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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Nov 2007 04:04:57 -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/2007/Nov/28/t119624727847hfdfh7ov0hrtr.htm/, Retrieved Thu, 02 May 2024 09:25:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7018, Retrieved Thu, 02 May 2024 09:25:06 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

215

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

-       [(Partial) Autocorrelation Function] [Inducing Stationa...] [2007-11-28 11:04:57] [157a0cf3c12a7482b4e6935b4c49d48f] [Current]

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Summary of compuational 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 compuational 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=7018&T=0

[TABLE]
[ROW][C]Summary of compuational 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=7018&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7018&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 compuational 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
0	1	8.4853	0
1	0.968718	8.2198	0
2	0.928889	7.8819	0
3	0.890042	7.5523	0
4	0.851435	7.2247	0
5	0.811723	6.8877	0
6	0.773496	6.5633	0
7	0.737276	6.256	0
8	0.702963	5.9648	0
9	0.658283	5.5857	0
10	0.614095	5.2108	1e-06
11	0.574607	4.8757	3e-06
12	0.532969	4.5224	1.2e-05
13	0.489589	4.1543	4.4e-05
14	0.445308	3.7786	0.000161
15	0.406034	3.4453	0.000478
16	0.373073	3.1656	0.001134
17	0.3367	2.857	0.002793

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.968718 & 8.2198 & 0 \tabularnewline
2 & 0.928889 & 7.8819 & 0 \tabularnewline
3 & 0.890042 & 7.5523 & 0 \tabularnewline
4 & 0.851435 & 7.2247 & 0 \tabularnewline
5 & 0.811723 & 6.8877 & 0 \tabularnewline
6 & 0.773496 & 6.5633 & 0 \tabularnewline
7 & 0.737276 & 6.256 & 0 \tabularnewline
8 & 0.702963 & 5.9648 & 0 \tabularnewline
9 & 0.658283 & 5.5857 & 0 \tabularnewline
10 & 0.614095 & 5.2108 & 1e-06 \tabularnewline
11 & 0.574607 & 4.8757 & 3e-06 \tabularnewline
12 & 0.532969 & 4.5224 & 1.2e-05 \tabularnewline
13 & 0.489589 & 4.1543 & 4.4e-05 \tabularnewline
14 & 0.445308 & 3.7786 & 0.000161 \tabularnewline
15 & 0.406034 & 3.4453 & 0.000478 \tabularnewline
16 & 0.373073 & 3.1656 & 0.001134 \tabularnewline
17 & 0.3367 & 2.857 & 0.002793 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7018&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]0[/C][C]1[/C][C]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.968718[/C][C]8.2198[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.928889[/C][C]7.8819[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.890042[/C][C]7.5523[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.851435[/C][C]7.2247[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.811723[/C][C]6.8877[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.773496[/C][C]6.5633[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.737276[/C][C]6.256[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.702963[/C][C]5.9648[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.658283[/C][C]5.5857[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.614095[/C][C]5.2108[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.574607[/C][C]4.8757[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.532969[/C][C]4.5224[/C][C]1.2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.489589[/C][C]4.1543[/C][C]4.4e-05[/C][/ROW]
[ROW][C]14[/C][C]0.445308[/C][C]3.7786[/C][C]0.000161[/C][/ROW]
[ROW][C]15[/C][C]0.406034[/C][C]3.4453[/C][C]0.000478[/C][/ROW]
[ROW][C]16[/C][C]0.373073[/C][C]3.1656[/C][C]0.001134[/C][/ROW]
[ROW][C]17[/C][C]0.3367[/C][C]2.857[/C][C]0.002793[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7018&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7018&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
0	1	8.4853	0
1	0.968718	8.2198	0
2	0.928889	7.8819	0
3	0.890042	7.5523	0
4	0.851435	7.2247	0
5	0.811723	6.8877	0
6	0.773496	6.5633	0
7	0.737276	6.256	0
8	0.702963	5.9648	0
9	0.658283	5.5857	0
10	0.614095	5.2108	1e-06
11	0.574607	4.8757	3e-06
12	0.532969	4.5224	1.2e-05
13	0.489589	4.1543	4.4e-05
14	0.445308	3.7786	0.000161
15	0.406034	3.4453	0.000478
16	0.373073	3.1656	0.001134
17	0.3367	2.857	0.002793

