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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 08:23:49 +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/17/t1481959684l10kk5q472swbng.htm/, Retrieved Fri, 01 Nov 2024 03:46:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300601, Retrieved Fri, 01 Nov 2024 03:46:13 +0000

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Estimated Impact

145

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

-       [(Partial) Autocorrelation Function] [N 2460- ACF (2)] [2016-12-17 07:23:49] [86c7fb9c8a0af864c0a27e2f433e80d7] [Current]

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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	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=300601&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=300601&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300601&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	-0.166713	-1.7722	0.039529
2	-0.340903	-3.6238	0.000218
3	-0.047725	-0.5073	0.306458
4	0.129254	1.374	0.086083
5	-0.038782	-0.4123	0.340466
6	-0.045274	-0.4813	0.315627
7	0.017736	0.1885	0.425399
8	-0.034935	-0.3714	0.35553
9	0.046337	0.4926	0.311637
10	0.18411	1.9571	0.0264
11	0.040699	0.4326	0.333051
12	-0.466117	-4.9549	1e-06
13	0.099839	1.0613	0.145407
14	0.135675	1.4422	0.075999
15	0.07843	0.8337	0.203097
16	-0.128679	-1.3679	0.087033
17	0.018338	0.1949	0.422898
18	0.093658	0.9956	0.160785
19	-0.010863	-0.1155	0.454136
20	-0.089944	-0.9561	0.170527
21	0.057947	0.616	0.269573

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.166713 & -1.7722 & 0.039529 \tabularnewline
2 & -0.340903 & -3.6238 & 0.000218 \tabularnewline
3 & -0.047725 & -0.5073 & 0.306458 \tabularnewline
4 & 0.129254 & 1.374 & 0.086083 \tabularnewline
5 & -0.038782 & -0.4123 & 0.340466 \tabularnewline
6 & -0.045274 & -0.4813 & 0.315627 \tabularnewline
7 & 0.017736 & 0.1885 & 0.425399 \tabularnewline
8 & -0.034935 & -0.3714 & 0.35553 \tabularnewline
9 & 0.046337 & 0.4926 & 0.311637 \tabularnewline
10 & 0.18411 & 1.9571 & 0.0264 \tabularnewline
11 & 0.040699 & 0.4326 & 0.333051 \tabularnewline
12 & -0.466117 & -4.9549 & 1e-06 \tabularnewline
13 & 0.099839 & 1.0613 & 0.145407 \tabularnewline
14 & 0.135675 & 1.4422 & 0.075999 \tabularnewline
15 & 0.07843 & 0.8337 & 0.203097 \tabularnewline
16 & -0.128679 & -1.3679 & 0.087033 \tabularnewline
17 & 0.018338 & 0.1949 & 0.422898 \tabularnewline
