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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

Tue, 06 Dec 2011 15:53:20 -0500

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/2011/Dec/06/t1323204834k329sh3nfa5ci33.htm/, Retrieved Mon, 29 Apr 2024 07:25:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151934, Retrieved Mon, 29 Apr 2024 07:25:32 +0000

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User-defined keywords

Estimated Impact

102

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

-       [(Partial) Autocorrelation Function] [WS 9 Partial Auto...] [2011-12-06 20:53:20] [6140f0163e532fc168d2f211324acd0a] [Current]
- R P     [(Partial) Autocorrelation Function] [WS 9 Partial Auto...] [2011-12-06 21:05:30] [f5fdea4413921432bb019d1f20c4f2ec] 
- RMP       [Spectral Analysis] [WS 9 Spectral Ana...] [2011-12-06 21:16:41] [f5fdea4413921432bb019d1f20c4f2ec] 
- R P         [Spectral Analysis] [WS 9 Spectral Ana...] [2011-12-06 21:35:07] [f5fdea4413921432bb019d1f20c4f2ec] 
-   P           [Spectral Analysis] [WS 9 Spectral Ana...] [2011-12-06 21:52:54] [f5fdea4413921432bb019d1f20c4f2ec] 
-   P             [Spectral Analysis] [WS 9 Spectral Ana...] [2011-12-16 12:23:12] [74be16979710d4c4e7c6647856088456] 
- RMP           [Variance Reduction Matrix] [WS 9 Variance Red...] [2011-12-06 22:12:11] [f5fdea4413921432bb019d1f20c4f2ec] 
- RMP           [Standard Deviation-Mean Plot] [Ws 9 Standard Dev...] [2011-12-06 22:25:52] [f5fdea4413921432bb019d1f20c4f2ec] 
- RMP           [ARIMA Backward Selection] [WS 9 ARIMA Backwa...] [2011-12-06 22:41:23] [f5fdea4413921432bb019d1f20c4f2ec] 
-   P           [Spectral Analysis] [WS 9 Spectral Ana...] [2011-12-16 11:57:04] [74be16979710d4c4e7c6647856088456] 
- R P         [Spectral Analysis] [WS 9 Spectral Ana...] [2011-12-16 11:52:18] [74be16979710d4c4e7c6647856088456] 

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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	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151934&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151934&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151934&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.741134	5.1347	3e-06
2	0.666796	4.6197	1.5e-05
3	0.620484	4.2988	4.2e-05
4	0.553977	3.8381	0.000181
5	0.433119	3.0007	0.002132
6	0.349114	2.4187	0.009708
7	0.291901	2.0224	0.024366
8	0.167444	1.1601	0.125876
9	0.08712	0.6036	0.274481
10	-0.002837	-0.0197	0.4922
11	-0.102681	-0.7114	0.240141
12	-0.248602	-1.7224	0.045721
13	-0.241773	-1.6751	0.050214
14	-0.262595	-1.8193	0.037552
15	-0.333111	-2.3079	0.012681
16	-0.378163	-2.62	0.005869
17	-0.380642	-2.6372	0.005616

