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Author's title

Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 26 Dec 2010 15:54:08 +0000

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/2010/Dec/26/t12933787249x9im11tp24ps1c.htm/, Retrieved Mon, 06 May 2024 11:20:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115682, Retrieved Mon, 06 May 2024 11:20:06 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

134

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [b98453cac15ba1066b407e146608df68]
- RMP           [(Partial) Autocorrelation Function] [WS6 - autocorrelatie] [2010-12-14 19:09:35] [8ed0bd3560b9ca2814a2ed0a29182575]
-   PD            [(Partial) Autocorrelation Function] [Partial autocorre...] [2010-12-26 15:52:58] [8ed0bd3560b9ca2814a2ed0a29182575]
-    D                [(Partial) Autocorrelation Function] [Partial autocorre...] [2010-12-26 15:54:08] [c9d5faca36bd2ada281161976df30bf1] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115682&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115682&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115682&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.30901	3.3709	0.000505
2	-0.026088	-0.2846	0.388229
3	0.028875	0.315	0.376661
4	0.072783	0.794	0.214397
5	0.011891	0.1297	0.448507
6	-0.102897	-1.1225	0.13196
7	-0.16884	-1.8418	0.033995
8	-0.09068	-0.9892	0.162285
9	-0.019811	-0.2161	0.414634
10	-0.047109	-0.5139	0.304139
11	-0.028031	-0.3058	0.380154
12	-0.107713	-1.175	0.121168
13	-0.074664	-0.8145	0.208497
14	0.018395	0.2007	0.420651
15	0.069472	0.7578	0.225021
16	0.068779	0.7503	0.22728
17	0.092505	1.0091	0.157485
18	0.130479	1.4234	0.078625
19	0.18973	2.0697	0.020322
20	0.047175	0.5146	0.303889