18 & 0.093658 & 0.9956 & 0.160785 \tabularnewline
19 & -0.010863 & -0.1155 & 0.454136 \tabularnewline
20 & -0.089944 & -0.9561 & 0.170527 \tabularnewline
21 & 0.057947 & 0.616 & 0.269573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300601&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]-0.166713[/C][C]-1.7722[/C][C]0.039529[/C][/ROW]
[ROW][C]2[/C][C]-0.340903[/C][C]-3.6238[/C][C]0.000218[/C][/ROW]
[ROW][C]3[/C][C]-0.047725[/C][C]-0.5073[/C][C]0.306458[/C][/ROW]
[ROW][C]4[/C][C]0.129254[/C][C]1.374[/C][C]0.086083[/C][/ROW]
[ROW][C]5[/C][C]-0.038782[/C][C]-0.4123[/C][C]0.340466[/C][/ROW]
[ROW][C]6[/C][C]-0.045274[/C][C]-0.4813[/C][C]0.315627[/C][/ROW]
[ROW][C]7[/C][C]0.017736[/C][C]0.1885[/C][C]0.425399[/C][/ROW]
[ROW][C]8[/C][C]-0.034935[/C][C]-0.3714[/C][C]0.35553[/C][/ROW]
[ROW][C]9[/C][C]0.046337[/C][C]0.4926[/C][C]0.311637[/C][/ROW]
[ROW][C]10[/C][C]0.18411[/C][C]1.9571[/C][C]0.0264[/C][/ROW]
[ROW][C]11[/C][C]0.040699[/C][C]0.4326[/C][C]0.333051[/C][/ROW]
[ROW][C]12[/C][C]-0.466117[/C][C]-4.9549[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.099839[/C][C]1.0613[/C][C]0.145407[/C][/ROW]
[ROW][C]14[/C][C]0.135675[/C][C]1.4422[/C][C]0.075999[/C][/ROW]
[ROW][C]15[/C][C]0.07843[/C][C]0.8337[/C][C]0.203097[/C][/ROW]
[ROW][C]16[/C][C]-0.128679[/C][C]-1.3679[/C][C]0.087033[/C][/ROW]
[ROW][C]17[/C][C]0.018338[/C][C]0.1949[/C][C]0.422898[/C][/ROW]
[ROW][C]18[/C][C]0.093658[/C][C]0.9956[/C][C]0.160785[/C][/ROW]
[ROW][C]19[/C][C]-0.010863[/C][C]-0.1155[/C][C]0.454136[/C][/ROW]
[ROW][C]20[/C][C]-0.089944[/C][C]-0.9561[/C][C]0.170527[/C][/ROW]
[ROW][C]21[/C][C]0.057947[/C][C]0.616[/C][C]0.269573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300601&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300601&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	-0.166713	-1.7722	0.039529
2	-0.340903	-3.6238	0.000218
3	-0.047725	-0.5073	0.306458
4	0.129254	1.374	0.086083
5	-0.038782	-0.4123	0.340466
6	-0.045274	-0.4813	0.315627
7	0.017736	0.1885	0.425399
8	-0.034935	-0.3714	0.35553
9	0.046337	0.4926	0.311637
10	0.18411	1.9571	0.0264
11	0.040699	0.4326	0.333051
12	-0.466117	-4.9549	1e-06
13	0.099839	1.0613	0.145407
14	0.135675	1.4422	0.075999
15	0.07843	0.8337	0.203097
16	-0.128679	-1.3679	0.087033
17	0.018338	0.1949	0.422898
18	0.093658	0.9956	0.160785
19	-0.010863	-0.1155	0.454136
20	-0.089944	-0.9561	0.170527
21	0.057947	0.616	0.269573