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.741134 & 5.1347 & 3e-06 \tabularnewline
2 & 0.666796 & 4.6197 & 1.5e-05 \tabularnewline
3 & 0.620484 & 4.2988 & 4.2e-05 \tabularnewline
4 & 0.553977 & 3.8381 & 0.000181 \tabularnewline
5 & 0.433119 & 3.0007 & 0.002132 \tabularnewline
6 & 0.349114 & 2.4187 & 0.009708 \tabularnewline
7 & 0.291901 & 2.0224 & 0.024366 \tabularnewline
8 & 0.167444 & 1.1601 & 0.125876 \tabularnewline
9 & 0.08712 & 0.6036 & 0.274481 \tabularnewline
10 & -0.002837 & -0.0197 & 0.4922 \tabularnewline
11 & -0.102681 & -0.7114 & 0.240141 \tabularnewline
12 & -0.248602 & -1.7224 & 0.045721 \tabularnewline
13 & -0.241773 & -1.6751 & 0.050214 \tabularnewline
14 & -0.262595 & -1.8193 & 0.037552 \tabularnewline
15 & -0.333111 & -2.3079 & 0.012681 \tabularnewline
16 & -0.378163 & -2.62 & 0.005869 \tabularnewline
17 & -0.380642 & -2.6372 & 0.005616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151934&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]0.741134[/C][C]5.1347[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]0.666796[/C][C]4.6197[/C][C]1.5e-05[/C][/ROW]
[ROW][C]3[/C][C]0.620484[/C][C]4.2988[/C][C]4.2e-05[/C][/ROW]
[ROW][C]4[/C][C]0.553977[/C][C]3.8381[/C][C]0.000181[/C][/ROW]
[ROW][C]5[/C][C]0.433119[/C][C]3.0007[/C][C]0.002132[/C][/ROW]
[ROW][C]6[/C][C]0.349114[/C][C]2.4187[/C][C]0.009708[/C][/ROW]
[ROW][C]7[/C][C]0.291901[/C][C]2.0224[/C][C]0.024366[/C][/ROW]
[ROW][C]8[/C][C]0.167444[/C][C]1.1601[/C][C]0.125876[/C][/ROW]
[ROW][C]9[/C][C]0.08712[/C][C]0.6036[/C][C]0.274481[/C][/ROW]
[ROW][C]10[/C][C]-0.002837[/C][C]-0.0197[/C][C]0.4922[/C][/ROW]
[ROW][C]11[/C][C]-0.102681[/C][C]-0.7114[/C][C]0.240141[/C][/ROW]
[ROW][C]12[/C][C]-0.248602[/C][C]-1.7224[/C][C]0.045721[/C][/ROW]
[ROW][C]13[/C][C]-0.241773[/C][C]-1.6751[/C][C]0.050214[/C][/ROW]
[ROW][C]14[/C][C]-0.262595[/C][C]-1.8193[/C][C]0.037552[/C][/ROW]
[ROW][C]15[/C][C]-0.333111[/C][C]-2.3079[/C][C]0.012681[/C][/ROW]
[ROW][C]16[/C][C]-0.378163[/C][C]-2.62[/C][C]0.005869[/C][/ROW]
[ROW][C]17[/C][C]-0.380642[/C][C]-2.6372[/C][C]0.005616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151934&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151934&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	0.741134	5.1347	3e-06
2	0.666796	4.6197	1.5e-05
3	0.620484	4.2988	4.2e-05
4	0.553977	3.8381	0.000181
5	0.433119	3.0007	0.002132
6	0.349114	2.4187	0.009708
7	0.291901	2.0224	0.024366
8	0.167444	1.1601	0.125876
9	0.08712	0.6036	0.274481
10	-0.002837	-0.0197	0.4922
11	-0.102681	-0.7114	0.240141
12	-0.248602	-1.7224	0.045721
13	-0.241773	-1.6751	0.050214
14	-0.262595	-1.8193	0.037552
15	-0.333111	-2.3079	0.012681
16	-0.378163	-2.62	0.005869
17	-0.380642	-2.6372	0.005616

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.741134	5.1347	3e-06
2	0.260732	1.8064	0.038563
3	0.14738	1.0211	0.156168
4	0.020973	0.1453	0.44254
5	-0.154414	-1.0698	0.145027
6	-0.085541	-0.5926	0.2781
7	-0.009582	-0.0664	0.473673
8	-0.158192	-1.096	0.139277
9	-0.054651	-0.3786	0.353315
10	-0.098485	-0.6823	0.249158
11	-0.12708	-0.8804	0.191506
12	-0.234898	-1.6274	0.055098
13	0.124116	0.8599	0.197058
14	0.085185	0.5902	0.278919
15	-0.048727	-0.3376	0.368571
16	-0.077412	-0.5363	0.297105
17	-0.049222	-0.341	0.367288

