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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationFri, 07 Dec 2007 05:57:10 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/07/t1197031629my1lw5x6gfmxh7x.htm/, Retrieved Sun, 28 Apr 2024 23:59:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2800, Retrieved Sun, 28 Apr 2024 23:59:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2007-12-07 12:57:10] [9bb499d88394279c02e6a8b8cf177cf7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18.33
22.6
24.9
24.8
23.8
25.1
26
27.4
27.3
24.3
28.4
24.4
30.3
31.5
29.8
25.3
25.6
26.7
27.4
28.6
26.3
28.5
28.4
29.4
30.3
29.6
32.1
32.4
36.3
34.6
36.3
40.3
40.4
45.4
39
35.7
40.2
41.7
49.1
49.6
47
52
53.1
57.8
57.9
54.6
51.3
52.7
58.5
56.6
57.9
64.4
65.1
64.6
68.9
68.8
59.3
55
55.4
58
50.8
54.6
58.6
63.6
64.5
66.9
71.9
68.7
74.2
75.8

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2800&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2800&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2800&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Autocorrelation Function
Time lag kACF(k)T-STATP-value
017.61580
10.7349745.59740
20.5526794.20914.5e-05
30.4741443.6110.000319
40.4721063.59550.000335
50.4542293.45930.000511
60.3074012.34110.011343
70.1823221.38850.085144
80.0483270.3680.357089
90.0641230.48830.313573
100.089370.68060.249409
11-0.017249-0.13140.552029
12-0.242803-1.84910.965231
13-0.299585-2.28160.986898
14-0.229864-1.75060.957348
15-0.156631-1.19290.88111
16-0.202337-1.5410.935616
17-0.296907-2.26120.986243

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6158 & 0 \tabularnewline
1 & 0.734974 & 5.5974 & 0 \tabularnewline
2 & 0.552679 & 4.2091 & 4.5e-05 \tabularnewline
3 & 0.474144 & 3.611 & 0.000319 \tabularnewline
4 & 0.472106 & 3.5955 & 0.000335 \tabularnewline
5 & 0.454229 & 3.4593 & 0.000511 \tabularnewline
6 & 0.307401 & 2.3411 & 0.011343 \tabularnewline
7 & 0.182322 & 1.3885 & 0.085144 \tabularnewline
8 & 0.048327 & 0.368 & 0.357089 \tabularnewline
9 & 0.064123 & 0.4883 & 0.313573 \tabularnewline
10 & 0.08937 & 0.6806 & 0.249409 \tabularnewline
11 & -0.017249 & -0.1314 & 0.552029 \tabularnewline
12 & -0.242803 & -1.8491 & 0.965231 \tabularnewline
13 & -0.299585 & -2.2816 & 0.986898 \tabularnewline
14 & -0.229864 & -1.7506 & 0.957348 \tabularnewline
15 & -0.156631 & -1.1929 & 0.88111 \tabularnewline
16 & -0.202337 & -1.541 & 0.935616 \tabularnewline
17 & -0.296907 & -2.2612 & 0.986243 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2800&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]0[/C][C]1[/C][C]7.6158[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.734974[/C][C]5.5974[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.552679[/C][C]4.2091[/C][C]4.5e-05[/C][/ROW]
[ROW][C]3[/C][C]0.474144[/C][C]3.611[/C][C]0.000319[/C][/ROW]
[ROW][C]4[/C][C]0.472106[/C][C]3.5955[/C][C]0.000335[/C][/ROW]
[ROW][C]5[/C][C]0.454229[/C][C]3.4593[/C][C]0.000511[/C][/ROW]
[ROW][C]6[/C][C]0.307401[/C][C]2.3411[/C][C]0.011343[/C][/ROW]
[ROW][C]7[/C][C]0.182322[/C][C]1.3885[/C][C]0.085144[/C][/ROW]
[ROW][C]8[/C][C]0.048327[/C][C]0.368[/C][C]0.357089[/C][/ROW]
[ROW][C]9[/C][C]0.064123[/C][C]0.4883[/C][C]0.313573[/C][/ROW]
[ROW][C]10[/C][C]0.08937[/C][C]0.6806[/C][C]0.249409[/C][/ROW]
[ROW][C]11[/C][C]-0.017249[/C][C]-0.1314[/C][C]0.552029[/C][/ROW]
[ROW][C]12[/C][C]-0.242803[/C][C]-1.8491[/C][C]0.965231[/C][/ROW]
[ROW][C]13[/C][C]-0.299585[/C][C]-2.2816[/C][C]0.986898[/C][/ROW]
[ROW][C]14[/C][C]-0.229864[/C][C]-1.7506[/C][C]0.957348[/C][/ROW]
[ROW][C]15[/C][C]-0.156631[/C][C]-1.1929[/C][C]0.88111[/C][/ROW]
[ROW][C]16[/C][C]-0.202337[/C][C]-1.541[/C][C]0.935616[/C][/ROW]
[ROW][C]17[/C][C]-0.296907[/C][C]-2.2612[/C][C]0.986243[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2800&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2800&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
017.61580
10.7349745.59740
20.5526794.20914.5e-05
30.4741443.6110.000319
40.4721063.59550.000335
50.4542293.45930.000511
60.3074012.34110.011343
70.1823221.38850.085144
80.0483270.3680.357089
90.0641230.48830.313573
100.089370.68060.249409
11-0.017249-0.13140.552029
12-0.242803-1.84910.965231
13-0.299585-2.28160.986898
14-0.229864-1.75060.957348
15-0.156631-1.19290.88111
16-0.202337-1.5410.935616
17-0.296907-2.26120.986243






