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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Apr 2010 18:11:36 +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/Apr/28/t12724783290f5m86hhas4kwt2.htm/, Retrieved Fri, 19 Apr 2024 01:29:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=75003, Retrieved Fri, 19 Apr 2024 01:29:42 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W21

Estimated Impact

140

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

-     [Mean Plot] [Het verkoopcijfer...] [2010-04-24 13:28:58] [e6858d370c345b8be9ebab3064023a2f]
- RMP     [(Partial) Autocorrelation Function] [Het verkoopcijfer...] [2010-04-28 18:11:36] [b9d93a00608bcde4713420de1fa47366] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75003&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75003&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75003&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.575952	-5.2787	1e-06
2	0.126011	1.1549	0.1257
3	-0.088392	-0.8101	0.21008
4	0.082692	0.7579	0.225321
5	0.080804	0.7406	0.230506
6	-0.200483	-1.8375	0.034839
7	0.077731	0.7124	0.23909
8	0.088771	0.8136	0.209088
9	-0.089033	-0.816	0.208403
10	0.156474	1.4341	0.077626
11	-0.579842	-5.3143	0
12	0.847317	7.7658	0
13	-0.48905	-4.4822	1.2e-05
14	0.114367	1.0482	0.148778
15	-0.091766	-0.841	0.201355
16	0.076522	0.7013	0.242515
17	0.073492	0.6736	0.25122
18	-0.182855	-1.6759	0.048739
19	0.074821	0.6857	0.247381

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.575952 & -5.2787 & 1e-06 \tabularnewline
2 & 0.126011 & 1.1549 & 0.1257 \tabularnewline
3 & -0.088392 & -0.8101 & 0.21008 \tabularnewline
4 & 0.082692 & 0.7579 & 0.225321 \tabularnewline
5 & 0.080804 & 0.7406 & 0.230506 \tabularnewline
6 & -0.200483 & -1.8375 & 0.034839 \tabularnewline
7 & 0.077731 & 0.7124 & 0.23909 \tabularnewline
8 & 0.088771 & 0.8136 & 0.209088 \tabularnewline
9 & -0.089033 & -0.816 & 0.208403 \tabularnewline
10 & 0.156474 & 1.4341 & 0.077626 \tabularnewline
11 & -0.579842 & -5.3143 & 0 \tabularnewline
12 & 0.847317 & 7.7658 & 0 \tabularnewline
13 & -0.48905 & -4.4822 & 1.2e-05 \tabularnewline
14 & 0.114367 & 1.0482 & 0.148778 \tabularnewline
15 & -0.091766 & -0.841 & 0.201355 \tabularnewline
16 & 0.076522 & 0.7013 & 0.242515 \tabularnewline
17 & 0.073492 & 0.6736 & 0.25122 \tabularnewline
18 & -0.182855 & -1.6759 & 0.048739 \tabularnewline
19 & 0.074821 & 0.6857 & 0.247381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75003&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]-0.575952[/C][C]-5.2787[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.126011[/C][C]1.1549[/C][C]0.1257[/C][/ROW]
[ROW][C]3[/C][C]-0.088392[/C][C]-0.8101[/C][C]0.21008[/C][/ROW]
[ROW][C]4[/C][C]0.082692[/C][C]0.7579[/C][C]0.225321[/C][/ROW]
[ROW][C]5[/C][C]0.080804[/C][C]0.7406[/C][C]0.230506[/C][/ROW]
[ROW][C]6[/C][C]-0.200483[/C][C]-1.8375[/C][C]0.034839[/C][/ROW]
[ROW][C]7[/C][C]0.077731[/C][C]0.7124[/C][C]0.23909[/C][/ROW]
[ROW][C]8[/C][C]0.088771[/C][C]0.8136[/C][C]0.209088[/C][/ROW]
[ROW][C]9[/C][C]-0.089033[/C][C]-0.816[/C][C]0.208403[/C][/ROW]
[ROW][C]10[/C][C]0.156474[/C][C]1.4341[/C][C]0.077626[/C][/ROW]
[ROW][C]11[/C][C]-0.579842[/C][C]-5.3143[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.847317[/C][C]7.7658[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.48905[/C][C]-4.4822[/C][C]1.2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.114367[/C][C]1.0482[/C][C]0.148778[/C][/ROW]
[ROW][C]15[/C][C]-0.091766[/C][C]-0.841[/C][C]0.201355[/C][/ROW]
[ROW][C]16[/C][C]0.076522[/C][C]0.7013[/C][C]0.242515[/C][/ROW]
[ROW][C]17[/C][C]0.073492[/C][C]0.6736[/C][C]0.25122[/C][/ROW]
[ROW][C]18[/C][C]-0.182855[/C][C]-1.6759[/C][C]0.048739[/C][/ROW]
[ROW][C]19[/C][C]0.074821[/C][C]0.6857[/C][C]0.247381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75003&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75003&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	-0.575952	-5.2787	1e-06
2	0.126011	1.1549	0.1257
3	-0.088392	-0.8101	0.21008
4	0.082692	0.7579	0.225321
5	0.080804	0.7406	0.230506
6	-0.200483	-1.8375	0.034839
7	0.077731	0.7124	0.23909
8	0.088771	0.8136	0.209088
9	-0.089033	-0.816	0.208403
10	0.156474	1.4341	0.077626
11	-0.579842	-5.3143	0
12	0.847317	7.7658	0
13	-0.48905	-4.4822	1.2e-05
14	0.114367	1.0482	0.148778
15	-0.091766	-0.841	0.201355
16	0.076522	0.7013	0.242515
17	0.073492	0.6736	0.25122
18	-0.182855	-1.6759	0.048739
19	0.074821	0.6857	0.247381

