Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Oct 2014 20:31:26 +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/2014/Oct/19/t1413747105fccsj5cj2vlnooc.htm/, Retrieved Sat, 11 May 2024 22:36:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243754, Retrieved Sat, 11 May 2024 22:36:56 +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] [] [2014-10-19 19:31:26] [062c419fa600f620f2df94d64c8876ba] [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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243754&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243754&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243754&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.498088	-4.8548	2e-06
2	-0.025113	-0.2448	0.403583
3	0.041022	0.3998	0.345087
4	0.123895	1.2076	0.115104
5	-0.23117	-2.2532	0.013274
6	0.190906	1.8607	0.032938
7	-0.043354	-0.4226	0.336784
8	-0.078719	-0.7673	0.222417
9	0.08398	0.8185	0.207549
10	-0.022193	-0.2163	0.414606
11	-0.086645	-0.8445	0.200252
12	0.237496	2.3148	0.011388
13	-0.228606	-2.2282	0.014114
14	0.139542	1.3601	0.08851
15	-0.082249	-0.8017	0.212373
16	0.089305	0.8704	0.193128
17	-0.157734	-1.5374	0.06376
18	0.204427	1.9925	0.024592
19	-0.219162	-2.1361	0.01762

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.498088 & -4.8548 & 2e-06 \tabularnewline
2 & -0.025113 & -0.2448 & 0.403583 \tabularnewline
3 & 0.041022 & 0.3998 & 0.345087 \tabularnewline
4 & 0.123895 & 1.2076 & 0.115104 \tabularnewline
5 & -0.23117 & -2.2532 & 0.013274 \tabularnewline
6 & 0.190906 & 1.8607 & 0.032938 \tabularnewline
7 & -0.043354 & -0.4226 & 0.336784 \tabularnewline
8 & -0.078719 & -0.7673 & 0.222417 \tabularnewline
9 & 0.08398 & 0.8185 & 0.207549 \tabularnewline
10 & -0.022193 & -0.2163 & 0.414606 \tabularnewline
11 & -0.086645 & -0.8445 & 0.200252 \tabularnewline
12 & 0.237496 & 2.3148 & 0.011388 \tabularnewline
13 & -0.228606 & -2.2282 & 0.014114 \tabularnewline
14 & 0.139542 & 1.3601 & 0.08851 \tabularnewline
15 & -0.082249 & -0.8017 & 0.212373 \tabularnewline
16 & 0.089305 & 0.8704 & 0.193128 \tabularnewline
17 & -0.157734 & -1.5374 & 0.06376 \tabularnewline
18 & 0.204427 & 1.9925 & 0.024592 \tabularnewline
19 & -0.219162 & -2.1361 & 0.01762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243754&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]-0.498088[/C][C]-4.8548[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.025113[/C][C]-0.2448[/C][C]0.403583[/C][/ROW]
[ROW][C]3[/C][C]0.041022[/C][C]0.3998[/C][C]0.345087[/C][/ROW]
[ROW][C]4[/C][C]0.123895[/C][C]1.2076[/C][C]0.115104[/C][/ROW]
[ROW][C]5[/C][C]-0.23117[/C][C]-2.2532[/C][C]0.013274[/C][/ROW]
[ROW][C]6[/C][C]0.190906[/C][C]1.8607[/C][C]0.032938[/C][/ROW]
[ROW][C]7[/C][C]-0.043354[/C][C]-0.4226[/C][C]0.336784[/C][/ROW]
[ROW][C]8[/C][C]-0.078719[/C][C]-0.7673[/C][C]0.222417[/C][/ROW]
[ROW][C]9[/C][C]0.08398[/C][C]0.8185[/C][C]0.207549[/C][/ROW]
[ROW][C]10[/C][C]-0.022193[/C][C]-0.2163[/C][C]0.414606[/C][/ROW]
[ROW][C]11[/C][C]-0.086645[/C][C]-0.8445[/C][C]0.200252[/C][/ROW]
[ROW][C]12[/C][C]0.237496[/C][C]2.3148[/C][C]0.011388[/C][/ROW]
[ROW][C]13[/C][C]-0.228606[/C][C]-2.2282[/C][C]0.014114[/C][/ROW]
[ROW][C]14[/C][C]0.139542[/C][C]1.3601[/C][C]0.08851[/C][/ROW]
[ROW][C]15[/C][C]-0.082249[/C][C]-0.8017[/C][C]0.212373[/C][/ROW]
[ROW][C]16[/C][C]0.089305[/C][C]0.8704[/C][C]0.193128[/C][/ROW]
[ROW][C]17[/C][C]-0.157734[/C][C]-1.5374[/C][C]0.06376[/C][/ROW]
[ROW][C]18[/C][C]0.204427[/C][C]1.9925[/C][C]0.024592[/C][/ROW]
[ROW][C]19[/C][C]-0.219162[/C][C]-2.1361[/C][C]0.01762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243754&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243754&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	-0.498088	-4.8548	2e-06
2	-0.025113	-0.2448	0.403583
3	0.041022	0.3998	0.345087
4	0.123895	1.2076	0.115104
5	-0.23117	-2.2532	0.013274
6	0.190906	1.8607	0.032938
7	-0.043354	-0.4226	0.336784
8	-0.078719	-0.7673	0.222417
9	0.08398	0.8185	0.207549
10	-0.022193	-0.2163	0.414606
11	-0.086645	-0.8445	0.200252
12	0.237496	2.3148	0.011388
13	-0.228606	-2.2282	0.014114
14	0.139542	1.3601	0.08851
15	-0.082249	-0.8017	0.212373
16	0.089305	0.8704	0.193128
17	-0.157734	-1.5374	0.06376
18	0.204427	1.9925	0.024592
19	-0.219162	-2.1361	0.01762

