Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 07 Dec 2008 03:42:19 -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/07/t1228646574dhwuu2cmtu90fux.htm/, Retrieved Sun, 19 May 2024 09:26:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29853, Retrieved Sun, 19 May 2024 09:26:49 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

205

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP     [(Partial) Autocorrelation Function] [] [2008-12-07 10:42:19] [d41d8cd98f00b204e9800998ecf8427e] [Current]

Feedback Forum

2008-12-13 13:34:30 [Julie Govaerts] [reply] 
Het langzaam dalend patroon duidt op een LT-trend, de bulten bij lags 12, 24, 36, 48, ... wijzen op seizonaliteit. Om de tijdreeks stationair te willen maken, moeten we zowel seizonaal als niet-seizonaal differentiëren.
2008-12-16 14:29:18 [Peter Van Doninck] [reply] 
De student heeft lambda gelijkgesteld aan 0,3 (waarom deze waarde???). Dit mocht hier echter nog niet! Wanneer de correcte lambda waarde gebruikt wordt, dan is het hangmatpatroon nog uitgesprokener! De lange termijntrend, die tevens dalend is, valt hier wel op. Ook de seizoenale trend is hier duidelijk aanwezig.

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29853&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]3 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=29853&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29853&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.95528	18.4248	0
2	0.909937	17.5502	0
3	0.873708	16.8515	0
4	0.856671	16.5229	0
5	0.845505	16.3075	0
6	0.813939	15.6987	0
7	0.791934	15.2743	0
8	0.752468	14.5131	0
9	0.721874	13.923	0
10	0.711332	13.7197	0
11	0.715476	13.7996	0
12	0.719784	13.8827	0
13	0.666073	12.8468	0
14	0.614968	11.8611	0
15	0.578525	11.1582	0
16	0.564748	10.8925	0
17	0.562121	10.8418	0
18	0.543748	10.4874	0
19	0.537394	10.3649	0
20	0.513742	9.9087	0
21	0.49925	9.6292	0
22	0.505261	9.7451	0
23	0.522349	10.0747	0
24	0.541349	10.4412	0
25	0.503323	9.7077	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95528 & 18.4248 & 0 \tabularnewline
2 & 0.909937 & 17.5502 & 0 \tabularnewline
3 & 0.873708 & 16.8515 & 0 \tabularnewline
4 & 0.856671 & 16.5229 & 0 \tabularnewline
5 & 0.845505 & 16.3075 & 0 \tabularnewline
6 & 0.813939 & 15.6987 & 0 \tabularnewline
7 & 0.791934 & 15.2743 & 0 \tabularnewline
8 & 0.752468 & 14.5131 & 0 \tabularnewline
9 & 0.721874 & 13.923 & 0 \tabularnewline
10 & 0.711332 & 13.7197 & 0 \tabularnewline
11 & 0.715476 & 13.7996 & 0 \tabularnewline
12 & 0.719784 & 13.8827 & 0 \tabularnewline
13 & 0.666073 & 12.8468 & 0 \tabularnewline
14 & 0.614968 & 11.8611 & 0 \tabularnewline
15 & 0.578525 & 11.1582 & 0 \tabularnewline
16 & 0.564748 & 10.8925 & 0 \tabularnewline
17 & 0.562121 & 10.8418 & 0 \tabularnewline
18 & 0.543748 & 10.4874 & 0 \tabularnewline
19 & 0.537394 & 10.3649 & 0 \tabularnewline
20 & 0.513742 & 9.9087 & 0 \tabularnewline
21 & 0.49925 & 9.6292 & 0 \tabularnewline
22 & 0.505261 & 9.7451 & 0 \tabularnewline
23 & 0.522349 & 10.0747 & 0 \tabularnewline
24 & 0.541349 & 10.4412 & 0 \tabularnewline
