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

Fri, 16 Dec 2016 09:38:21 +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/2016/Dec/16/t14818775601iu7jvc3jd65fcs.htm/, Retrieved Fri, 03 May 2024 01:51:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300121, Retrieved Fri, 03 May 2024 01:51:30 +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] [] [2016-12-16 08:38:21] [219800a2f11ddd28e3280d87dbde8c8d] [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	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=300121&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=300121&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300121&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	-0.36121	-3.8567	9.5e-05
2	-0.231202	-2.4686	0.007525
3	0.25335	2.705	0.003939
4	-0.201691	-2.1535	0.016694
5	0.054761	0.5847	0.279958
6	0.184084	1.9655	0.025895
7	-0.332501	-3.5501	0.00028
8	0.104896	1.12	0.132537
9	0.218908	2.3373	0.010584
10	-0.185796	-1.9838	0.024843
11	0.060786	0.649	0.258816
12	-0.04955	-0.529	0.298901
13	-0.098834	-1.0553	0.146768
14	0.140483	1.5	0.068196
15	-0.05106	-0.5452	0.293351
16	-0.07571	-0.8084	0.210282
17	0.115422	1.2324	0.110172
18	0.090414	0.9654	0.168205
19	-0.149886	-1.6003	0.056145
20	0.137555	1.4687	0.072335

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.36121 & -3.8567 & 9.5e-05 \tabularnewline
2 & -0.231202 & -2.4686 & 0.007525 \tabularnewline
3 & 0.25335 & 2.705 & 0.003939 \tabularnewline
4 & -0.201691 & -2.1535 & 0.016694 \tabularnewline
5 & 0.054761 & 0.5847 & 0.279958 \tabularnewline
6 & 0.184084 & 1.9655 & 0.025895 \tabularnewline
7 & -0.332501 & -3.5501 & 0.00028 \tabularnewline
8 & 0.104896 & 1.12 & 0.132537 \tabularnewline
9 & 0.218908 & 2.3373 & 0.010584 \tabularnewline
10 & -0.185796 & -1.9838 & 0.024843 \tabularnewline
11 & 0.060786 & 0.649 & 0.258816 \tabularnewline
12 & -0.04955 & -0.529 & 0.298901 \tabularnewline
13 & -0.098834 & -1.0553 & 0.146768 \tabularnewline
14 & 0.140483 & 1.5 & 0.068196 \tabularnewline
15 & -0.05106 & -0.5452 & 0.293351 \tabularnewline
16 & -0.07571 & -0.8084 & 0.210282 \tabularnewline
17 & 0.115422 & 1.2324 & 0.110172 \tabularnewline
18 & 0.090414 & 0.9654 & 0.168205 \tabularnewline
