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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 17 Dec 2008 10:55:34 -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/2008/Dec/17/t1229536611vp3zfr9v4j40lmp.htm/, Retrieved Sun, 19 May 2024 07:58:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34453, Retrieved Sun, 19 May 2024 07:58:40 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

151

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

-       [(Partial) Autocorrelation Function] [VSA d=1; D=0] [2008-12-17 17:55:34] [d41d8cd98f00b204e9800998ecf8427e] [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=34453&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=34453&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34453&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	-0.226174	-4.4894	5e-06
2	-0.090783	-1.802	0.036156
3	0.0888	1.7626	0.039369
4	-0.040499	-0.8039	0.210973
5	0.003961	0.0786	0.468683
6	-0.027462	-0.5451	0.292996
7	-0.065854	-1.3072	0.095961
8	0.113433	2.2516	0.012449
9	-0.049589	-0.9843	0.162783
10	0.066575	1.3215	0.093554
11	0.048933	0.9713	0.165998
12	-0.054634	-1.0845	0.139414
13	0.036698	0.7284	0.23339
14	-0.012876	-0.2556	0.399202
15	-0.141862	-2.8159	0.002554
16	0.040161	0.7972	0.212913
17	0.062497	1.2405	0.107758
18	-0.074078	-1.4704	0.071125
19	-0.016253	-0.3226	0.373578
20	0.025607	0.5083	0.305766
21	-0.062514	-1.2409	0.107695
22	0.032942	0.6539	0.256782
23	-0.020523	-0.4074	0.341982
24	-0.012388	-0.2459	0.402948
25	-0.007924	-0.1573	0.437551

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.226174 & -4.4894 & 5e-06 \tabularnewline
2 & -0.090783 & -1.802 & 0.036156 \tabularnewline
3 & 0.0888 & 1.7626 & 0.039369 \tabularnewline
4 & -0.040499 & -0.8039 & 0.210973 \tabularnewline
5 & 0.003961 & 0.0786 & 0.468683 \tabularnewline
6 & -0.027462 & -0.5451 & 0.292996 \tabularnewline
7 & -0.065854 & -1.3072 & 0.095961 \tabularnewline
8 & 0.113433 & 2.2516 & 0.012449 \tabularnewline
9 & -0.049589 & -0.9843 & 0.162783 \tabularnewline
10 & 0.066575 & 1.3215 & 0.093554 \tabularnewline
11 & 0.048933 & 0.9713 & 0.165998 \tabularnewline
12 & -0.054634 & -1.0845 & 0.139414 \tabularnewline
13 & 0.036698 & 0.7284 & 0.23339 \tabularnewline
14 & -0.012876 & -0.2556 & 0.399202 \tabularnewline
15 & -0.141862 & -2.8159 & 0.002554 \tabularnewline
16 & 0.040161 & 0.7972 & 0.212913 \tabularnewline
17 & 0.062497 & 1.2405 & 0.107758 \tabularnewline
18 & -0.074078 & -1.4704 & 0.071125 \tabularnewline
19 & -0.016253 & -0.3226 & 0.373578 \tabularnewline
20 & 0.025607 & 0.5083 & 0.305766 \tabularnewline
21 & -0.062514 & -1.2409 & 0.107695 \tabularnewline
22 & 0.032942 & 0.6539 & 0.256782 \tabularnewline
23 & -0.020523 & -0.4074 & 0.341982 \tabularnewline