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.968718	8.2198	0
1	-0.154672	-1.3124	0.903229
2	0.014394	0.1221	0.451565
3	-0.023608	-0.2003	0.579101
4	-0.038827	-0.3295	0.628618
5	0.007897	0.067	0.473382
6	0.003482	0.0295	0.488254
7	0.004107	0.0348	0.486149
8	-0.198945	-1.6881	0.952141
9	0.031936	0.271	0.393587
10	0.035225	0.2989	0.382941
11	-0.082934	-0.7037	0.75806
12	-0.03174	-0.2693	0.605774
13	-0.048794	-0.414	0.659959
14	0.052947	0.4493	0.327294
15	0.048664	0.4129	0.340443
16	-0.075063	-0.6369	0.736905
17	-0.012932	-0.1097	0.543537

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.968718 & 8.2198 & 0 \tabularnewline
1 & -0.154672 & -1.3124 & 0.903229 \tabularnewline
2 & 0.014394 & 0.1221 & 0.451565 \tabularnewline
3 & -0.023608 & -0.2003 & 0.579101 \tabularnewline
4 & -0.038827 & -0.3295 & 0.628618 \tabularnewline
5 & 0.007897 & 0.067 & 0.473382 \tabularnewline
6 & 0.003482 & 0.0295 & 0.488254 \tabularnewline
7 & 0.004107 & 0.0348 & 0.486149 \tabularnewline
8 & -0.198945 & -1.6881 & 0.952141 \tabularnewline
9 & 0.031936 & 0.271 & 0.393587 \tabularnewline
10 & 0.035225 & 0.2989 & 0.382941 \tabularnewline
11 & -0.082934 & -0.7037 & 0.75806 \tabularnewline
12 & -0.03174 & -0.2693 & 0.605774 \tabularnewline
13 & -0.048794 & -0.414 & 0.659959 \tabularnewline
14 & 0.052947 & 0.4493 & 0.327294 \tabularnewline
15 & 0.048664 & 0.4129 & 0.340443 \tabularnewline
16 & -0.075063 & -0.6369 & 0.736905 \tabularnewline
17 & -0.012932 & -0.1097 & 0.543537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7018&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]0[/C][C]0.968718[/C][C]8.2198[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.154672[/C][C]-1.3124[/C][C]0.903229[/C][/ROW]
[ROW][C]2[/C][C]0.014394[/C][C]0.1221[/C][C]0.451565[/C][/ROW]
[ROW][C]3[/C][C]-0.023608[/C][C]-0.2003[/C][C]0.579101[/C][/ROW]
[ROW][C]4[/C][C]-0.038827[/C][C]-0.3295[/C][C]0.628618[/C][/ROW]
[ROW][C]5[/C][C]0.007897[/C][C]0.067[/C][C]0.473382[/C][/ROW]
[ROW][C]6[/C][C]0.003482[/C][C]0.0295[/C][C]0.488254[/C][/ROW]
[ROW][C]7[/C][C]0.004107[/C][C]0.0348[/C][C]0.486149[/C][/ROW]
[ROW][C]8[/C][C]-0.198945[/C][C]-1.6881[/C][C]0.952141[/C][/ROW]
[ROW][C]9[/C][C]0.031936[/C][C]0.271[/C][C]0.393587[/C][/ROW]
[ROW][C]10[/C][C]0.035225[/C][C]0.2989[/C][C]0.382941[/C][/ROW]
[ROW][C]11[/C][C]-0.082934[/C][C]-0.7037[/C][C]0.75806[/C][/ROW]
[ROW][C]12[/C][C]-0.03174[/C][C]-0.2693[/C][C]0.605774[/C][/ROW]
[ROW][C]13[/C][C]-0.048794[/C][C]-0.414[/C][C]0.659959[/C][/ROW]
[ROW][C]14[/C][C]0.052947[/C][C]0.4493[/C][C]0.327294[/C][/ROW]
[ROW][C]15[/C][C]0.048664[/C][C]0.4129[/C][C]0.340443[/C][/ROW]
[ROW][C]16[/C][C]-0.075063[/C][C]-0.6369[/C][C]0.736905[/C][/ROW]
[ROW][C]17[/C][C]-0.012932[/C][C]-0.1097[/C][C]0.543537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7018&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7018&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
0	0.968718	8.2198	0
1	-0.154672	-1.3124	0.903229
2	0.014394	0.1221	0.451565
3	-0.023608	-0.2003	0.579101
4	-0.038827	-0.3295	0.628618
5	0.007897	0.067	0.473382
6	0.003482	0.0295	0.488254
7	0.004107	0.0348	0.486149
8	-0.198945	-1.6881	0.952141
9	0.031936	0.271	0.393587
10	0.035225	0.2989	0.382941
11	-0.082934	-0.7037	0.75806
12	-0.03174	-0.2693	0.605774
13	-0.048794	-0.414	0.659959
14	0.052947	0.4493	0.327294
15	0.048664	0.4129	0.340443
16	-0.075063	-0.6369	0.736905
17	-0.012932	-0.1097	0.543537

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1.2 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1.2 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code