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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, 14 Dec 2009 02:49:31 -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/14/t12607842365vvyrdhhl8wcmr6.htm/, Retrieved Sun, 05 May 2024 18:46:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67480, Retrieved Sun, 05 May 2024 18:46:16 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

133

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

-     [Variance Reduction Matrix] [VRM invoer] [2008-12-17 15:09:52] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [Autocorrelation F...] [2009-12-14 09:49:31] [91da2e1ebdd83187f2515f461585cbee] [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=67480&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=67480&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67480&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	-0.501527	-5.9341	0
2	0.005812	0.0688	0.472636
3	0.385683	4.5635	5e-06
4	-0.326338	-3.8613	8.6e-05
5	0.116704	1.3809	0.084761
6	0.165171	1.9543	0.026328
7	-0.369534	-4.3724	1.2e-05
8	0.226519	2.6802	0.00412
9	-0.041477	-0.4908	0.31218
10	-0.167321	-1.9798	0.024845
11	0.102971	1.2184	0.112565
12	-0.089558	-1.0597	0.14556
13	-0.050137	-0.5932	0.276991
14	0.078855	0.933	0.176208
15	0.042883	0.5074	0.306336
16	-0.225712	-2.6707	0.004233
17	0.221243	2.6178	0.004912
18	-0.025672	-0.3038	0.380882
19	-0.158187	-1.8717	0.031667
20	0.207305	2.4529	0.007701
21	-0.066182	-0.7831	0.217454

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.501527 & -5.9341 & 0 \tabularnewline
2 & 0.005812 & 0.0688 & 0.472636 \tabularnewline
3 & 0.385683 & 4.5635 & 5e-06 \tabularnewline
4 & -0.326338 & -3.8613 & 8.6e-05 \tabularnewline
5 & 0.116704 & 1.3809 & 0.084761 \tabularnewline
6 & 0.165171 & 1.9543 & 0.026328 \tabularnewline
7 & -0.369534 & -4.3724 & 1.2e-05 \tabularnewline
8 & 0.226519 & 2.6802 & 0.00412 \tabularnewline
9 & -0.041477 & -0.4908 & 0.31218 \tabularnewline
10 & -0.167321 & -1.9798 & 0.024845 \tabularnewline
11 & 0.102971 & 1.2184 & 0.112565 \tabularnewline
12 & -0.089558 & -1.0597 & 0.14556 \tabularnewline
13 & -0.050137 & -0.5932 & 0.276991 \tabularnewline
14 & 0.078855 & 0.933 & 0.176208 \tabularnewline
15 & 0.042883 & 0.5074 & 0.306336 \tabularnewline
16 & -0.225712 & -2.6707 & 0.004233 \tabularnewline
17 & 0.221243 & 2.6178 & 0.004912 \tabularnewline