25 & 0.503323 & 9.7077 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29853&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]0.95528[/C][C]18.4248[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.909937[/C][C]17.5502[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.873708[/C][C]16.8515[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.856671[/C][C]16.5229[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.845505[/C][C]16.3075[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.813939[/C][C]15.6987[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.791934[/C][C]15.2743[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.752468[/C][C]14.5131[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.721874[/C][C]13.923[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.711332[/C][C]13.7197[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.715476[/C][C]13.7996[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.719784[/C][C]13.8827[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.666073[/C][C]12.8468[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.614968[/C][C]11.8611[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.578525[/C][C]11.1582[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.564748[/C][C]10.8925[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.562121[/C][C]10.8418[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.543748[/C][C]10.4874[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.537394[/C][C]10.3649[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.513742[/C][C]9.9087[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.49925[/C][C]9.6292[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.505261[/C][C]9.7451[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.522349[/C][C]10.0747[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.541349[/C][C]10.4412[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.503323[/C][C]9.7077[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29853&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29853&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	0.95528	18.4248	0
2	0.909937	17.5502	0
3	0.873708	16.8515	0
4	0.856671	16.5229	0
5	0.845505	16.3075	0
6	0.813939	15.6987	0
7	0.791934	15.2743	0
8	0.752468	14.5131	0
9	0.721874	13.923	0
10	0.711332	13.7197	0
11	0.715476	13.7996	0
12	0.719784	13.8827	0
13	0.666073	12.8468	0
14	0.614968	11.8611	0
15	0.578525	11.1582	0
16	0.564748	10.8925	0
17	0.562121	10.8418	0
18	0.543748	10.4874	0
19	0.537394	10.3649	0
20	0.513742	9.9087	0
21	0.49925	9.6292	0
22	0.505261	9.7451	0
23	0.522349	10.0747	0
24	0.541349	10.4412	0
25	0.503323	9.7077	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.95528	18.4248	0
2	-0.029997	-0.5786	0.281617
3	0.080629	1.5551	0.060384
4	0.199852	3.8546	6.8e-05
5	0.070202	1.354	0.088278
6	-0.206526	-3.9833	4.1e-05
7	0.162089	3.1263	0.000955
8	-0.245704	-4.739	2e-06
9	0.046531	0.8975	0.185029
10	0.237191	4.5748	3e-06
11	0.157028	3.0287	0.001314
12	-0.031148	-0.6008	0.274182
13	-0.55582	-10.7203	0
14	0.04326	0.8344	0.202305
15	0.138263	2.6667	0.003997
16	0.087582	1.6892	0.046008
17	0.150558	2.9039	0.001953
18	0.051791	0.9989	0.159244
19	0.109873	2.1192	0.01737
20	-0.063508	-1.2249	0.110695
21	0.000424	0.0082	0.496743
22	0.077982	1.5041	0.066707
23	-0.039941	-0.7704	0.220789
24	0.067972	1.311	0.095335
25	-0.275369	-5.3111	0

