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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 06 Dec 2011 09:36:38 -0500

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/2011/Dec/06/t132318220892zwkx70oqapwwe.htm/, Retrieved Mon, 29 Apr 2024 04:13:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151618, Retrieved Mon, 29 Apr 2024 04:13:37 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

135

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

F     [(Partial) Autocorrelation Function] [WS9] [2010-12-08 16:30:25] [ebb35fb07def4d07c0eb7ec8d2fd3b0e]
- R  D  [(Partial) Autocorrelation Function] [] [2011-12-06 13:43:04] [74be16979710d4c4e7c6647856088456]
-    D      [(Partial) Autocorrelation Function] [] [2011-12-06 14:36:38] [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	'AstonUniversity' @ aston.wessa.net

\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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151618&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151618&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151618&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.671145	4.698	1.1e-05
2	0.537072	3.7595	0.000227
3	0.582041	4.0743	8.4e-05
4	0.464837	3.2539	0.001033
5	0.371266	2.5989	0.006161
6	0.342892	2.4002	0.010114
7	0.146316	1.0242	0.155383
8	0.143583	1.0051	0.159897
9	0.029329	0.2053	0.419092
10	-0.163124	-1.1419	0.129529
11	-0.070812	-0.4957	0.311167
12	-0.00521	-0.0365	0.485528
13	-0.262402	-1.8368	0.036154
14	-0.313351	-2.1935	0.016525
15	-0.314804	-2.2036	0.01614
16	-0.367041	-2.5693	0.006643

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.671145 & 4.698 & 1.1e-05 \tabularnewline
2 & 0.537072 & 3.7595 & 0.000227 \tabularnewline
3 & 0.582041 & 4.0743 & 8.4e-05 \tabularnewline
4 & 0.464837 & 3.2539 & 0.001033 \tabularnewline
5 & 0.371266 & 2.5989 & 0.006161 \tabularnewline
6 & 0.342892 & 2.4002 & 0.010114 \tabularnewline
7 & 0.146316 & 1.0242 & 0.155383 \tabularnewline
8 & 0.143583 & 1.0051 & 0.159897 \tabularnewline
9 & 0.029329 & 0.2053 & 0.419092 \tabularnewline
10 & -0.163124 & -1.1419 & 0.129529 \tabularnewline
11 & -0.070812 & -0.4957 & 0.311167 \tabularnewline
12 & -0.00521 & -0.0365 & 0.485528 \tabularnewline
13 & -0.262402 & -1.8368 & 0.036154 \tabularnewline
14 & -0.313351 & -2.1935 & 0.016525 \tabularnewline
15 & -0.314804 & -2.2036 & 0.01614 \tabularnewline
16 & -0.367041 & -2.5693 & 0.006643 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151618&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]0.671145[/C][C]4.698[/C][C]1.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.537072[/C][C]3.7595[/C][C]0.000227[/C][/ROW]
[ROW][C]3[/C][C]0.582041[/C][C]4.0743[/C][C]8.4e-05[/C][/ROW]
[ROW][C]4[/C][C]0.464837[/C][C]3.2539[/C][C]0.001033[/C][/ROW]
[ROW][C]5[/C][C]0.371266[/C][C]2.5989[/C][C]0.006161[/C][/ROW]
[ROW][C]6[/C][C]0.342892[/C][C]2.4002[/C][C]0.010114[/C][/ROW]
[ROW][C]7[/C][C]0.146316[/C][C]1.0242[/C][C]0.155383[/C][/ROW]
[ROW][C]8[/C][C]0.143583[/C][C]1.0051[/C][C]0.159897[/C][/ROW]
[ROW][C]9[/C][C]0.029329[/C][C]0.2053[/C][C]0.419092[/C][/ROW]
[ROW][C]10[/C][C]-0.163124[/C][C]-1.1419[/C][C]0.129529[/C][/ROW]
[ROW][C]11[/C][C]-0.070812[/C][C]-0.4957[/C][C]0.311167[/C][/ROW]
[ROW][C]12[/C][C]-0.00521[/C][C]-0.0365[/C][C]0.485528[/C][/ROW]
[ROW][C]13[/C][C]-0.262402[/C][C]-1.8368[/C][C]0.036154[/C][/ROW]
[ROW][C]14[/C][C]-0.313351[/C][C]-2.1935[/C][C]0.016525[/C][/ROW]
[ROW][C]15[/C][C]-0.314804[/C][C]-2.2036[/C][C]0.01614[/C][/ROW]
[ROW][C]16[/C][C]-0.367041[/C][C]-2.5693[/C][C]0.006643[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151618&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151618&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	0.671145	4.698	1.1e-05
2	0.537072	3.7595	0.000227
3	0.582041	4.0743	8.4e-05
4	0.464837	3.2539	0.001033
5	0.371266	2.5989	0.006161
6	0.342892	2.4002	0.010114
7	0.146316	1.0242	0.155383
8	0.143583	1.0051	0.159897
9	0.029329	0.2053	0.419092
10	-0.163124	-1.1419	0.129529
11	-0.070812	-0.4957	0.311167
12	-0.00521	-0.0365	0.485528
13	-0.262402	-1.8368	0.036154
14	-0.313351	-2.1935	0.016525
15	-0.314804	-2.2036	0.01614
16	-0.367041	-2.5693	0.006643