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.166713	-1.7722	0.039529
2	-0.379237	-4.0313	5e-05
3	-0.227462	-2.4179	0.008603
4	-0.089787	-0.9545	0.170946
5	-0.153146	-1.628	0.053159
6	-0.107736	-1.1453	0.127262
7	-0.085589	-0.9098	0.182427
8	-0.148058	-1.5739	0.059156
9	-0.043266	-0.4599	0.323227
10	0.171086	1.8187	0.035805
11	0.216934	2.306	0.011466
12	-0.317042	-3.3702	0.000514
13	-0.017611	-0.1872	0.425915
14	-0.176092	-1.8719	0.031904
15	0.010537	0.112	0.455507
16	-0.079438	-0.8444	0.200105
17	-0.03589	-0.3815	0.351767
18	0.028062	0.2983	0.383008
19	-0.00964	-0.1025	0.45928
20	-0.111607	-1.1864	0.118977
21	0.075137	0.7987	0.213066

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.166713 & -1.7722 & 0.039529 \tabularnewline
2 & -0.379237 & -4.0313 & 5e-05 \tabularnewline
3 & -0.227462 & -2.4179 & 0.008603 \tabularnewline
4 & -0.089787 & -0.9545 & 0.170946 \tabularnewline
5 & -0.153146 & -1.628 & 0.053159 \tabularnewline
6 & -0.107736 & -1.1453 & 0.127262 \tabularnewline
7 & -0.085589 & -0.9098 & 0.182427 \tabularnewline
8 & -0.148058 & -1.5739 & 0.059156 \tabularnewline
9 & -0.043266 & -0.4599 & 0.323227 \tabularnewline
10 & 0.171086 & 1.8187 & 0.035805 \tabularnewline
11 & 0.216934 & 2.306 & 0.011466 \tabularnewline
12 & -0.317042 & -3.3702 & 0.000514 \tabularnewline
13 & -0.017611 & -0.1872 & 0.425915 \tabularnewline
14 & -0.176092 & -1.8719 & 0.031904 \tabularnewline
15 & 0.010537 & 0.112 & 0.455507 \tabularnewline
16 & -0.079438 & -0.8444 & 0.200105 \tabularnewline
17 & -0.03589 & -0.3815 & 0.351767 \tabularnewline
18 & 0.028062 & 0.2983 & 0.383008 \tabularnewline
19 & -0.00964 & -0.1025 & 0.45928 \tabularnewline
20 & -0.111607 & -1.1864 & 0.118977 \tabularnewline
21 & 0.075137 & 0.7987 & 0.213066 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300601&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]-0.166713[/C][C]-1.7722[/C][C]0.039529[/C][/ROW]
[ROW][C]2[/C][C]-0.379237[/C][C]-4.0313[/C][C]5e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.227462[/C][C]-2.4179[/C][C]0.008603[/C][/ROW]
[ROW][C]4[/C][C]-0.089787[/C][C]-0.9545[/C][C]0.170946[/C][/ROW]
[ROW][C]5[/C][C]-0.153146[/C][C]-1.628[/C][C]0.053159[/C][/ROW]
[ROW][C]6[/C][C]-0.107736[/C][C]-1.1453[/C][C]0.127262[/C][/ROW]
[ROW][C]7[/C][C]-0.085589[/C][C]-0.9098[/C][C]0.182427[/C][/ROW]
[ROW][C]8[/C][C]-0.148058[/C][C]-1.5739[/C][C]0.059156[/C][/ROW]
[ROW][C]9[/C][C]-0.043266[/C][C]-0.4599[/C][C]0.323227[/C][/ROW]
[ROW][C]10[/C][C]0.171086[/C][C]1.8187[/C][C]0.035805[/C][/ROW]
[ROW][C]11[/C][C]0.216934[/C][C]2.306[/C][C]0.011466[/C][/ROW]
[ROW][C]12[/C][C]-0.317042[/C][C]-3.3702[/C][C]0.000514[/C][/ROW]
[ROW][C]13[/C][C]-0.017611[/C][C]-0.1872[/C][C]0.425915[/C][/ROW]
[ROW][C]14[/C][C]-0.176092[/C][C]-1.8719[/C][C]0.031904[/C][/ROW]
[ROW][C]15[/C][C]0.010537[/C][C]0.112[/C][C]0.455507[/C][/ROW]
[ROW][C]16[/C][C]-0.079438[/C][C]-0.8444[/C][C]0.200105[/C][/ROW]
[ROW][C]17[/C][C]-0.03589[/C][C]-0.3815[/C][C]0.351767[/C][/ROW]
[ROW][C]18[/C][C]0.028062[/C][C]0.2983[/C][C]0.383008[/C][/ROW]
[ROW][C]19[/C][C]-0.00964[/C][C]-0.1025[/C][C]0.45928[/C][/ROW]
[ROW][C]20[/C][C]-0.111607[/C][C]-1.1864[/C][C]0.118977[/C][/ROW]
[ROW][C]21[/C][C]0.075137[/C][C]0.7987[/C][C]0.213066[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300601&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300601&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	-0.166713	-1.7722	0.039529
2	-0.379237	-4.0313	5e-05
3	-0.227462	-2.4179	0.008603
4	-0.089787	-0.9545	0.170946
5	-0.153146	-1.628	0.053159
6	-0.107736	-1.1453	0.127262
7	-0.085589	-0.9098	0.182427
8	-0.148058	-1.5739	0.059156
9	-0.043266	-0.4599	0.323227
10	0.171086	1.8187	0.035805
11	0.216934	2.306	0.011466
12	-0.317042	-3.3702	0.000514
13	-0.017611	-0.1872	0.425915
14	-0.176092	-1.8719	0.031904
15	0.010537	0.112	0.455507
16	-0.079438	-0.8444	0.200105
17	-0.03589	-0.3815	0.351767
18	0.028062	0.2983	0.383008
19	-0.00964	-0.1025	0.45928
20	-0.111607	-1.1864	0.118977
21	0.075137	0.7987	0.213066

Figure 1

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Figure 2

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Figure 3

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Parameters (Session):

par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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