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95528 & 18.4248 & 0 \tabularnewline
2 & -0.029997 & -0.5786 & 0.281617 \tabularnewline
3 & 0.080629 & 1.5551 & 0.060384 \tabularnewline
4 & 0.199852 & 3.8546 & 6.8e-05 \tabularnewline
5 & 0.070202 & 1.354 & 0.088278 \tabularnewline
6 & -0.206526 & -3.9833 & 4.1e-05 \tabularnewline
7 & 0.162089 & 3.1263 & 0.000955 \tabularnewline
8 & -0.245704 & -4.739 & 2e-06 \tabularnewline
9 & 0.046531 & 0.8975 & 0.185029 \tabularnewline
10 & 0.237191 & 4.5748 & 3e-06 \tabularnewline
11 & 0.157028 & 3.0287 & 0.001314 \tabularnewline
12 & -0.031148 & -0.6008 & 0.274182 \tabularnewline
13 & -0.55582 & -10.7203 & 0 \tabularnewline
14 & 0.04326 & 0.8344 & 0.202305 \tabularnewline
15 & 0.138263 & 2.6667 & 0.003997 \tabularnewline
16 & 0.087582 & 1.6892 & 0.046008 \tabularnewline
17 & 0.150558 & 2.9039 & 0.001953 \tabularnewline
18 & 0.051791 & 0.9989 & 0.159244 \tabularnewline
19 & 0.109873 & 2.1192 & 0.01737 \tabularnewline
20 & -0.063508 & -1.2249 & 0.110695 \tabularnewline
21 & 0.000424 & 0.0082 & 0.496743 \tabularnewline
22 & 0.077982 & 1.5041 & 0.066707 \tabularnewline
23 & -0.039941 & -0.7704 & 0.220789 \tabularnewline
24 & 0.067972 & 1.311 & 0.095335 \tabularnewline
25 & -0.275369 & -5.3111 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29853&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]0.95528[/C][C]18.4248[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.029997[/C][C]-0.5786[/C][C]0.281617[/C][/ROW]
[ROW][C]3[/C][C]0.080629[/C][C]1.5551[/C][C]0.060384[/C][/ROW]
[ROW][C]4[/C][C]0.199852[/C][C]3.8546[/C][C]6.8e-05[/C][/ROW]
[ROW][C]5[/C][C]0.070202[/C][C]1.354[/C][C]0.088278[/C][/ROW]
[ROW][C]6[/C][C]-0.206526[/C][C]-3.9833[/C][C]4.1e-05[/C][/ROW]
[ROW][C]7[/C][C]0.162089[/C][C]3.1263[/C][C]0.000955[/C][/ROW]
[ROW][C]8[/C][C]-0.245704[/C][C]-4.739[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]0.046531[/C][C]0.8975[/C][C]0.185029[/C][/ROW]
[ROW][C]10[/C][C]0.237191[/C][C]4.5748[/C][C]3e-06[/C][/ROW]
[ROW][C]11[/C][C]0.157028[/C][C]3.0287[/C][C]0.001314[/C][/ROW]
[ROW][C]12[/C][C]-0.031148[/C][C]-0.6008[/C][C]0.274182[/C][/ROW]
[ROW][C]13[/C][C]-0.55582[/C][C]-10.7203[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.04326[/C][C]0.8344[/C][C]0.202305[/C][/ROW]
[ROW][C]15[/C][C]0.138263[/C][C]2.6667[/C][C]0.003997[/C][/ROW]
[ROW][C]16[/C][C]0.087582[/C][C]1.6892[/C][C]0.046008[/C][/ROW]
[ROW][C]17[/C][C]0.150558[/C][C]2.9039[/C][C]0.001953[/C][/ROW]
[ROW][C]18[/C][C]0.051791[/C][C]0.9989[/C][C]0.159244[/C][/ROW]
[ROW][C]19[/C][C]0.109873[/C][C]2.1192[/C][C]0.01737[/C][/ROW]
[ROW][C]20[/C][C]-0.063508[/C][C]-1.2249[/C][C]0.110695[/C][/ROW]
[ROW][C]21[/C][C]0.000424[/C][C]0.0082[/C][C]0.496743[/C][/ROW]
[ROW][C]22[/C][C]0.077982[/C][C]1.5041[/C][C]0.066707[/C][/ROW]
[ROW][C]23[/C][C]-0.039941[/C][C]-0.7704[/C][C]0.220789[/C][/ROW]
[ROW][C]24[/C][C]0.067972[/C][C]1.311[/C][C]0.095335[/C][/ROW]
[ROW][C]25[/C][C]-0.275369[/C][C]-5.3111[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29853&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29853&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	0.95528	18.4248	0
2	-0.029997	-0.5786	0.281617
3	0.080629	1.5551	0.060384
4	0.199852	3.8546	6.8e-05
5	0.070202	1.354	0.088278
6	-0.206526	-3.9833	4.1e-05
7	0.162089	3.1263	0.000955
8	-0.245704	-4.739	2e-06
9	0.046531	0.8975	0.185029
10	0.237191	4.5748	3e-06
11	0.157028	3.0287	0.001314
12	-0.031148	-0.6008	0.274182
13	-0.55582	-10.7203	0
14	0.04326	0.8344	0.202305
15	0.138263	2.6667	0.003997
16	0.087582	1.6892	0.046008
17	0.150558	2.9039	0.001953
18	0.051791	0.9989	0.159244
19	0.109873	2.1192	0.01737
20	-0.063508	-1.2249	0.110695
21	0.000424	0.0082	0.496743
22	0.077982	1.5041	0.066707
23	-0.039941	-0.7704	0.220789
24	0.067972	1.311	0.095335
25	-0.275369	-5.3111	0

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.3 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.3 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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