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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 16 Dec 2009 06:18:32 -0700

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/2009/Dec/16/t1260969568mmn78uu70wezbrd.htm/, Retrieved Tue, 30 Apr 2024 15:47:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68303, Retrieved Tue, 30 Apr 2024 15:47:52 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

129

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

-     [ARIMA Forecasting] [] [2009-12-07 09:54:52] [b98453cac15ba1066b407e146608df68]
-   PD  [ARIMA Forecasting] [WS10] [2009-12-11 16:05:20] [90e6802d28d0afa9b030a19cd25ed2b0]
- RMP       [(Partial) Autocorrelation Function] [Verbetering works...] [2009-12-16 13:18:32] [3d2053c5f7c50d3c075d87ce0bd87294] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68303&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68303&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.879885	6.8721	0
2	0.736405	5.7515	0
3	0.633609	4.9486	3e-06
4	0.582572	4.55	1.3e-05
5	0.562305	4.3917	2.3e-05
6	0.508698	3.9731	9.5e-05
7	0.413243	3.2275	0.001005
8	0.304705	2.3798	0.010231
9	0.238008	1.8589	0.033933
10	0.220833	1.7248	0.044817
11	0.234321	1.8301	0.036061
12	0.22133	1.7286	0.044466
13	0.084316	0.6585	0.256338
14	-0.047453	-0.3706	0.356103
15	-0.138889	-1.0848	0.141149
16	-0.172079	-1.344	0.091966
17	-0.170623	-1.3326	0.093808

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.879885 & 6.8721 & 0 \tabularnewline
2 & 0.736405 & 5.7515 & 0 \tabularnewline
3 & 0.633609 & 4.9486 & 3e-06 \tabularnewline
4 & 0.582572 & 4.55 & 1.3e-05 \tabularnewline
5 & 0.562305 & 4.3917 & 2.3e-05 \tabularnewline
6 & 0.508698 & 3.9731 & 9.5e-05 \tabularnewline
7 & 0.413243 & 3.2275 & 0.001005 \tabularnewline
8 & 0.304705 & 2.3798 & 0.010231 \tabularnewline
9 & 0.238008 & 1.8589 & 0.033933 \tabularnewline
10 & 0.220833 & 1.7248 & 0.044817 \tabularnewline
11 & 0.234321 & 1.8301 & 0.036061 \tabularnewline
12 & 0.22133 & 1.7286 & 0.044466 \tabularnewline
13 & 0.084316 & 0.6585 & 0.256338 \tabularnewline
14 & -0.047453 & -0.3706 & 0.356103 \tabularnewline
15 & -0.138889 & -1.0848 & 0.141149 \tabularnewline
16 & -0.172079 & -1.344 & 0.091966 \tabularnewline
17 & -0.170623 & -1.3326 & 0.093808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68303&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]0.879885[/C][C]6.8721[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.736405[/C][C]5.7515[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.633609[/C][C]4.9486[/C][C]3e-06[/C][/ROW]
[ROW][C]4[/C][C]0.582572[/C][C]4.55[/C][C]1.3e-05[/C][/ROW]
[ROW][C]5[/C][C]0.562305[/C][C]4.3917[/C][C]2.3e-05[/C][/ROW]
[ROW][C]6[/C][C]0.508698[/C][C]3.9731[/C][C]9.5e-05[/C][/ROW]
[ROW][C]7[/C][C]0.413243[/C][C]3.2275[/C][C]0.001005[/C][/ROW]
[ROW][C]8[/C][C]0.304705[/C][C]2.3798[/C][C]0.010231[/C][/ROW]
[ROW][C]9[/C][C]0.238008[/C][C]1.8589[/C][C]0.033933[/C][/ROW]
[ROW][C]10[/C][C]0.220833[/C][C]1.7248[/C][C]0.044817[/C][/ROW]
[ROW][C]11[/C][C]0.234321[/C][C]1.8301[/C][C]0.036061[/C][/ROW]
[ROW][C]12[/C][C]0.22133[/C][C]1.7286[/C][C]0.044466[/C][/ROW]
[ROW][C]13[/C][C]0.084316[/C][C]0.6585[/C][C]0.256338[/C][/ROW]
[ROW][C]14[/C][C]-0.047453[/C][C]-0.3706[/C][C]0.356103[/C][/ROW]
[ROW][C]15[/C][C]-0.138889[/C][C]-1.0848[/C][C]0.141149[/C][/ROW]
[ROW][C]16[/C][C]-0.172079[/C][C]-1.344[/C][C]0.091966[/C][/ROW]
[ROW][C]17[/C][C]-0.170623[/C][C]-1.3326[/C][C]0.093808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68303&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	0.879885	6.8721	0
2	0.736405	5.7515	0
3	0.633609	4.9486	3e-06
4	0.582572	4.55	1.3e-05
5	0.562305	4.3917	2.3e-05
6	0.508698	3.9731	9.5e-05
7	0.413243	3.2275	0.001005
8	0.304705	2.3798	0.010231
9	0.238008	1.8589	0.033933
10	0.220833	1.7248	0.044817
11	0.234321	1.8301	0.036061
12	0.22133	1.7286	0.044466
13	0.084316	0.6585	0.256338
14	-0.047453	-0.3706	0.356103
15	-0.138889	-1.0848	0.141149
16	-0.172079	-1.344	0.091966
17	-0.170623	-1.3326	0.093808

