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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

Mon, 03 Dec 2012 14:57:39 -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/2012/Dec/03/t1354564681b559lbtpbmp3nb2.htm/, Retrieved Sun, 28 Apr 2024 07:24:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=195996, Retrieved Sun, 28 Apr 2024 07:24:26 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

109

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

-     [(Partial) Autocorrelation Function] [Workshop 9 - auto...] [2012-12-03 19:55:49] [c85dbc843174c8f40de92b1c92b5205a]
- R P     [(Partial) Autocorrelation Function] [Workshop 9 - auto...] [2012-12-03 19:57:39] [729cfeb7382ca95684eaaf6b24800101] [Current]
-   P       [(Partial) Autocorrelation Function] [Workshop 9 - auto...] [2012-12-03 19:59:54] [c85dbc843174c8f40de92b1c92b5205a] 
- RMP       [Spectral Analysis] [Workshop 9 - peri...] [2012-12-03 20:02:49] [c85dbc843174c8f40de92b1c92b5205a] 
- R P         [Spectral Analysis] [Workshop 9 - peri...] [2012-12-03 20:04:57] [c85dbc843174c8f40de92b1c92b5205a] 
- RMP           [Variance Reduction Matrix] [Workshop 9 - vari...] [2012-12-03 20:17:14] [c85dbc843174c8f40de92b1c92b5205a] 
- RMP           [Standard Deviation-Mean Plot] [Workshop 9 - mean...] [2012-12-03 20:19:24] [c85dbc843174c8f40de92b1c92b5205a] 
- RMP           [ARIMA Backward Selection] [Workshop 9 - ARIM...] [2012-12-03 20:32:52] [c85dbc843174c8f40de92b1c92b5205a] 
-   P             [ARIMA Backward Selection] [Workshop 9 - ARIM...] [2012-12-04 11:24:44] [c85dbc843174c8f40de92b1c92b5205a] 
- RMP             [Skewness and Kurtosis Test] [Workshop 9 - skew...] [2012-12-04 11:43:19] [c85dbc843174c8f40de92b1c92b5205a] 
- RMP             [ARIMA Forecasting] [Workshop 9 - ARIM...] [2012-12-04 11:52:28] [c85dbc843174c8f40de92b1c92b5205a] 

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Dataseries X:

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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	'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195996&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195996&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195996&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.044924	-0.5102	0.305378
2	-0.255508	-2.902	0.002181
3	0.082914	0.9417	0.174048
4	0.052502	0.5963	0.276009
5	-0.068975	-0.7834	0.217412
6	-0.092466	-1.0502	0.147793
7	0.222992	2.5327	0.006259
8	0.086507	0.9825	0.163839
9	-0.08435	-0.958	0.169921
10	-0.002025	-0.023	0.490845
11	-0.006141	-0.0697	0.47225
12	-0.049895	-0.5667	0.285951
13	0.036293	0.4122	0.340433
14	0.026542	0.3015	0.381773
15	-0.055268	-0.6277	0.265647
16	-0.008131	-0.0924	0.46328
17	-0.055853	-0.6344	0.263482
18	0.038861	0.4414	0.32984
19	-0.025324	-0.2876	0.387048
20	-0.076076	-0.8641	0.194581
21	0.019734	0.2241	0.411503