19 & -0.149886 & -1.6003 & 0.056145 \tabularnewline
20 & 0.137555 & 1.4687 & 0.072335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300121&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]-0.36121[/C][C]-3.8567[/C][C]9.5e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.231202[/C][C]-2.4686[/C][C]0.007525[/C][/ROW]
[ROW][C]3[/C][C]0.25335[/C][C]2.705[/C][C]0.003939[/C][/ROW]
[ROW][C]4[/C][C]-0.201691[/C][C]-2.1535[/C][C]0.016694[/C][/ROW]
[ROW][C]5[/C][C]0.054761[/C][C]0.5847[/C][C]0.279958[/C][/ROW]
[ROW][C]6[/C][C]0.184084[/C][C]1.9655[/C][C]0.025895[/C][/ROW]
[ROW][C]7[/C][C]-0.332501[/C][C]-3.5501[/C][C]0.00028[/C][/ROW]
[ROW][C]8[/C][C]0.104896[/C][C]1.12[/C][C]0.132537[/C][/ROW]
[ROW][C]9[/C][C]0.218908[/C][C]2.3373[/C][C]0.010584[/C][/ROW]
[ROW][C]10[/C][C]-0.185796[/C][C]-1.9838[/C][C]0.024843[/C][/ROW]
[ROW][C]11[/C][C]0.060786[/C][C]0.649[/C][C]0.258816[/C][/ROW]
[ROW][C]12[/C][C]-0.04955[/C][C]-0.529[/C][C]0.298901[/C][/ROW]
[ROW][C]13[/C][C]-0.098834[/C][C]-1.0553[/C][C]0.146768[/C][/ROW]
[ROW][C]14[/C][C]0.140483[/C][C]1.5[/C][C]0.068196[/C][/ROW]
[ROW][C]15[/C][C]-0.05106[/C][C]-0.5452[/C][C]0.293351[/C][/ROW]
[ROW][C]16[/C][C]-0.07571[/C][C]-0.8084[/C][C]0.210282[/C][/ROW]
[ROW][C]17[/C][C]0.115422[/C][C]1.2324[/C][C]0.110172[/C][/ROW]
[ROW][C]18[/C][C]0.090414[/C][C]0.9654[/C][C]0.168205[/C][/ROW]
[ROW][C]19[/C][C]-0.149886[/C][C]-1.6003[/C][C]0.056145[/C][/ROW]
[ROW][C]20[/C][C]0.137555[/C][C]1.4687[/C][C]0.072335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300121&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300121&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	-0.36121	-3.8567	9.5e-05
2	-0.231202	-2.4686	0.007525
3	0.25335	2.705	0.003939
4	-0.201691	-2.1535	0.016694
5	0.054761	0.5847	0.279958
6	0.184084	1.9655	0.025895
7	-0.332501	-3.5501	0.00028
8	0.104896	1.12	0.132537
9	0.218908	2.3373	0.010584
10	-0.185796	-1.9838	0.024843
11	0.060786	0.649	0.258816
12	-0.04955	-0.529	0.298901
13	-0.098834	-1.0553	0.146768
14	0.140483	1.5	0.068196
15	-0.05106	-0.5452	0.293351
16	-0.07571	-0.8084	0.210282
17	0.115422	1.2324	0.110172
18	0.090414	0.9654	0.168205
19	-0.149886	-1.6003	0.056145
20	0.137555	1.4687	0.072335