24 & -0.012388 & -0.2459 & 0.402948 \tabularnewline
25 & -0.007924 & -0.1573 & 0.437551 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34453&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]-0.226174[/C][C]-4.4894[/C][C]5e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.090783[/C][C]-1.802[/C][C]0.036156[/C][/ROW]
[ROW][C]3[/C][C]0.0888[/C][C]1.7626[/C][C]0.039369[/C][/ROW]
[ROW][C]4[/C][C]-0.040499[/C][C]-0.8039[/C][C]0.210973[/C][/ROW]
[ROW][C]5[/C][C]0.003961[/C][C]0.0786[/C][C]0.468683[/C][/ROW]
[ROW][C]6[/C][C]-0.027462[/C][C]-0.5451[/C][C]0.292996[/C][/ROW]
[ROW][C]7[/C][C]-0.065854[/C][C]-1.3072[/C][C]0.095961[/C][/ROW]
[ROW][C]8[/C][C]0.113433[/C][C]2.2516[/C][C]0.012449[/C][/ROW]
[ROW][C]9[/C][C]-0.049589[/C][C]-0.9843[/C][C]0.162783[/C][/ROW]
[ROW][C]10[/C][C]0.066575[/C][C]1.3215[/C][C]0.093554[/C][/ROW]
[ROW][C]11[/C][C]0.048933[/C][C]0.9713[/C][C]0.165998[/C][/ROW]
[ROW][C]12[/C][C]-0.054634[/C][C]-1.0845[/C][C]0.139414[/C][/ROW]
[ROW][C]13[/C][C]0.036698[/C][C]0.7284[/C][C]0.23339[/C][/ROW]
[ROW][C]14[/C][C]-0.012876[/C][C]-0.2556[/C][C]0.399202[/C][/ROW]
[ROW][C]15[/C][C]-0.141862[/C][C]-2.8159[/C][C]0.002554[/C][/ROW]
[ROW][C]16[/C][C]0.040161[/C][C]0.7972[/C][C]0.212913[/C][/ROW]
[ROW][C]17[/C][C]0.062497[/C][C]1.2405[/C][C]0.107758[/C][/ROW]
[ROW][C]18[/C][C]-0.074078[/C][C]-1.4704[/C][C]0.071125[/C][/ROW]
[ROW][C]19[/C][C]-0.016253[/C][C]-0.3226[/C][C]0.373578[/C][/ROW]
[ROW][C]20[/C][C]0.025607[/C][C]0.5083[/C][C]0.305766[/C][/ROW]
[ROW][C]21[/C][C]-0.062514[/C][C]-1.2409[/C][C]0.107695[/C][/ROW]
[ROW][C]22[/C][C]0.032942[/C][C]0.6539[/C][C]0.256782[/C][/ROW]
[ROW][C]23[/C][C]-0.020523[/C][C]-0.4074[/C][C]0.341982[/C][/ROW]
[ROW][C]24[/C][C]-0.012388[/C][C]-0.2459[/C][C]0.402948[/C][/ROW]
[ROW][C]25[/C][C]-0.007924[/C][C]-0.1573[/C][C]0.437551[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34453&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34453&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	-0.226174	-4.4894	5e-06
2	-0.090783	-1.802	0.036156
3	0.0888	1.7626	0.039369
4	-0.040499	-0.8039	0.210973
5	0.003961	0.0786	0.468683
6	-0.027462	-0.5451	0.292996
7	-0.065854	-1.3072	0.095961
8	0.113433	2.2516	0.012449
9	-0.049589	-0.9843	0.162783
10	0.066575	1.3215	0.093554
11	0.048933	0.9713	0.165998
12	-0.054634	-1.0845	0.139414
13	0.036698	0.7284	0.23339
14	-0.012876	-0.2556	0.399202
15	-0.141862	-2.8159	0.002554
16	0.040161	0.7972	0.212913
17	0.062497	1.2405	0.107758
18	-0.074078	-1.4704	0.071125
19	-0.016253	-0.3226	0.373578
20	0.025607	0.5083	0.305766
21	-0.062514	-1.2409	0.107695
22	0.032942	0.6539	0.256782
23	-0.020523	-0.4074	0.341982
24	-0.012388	-0.2459	0.402948
25	-0.007924	-0.1573	0.437551

