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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 17 Oct 2014 16:00:06 +0100

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/2014/Oct/17/t1413558028pddsidtlrqskg64.htm/, Retrieved Fri, 10 May 2024 19:57:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243311, Retrieved Fri, 10 May 2024 19:57:51 +0000

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Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2014-10-17 15:00:06] [5cf6a598f846f655ef95f65053f7ffc6] [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' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243311&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243311&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243311&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' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.097504	-0.7553	0.226524
2	0.120286	0.9317	0.177604
3	-0.150762	-1.1678	0.123754
4	0.256795	1.9891	0.025626
5	0.062472	0.4839	0.315107
6	-0.039167	-0.3034	0.381324
7	-0.001361	-0.0105	0.495812
8	-0.150088	-1.1626	0.124802
9	0.151767	1.1756	0.122202
10	-0.069327	-0.537	0.296626
11	0.120727	0.9351	0.176731
12	-0.116748	-0.9043	0.184719
13	0.066901	0.5182	0.303109
14	-0.0146	-0.1131	0.455169
15	0.092826	0.719	0.237458
16	-0.194564	-1.5071	0.068518
17	-0.060686	-0.4701	0.320005
18	0.012157	0.0942	0.462646
19	0.043951	0.3404	0.367356
20	-0.038191	-0.2958	0.384191
21	-0.030854	-0.239	0.405962
22	-0.013888	-0.1076	0.457345
23	-0.066493	-0.5151	0.304205
24	0.018899	0.1464	0.442051

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.097504 & -0.7553 & 0.226524 \tabularnewline
2 & 0.120286 & 0.9317 & 0.177604 \tabularnewline
3 & -0.150762 & -1.1678 & 0.123754 \tabularnewline
4 & 0.256795 & 1.9891 & 0.025626 \tabularnewline
5 & 0.062472 & 0.4839 & 0.315107 \tabularnewline
6 & -0.039167 & -0.3034 & 0.381324 \tabularnewline
7 & -0.001361 & -0.0105 & 0.495812 \tabularnewline
8 & -0.150088 & -1.1626 & 0.124802 \tabularnewline
9 & 0.151767 & 1.1756 & 0.122202 \tabularnewline
10 & -0.069327 & -0.537 & 0.296626 \tabularnewline
11 & 0.120727 & 0.9351 & 0.176731 \tabularnewline
12 & -0.116748 & -0.9043 & 0.184719 \tabularnewline
13 & 0.066901 & 0.5182 & 0.303109 \tabularnewline
14 & -0.0146 & -0.1131 & 0.455169 \tabularnewline
15 & 0.092826 & 0.719 & 0.237458 \tabularnewline
16 & -0.194564 & -1.5071 & 0.068518 \tabularnewline
17 & -0.060686 & -0.4701 & 0.320005 \tabularnewline
18 & 0.012157 & 0.0942 & 0.462646 \tabularnewline
19 & 0.043951 & 0.3404 & 0.367356 \tabularnewline
20 & -0.038191 & -0.2958 & 0.384191 \tabularnewline
21 & -0.030854 & -0.239 & 0.405962 \tabularnewline