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.879885	6.8721	0
2	-0.16737	-1.3072	0.098025
3	0.11152	0.871	0.193586
4	0.135711	1.0599	0.146676
5	0.090366	0.7058	0.241506
6	-0.138198	-1.0794	0.142338
7	-0.134922	-1.0538	0.148072
8	-0.089469	-0.6988	0.243675
9	0.071157	0.5558	0.290205
10	0.072024	0.5625	0.28791
11	0.102487	0.8004	0.213279
12	-0.053171	-0.4153	0.339698
13	-0.490726	-3.8327	0.000151
14	0.030109	0.2352	0.407436
15	-0.078537	-0.6134	0.270948
16	0.031417	0.2454	0.403494
17	0.046633	0.3642	0.358477

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.879885 & 6.8721 & 0 \tabularnewline
2 & -0.16737 & -1.3072 & 0.098025 \tabularnewline
3 & 0.11152 & 0.871 & 0.193586 \tabularnewline
4 & 0.135711 & 1.0599 & 0.146676 \tabularnewline
5 & 0.090366 & 0.7058 & 0.241506 \tabularnewline
6 & -0.138198 & -1.0794 & 0.142338 \tabularnewline
7 & -0.134922 & -1.0538 & 0.148072 \tabularnewline
8 & -0.089469 & -0.6988 & 0.243675 \tabularnewline
9 & 0.071157 & 0.5558 & 0.290205 \tabularnewline
10 & 0.072024 & 0.5625 & 0.28791 \tabularnewline
11 & 0.102487 & 0.8004 & 0.213279 \tabularnewline
12 & -0.053171 & -0.4153 & 0.339698 \tabularnewline
13 & -0.490726 & -3.8327 & 0.000151 \tabularnewline
14 & 0.030109 & 0.2352 & 0.407436 \tabularnewline
15 & -0.078537 & -0.6134 & 0.270948 \tabularnewline
16 & 0.031417 & 0.2454 & 0.403494 \tabularnewline
17 & 0.046633 & 0.3642 & 0.358477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68303&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]0.879885[/C][C]6.8721[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.16737[/C][C]-1.3072[/C][C]0.098025[/C][/ROW]
[ROW][C]3[/C][C]0.11152[/C][C]0.871[/C][C]0.193586[/C][/ROW]
[ROW][C]4[/C][C]0.135711[/C][C]1.0599[/C][C]0.146676[/C][/ROW]
[ROW][C]5[/C][C]0.090366[/C][C]0.7058[/C][C]0.241506[/C][/ROW]
[ROW][C]6[/C][C]-0.138198[/C][C]-1.0794[/C][C]0.142338[/C][/ROW]
[ROW][C]7[/C][C]-0.134922[/C][C]-1.0538[/C][C]0.148072[/C][/ROW]
[ROW][C]8[/C][C]-0.089469[/C][C]-0.6988[/C][C]0.243675[/C][/ROW]
[ROW][C]9[/C][C]0.071157[/C][C]0.5558[/C][C]0.290205[/C][/ROW]
[ROW][C]10[/C][C]0.072024[/C][C]0.5625[/C][C]0.28791[/C][/ROW]
[ROW][C]11[/C][C]0.102487[/C][C]0.8004[/C][C]0.213279[/C][/ROW]
[ROW][C]12[/C][C]-0.053171[/C][C]-0.4153[/C][C]0.339698[/C][/ROW]
[ROW][C]13[/C][C]-0.490726[/C][C]-3.8327[/C][C]0.000151[/C][/ROW]
[ROW][C]14[/C][C]0.030109[/C][C]0.2352[/C][C]0.407436[/C][/ROW]
[ROW][C]15[/C][C]-0.078537[/C][C]-0.6134[/C][C]0.270948[/C][/ROW]
[ROW][C]16[/C][C]0.031417[/C][C]0.2454[/C][C]0.403494[/C][/ROW]
[ROW][C]17[/C][C]0.046633[/C][C]0.3642[/C][C]0.358477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68303&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68303&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	0.879885	6.8721	0
2	-0.16737	-1.3072	0.098025
3	0.11152	0.871	0.193586
4	0.135711	1.0599	0.146676
5	0.090366	0.7058	0.241506
6	-0.138198	-1.0794	0.142338
7	-0.134922	-1.0538	0.148072
8	-0.089469	-0.6988	0.243675
9	0.071157	0.5558	0.290205
10	0.072024	0.5625	0.28791
11	0.102487	0.8004	0.213279
12	-0.053171	-0.4153	0.339698
13	-0.490726	-3.8327	0.000151
14	0.030109	0.2352	0.407436
15	-0.078537	-0.6134	0.270948
16	0.031417	0.2454	0.403494
17	0.046633	0.3642	0.358477

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code