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.30901 & 3.3709 & 0.000505 \tabularnewline
2 & -0.026088 & -0.2846 & 0.388229 \tabularnewline
3 & 0.028875 & 0.315 & 0.376661 \tabularnewline
4 & 0.072783 & 0.794 & 0.214397 \tabularnewline
5 & 0.011891 & 0.1297 & 0.448507 \tabularnewline
6 & -0.102897 & -1.1225 & 0.13196 \tabularnewline
7 & -0.16884 & -1.8418 & 0.033995 \tabularnewline
8 & -0.09068 & -0.9892 & 0.162285 \tabularnewline
9 & -0.019811 & -0.2161 & 0.414634 \tabularnewline
10 & -0.047109 & -0.5139 & 0.304139 \tabularnewline
11 & -0.028031 & -0.3058 & 0.380154 \tabularnewline
12 & -0.107713 & -1.175 & 0.121168 \tabularnewline
13 & -0.074664 & -0.8145 & 0.208497 \tabularnewline
14 & 0.018395 & 0.2007 & 0.420651 \tabularnewline
15 & 0.069472 & 0.7578 & 0.225021 \tabularnewline
16 & 0.068779 & 0.7503 & 0.22728 \tabularnewline
17 & 0.092505 & 1.0091 & 0.157485 \tabularnewline
18 & 0.130479 & 1.4234 & 0.078625 \tabularnewline
19 & 0.18973 & 2.0697 & 0.020322 \tabularnewline
20 & 0.047175 & 0.5146 & 0.303889 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115682&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]0.30901[/C][C]3.3709[/C][C]0.000505[/C][/ROW]
[ROW][C]2[/C][C]-0.026088[/C][C]-0.2846[/C][C]0.388229[/C][/ROW]
[ROW][C]3[/C][C]0.028875[/C][C]0.315[/C][C]0.376661[/C][/ROW]
[ROW][C]4[/C][C]0.072783[/C][C]0.794[/C][C]0.214397[/C][/ROW]
[ROW][C]5[/C][C]0.011891[/C][C]0.1297[/C][C]0.448507[/C][/ROW]
[ROW][C]6[/C][C]-0.102897[/C][C]-1.1225[/C][C]0.13196[/C][/ROW]
[ROW][C]7[/C][C]-0.16884[/C][C]-1.8418[/C][C]0.033995[/C][/ROW]
[ROW][C]8[/C][C]-0.09068[/C][C]-0.9892[/C][C]0.162285[/C][/ROW]
[ROW][C]9[/C][C]-0.019811[/C][C]-0.2161[/C][C]0.414634[/C][/ROW]
[ROW][C]10[/C][C]-0.047109[/C][C]-0.5139[/C][C]0.304139[/C][/ROW]
[ROW][C]11[/C][C]-0.028031[/C][C]-0.3058[/C][C]0.380154[/C][/ROW]
[ROW][C]12[/C][C]-0.107713[/C][C]-1.175[/C][C]0.121168[/C][/ROW]
[ROW][C]13[/C][C]-0.074664[/C][C]-0.8145[/C][C]0.208497[/C][/ROW]
[ROW][C]14[/C][C]0.018395[/C][C]0.2007[/C][C]0.420651[/C][/ROW]
[ROW][C]15[/C][C]0.069472[/C][C]0.7578[/C][C]0.225021[/C][/ROW]
[ROW][C]16[/C][C]0.068779[/C][C]0.7503[/C][C]0.22728[/C][/ROW]
[ROW][C]17[/C][C]0.092505[/C][C]1.0091[/C][C]0.157485[/C][/ROW]
[ROW][C]18[/C][C]0.130479[/C][C]1.4234[/C][C]0.078625[/C][/ROW]
[ROW][C]19[/C][C]0.18973[/C][C]2.0697[/C][C]0.020322[/C][/ROW]
[ROW][C]20[/C][C]0.047175[/C][C]0.5146[/C][C]0.303889[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115682&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115682&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	0.30901	3.3709	0.000505
2	-0.026088	-0.2846	0.388229
3	0.028875	0.315	0.376661
4	0.072783	0.794	0.214397
5	0.011891	0.1297	0.448507
6	-0.102897	-1.1225	0.13196
7	-0.16884	-1.8418	0.033995
8	-0.09068	-0.9892	0.162285
9	-0.019811	-0.2161	0.414634
10	-0.047109	-0.5139	0.304139
11	-0.028031	-0.3058	0.380154
12	-0.107713	-1.175	0.121168
13	-0.074664	-0.8145	0.208497
14	0.018395	0.2007	0.420651
15	0.069472	0.7578	0.225021
16	0.068779	0.7503	0.22728
17	0.092505	1.0091	0.157485
18	0.130479	1.4234	0.078625
19	0.18973	2.0697	0.020322
20	0.047175	0.5146	0.303889

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.30901	3.3709	0.000505
2	-0.134409	-1.4662	0.072612
3	0.08957	0.9771	0.165253
4	0.034402	0.3753	0.354059
5	-0.020763	-0.2265	0.410603
6	-0.102619	-1.1194	0.132603
7	-0.12028	-1.3121	0.096006
8	-0.018501	-0.2018	0.420201
9	-0.001978	-0.0216	0.491408
10	-0.033025	-0.3603	0.359645
11	0.021012	0.2292	0.409549
12	-0.130127	-1.4195	0.079181
13	-0.02311	-0.2521	0.400699
14	0.010693	0.1166	0.453668
15	0.051936	0.5666	0.286041
16	0.049832	0.5436	0.293865
17	0.072392	0.7897	0.215636
18	0.076202	0.8313	0.203744
19	0.113156	1.2344	0.109746
20	-0.076358	-0.833	0.203267