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.671145	4.698	1.1e-05
2	0.157645	1.1035	0.137597
3	0.322088	2.2546	0.01433
4	-0.078493	-0.5495	0.292595
5	-0.013255	-0.0928	0.463227
6	-0.022403	-0.1568	0.438016
7	-0.302636	-2.1185	0.019616
8	0.134175	0.9392	0.176112
9	-0.297889	-2.0852	0.02114
10	-0.154985	-1.0849	0.141638
11	0.248864	1.742	0.043887
12	0.157684	1.1038	0.137538
13	-0.331279	-2.319	0.012305
14	-0.192669	-1.3487	0.09182
15	-0.081794	-0.5726	0.28478
16	0.000829	0.0058	0.497696

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.671145 & 4.698 & 1.1e-05 \tabularnewline
2 & 0.157645 & 1.1035 & 0.137597 \tabularnewline
3 & 0.322088 & 2.2546 & 0.01433 \tabularnewline
4 & -0.078493 & -0.5495 & 0.292595 \tabularnewline
5 & -0.013255 & -0.0928 & 0.463227 \tabularnewline
6 & -0.022403 & -0.1568 & 0.438016 \tabularnewline
7 & -0.302636 & -2.1185 & 0.019616 \tabularnewline
8 & 0.134175 & 0.9392 & 0.176112 \tabularnewline
9 & -0.297889 & -2.0852 & 0.02114 \tabularnewline
10 & -0.154985 & -1.0849 & 0.141638 \tabularnewline
11 & 0.248864 & 1.742 & 0.043887 \tabularnewline
12 & 0.157684 & 1.1038 & 0.137538 \tabularnewline
13 & -0.331279 & -2.319 & 0.012305 \tabularnewline
14 & -0.192669 & -1.3487 & 0.09182 \tabularnewline
15 & -0.081794 & -0.5726 & 0.28478 \tabularnewline
16 & 0.000829 & 0.0058 & 0.497696 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151618&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]0.671145[/C][C]4.698[/C][C]1.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.157645[/C][C]1.1035[/C][C]0.137597[/C][/ROW]
[ROW][C]3[/C][C]0.322088[/C][C]2.2546[/C][C]0.01433[/C][/ROW]
[ROW][C]4[/C][C]-0.078493[/C][C]-0.5495[/C][C]0.292595[/C][/ROW]
[ROW][C]5[/C][C]-0.013255[/C][C]-0.0928[/C][C]0.463227[/C][/ROW]
[ROW][C]6[/C][C]-0.022403[/C][C]-0.1568[/C][C]0.438016[/C][/ROW]
[ROW][C]7[/C][C]-0.302636[/C][C]-2.1185[/C][C]0.019616[/C][/ROW]
[ROW][C]8[/C][C]0.134175[/C][C]0.9392[/C][C]0.176112[/C][/ROW]
[ROW][C]9[/C][C]-0.297889[/C][C]-2.0852[/C][C]0.02114[/C][/ROW]
[ROW][C]10[/C][C]-0.154985[/C][C]-1.0849[/C][C]0.141638[/C][/ROW]
[ROW][C]11[/C][C]0.248864[/C][C]1.742[/C][C]0.043887[/C][/ROW]
[ROW][C]12[/C][C]0.157684[/C][C]1.1038[/C][C]0.137538[/C][/ROW]
[ROW][C]13[/C][C]-0.331279[/C][C]-2.319[/C][C]0.012305[/C][/ROW]
[ROW][C]14[/C][C]-0.192669[/C][C]-1.3487[/C][C]0.09182[/C][/ROW]
[ROW][C]15[/C][C]-0.081794[/C][C]-0.5726[/C][C]0.28478[/C][/ROW]
[ROW][C]16[/C][C]0.000829[/C][C]0.0058[/C][C]0.497696[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151618&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151618&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	0.671145	4.698	1.1e-05
2	0.157645	1.1035	0.137597
3	0.322088	2.2546	0.01433
4	-0.078493	-0.5495	0.292595
5	-0.013255	-0.0928	0.463227
6	-0.022403	-0.1568	0.438016
7	-0.302636	-2.1185	0.019616
8	0.134175	0.9392	0.176112
9	-0.297889	-2.0852	0.02114
10	-0.154985	-1.0849	0.141638
11	0.248864	1.742	0.043887
12	0.157684	1.1038	0.137538
13	-0.331279	-2.319	0.012305
14	-0.192669	-1.3487	0.09182
15	-0.081794	-0.5726	0.28478
16	0.000829	0.0058	0.497696

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 ; 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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code