18 & -0.025672 & -0.3038 & 0.380882 \tabularnewline
19 & -0.158187 & -1.8717 & 0.031667 \tabularnewline
20 & 0.207305 & 2.4529 & 0.007701 \tabularnewline
21 & -0.066182 & -0.7831 & 0.217454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67480&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]-0.501527[/C][C]-5.9341[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.005812[/C][C]0.0688[/C][C]0.472636[/C][/ROW]
[ROW][C]3[/C][C]0.385683[/C][C]4.5635[/C][C]5e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.326338[/C][C]-3.8613[/C][C]8.6e-05[/C][/ROW]
[ROW][C]5[/C][C]0.116704[/C][C]1.3809[/C][C]0.084761[/C][/ROW]
[ROW][C]6[/C][C]0.165171[/C][C]1.9543[/C][C]0.026328[/C][/ROW]
[ROW][C]7[/C][C]-0.369534[/C][C]-4.3724[/C][C]1.2e-05[/C][/ROW]
[ROW][C]8[/C][C]0.226519[/C][C]2.6802[/C][C]0.00412[/C][/ROW]
[ROW][C]9[/C][C]-0.041477[/C][C]-0.4908[/C][C]0.31218[/C][/ROW]
[ROW][C]10[/C][C]-0.167321[/C][C]-1.9798[/C][C]0.024845[/C][/ROW]
[ROW][C]11[/C][C]0.102971[/C][C]1.2184[/C][C]0.112565[/C][/ROW]
[ROW][C]12[/C][C]-0.089558[/C][C]-1.0597[/C][C]0.14556[/C][/ROW]
[ROW][C]13[/C][C]-0.050137[/C][C]-0.5932[/C][C]0.276991[/C][/ROW]
[ROW][C]14[/C][C]0.078855[/C][C]0.933[/C][C]0.176208[/C][/ROW]
[ROW][C]15[/C][C]0.042883[/C][C]0.5074[/C][C]0.306336[/C][/ROW]
[ROW][C]16[/C][C]-0.225712[/C][C]-2.6707[/C][C]0.004233[/C][/ROW]
[ROW][C]17[/C][C]0.221243[/C][C]2.6178[/C][C]0.004912[/C][/ROW]
[ROW][C]18[/C][C]-0.025672[/C][C]-0.3038[/C][C]0.380882[/C][/ROW]
[ROW][C]19[/C][C]-0.158187[/C][C]-1.8717[/C][C]0.031667[/C][/ROW]
[ROW][C]20[/C][C]0.207305[/C][C]2.4529[/C][C]0.007701[/C][/ROW]
[ROW][C]21[/C][C]-0.066182[/C][C]-0.7831[/C][C]0.217454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67480&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67480&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	-0.501527	-5.9341	0
2	0.005812	0.0688	0.472636
3	0.385683	4.5635	5e-06
4	-0.326338	-3.8613	8.6e-05
5	0.116704	1.3809	0.084761
6	0.165171	1.9543	0.026328
7	-0.369534	-4.3724	1.2e-05
8	0.226519	2.6802	0.00412
9	-0.041477	-0.4908	0.31218
10	-0.167321	-1.9798	0.024845
11	0.102971	1.2184	0.112565
12	-0.089558	-1.0597	0.14556
13	-0.050137	-0.5932	0.276991
14	0.078855	0.933	0.176208
15	0.042883	0.5074	0.306336
16	-0.225712	-2.6707	0.004233
17	0.221243	2.6178	0.004912
18	-0.025672	-0.3038	0.380882
19	-0.158187	-1.8717	0.031667
20	0.207305	2.4529	0.007701
21	-0.066182	-0.7831	0.217454