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.498088	-4.8548	2e-06
2	-0.363348	-3.5415	0.000309
3	-0.240577	-2.3449	0.010558
4	0.036238	0.3532	0.362358
5	-0.168969	-1.6469	0.051441
6	0.017231	0.1679	0.433491
7	0.031338	0.3054	0.380347
8	-0.074678	-0.7279	0.234242
9	0.039529	0.3853	0.350444
10	-0.034178	-0.3331	0.369887
11	-0.108305	-1.0556	0.146909
12	0.218226	2.127	0.018005
13	-0.053735	-0.5237	0.300839
14	0.151075	1.4725	0.072097
15	0.002892	0.0282	0.488785
16	0.031797	0.3099	0.378649
17	-0.02291	-0.2233	0.411891
18	0.033422	0.3258	0.372661
19	-0.127192	-1.2397	0.109068

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.498088 & -4.8548 & 2e-06 \tabularnewline
2 & -0.363348 & -3.5415 & 0.000309 \tabularnewline
3 & -0.240577 & -2.3449 & 0.010558 \tabularnewline
4 & 0.036238 & 0.3532 & 0.362358 \tabularnewline
5 & -0.168969 & -1.6469 & 0.051441 \tabularnewline
6 & 0.017231 & 0.1679 & 0.433491 \tabularnewline
7 & 0.031338 & 0.3054 & 0.380347 \tabularnewline
8 & -0.074678 & -0.7279 & 0.234242 \tabularnewline
9 & 0.039529 & 0.3853 & 0.350444 \tabularnewline
10 & -0.034178 & -0.3331 & 0.369887 \tabularnewline
11 & -0.108305 & -1.0556 & 0.146909 \tabularnewline
12 & 0.218226 & 2.127 & 0.018005 \tabularnewline
13 & -0.053735 & -0.5237 & 0.300839 \tabularnewline
14 & 0.151075 & 1.4725 & 0.072097 \tabularnewline
15 & 0.002892 & 0.0282 & 0.488785 \tabularnewline
16 & 0.031797 & 0.3099 & 0.378649 \tabularnewline
17 & -0.02291 & -0.2233 & 0.411891 \tabularnewline
18 & 0.033422 & 0.3258 & 0.372661 \tabularnewline
19 & -0.127192 & -1.2397 & 0.109068 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243754&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]-0.498088[/C][C]-4.8548[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.363348[/C][C]-3.5415[/C][C]0.000309[/C][/ROW]
[ROW][C]3[/C][C]-0.240577[/C][C]-2.3449[/C][C]0.010558[/C][/ROW]
[ROW][C]4[/C][C]0.036238[/C][C]0.3532[/C][C]0.362358[/C][/ROW]
[ROW][C]5[/C][C]-0.168969[/C][C]-1.6469[/C][C]0.051441[/C][/ROW]
[ROW][C]6[/C][C]0.017231[/C][C]0.1679[/C][C]0.433491[/C][/ROW]
[ROW][C]7[/C][C]0.031338[/C][C]0.3054[/C][C]0.380347[/C][/ROW]
[ROW][C]8[/C][C]-0.074678[/C][C]-0.7279[/C][C]0.234242[/C][/ROW]
[ROW][C]9[/C][C]0.039529[/C][C]0.3853[/C][C]0.350444[/C][/ROW]
[ROW][C]10[/C][C]-0.034178[/C][C]-0.3331[/C][C]0.369887[/C][/ROW]
[ROW][C]11[/C][C]-0.108305[/C][C]-1.0556[/C][C]0.146909[/C][/ROW]
[ROW][C]12[/C][C]0.218226[/C][C]2.127[/C][C]0.018005[/C][/ROW]
[ROW][C]13[/C][C]-0.053735[/C][C]-0.5237[/C][C]0.300839[/C][/ROW]
[ROW][C]14[/C][C]0.151075[/C][C]1.4725[/C][C]0.072097[/C][/ROW]
[ROW][C]15[/C][C]0.002892[/C][C]0.0282[/C][C]0.488785[/C][/ROW]
[ROW][C]16[/C][C]0.031797[/C][C]0.3099[/C][C]0.378649[/C][/ROW]
[ROW][C]17[/C][C]-0.02291[/C][C]-0.2233[/C][C]0.411891[/C][/ROW]
[ROW][C]18[/C][C]0.033422[/C][C]0.3258[/C][C]0.372661[/C][/ROW]
[ROW][C]19[/C][C]-0.127192[/C][C]-1.2397[/C][C]0.109068[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243754&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243754&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	-0.498088	-4.8548	2e-06
2	-0.363348	-3.5415	0.000309
3	-0.240577	-2.3449	0.010558
4	0.036238	0.3532	0.362358
5	-0.168969	-1.6469	0.051441
6	0.017231	0.1679	0.433491
7	0.031338	0.3054	0.380347
8	-0.074678	-0.7279	0.234242
9	0.039529	0.3853	0.350444
10	-0.034178	-0.3331	0.369887
11	-0.108305	-1.0556	0.146909
12	0.218226	2.127	0.018005
13	-0.053735	-0.5237	0.300839
14	0.151075	1.4725	0.072097
15	0.002892	0.0282	0.488785
16	0.031797	0.3099	0.378649
17	-0.02291	-0.2233	0.411891
18	0.033422	0.3258	0.372661
19	-0.127192	-1.2397	0.109068

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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)
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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code