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.575952	-5.2787	1e-06
2	-0.307819	-2.8212	0.002985
3	-0.282273	-2.5871	0.005701
4	-0.15907	-1.4579	0.074299
5	0.113259	1.038	0.151117
6	-0.079368	-0.7274	0.234497
7	-0.14721	-1.3492	0.090449
8	0.053079	0.4865	0.313947
9	-0.013233	-0.1213	0.451879
10	0.236041	2.1633	0.016678
11	-0.646527	-5.9255	0
12	0.476852	4.3704	1.8e-05
13	0.086729	0.7949	0.214459
14	0.023011	0.2109	0.416737
15	-0.030922	-0.2834	0.388781
16	-0.025126	-0.2303	0.409217
17	-0.089278	-0.8182	0.207765
18	-0.020025	-0.1835	0.427413
19	0.022778	0.2088	0.417569

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.575952 & -5.2787 & 1e-06 \tabularnewline
2 & -0.307819 & -2.8212 & 0.002985 \tabularnewline
3 & -0.282273 & -2.5871 & 0.005701 \tabularnewline
4 & -0.15907 & -1.4579 & 0.074299 \tabularnewline
5 & 0.113259 & 1.038 & 0.151117 \tabularnewline
6 & -0.079368 & -0.7274 & 0.234497 \tabularnewline
7 & -0.14721 & -1.3492 & 0.090449 \tabularnewline
8 & 0.053079 & 0.4865 & 0.313947 \tabularnewline
9 & -0.013233 & -0.1213 & 0.451879 \tabularnewline
10 & 0.236041 & 2.1633 & 0.016678 \tabularnewline
11 & -0.646527 & -5.9255 & 0 \tabularnewline
12 & 0.476852 & 4.3704 & 1.8e-05 \tabularnewline
13 & 0.086729 & 0.7949 & 0.214459 \tabularnewline
14 & 0.023011 & 0.2109 & 0.416737 \tabularnewline
15 & -0.030922 & -0.2834 & 0.388781 \tabularnewline
16 & -0.025126 & -0.2303 & 0.409217 \tabularnewline
17 & -0.089278 & -0.8182 & 0.207765 \tabularnewline
18 & -0.020025 & -0.1835 & 0.427413 \tabularnewline
19 & 0.022778 & 0.2088 & 0.417569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75003&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]-0.575952[/C][C]-5.2787[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.307819[/C][C]-2.8212[/C][C]0.002985[/C][/ROW]
[ROW][C]3[/C][C]-0.282273[/C][C]-2.5871[/C][C]0.005701[/C][/ROW]
[ROW][C]4[/C][C]-0.15907[/C][C]-1.4579[/C][C]0.074299[/C][/ROW]
[ROW][C]5[/C][C]0.113259[/C][C]1.038[/C][C]0.151117[/C][/ROW]
[ROW][C]6[/C][C]-0.079368[/C][C]-0.7274[/C][C]0.234497[/C][/ROW]
[ROW][C]7[/C][C]-0.14721[/C][C]-1.3492[/C][C]0.090449[/C][/ROW]
[ROW][C]8[/C][C]0.053079[/C][C]0.4865[/C][C]0.313947[/C][/ROW]
[ROW][C]9[/C][C]-0.013233[/C][C]-0.1213[/C][C]0.451879[/C][/ROW]
[ROW][C]10[/C][C]0.236041[/C][C]2.1633[/C][C]0.016678[/C][/ROW]
[ROW][C]11[/C][C]-0.646527[/C][C]-5.9255[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.476852[/C][C]4.3704[/C][C]1.8e-05[/C][/ROW]
[ROW][C]13[/C][C]0.086729[/C][C]0.7949[/C][C]0.214459[/C][/ROW]
[ROW][C]14[/C][C]0.023011[/C][C]0.2109[/C][C]0.416737[/C][/ROW]
[ROW][C]15[/C][C]-0.030922[/C][C]-0.2834[/C][C]0.388781[/C][/ROW]
[ROW][C]16[/C][C]-0.025126[/C][C]-0.2303[/C][C]0.409217[/C][/ROW]
[ROW][C]17[/C][C]-0.089278[/C][C]-0.8182[/C][C]0.207765[/C][/ROW]
[ROW][C]18[/C][C]-0.020025[/C][C]-0.1835[/C][C]0.427413[/C][/ROW]
[ROW][C]19[/C][C]0.022778[/C][C]0.2088[/C][C]0.417569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75003&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75003&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	-0.575952	-5.2787	1e-06
2	-0.307819	-2.8212	0.002985
3	-0.282273	-2.5871	0.005701
4	-0.15907	-1.4579	0.074299
5	0.113259	1.038	0.151117
6	-0.079368	-0.7274	0.234497
7	-0.14721	-1.3492	0.090449
8	0.053079	0.4865	0.313947
9	-0.013233	-0.1213	0.451879
10	0.236041	2.1633	0.016678
11	-0.646527	-5.9255	0
12	0.476852	4.3704	1.8e-05
13	0.086729	0.7949	0.214459
14	0.023011	0.2109	0.416737
15	-0.030922	-0.2834	0.388781
16	-0.025126	-0.2303	0.409217
17	-0.089278	-0.8182	0.207765
18	-0.020025	-0.1835	0.427413
19	0.022778	0.2088	0.417569

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 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code