22 & -0.013888 & -0.1076 & 0.457345 \tabularnewline
23 & -0.066493 & -0.5151 & 0.304205 \tabularnewline
24 & 0.018899 & 0.1464 & 0.442051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243311&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]-0.097504[/C][C]-0.7553[/C][C]0.226524[/C][/ROW]
[ROW][C]2[/C][C]0.120286[/C][C]0.9317[/C][C]0.177604[/C][/ROW]
[ROW][C]3[/C][C]-0.150762[/C][C]-1.1678[/C][C]0.123754[/C][/ROW]
[ROW][C]4[/C][C]0.256795[/C][C]1.9891[/C][C]0.025626[/C][/ROW]
[ROW][C]5[/C][C]0.062472[/C][C]0.4839[/C][C]0.315107[/C][/ROW]
[ROW][C]6[/C][C]-0.039167[/C][C]-0.3034[/C][C]0.381324[/C][/ROW]
[ROW][C]7[/C][C]-0.001361[/C][C]-0.0105[/C][C]0.495812[/C][/ROW]
[ROW][C]8[/C][C]-0.150088[/C][C]-1.1626[/C][C]0.124802[/C][/ROW]
[ROW][C]9[/C][C]0.151767[/C][C]1.1756[/C][C]0.122202[/C][/ROW]
[ROW][C]10[/C][C]-0.069327[/C][C]-0.537[/C][C]0.296626[/C][/ROW]
[ROW][C]11[/C][C]0.120727[/C][C]0.9351[/C][C]0.176731[/C][/ROW]
[ROW][C]12[/C][C]-0.116748[/C][C]-0.9043[/C][C]0.184719[/C][/ROW]
[ROW][C]13[/C][C]0.066901[/C][C]0.5182[/C][C]0.303109[/C][/ROW]
[ROW][C]14[/C][C]-0.0146[/C][C]-0.1131[/C][C]0.455169[/C][/ROW]
[ROW][C]15[/C][C]0.092826[/C][C]0.719[/C][C]0.237458[/C][/ROW]
[ROW][C]16[/C][C]-0.194564[/C][C]-1.5071[/C][C]0.068518[/C][/ROW]
[ROW][C]17[/C][C]-0.060686[/C][C]-0.4701[/C][C]0.320005[/C][/ROW]
[ROW][C]18[/C][C]0.012157[/C][C]0.0942[/C][C]0.462646[/C][/ROW]
[ROW][C]19[/C][C]0.043951[/C][C]0.3404[/C][C]0.367356[/C][/ROW]
[ROW][C]20[/C][C]-0.038191[/C][C]-0.2958[/C][C]0.384191[/C][/ROW]
[ROW][C]21[/C][C]-0.030854[/C][C]-0.239[/C][C]0.405962[/C][/ROW]
[ROW][C]22[/C][C]-0.013888[/C][C]-0.1076[/C][C]0.457345[/C][/ROW]
[ROW][C]23[/C][C]-0.066493[/C][C]-0.5151[/C][C]0.304205[/C][/ROW]
[ROW][C]24[/C][C]0.018899[/C][C]0.1464[/C][C]0.442051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243311&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243311&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	-0.097504	-0.7553	0.226524
2	0.120286	0.9317	0.177604
3	-0.150762	-1.1678	0.123754
4	0.256795	1.9891	0.025626
5	0.062472	0.4839	0.315107
6	-0.039167	-0.3034	0.381324
7	-0.001361	-0.0105	0.495812
8	-0.150088	-1.1626	0.124802
9	0.151767	1.1756	0.122202
10	-0.069327	-0.537	0.296626
11	0.120727	0.9351	0.176731
12	-0.116748	-0.9043	0.184719
13	0.066901	0.5182	0.303109
14	-0.0146	-0.1131	0.455169
15	0.092826	0.719	0.237458
16	-0.194564	-1.5071	0.068518
17	-0.060686	-0.4701	0.320005
18	0.012157	0.0942	0.462646
19	0.043951	0.3404	0.367356
20	-0.038191	-0.2958	0.384191
21	-0.030854	-0.239	0.405962
22	-0.013888	-0.1076	0.457345
23	-0.066493	-0.5151	0.304205
24	0.018899	0.1464	0.442051

