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*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 14:04:03 +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/t1481893497pp47ru6hiatjmrz.htm/, Retrieved Fri, 01 Nov 2024 03:27:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300237, Retrieved Fri, 01 Nov 2024 03:27:23 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

133

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

-     [(Partial) Autocorrelation Function] [autocorrelation N247] [2016-12-16 08:48:05] [5ad8e5538a25411d3c3b0ec85050bd51]
- R P     [(Partial) Autocorrelation Function] [Autocorrelation N...] [2016-12-16 13:04:03] [b95f76f605693b3a3343a287ab24f42a] [Current]
- R         [(Partial) Autocorrelation Function] [autocorrelation m...] [2016-12-18 19:18:14] [d1d385d9b7e195437bdc484ddbefdda4] 
- R         [(Partial) Autocorrelation Function] [1x d] [2016-12-18 21:05:51] [d1d385d9b7e195437bdc484ddbefdda4] 

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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=300237&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=300237&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300237&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	0.865233	9.2382	0
2	0.836928	8.9359	0
3	0.841362	8.9833	0
4	0.818772	8.7421	0
5	0.791554	8.4515	0
6	0.776145	8.287	0
7	0.762583	8.1422	0
8	0.722117	7.7101	0
9	0.699244	7.4659	0
10	0.649926	6.9393	0
11	0.642797	6.8632	0
12	0.706937	7.548	0
13	0.60835	6.4954	0
14	0.583299	6.2279	0
15	0.581907	6.2131	0
16	0.554349	5.9188	0
17	0.52921	5.6504	0
18	0.508534	5.4297	0
19	0.489969	5.2314	0
20	0.4633	4.9467	1e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.865233 & 9.2382 & 0 \tabularnewline
2 & 0.836928 & 8.9359 & 0 \tabularnewline
3 & 0.841362 & 8.9833 & 0 \tabularnewline
4 & 0.818772 & 8.7421 & 0 \tabularnewline
5 & 0.791554 & 8.4515 & 0 \tabularnewline
6 & 0.776145 & 8.287 & 0 \tabularnewline
7 & 0.762583 & 8.1422 & 0 \tabularnewline
8 & 0.722117 & 7.7101 & 0 \tabularnewline
9 & 0.699244 & 7.4659 & 0 \tabularnewline
10 & 0.649926 & 6.9393 & 0 \tabularnewline
11 & 0.642797 & 6.8632 & 0 \tabularnewline
12 & 0.706937 & 7.548 & 0 \tabularnewline
13 & 0.60835 & 6.4954 & 0 \tabularnewline
14 & 0.583299 & 6.2279 & 0 \tabularnewline
15 & 0.581907 & 6.2131 & 0 \tabularnewline
16 & 0.554349 & 5.9188 & 0 \tabularnewline
17 & 0.52921 & 5.6504 & 0 \tabularnewline
18 & 0.508534 & 5.4297 & 0 \tabularnewline
19 & 0.489969 & 5.2314 & 0 \tabularnewline
20 & 0.4633 & 4.9467 & 1e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300237&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]0.865233[/C][C]9.2382[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.836928[/C][C]8.9359[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.841362[/C][C]8.9833[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.818772[/C][C]8.7421[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.791554[/C][C]8.4515[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.776145[/C][C]8.287[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.762583[/C][C]8.1422[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.722117[/C][C]7.7101[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.699244[/C][C]7.4659[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.649926[/C][C]6.9393[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.642797[/C][C]6.8632[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.706937[/C][C]7.548[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.60835[/C][C]6.4954[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.583299[/C][C]6.2279[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.581907[/C][C]6.2131[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.554349[/C][C]5.9188[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.52921[/C][C]5.6504[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.508534[/C][C]5.4297[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.489969[/C][C]5.2314[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.4633[/C][C]4.9467[/C][C]1e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300237&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300237&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	0.865233	9.2382	0
2	0.836928	8.9359	0
3	0.841362	8.9833	0
4	0.818772	8.7421	0
5	0.791554	8.4515	0
6	0.776145	8.287	0
7	0.762583	8.1422	0
8	0.722117	7.7101	0
9	0.699244	7.4659	0
10	0.649926	6.9393	0
11	0.642797	6.8632	0
12	0.706937	7.548	0
13	0.60835	6.4954	0
14	0.583299	6.2279	0
15	0.581907	6.2131	0
16	0.554349	5.9188	0
17	0.52921	5.6504	0
18	0.508534	5.4297	0
19	0.489969	5.2314	0
20	0.4633	4.9467	1e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.865233	9.2382	0
2	0.351274	3.7506	0.000139
3	0.307057	3.2785	0.000692
4	0.109456	1.1687	0.122487
5	0.01824	0.1947	0.422968
6	0.018606	0.1987	0.421444
7	0.025561	0.2729	0.392706
8	-0.101563	-1.0844	0.140238
9	-0.04296	-0.4587	0.323666
10	-0.181281	-1.9356	0.0277
11	0.052205	0.5574	0.289174
12	0.470535	5.0239	1e-06
13	-0.343126	-3.6636	0.000189
14	-0.076496	-0.8167	0.207887
15	-0.01462	-0.1561	0.438116
16	-0.030388	-0.3245	0.373095
17	0.095797	1.0228	0.154276
18	-0.127694	-1.3634	0.087722
19	-0.127811	-1.3647	0.087525
20	0.12402	1.3242	0.094048