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.226174	-4.4894	5e-06
2	-0.149589	-2.9693	0.001584
3	0.03381	0.6711	0.251271
4	-0.024818	-0.4926	0.311278
5	0.003634	0.0721	0.471265
6	-0.039027	-0.7747	0.219503
7	-0.084198	-1.6713	0.04773
8	0.074518	1.4791	0.069951
9	-0.016488	-0.3273	0.371817
10	0.085662	1.7003	0.044928
11	0.068755	1.3648	0.086555
12	-0.00479	-0.0951	0.462148
13	0.022968	0.4559	0.324354
14	-0.007708	-0.153	0.439235
15	-0.135811	-2.6958	0.003662
16	-0.043431	-0.8621	0.194586
17	0.056941	1.1302	0.129531
18	-0.043609	-0.8656	0.193614
19	-0.050742	-1.0072	0.157228
20	-0.011194	-0.2222	0.412141
21	-0.093772	-1.8613	0.031722
22	-0.009378	-0.1861	0.426214
23	-0.003059	-0.0607	0.475808
24	-0.00968	-0.1922	0.423862
25	-0.015764	-0.3129	0.377257

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.226174 & -4.4894 & 5e-06 \tabularnewline
2 & -0.149589 & -2.9693 & 0.001584 \tabularnewline
3 & 0.03381 & 0.6711 & 0.251271 \tabularnewline
4 & -0.024818 & -0.4926 & 0.311278 \tabularnewline
5 & 0.003634 & 0.0721 & 0.471265 \tabularnewline
6 & -0.039027 & -0.7747 & 0.219503 \tabularnewline
7 & -0.084198 & -1.6713 & 0.04773 \tabularnewline
8 & 0.074518 & 1.4791 & 0.069951 \tabularnewline
9 & -0.016488 & -0.3273 & 0.371817 \tabularnewline
10 & 0.085662 & 1.7003 & 0.044928 \tabularnewline
11 & 0.068755 & 1.3648 & 0.086555 \tabularnewline
12 & -0.00479 & -0.0951 & 0.462148 \tabularnewline
13 & 0.022968 & 0.4559 & 0.324354 \tabularnewline
14 & -0.007708 & -0.153 & 0.439235 \tabularnewline
15 & -0.135811 & -2.6958 & 0.003662 \tabularnewline
16 & -0.043431 & -0.8621 & 0.194586 \tabularnewline
17 & 0.056941 & 1.1302 & 0.129531 \tabularnewline
18 & -0.043609 & -0.8656 & 0.193614 \tabularnewline
19 & -0.050742 & -1.0072 & 0.157228 \tabularnewline
20 & -0.011194 & -0.2222 & 0.412141 \tabularnewline
21 & -0.093772 & -1.8613 & 0.031722 \tabularnewline
22 & -0.009378 & -0.1861 & 0.426214 \tabularnewline
23 & -0.003059 & -0.0607 & 0.475808 \tabularnewline
24 & -0.00968 & -0.1922 & 0.423862 \tabularnewline
25 & -0.015764 & -0.3129 & 0.377257 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34453&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]-0.226174[/C][C]-4.4894[/C][C]5e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.149589[/C][C]-2.9693[/C][C]0.001584[/C][/ROW]
[ROW][C]3[/C][C]0.03381[/C][C]0.6711[/C][C]0.251271[/C][/ROW]
[ROW][C]4[/C][C]-0.024818[/C][C]-0.4926[/C][C]0.311278[/C][/ROW]
[ROW][C]5[/C][C]0.003634[/C][C]0.0721[/C][C]0.471265[/C][/ROW]
[ROW][C]6[/C][C]-0.039027[/C][C]-0.7747[/C][C]0.219503[/C][/ROW]
[ROW][C]7[/C][C]-0.084198[/C][C]-1.6713[/C][C]0.04773[/C][/ROW]
[ROW][C]8[/C][C]0.074518[/C][C]1.4791[/C][C]0.069951[/C][/ROW]
[ROW][C]9[/C][C]-0.016488[/C][C]-0.3273[/C][C]0.371817[/C][/ROW]
[ROW][C]10[/C][C]0.085662[/C][C]1.7003[/C][C]0.044928[/C][/ROW]
[ROW][C]11[/C][C]0.068755[/C][C]1.3648[/C][C]0.086555[/C][/ROW]
[ROW][C]12[/C][C]-0.00479[/C][C]-0.0951[/C][C]0.462148[/C][/ROW]
[ROW][C]13[/C][C]0.022968[/C][C]0.4559[/C][C]0.324354[/C][/ROW]
[ROW][C]14[/C][C]-0.007708[/C][C]-0.153[/C][C]0.439235[/C][/ROW]
[ROW][C]15[/C][C]-0.135811[/C][C]-2.6958[/C][C]0.003662[/C][/ROW]
[ROW][C]16[/C][C]-0.043431[/C][C]-0.8621[/C][C]0.194586[/C][/ROW]
[ROW][C]17[/C][C]0.056941[/C][C]1.1302[/C][C]0.129531[/C][/ROW]
[ROW][C]18[/C][C]-0.043609[/C][C]-0.8656[/C][C]0.193614[/C][/ROW]
[ROW][C]19[/C][C]-0.050742[/C][C]-1.0072[/C][C]0.157228[/C][/ROW]
[ROW][C]20[/C][C]-0.011194[/C][C]-0.2222[/C][C]0.412141[/C][/ROW]
[ROW][C]21[/C][C]-0.093772[/C][C]-1.8613[/C][C]0.031722[/C][/ROW]
[ROW][C]22[/C][C]-0.009378[/C][C]-0.1861[/C][C]0.426214[/C][/ROW]
[ROW][C]23[/C][C]-0.003059[/C][C]-0.0607[/C][C]0.475808[/C][/ROW]
[ROW][C]24[/C][C]-0.00968[/C][C]-0.1922[/C][C]0.423862[/C][/ROW]
[ROW][C]25[/C][C]-0.015764[/C][C]-0.3129[/C][C]0.377257[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34453&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34453&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	-0.226174	-4.4894	5e-06
2	-0.149589	-2.9693	0.001584
3	0.03381	0.6711	0.251271
4	-0.024818	-0.4926	0.311278
5	0.003634	0.0721	0.471265
6	-0.039027	-0.7747	0.219503
7	-0.084198	-1.6713	0.04773
8	0.074518	1.4791	0.069951
9	-0.016488	-0.3273	0.371817
10	0.085662	1.7003	0.044928
11	0.068755	1.3648	0.086555
12	-0.00479	-0.0951	0.462148
13	0.022968	0.4559	0.324354
14	-0.007708	-0.153	0.439235
15	-0.135811	-2.6958	0.003662
16	-0.043431	-0.8621	0.194586
17	0.056941	1.1302	0.129531
18	-0.043609	-0.8656	0.193614
19	-0.050742	-1.0072	0.157228
20	-0.011194	-0.2222	0.412141
21	-0.093772	-1.8613	0.031722
22	-0.009378	-0.1861	0.426214
23	-0.003059	-0.0607	0.475808
24	-0.00968	-0.1922	0.423862
25	-0.015764	-0.3129	0.377257

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 = 0 ; par5 = 1 ;

Parameters (R input):

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

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 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