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.044924 & -0.5102 & 0.305378 \tabularnewline
2 & -0.255508 & -2.902 & 0.002181 \tabularnewline
3 & 0.082914 & 0.9417 & 0.174048 \tabularnewline
4 & 0.052502 & 0.5963 & 0.276009 \tabularnewline
5 & -0.068975 & -0.7834 & 0.217412 \tabularnewline
6 & -0.092466 & -1.0502 & 0.147793 \tabularnewline
7 & 0.222992 & 2.5327 & 0.006259 \tabularnewline
8 & 0.086507 & 0.9825 & 0.163839 \tabularnewline
9 & -0.08435 & -0.958 & 0.169921 \tabularnewline
10 & -0.002025 & -0.023 & 0.490845 \tabularnewline
11 & -0.006141 & -0.0697 & 0.47225 \tabularnewline
12 & -0.049895 & -0.5667 & 0.285951 \tabularnewline
13 & 0.036293 & 0.4122 & 0.340433 \tabularnewline
14 & 0.026542 & 0.3015 & 0.381773 \tabularnewline
15 & -0.055268 & -0.6277 & 0.265647 \tabularnewline
16 & -0.008131 & -0.0924 & 0.46328 \tabularnewline
17 & -0.055853 & -0.6344 & 0.263482 \tabularnewline
18 & 0.038861 & 0.4414 & 0.32984 \tabularnewline
19 & -0.025324 & -0.2876 & 0.387048 \tabularnewline
20 & -0.076076 & -0.8641 & 0.194581 \tabularnewline
21 & 0.019734 & 0.2241 & 0.411503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195996&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]-0.044924[/C][C]-0.5102[/C][C]0.305378[/C][/ROW]
[ROW][C]2[/C][C]-0.255508[/C][C]-2.902[/C][C]0.002181[/C][/ROW]
[ROW][C]3[/C][C]0.082914[/C][C]0.9417[/C][C]0.174048[/C][/ROW]
[ROW][C]4[/C][C]0.052502[/C][C]0.5963[/C][C]0.276009[/C][/ROW]
[ROW][C]5[/C][C]-0.068975[/C][C]-0.7834[/C][C]0.217412[/C][/ROW]
[ROW][C]6[/C][C]-0.092466[/C][C]-1.0502[/C][C]0.147793[/C][/ROW]
[ROW][C]7[/C][C]0.222992[/C][C]2.5327[/C][C]0.006259[/C][/ROW]
[ROW][C]8[/C][C]0.086507[/C][C]0.9825[/C][C]0.163839[/C][/ROW]
[ROW][C]9[/C][C]-0.08435[/C][C]-0.958[/C][C]0.169921[/C][/ROW]
[ROW][C]10[/C][C]-0.002025[/C][C]-0.023[/C][C]0.490845[/C][/ROW]
[ROW][C]11[/C][C]-0.006141[/C][C]-0.0697[/C][C]0.47225[/C][/ROW]
[ROW][C]12[/C][C]-0.049895[/C][C]-0.5667[/C][C]0.285951[/C][/ROW]
[ROW][C]13[/C][C]0.036293[/C][C]0.4122[/C][C]0.340433[/C][/ROW]
[ROW][C]14[/C][C]0.026542[/C][C]0.3015[/C][C]0.381773[/C][/ROW]
[ROW][C]15[/C][C]-0.055268[/C][C]-0.6277[/C][C]0.265647[/C][/ROW]
[ROW][C]16[/C][C]-0.008131[/C][C]-0.0924[/C][C]0.46328[/C][/ROW]
[ROW][C]17[/C][C]-0.055853[/C][C]-0.6344[/C][C]0.263482[/C][/ROW]
[ROW][C]18[/C][C]0.038861[/C][C]0.4414[/C][C]0.32984[/C][/ROW]
[ROW][C]19[/C][C]-0.025324[/C][C]-0.2876[/C][C]0.387048[/C][/ROW]
[ROW][C]20[/C][C]-0.076076[/C][C]-0.8641[/C][C]0.194581[/C][/ROW]
[ROW][C]21[/C][C]0.019734[/C][C]0.2241[/C][C]0.411503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195996&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195996&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	-0.044924	-0.5102	0.305378
2	-0.255508	-2.902	0.002181
3	0.082914	0.9417	0.174048
4	0.052502	0.5963	0.276009
5	-0.068975	-0.7834	0.217412
6	-0.092466	-1.0502	0.147793
7	0.222992	2.5327	0.006259
8	0.086507	0.9825	0.163839
9	-0.08435	-0.958	0.169921
10	-0.002025	-0.023	0.490845
11	-0.006141	-0.0697	0.47225
12	-0.049895	-0.5667	0.285951
13	0.036293	0.4122	0.340433
14	0.026542	0.3015	0.381773
15	-0.055268	-0.6277	0.265647
16	-0.008131	-0.0924	0.46328
17	-0.055853	-0.6344	0.263482
18	0.038861	0.4414	0.32984
19	-0.025324	-0.2876	0.387048
20	-0.076076	-0.8641	0.194581
21	0.019734	0.2241	0.411503

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.044924	-0.5102	0.305378
2	-0.258047	-2.9309	0.002
3	0.061062	0.6935	0.244612
4	-0.006925	-0.0787	0.468714
5	-0.03274	-0.3719	0.355305
6	-0.096902	-1.1006	0.13656
7	0.204	2.317	0.01104
8	0.069455	0.7889	0.215821
9	0.041964	0.4766	0.317219
10	0.005053	0.0574	0.47716
11	-0.038768	-0.4403	0.33022
12	-0.050045	-0.5684	0.285373
13	0.064978	0.738	0.230926
14	-0.024043	-0.2731	0.392617
15	-0.070369	-0.7992	0.212812
16	-0.020258	-0.2301	0.409196
17	-0.100489	-1.1413	0.127921
18	0.050701	0.5759	0.282858
19	-0.028392	-0.3225	0.373807
20	-0.073704	-0.8371	0.202039
21	-0.02998	-0.3405	0.367014

