C][C]8.4633[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.569849[/C][C]8.2971[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.541555[/C][C]7.8852[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.495064[/C][C]7.2082[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.522837[/C][C]7.6126[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310532&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310532&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	0.812942	11.8366	0
2	0.749845	10.9179	0
3	0.782707	11.3964	0
4	0.755884	11.0058	0
5	0.74463	10.842	0
6	0.747929	10.89	0
7	0.71404	10.3966	0
8	0.69945	10.1841	0
9	0.697157	10.1508	0
10	0.650787	9.4756	0
11	0.678221	9.8751	0
12	0.757998	11.0366	0
13	0.656294	9.5558	0
14	0.62881	9.1556	0
15	0.659577	9.6036	0
16	0.627827	9.1413	0
17	0.624652	9.0951	0
18	0.622916	9.0698	0
19	0.581259	8.4633	0
20	0.569849	8.2971	0
21	0.541555	7.8852	0
22	0.495064	7.2082	0
23	0.522837	7.6126	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.812942	11.8366	0
2	0.262353	3.8199	8.8e-05
3	0.379289	5.5225	0
4	0.110569	1.6099	0.054453
5	0.154062	2.2432	0.01296
6	0.109735	1.5978	0.055793
7	-0.008216	-0.1196	0.452447
8	0.02495	0.3633	0.358381
9	0.019407	0.2826	0.388893
10	-0.105433	-1.5351	0.063121
11	0.149735	2.1802	0.015173
12	0.340337	4.9554	1e-06
13	-0.230237	-3.3523	0.000474
14	-0.015715	-0.2288	0.409617
15	-0.005333	-0.0776	0.469091
16	-0.048144	-0.701	0.242039
17	0.017713	0.2579	0.398363
18	-0.035302	-0.514	0.303894
19	-0.065017	-0.9467	0.172445
20	-0.022118	-0.322	0.373869
21	-0.130237	-1.8963	0.029641
22	-0.051192	-0.7454	0.228437
23	0.052181	0.7598	0.224121

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.812942 & 11.8366 & 0 \tabularnewline
2 & 0.262353 & 3.8199 & 8.8e-05 \tabularnewline
3 & 0.379289 & 5.5225 & 0 \tabularnewline
4 & 0.110569 & 1.6099 & 0.054453 \tabularnewline
5 & 0.154062 & 2.2432 & 0.01296 \tabularnewline
6 & 0.109735 & 1.5978 & 0.055793 \tabularnewline
7 & -0.008216 & -0.1196 & 0.452447 \tabularnewline
8 & 0.02495 & 0.3633 & 0.358381 \tabularnewline
9 & 0.019407 & 0.2826 & 0.388893 \tabularnewline
10 & -0.105433 & -1.5351 & 0.063121 \tabularnewline
11 & 0.149735 & 2.1802 & 0.015173 \tabularnewline
12 & 0.340337 & 4.9554 & 1e-06 \tabularnewline
13 & -0.230237 & -3.3523 & 0.000474 \tabularnewline
14 & -0.015715 & -0.2288 & 0.409617 \tabularnewline
15 & -0.005333 & -0.0776 & 0.469091 \tabularnewline
16 & -0.048144 & -0.701 & 0.242039 \tabularnewline
17 & 0.017713 & 0.2579 & 0.398363 \tabularnewline
18 & -0.035302 & -0.514 & 0.303894 \tabularnewline
19 & -0.065017 & -0.9467 & 0.172445 \tabularnewline
20 & -0.022118 & -0.322 & 0.373869 \tabularnewline
21 & -0.130237 & -1.8963 & 0.029641 \tabularnewline
22 & -0.051192 & -0.7454 & 0.228437 \tabularnewline
23 & 0.052181 & 0.7598 & 0.224121 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310532&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]0.812942[/C][C]11.8366[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.262353[/C][C]3.8199[/C][C]8.8e-05[/C][/ROW]
[ROW][C]3[/C][C]0.379289[/C][C]5.5225[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.110569[/C][C]1.6099[/C][C]0.054453[/C][/ROW]
[ROW][C]5[/C][C]0.154062[/C][C]2.2432[/C][C]0.01296[/C][/ROW]
[ROW][C]6[/C][C]0.109735[/C][C]1.5978[/C][C]0.055793[/C][/ROW]
[ROW][C]7[/C][C]-0.008216[/C][C]-0.1196[/C][C]0.452447[/C][/ROW]
[ROW][C]8[/C][C]0.02495[/C][C]0.3633[/C][C]0.358381[/C][/ROW]
[ROW][C]9[/C][C]0.019407[/C][C]0.2826[/C][C]0.388893[/C][/ROW]
[ROW][C]10[/C][C]-0.105433[/C][C]-1.5351[/C][C]0.063121[/C][/ROW]
[ROW][C]11[/C][C]0.149735[/C][C]2.1802[/C][C]0.015173[/C][/ROW]
[ROW][C]12[/C][C]0.340337[/C][C]4.9554[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.230237[/C][C]-3.3523[/C][C]0.000474[/C][/ROW]
[ROW][C]14[/C][C]-0.015715[/C][C]-0.2288[/C][C]0.409617[/C][/ROW]
[ROW][C]15[/C][C]-0.005333[/C][C]-0.0776[/C][C]0.469091[/C][/ROW]
[ROW][C]16[/C][C]-0.048144[/C][C]-0.701[/C][C]0.242039[/C][/ROW]
[ROW][C]17[/C][C]0.017713[/C][C]0.2579[/C][C]0.398363[/C][/ROW]
[ROW][C]18[/C][C]-0.035302[/C][C]-0.514[/C][C]0.303894[/C][/ROW]
[ROW][C]19[/C][C]-0.065017[/C][C]-0.9467[/C][C]0.172445[/C][/ROW]
[ROW][C]20[/C][C]-0.022118[/C][C]-0.322[/C][C]0.373869[/C][/ROW]
[ROW][C]21[/C][C]-0.130237[/C][C]-1.8963[/C][C]0.029641[/C][/ROW]
[ROW][C]22[/C][C]-0.051192[/C][C]-0.7454[/C][C]0.228437[/C][/ROW]
[ROW][C]23[/C][C]0.052181[/C][C]0.7598[/C][C]0.224121[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310532&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310532&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	0.812942	11.8366	0
2	0.262353	3.8199	8.8e-05
3	0.379289	5.5225	0
4	0.110569	1.6099	0.054453
5	0.154062	2.2432	0.01296
6	0.109735	1.5978	0.055793
7	-0.008216	-0.1196	0.452447
8	0.02495	0.3633	0.358381
9	0.019407	0.2826	0.388893
10	-0.105433	-1.5351	0.063121
11	0.149735	2.1802	0.015173
12	0.340337	4.9554	1e-06
13	-0.230237	-3.3523	0.000474
14	-0.015715	-0.2288	0.409617
15	-0.005333	-0.0776	0.469091
16	-0.048144	-0.701	0.242039
17	0.017713	0.2579	0.398363
18	-0.035302	-0.514	0.303894
19	-0.065017	-0.9467	0.172445
20	-0.022118	-0.322	0.373869
21	-0.130237	-1.8963	0.029641
22	-0.051192	-0.7454	0.228437
23	0.052181	0.7598	0.224121

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)
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