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.741134 & 5.1347 & 3e-06 \tabularnewline
2 & 0.260732 & 1.8064 & 0.038563 \tabularnewline
3 & 0.14738 & 1.0211 & 0.156168 \tabularnewline
4 & 0.020973 & 0.1453 & 0.44254 \tabularnewline
5 & -0.154414 & -1.0698 & 0.145027 \tabularnewline
6 & -0.085541 & -0.5926 & 0.2781 \tabularnewline
7 & -0.009582 & -0.0664 & 0.473673 \tabularnewline
8 & -0.158192 & -1.096 & 0.139277 \tabularnewline
9 & -0.054651 & -0.3786 & 0.353315 \tabularnewline
10 & -0.098485 & -0.6823 & 0.249158 \tabularnewline
11 & -0.12708 & -0.8804 & 0.191506 \tabularnewline
12 & -0.234898 & -1.6274 & 0.055098 \tabularnewline
13 & 0.124116 & 0.8599 & 0.197058 \tabularnewline
14 & 0.085185 & 0.5902 & 0.278919 \tabularnewline
15 & -0.048727 & -0.3376 & 0.368571 \tabularnewline
16 & -0.077412 & -0.5363 & 0.297105 \tabularnewline
17 & -0.049222 & -0.341 & 0.367288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151934&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]0.741134[/C][C]5.1347[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]0.260732[/C][C]1.8064[/C][C]0.038563[/C][/ROW]
[ROW][C]3[/C][C]0.14738[/C][C]1.0211[/C][C]0.156168[/C][/ROW]
[ROW][C]4[/C][C]0.020973[/C][C]0.1453[/C][C]0.44254[/C][/ROW]
[ROW][C]5[/C][C]-0.154414[/C][C]-1.0698[/C][C]0.145027[/C][/ROW]
[ROW][C]6[/C][C]-0.085541[/C][C]-0.5926[/C][C]0.2781[/C][/ROW]
[ROW][C]7[/C][C]-0.009582[/C][C]-0.0664[/C][C]0.473673[/C][/ROW]
[ROW][C]8[/C][C]-0.158192[/C][C]-1.096[/C][C]0.139277[/C][/ROW]
[ROW][C]9[/C][C]-0.054651[/C][C]-0.3786[/C][C]0.353315[/C][/ROW]
[ROW][C]10[/C][C]-0.098485[/C][C]-0.6823[/C][C]0.249158[/C][/ROW]
[ROW][C]11[/C][C]-0.12708[/C][C]-0.8804[/C][C]0.191506[/C][/ROW]
[ROW][C]12[/C][C]-0.234898[/C][C]-1.6274[/C][C]0.055098[/C][/ROW]
[ROW][C]13[/C][C]0.124116[/C][C]0.8599[/C][C]0.197058[/C][/ROW]
[ROW][C]14[/C][C]0.085185[/C][C]0.5902[/C][C]0.278919[/C][/ROW]
[ROW][C]15[/C][C]-0.048727[/C][C]-0.3376[/C][C]0.368571[/C][/ROW]
[ROW][C]16[/C][C]-0.077412[/C][C]-0.5363[/C][C]0.297105[/C][/ROW]
[ROW][C]17[/C][C]-0.049222[/C][C]-0.341[/C][C]0.367288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151934&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151934&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	0.741134	5.1347	3e-06
2	0.260732	1.8064	0.038563
3	0.14738	1.0211	0.156168
4	0.020973	0.1453	0.44254
5	-0.154414	-1.0698	0.145027
6	-0.085541	-0.5926	0.2781
7	-0.009582	-0.0664	0.473673
8	-0.158192	-1.096	0.139277
9	-0.054651	-0.3786	0.353315
10	-0.098485	-0.6823	0.249158
11	-0.12708	-0.8804	0.191506
12	-0.234898	-1.6274	0.055098
13	0.124116	0.8599	0.197058
14	0.085185	0.5902	0.278919
15	-0.048727	-0.3376	0.368571
16	-0.077412	-0.5363	0.297105
17	-0.049222	-0.341	0.367288

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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)
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code