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.044924 & -0.5102 & 0.305378 \tabularnewline
2 & -0.258047 & -2.9309 & 0.002 \tabularnewline
3 & 0.061062 & 0.6935 & 0.244612 \tabularnewline
4 & -0.006925 & -0.0787 & 0.468714 \tabularnewline
5 & -0.03274 & -0.3719 & 0.355305 \tabularnewline
6 & -0.096902 & -1.1006 & 0.13656 \tabularnewline
7 & 0.204 & 2.317 & 0.01104 \tabularnewline
8 & 0.069455 & 0.7889 & 0.215821 \tabularnewline
9 & 0.041964 & 0.4766 & 0.317219 \tabularnewline
10 & 0.005053 & 0.0574 & 0.47716 \tabularnewline
11 & -0.038768 & -0.4403 & 0.33022 \tabularnewline
12 & -0.050045 & -0.5684 & 0.285373 \tabularnewline
13 & 0.064978 & 0.738 & 0.230926 \tabularnewline
14 & -0.024043 & -0.2731 & 0.392617 \tabularnewline
15 & -0.070369 & -0.7992 & 0.212812 \tabularnewline
16 & -0.020258 & -0.2301 & 0.409196 \tabularnewline
17 & -0.100489 & -1.1413 & 0.127921 \tabularnewline
18 & 0.050701 & 0.5759 & 0.282858 \tabularnewline
19 & -0.028392 & -0.3225 & 0.373807 \tabularnewline
20 & -0.073704 & -0.8371 & 0.202039 \tabularnewline
21 & -0.02998 & -0.3405 & 0.367014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195996&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]-0.044924[/C][C]-0.5102[/C][C]0.305378[/C][/ROW]
[ROW][C]2[/C][C]-0.258047[/C][C]-2.9309[/C][C]0.002[/C][/ROW]
[ROW][C]3[/C][C]0.061062[/C][C]0.6935[/C][C]0.244612[/C][/ROW]
[ROW][C]4[/C][C]-0.006925[/C][C]-0.0787[/C][C]0.468714[/C][/ROW]
[ROW][C]5[/C][C]-0.03274[/C][C]-0.3719[/C][C]0.355305[/C][/ROW]
[ROW][C]6[/C][C]-0.096902[/C][C]-1.1006[/C][C]0.13656[/C][/ROW]
[ROW][C]7[/C][C]0.204[/C][C]2.317[/C][C]0.01104[/C][/ROW]
[ROW][C]8[/C][C]0.069455[/C][C]0.7889[/C][C]0.215821[/C][/ROW]
[ROW][C]9[/C][C]0.041964[/C][C]0.4766[/C][C]0.317219[/C][/ROW]
[ROW][C]10[/C][C]0.005053[/C][C]0.0574[/C][C]0.47716[/C][/ROW]
[ROW][C]11[/C][C]-0.038768[/C][C]-0.4403[/C][C]0.33022[/C][/ROW]
[ROW][C]12[/C][C]-0.050045[/C][C]-0.5684[/C][C]0.285373[/C][/ROW]
[ROW][C]13[/C][C]0.064978[/C][C]0.738[/C][C]0.230926[/C][/ROW]
[ROW][C]14[/C][C]-0.024043[/C][C]-0.2731[/C][C]0.392617[/C][/ROW]
[ROW][C]15[/C][C]-0.070369[/C][C]-0.7992[/C][C]0.212812[/C][/ROW]
[ROW][C]16[/C][C]-0.020258[/C][C]-0.2301[/C][C]0.409196[/C][/ROW]
[ROW][C]17[/C][C]-0.100489[/C][C]-1.1413[/C][C]0.127921[/C][/ROW]
[ROW][C]18[/C][C]0.050701[/C][C]0.5759[/C][C]0.282858[/C][/ROW]
[ROW][C]19[/C][C]-0.028392[/C][C]-0.3225[/C][C]0.373807[/C][/ROW]
[ROW][C]20[/C][C]-0.073704[/C][C]-0.8371[/C][C]0.202039[/C][/ROW]
[ROW][C]21[/C][C]-0.02998[/C][C]-0.3405[/C][C]0.367014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195996&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195996&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	-0.044924	-0.5102	0.305378
2	-0.258047	-2.9309	0.002
3	0.061062	0.6935	0.244612
4	-0.006925	-0.0787	0.468714
5	-0.03274	-0.3719	0.355305
6	-0.096902	-1.1006	0.13656
7	0.204	2.317	0.01104
8	0.069455	0.7889	0.215821
9	0.041964	0.4766	0.317219
10	0.005053	0.0574	0.47716
11	-0.038768	-0.4403	0.33022
12	-0.050045	-0.5684	0.285373
13	0.064978	0.738	0.230926
14	-0.024043	-0.2731	0.392617
15	-0.070369	-0.7992	0.212812
16	-0.020258	-0.2301	0.409196
17	-0.100489	-1.1413	0.127921
18	0.050701	0.5759	0.282858
19	-0.028392	-0.3225	0.373807
20	-0.073704	-0.8371	0.202039
21	-0.02998	-0.3405	0.367014

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 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; 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