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.36121	-3.8567	9.5e-05
2	-0.415944	-4.4411	1e-05
3	-0.021057	-0.2248	0.411258
4	-0.245082	-2.6168	0.00504
5	-0.058423	-0.6238	0.267008
6	0.097086	1.0366	0.151059
7	-0.222713	-2.3779	0.009537
8	-0.10491	-1.1201	0.132505
9	0.07806	0.8335	0.203167
10	0.04484	0.4788	0.316513
11	0.046711	0.4987	0.309462
12	-0.096812	-1.0337	0.15174
13	-0.081334	-0.8684	0.193498
14	-0.087314	-0.9323	0.176587
15	-0.108113	-1.1543	0.125389
16	-0.064215	-0.6856	0.247171
17	-0.021375	-0.2282	0.409943
18	0.187188	1.9986	0.024015
19	-0.028759	-0.3071	0.379678
20	0.160634	1.7151	0.044522

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.36121 & -3.8567 & 9.5e-05 \tabularnewline
2 & -0.415944 & -4.4411 & 1e-05 \tabularnewline
3 & -0.021057 & -0.2248 & 0.411258 \tabularnewline
4 & -0.245082 & -2.6168 & 0.00504 \tabularnewline
5 & -0.058423 & -0.6238 & 0.267008 \tabularnewline
6 & 0.097086 & 1.0366 & 0.151059 \tabularnewline
7 & -0.222713 & -2.3779 & 0.009537 \tabularnewline
8 & -0.10491 & -1.1201 & 0.132505 \tabularnewline
9 & 0.07806 & 0.8335 & 0.203167 \tabularnewline
10 & 0.04484 & 0.4788 & 0.316513 \tabularnewline
11 & 0.046711 & 0.4987 & 0.309462 \tabularnewline
12 & -0.096812 & -1.0337 & 0.15174 \tabularnewline
13 & -0.081334 & -0.8684 & 0.193498 \tabularnewline
14 & -0.087314 & -0.9323 & 0.176587 \tabularnewline
15 & -0.108113 & -1.1543 & 0.125389 \tabularnewline
16 & -0.064215 & -0.6856 & 0.247171 \tabularnewline
17 & -0.021375 & -0.2282 & 0.409943 \tabularnewline
18 & 0.187188 & 1.9986 & 0.024015 \tabularnewline
19 & -0.028759 & -0.3071 & 0.379678 \tabularnewline
20 & 0.160634 & 1.7151 & 0.044522 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300121&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]-0.36121[/C][C]-3.8567[/C][C]9.5e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.415944[/C][C]-4.4411[/C][C]1e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.021057[/C][C]-0.2248[/C][C]0.411258[/C][/ROW]
[ROW][C]4[/C][C]-0.245082[/C][C]-2.6168[/C][C]0.00504[/C][/ROW]
[ROW][C]5[/C][C]-0.058423[/C][C]-0.6238[/C][C]0.267008[/C][/ROW]
[ROW][C]6[/C][C]0.097086[/C][C]1.0366[/C][C]0.151059[/C][/ROW]
[ROW][C]7[/C][C]-0.222713[/C][C]-2.3779[/C][C]0.009537[/C][/ROW]
[ROW][C]8[/C][C]-0.10491[/C][C]-1.1201[/C][C]0.132505[/C][/ROW]
[ROW][C]9[/C][C]0.07806[/C][C]0.8335[/C][C]0.203167[/C][/ROW]
[ROW][C]10[/C][C]0.04484[/C][C]0.4788[/C][C]0.316513[/C][/ROW]
[ROW][C]11[/C][C]0.046711[/C][C]0.4987[/C][C]0.309462[/C][/ROW]
[ROW][C]12[/C][C]-0.096812[/C][C]-1.0337[/C][C]0.15174[/C][/ROW]
[ROW][C]13[/C][C]-0.081334[/C][C]-0.8684[/C][C]0.193498[/C][/ROW]
[ROW][C]14[/C][C]-0.087314[/C][C]-0.9323[/C][C]0.176587[/C][/ROW]
[ROW][C]15[/C][C]-0.108113[/C][C]-1.1543[/C][C]0.125389[/C][/ROW]
[ROW][C]16[/C][C]-0.064215[/C][C]-0.6856[/C][C]0.247171[/C][/ROW]
[ROW][C]17[/C][C]-0.021375[/C][C]-0.2282[/C][C]0.409943[/C][/ROW]
[ROW][C]18[/C][C]0.187188[/C][C]1.9986[/C][C]0.024015[/C][/ROW]
[ROW][C]19[/C][C]-0.028759[/C][C]-0.3071[/C][C]0.379678[/C][/ROW]
[ROW][C]20[/C][C]0.160634[/C][C]1.7151[/C][C]0.044522[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300121&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300121&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	-0.36121	-3.8567	9.5e-05
2	-0.415944	-4.4411	1e-05
3	-0.021057	-0.2248	0.411258
4	-0.245082	-2.6168	0.00504
5	-0.058423	-0.6238	0.267008
6	0.097086	1.0366	0.151059
7	-0.222713	-2.3779	0.009537
8	-0.10491	-1.1201	0.132505
9	0.07806	0.8335	0.203167
10	0.04484	0.4788	0.316513
11	0.046711	0.4987	0.309462
12	-0.096812	-1.0337	0.15174
13	-0.081334	-0.8684	0.193498
14	-0.087314	-0.9323	0.176587
15	-0.108113	-1.1543	0.125389
16	-0.064215	-0.6856	0.247171
17	-0.021375	-0.2282	0.409943
18	0.187188	1.9986	0.024015
19	-0.028759	-0.3071	0.379678
20	0.160634	1.7151	0.044522

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 = 2 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; 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