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.097504	-0.7553	0.226524
2	0.111843	0.8663	0.19488
3	-0.132338	-1.0251	0.154718
4	0.229967	1.7813	0.039961
5	0.133058	1.0307	0.153419
6	-0.103845	-0.8044	0.212176
7	0.041283	0.3198	0.375124
8	-0.188507	-1.4602	0.07473
9	0.074433	0.5766	0.283198
10	0.008682	0.0672	0.473304
11	0.060722	0.4704	0.319905
12	0.013062	0.1012	0.459874
13	0.00025	0.0019	0.499231
14	0.002864	0.0222	0.491187
15	0.052484	0.4065	0.342897
16	-0.233717	-1.8104	0.037623
17	-0.058388	-0.4523	0.326351
18	0.033365	0.2584	0.398473
19	0.014287	0.1107	0.456125
20	0.022756	0.1763	0.430339
21	0.068094	0.5275	0.299913
22	-0.050483	-0.391	0.348577
23	-0.090526	-0.7012	0.242941
24	-0.071684	-0.5553	0.29039

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.097504 & -0.7553 & 0.226524 \tabularnewline
2 & 0.111843 & 0.8663 & 0.19488 \tabularnewline
3 & -0.132338 & -1.0251 & 0.154718 \tabularnewline
4 & 0.229967 & 1.7813 & 0.039961 \tabularnewline
5 & 0.133058 & 1.0307 & 0.153419 \tabularnewline
6 & -0.103845 & -0.8044 & 0.212176 \tabularnewline
7 & 0.041283 & 0.3198 & 0.375124 \tabularnewline
8 & -0.188507 & -1.4602 & 0.07473 \tabularnewline
9 & 0.074433 & 0.5766 & 0.283198 \tabularnewline
10 & 0.008682 & 0.0672 & 0.473304 \tabularnewline
11 & 0.060722 & 0.4704 & 0.319905 \tabularnewline
12 & 0.013062 & 0.1012 & 0.459874 \tabularnewline
13 & 0.00025 & 0.0019 & 0.499231 \tabularnewline
14 & 0.002864 & 0.0222 & 0.491187 \tabularnewline
15 & 0.052484 & 0.4065 & 0.342897 \tabularnewline
16 & -0.233717 & -1.8104 & 0.037623 \tabularnewline
17 & -0.058388 & -0.4523 & 0.326351 \tabularnewline
18 & 0.033365 & 0.2584 & 0.398473 \tabularnewline
19 & 0.014287 & 0.1107 & 0.456125 \tabularnewline
20 & 0.022756 & 0.1763 & 0.430339 \tabularnewline
21 & 0.068094 & 0.5275 & 0.299913 \tabularnewline
22 & -0.050483 & -0.391 & 0.348577 \tabularnewline
23 & -0.090526 & -0.7012 & 0.242941 \tabularnewline
24 & -0.071684 & -0.5553 & 0.29039 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243311&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]-0.097504[/C][C]-0.7553[/C][C]0.226524[/C][/ROW]
[ROW][C]2[/C][C]0.111843[/C][C]0.8663[/C][C]0.19488[/C][/ROW]
[ROW][C]3[/C][C]-0.132338[/C][C]-1.0251[/C][C]0.154718[/C][/ROW]
[ROW][C]4[/C][C]0.229967[/C][C]1.7813[/C][C]0.039961[/C][/ROW]
[ROW][C]5[/C][C]0.133058[/C][C]1.0307[/C][C]0.153419[/C][/ROW]
[ROW][C]6[/C][C]-0.103845[/C][C]-0.8044[/C][C]0.212176[/C][/ROW]
[ROW][C]7[/C][C]0.041283[/C][C]0.3198[/C][C]0.375124[/C][/ROW]
[ROW][C]8[/C][C]-0.188507[/C][C]-1.4602[/C][C]0.07473[/C][/ROW]
[ROW][C]9[/C][C]0.074433[/C][C]0.5766[/C][C]0.283198[/C][/ROW]
[ROW][C]10[/C][C]0.008682[/C][C]0.0672[/C][C]0.473304[/C][/ROW]
[ROW][C]11[/C][C]0.060722[/C][C]0.4704[/C][C]0.319905[/C][/ROW]
[ROW][C]12[/C][C]0.013062[/C][C]0.1012[/C][C]0.459874[/C][/ROW]
[ROW][C]13[/C][C]0.00025[/C][C]0.0019[/C][C]0.499231[/C][/ROW]
[ROW][C]14[/C][C]0.002864[/C][C]0.0222[/C][C]0.491187[/C][/ROW]
[ROW][C]15[/C][C]0.052484[/C][C]0.4065[/C][C]0.342897[/C][/ROW]
[ROW][C]16[/C][C]-0.233717[/C][C]-1.8104[/C][C]0.037623[/C][/ROW]
[ROW][C]17[/C][C]-0.058388[/C][C]-0.4523[/C][C]0.326351[/C][/ROW]
[ROW][C]18[/C][C]0.033365[/C][C]0.2584[/C][C]0.398473[/C][/ROW]
[ROW][C]19[/C][C]0.014287[/C][C]0.1107[/C][C]0.456125[/C][/ROW]
[ROW][C]20[/C][C]0.022756[/C][C]0.1763[/C][C]0.430339[/C][/ROW]
[ROW][C]21[/C][C]0.068094[/C][C]0.5275[/C][C]0.299913[/C][/ROW]
[ROW][C]22[/C][C]-0.050483[/C][C]-0.391[/C][C]0.348577[/C][/ROW]
[ROW][C]23[/C][C]-0.090526[/C][C]-0.7012[/C][C]0.242941[/C][/ROW]
[ROW][C]24[/C][C]-0.071684[/C][C]-0.5553[/C][C]0.29039[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243311&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243311&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	-0.097504	-0.7553	0.226524
2	0.111843	0.8663	0.19488
3	-0.132338	-1.0251	0.154718
4	0.229967	1.7813	0.039961
5	0.133058	1.0307	0.153419
6	-0.103845	-0.8044	0.212176
7	0.041283	0.3198	0.375124
8	-0.188507	-1.4602	0.07473
9	0.074433	0.5766	0.283198
10	0.008682	0.0672	0.473304
11	0.060722	0.4704	0.319905
12	0.013062	0.1012	0.459874
13	0.00025	0.0019	0.499231
14	0.002864	0.0222	0.491187
15	0.052484	0.4065	0.342897
16	-0.233717	-1.8104	0.037623
17	-0.058388	-0.4523	0.326351
18	0.033365	0.2584	0.398473
19	0.014287	0.1107	0.456125
20	0.022756	0.1763	0.430339
21	0.068094	0.5275	0.299913
22	-0.050483	-0.391	0.348577
23	-0.090526	-0.7012	0.242941
24	-0.071684	-0.5553	0.29039

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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