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.30901 & 3.3709 & 0.000505 \tabularnewline
2 & -0.134409 & -1.4662 & 0.072612 \tabularnewline
3 & 0.08957 & 0.9771 & 0.165253 \tabularnewline
4 & 0.034402 & 0.3753 & 0.354059 \tabularnewline
5 & -0.020763 & -0.2265 & 0.410603 \tabularnewline
6 & -0.102619 & -1.1194 & 0.132603 \tabularnewline
7 & -0.12028 & -1.3121 & 0.096006 \tabularnewline
8 & -0.018501 & -0.2018 & 0.420201 \tabularnewline
9 & -0.001978 & -0.0216 & 0.491408 \tabularnewline
10 & -0.033025 & -0.3603 & 0.359645 \tabularnewline
11 & 0.021012 & 0.2292 & 0.409549 \tabularnewline
12 & -0.130127 & -1.4195 & 0.079181 \tabularnewline
13 & -0.02311 & -0.2521 & 0.400699 \tabularnewline
14 & 0.010693 & 0.1166 & 0.453668 \tabularnewline
15 & 0.051936 & 0.5666 & 0.286041 \tabularnewline
16 & 0.049832 & 0.5436 & 0.293865 \tabularnewline
17 & 0.072392 & 0.7897 & 0.215636 \tabularnewline
18 & 0.076202 & 0.8313 & 0.203744 \tabularnewline
19 & 0.113156 & 1.2344 & 0.109746 \tabularnewline
20 & -0.076358 & -0.833 & 0.203267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115682&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]0.30901[/C][C]3.3709[/C][C]0.000505[/C][/ROW]
[ROW][C]2[/C][C]-0.134409[/C][C]-1.4662[/C][C]0.072612[/C][/ROW]
[ROW][C]3[/C][C]0.08957[/C][C]0.9771[/C][C]0.165253[/C][/ROW]
[ROW][C]4[/C][C]0.034402[/C][C]0.3753[/C][C]0.354059[/C][/ROW]
[ROW][C]5[/C][C]-0.020763[/C][C]-0.2265[/C][C]0.410603[/C][/ROW]
[ROW][C]6[/C][C]-0.102619[/C][C]-1.1194[/C][C]0.132603[/C][/ROW]
[ROW][C]7[/C][C]-0.12028[/C][C]-1.3121[/C][C]0.096006[/C][/ROW]
[ROW][C]8[/C][C]-0.018501[/C][C]-0.2018[/C][C]0.420201[/C][/ROW]
[ROW][C]9[/C][C]-0.001978[/C][C]-0.0216[/C][C]0.491408[/C][/ROW]
[ROW][C]10[/C][C]-0.033025[/C][C]-0.3603[/C][C]0.359645[/C][/ROW]
[ROW][C]11[/C][C]0.021012[/C][C]0.2292[/C][C]0.409549[/C][/ROW]
[ROW][C]12[/C][C]-0.130127[/C][C]-1.4195[/C][C]0.079181[/C][/ROW]
[ROW][C]13[/C][C]-0.02311[/C][C]-0.2521[/C][C]0.400699[/C][/ROW]
[ROW][C]14[/C][C]0.010693[/C][C]0.1166[/C][C]0.453668[/C][/ROW]
[ROW][C]15[/C][C]0.051936[/C][C]0.5666[/C][C]0.286041[/C][/ROW]
[ROW][C]16[/C][C]0.049832[/C][C]0.5436[/C][C]0.293865[/C][/ROW]
[ROW][C]17[/C][C]0.072392[/C][C]0.7897[/C][C]0.215636[/C][/ROW]
[ROW][C]18[/C][C]0.076202[/C][C]0.8313[/C][C]0.203744[/C][/ROW]
[ROW][C]19[/C][C]0.113156[/C][C]1.2344[/C][C]0.109746[/C][/ROW]
[ROW][C]20[/C][C]-0.076358[/C][C]-0.833[/C][C]0.203267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115682&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115682&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	0.30901	3.3709	0.000505
2	-0.134409	-1.4662	0.072612
3	0.08957	0.9771	0.165253
4	0.034402	0.3753	0.354059
5	-0.020763	-0.2265	0.410603
6	-0.102619	-1.1194	0.132603
7	-0.12028	-1.3121	0.096006
8	-0.018501	-0.2018	0.420201
9	-0.001978	-0.0216	0.491408
10	-0.033025	-0.3603	0.359645
11	0.021012	0.2292	0.409549
12	-0.130127	-1.4195	0.079181
13	-0.02311	-0.2521	0.400699
14	0.010693	0.1166	0.453668
15	0.051936	0.5666	0.286041
16	0.049832	0.5436	0.293865
17	0.072392	0.7897	0.215636
18	0.076202	0.8313	0.203744
19	0.113156	1.2344	0.109746
20	-0.076358	-0.833	0.203267

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; 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 (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