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.501527	-5.9341	0
2	-0.328292	-3.8844	7.9e-05
3	0.336787	3.9849	5.4e-05
4	0.097057	1.1484	0.126382
5	0.012483	0.1477	0.441394
6	0.095947	1.1353	0.129103
7	-0.240727	-2.8483	0.002529
8	-0.154508	-1.8282	0.034827
9	-0.095741	-1.1328	0.129612
10	-0.000286	-0.0034	0.498654
11	-0.094136	-1.1138	0.13363
12	-0.114798	-1.3583	0.088275
13	-0.060439	-0.7151	0.237861
14	-0.043262	-0.5119	0.304771
15	0.245388	2.9035	0.002145
16	-0.159068	-1.8821	0.030948
17	-0.066082	-0.7819	0.217798
18	-0.016515	-0.1954	0.422679
19	-0.096493	-1.1417	0.12776
20	-0.022624	-0.2677	0.394665
21	0.046804	0.5538	0.290302

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.501527 & -5.9341 & 0 \tabularnewline
2 & -0.328292 & -3.8844 & 7.9e-05 \tabularnewline
3 & 0.336787 & 3.9849 & 5.4e-05 \tabularnewline
4 & 0.097057 & 1.1484 & 0.126382 \tabularnewline
5 & 0.012483 & 0.1477 & 0.441394 \tabularnewline
6 & 0.095947 & 1.1353 & 0.129103 \tabularnewline
7 & -0.240727 & -2.8483 & 0.002529 \tabularnewline
8 & -0.154508 & -1.8282 & 0.034827 \tabularnewline
9 & -0.095741 & -1.1328 & 0.129612 \tabularnewline
10 & -0.000286 & -0.0034 & 0.498654 \tabularnewline
11 & -0.094136 & -1.1138 & 0.13363 \tabularnewline
12 & -0.114798 & -1.3583 & 0.088275 \tabularnewline
13 & -0.060439 & -0.7151 & 0.237861 \tabularnewline
14 & -0.043262 & -0.5119 & 0.304771 \tabularnewline
15 & 0.245388 & 2.9035 & 0.002145 \tabularnewline
16 & -0.159068 & -1.8821 & 0.030948 \tabularnewline
17 & -0.066082 & -0.7819 & 0.217798 \tabularnewline
18 & -0.016515 & -0.1954 & 0.422679 \tabularnewline
19 & -0.096493 & -1.1417 & 0.12776 \tabularnewline
20 & -0.022624 & -0.2677 & 0.394665 \tabularnewline
21 & 0.046804 & 0.5538 & 0.290302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67480&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]-0.501527[/C][C]-5.9341[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.328292[/C][C]-3.8844[/C][C]7.9e-05[/C][/ROW]
[ROW][C]3[/C][C]0.336787[/C][C]3.9849[/C][C]5.4e-05[/C][/ROW]
[ROW][C]4[/C][C]0.097057[/C][C]1.1484[/C][C]0.126382[/C][/ROW]
[ROW][C]5[/C][C]0.012483[/C][C]0.1477[/C][C]0.441394[/C][/ROW]
[ROW][C]6[/C][C]0.095947[/C][C]1.1353[/C][C]0.129103[/C][/ROW]
[ROW][C]7[/C][C]-0.240727[/C][C]-2.8483[/C][C]0.002529[/C][/ROW]
[ROW][C]8[/C][C]-0.154508[/C][C]-1.8282[/C][C]0.034827[/C][/ROW]
[ROW][C]9[/C][C]-0.095741[/C][C]-1.1328[/C][C]0.129612[/C][/ROW]
[ROW][C]10[/C][C]-0.000286[/C][C]-0.0034[/C][C]0.498654[/C][/ROW]
[ROW][C]11[/C][C]-0.094136[/C][C]-1.1138[/C][C]0.13363[/C][/ROW]
[ROW][C]12[/C][C]-0.114798[/C][C]-1.3583[/C][C]0.088275[/C][/ROW]
[ROW][C]13[/C][C]-0.060439[/C][C]-0.7151[/C][C]0.237861[/C][/ROW]
[ROW][C]14[/C][C]-0.043262[/C][C]-0.5119[/C][C]0.304771[/C][/ROW]
[ROW][C]15[/C][C]0.245388[/C][C]2.9035[/C][C]0.002145[/C][/ROW]
[ROW][C]16[/C][C]-0.159068[/C][C]-1.8821[/C][C]0.030948[/C][/ROW]
[ROW][C]17[/C][C]-0.066082[/C][C]-0.7819[/C][C]0.217798[/C][/ROW]
[ROW][C]18[/C][C]-0.016515[/C][C]-0.1954[/C][C]0.422679[/C][/ROW]
[ROW][C]19[/C][C]-0.096493[/C][C]-1.1417[/C][C]0.12776[/C][/ROW]
[ROW][C]20[/C][C]-0.022624[/C][C]-0.2677[/C][C]0.394665[/C][/ROW]
[ROW][C]21[/C][C]0.046804[/C][C]0.5538[/C][C]0.290302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67480&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67480&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	-0.501527	-5.9341	0
2	-0.328292	-3.8844	7.9e-05
3	0.336787	3.9849	5.4e-05
4	0.097057	1.1484	0.126382
5	0.012483	0.1477	0.441394
6	0.095947	1.1353	0.129103
7	-0.240727	-2.8483	0.002529
8	-0.154508	-1.8282	0.034827
9	-0.095741	-1.1328	0.129612
10	-0.000286	-0.0034	0.498654
11	-0.094136	-1.1138	0.13363
12	-0.114798	-1.3583	0.088275
13	-0.060439	-0.7151	0.237861
14	-0.043262	-0.5119	0.304771
15	0.245388	2.9035	0.002145
16	-0.159068	-1.8821	0.030948
17	-0.066082	-0.7819	0.217798
18	-0.016515	-0.1954	0.422679
19	-0.096493	-1.1417	0.12776
20	-0.022624	-0.2677	0.394665
21	0.046804	0.5538	0.290302

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code