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.865233 & 9.2382 & 0 \tabularnewline
2 & 0.351274 & 3.7506 & 0.000139 \tabularnewline
3 & 0.307057 & 3.2785 & 0.000692 \tabularnewline
4 & 0.109456 & 1.1687 & 0.122487 \tabularnewline
5 & 0.01824 & 0.1947 & 0.422968 \tabularnewline
6 & 0.018606 & 0.1987 & 0.421444 \tabularnewline
7 & 0.025561 & 0.2729 & 0.392706 \tabularnewline
8 & -0.101563 & -1.0844 & 0.140238 \tabularnewline
9 & -0.04296 & -0.4587 & 0.323666 \tabularnewline
10 & -0.181281 & -1.9356 & 0.0277 \tabularnewline
11 & 0.052205 & 0.5574 & 0.289174 \tabularnewline
12 & 0.470535 & 5.0239 & 1e-06 \tabularnewline
13 & -0.343126 & -3.6636 & 0.000189 \tabularnewline
14 & -0.076496 & -0.8167 & 0.207887 \tabularnewline
15 & -0.01462 & -0.1561 & 0.438116 \tabularnewline
16 & -0.030388 & -0.3245 & 0.373095 \tabularnewline
17 & 0.095797 & 1.0228 & 0.154276 \tabularnewline
18 & -0.127694 & -1.3634 & 0.087722 \tabularnewline
19 & -0.127811 & -1.3647 & 0.087525 \tabularnewline
20 & 0.12402 & 1.3242 & 0.094048 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300237&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]0.865233[/C][C]9.2382[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.351274[/C][C]3.7506[/C][C]0.000139[/C][/ROW]
[ROW][C]3[/C][C]0.307057[/C][C]3.2785[/C][C]0.000692[/C][/ROW]
[ROW][C]4[/C][C]0.109456[/C][C]1.1687[/C][C]0.122487[/C][/ROW]
[ROW][C]5[/C][C]0.01824[/C][C]0.1947[/C][C]0.422968[/C][/ROW]
[ROW][C]6[/C][C]0.018606[/C][C]0.1987[/C][C]0.421444[/C][/ROW]
[ROW][C]7[/C][C]0.025561[/C][C]0.2729[/C][C]0.392706[/C][/ROW]
[ROW][C]8[/C][C]-0.101563[/C][C]-1.0844[/C][C]0.140238[/C][/ROW]
[ROW][C]9[/C][C]-0.04296[/C][C]-0.4587[/C][C]0.323666[/C][/ROW]
[ROW][C]10[/C][C]-0.181281[/C][C]-1.9356[/C][C]0.0277[/C][/ROW]
[ROW][C]11[/C][C]0.052205[/C][C]0.5574[/C][C]0.289174[/C][/ROW]
[ROW][C]12[/C][C]0.470535[/C][C]5.0239[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.343126[/C][C]-3.6636[/C][C]0.000189[/C][/ROW]
[ROW][C]14[/C][C]-0.076496[/C][C]-0.8167[/C][C]0.207887[/C][/ROW]
[ROW][C]15[/C][C]-0.01462[/C][C]-0.1561[/C][C]0.438116[/C][/ROW]
[ROW][C]16[/C][C]-0.030388[/C][C]-0.3245[/C][C]0.373095[/C][/ROW]
[ROW][C]17[/C][C]0.095797[/C][C]1.0228[/C][C]0.154276[/C][/ROW]
[ROW][C]18[/C][C]-0.127694[/C][C]-1.3634[/C][C]0.087722[/C][/ROW]
[ROW][C]19[/C][C]-0.127811[/C][C]-1.3647[/C][C]0.087525[/C][/ROW]
[ROW][C]20[/C][C]0.12402[/C][C]1.3242[/C][C]0.094048[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300237&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300237&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	0.865233	9.2382	0
2	0.351274	3.7506	0.000139
3	0.307057	3.2785	0.000692
4	0.109456	1.1687	0.122487
5	0.01824	0.1947	0.422968
6	0.018606	0.1987	0.421444
7	0.025561	0.2729	0.392706
8	-0.101563	-1.0844	0.140238
9	-0.04296	-0.4587	0.323666
10	-0.181281	-1.9356	0.0277
11	0.052205	0.5574	0.289174
12	0.470535	5.0239	1e-06
13	-0.343126	-3.6636	0.000189
14	-0.076496	-0.8167	0.207887
15	-0.01462	-0.1561	0.438116
16	-0.030388	-0.3245	0.373095
17	0.095797	1.0228	0.154276
18	-0.127694	-1.3634	0.087722
19	-0.127811	-1.3647	0.087525
20	0.12402	1.3242	0.094048

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = -0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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