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
00.7349745.59740
10.0271680.20690.418405
20.1284240.9780.166056
30.1683791.28230.102413
40.0580820.44230.329944
5-0.217264-1.65460.948299
6-0.083257-0.63410.735736
7-0.206411-1.5720.939302
80.1364581.03920.151505
90.0655270.4990.30982
10-0.161134-1.22720.887639
11-0.374365-2.85110.996987
120.1006810.76680.223167
130.0873340.66510.254305
140.1315941.00220.160208
15-0.110447-0.84110.798137
16-0.045371-0.34550.634528
17-0.030175-0.22980.590474

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.734974 & 5.5974 & 0 \tabularnewline
1 & 0.027168 & 0.2069 & 0.418405 \tabularnewline
2 & 0.128424 & 0.978 & 0.166056 \tabularnewline
3 & 0.168379 & 1.2823 & 0.102413 \tabularnewline
4 & 0.058082 & 0.4423 & 0.329944 \tabularnewline
5 & -0.217264 & -1.6546 & 0.948299 \tabularnewline
6 & -0.083257 & -0.6341 & 0.735736 \tabularnewline
7 & -0.206411 & -1.572 & 0.939302 \tabularnewline
8 & 0.136458 & 1.0392 & 0.151505 \tabularnewline
9 & 0.065527 & 0.499 & 0.30982 \tabularnewline
10 & -0.161134 & -1.2272 & 0.887639 \tabularnewline
11 & -0.374365 & -2.8511 & 0.996987 \tabularnewline
12 & 0.100681 & 0.7668 & 0.223167 \tabularnewline
13 & 0.087334 & 0.6651 & 0.254305 \tabularnewline
14 & 0.131594 & 1.0022 & 0.160208 \tabularnewline
15 & -0.110447 & -0.8411 & 0.798137 \tabularnewline
16 & -0.045371 & -0.3455 & 0.634528 \tabularnewline
17 & -0.030175 & -0.2298 & 0.590474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2800&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]0[/C][C]0.734974[/C][C]5.5974[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.027168[/C][C]0.2069[/C][C]0.418405[/C][/ROW]
[ROW][C]2[/C][C]0.128424[/C][C]0.978[/C][C]0.166056[/C][/ROW]
[ROW][C]3[/C][C]0.168379[/C][C]1.2823[/C][C]0.102413[/C][/ROW]
[ROW][C]4[/C][C]0.058082[/C][C]0.4423[/C][C]0.329944[/C][/ROW]
[ROW][C]5[/C][C]-0.217264[/C][C]-1.6546[/C][C]0.948299[/C][/ROW]
[ROW][C]6[/C][C]-0.083257[/C][C]-0.6341[/C][C]0.735736[/C][/ROW]
[ROW][C]7[/C][C]-0.206411[/C][C]-1.572[/C][C]0.939302[/C][/ROW]
[ROW][C]8[/C][C]0.136458[/C][C]1.0392[/C][C]0.151505[/C][/ROW]
[ROW][C]9[/C][C]0.065527[/C][C]0.499[/C][C]0.30982[/C][/ROW]
[ROW][C]10[/C][C]-0.161134[/C][C]-1.2272[/C][C]0.887639[/C][/ROW]
[ROW][C]11[/C][C]-0.374365[/C][C]-2.8511[/C][C]0.996987[/C][/ROW]
[ROW][C]12[/C][C]0.100681[/C][C]0.7668[/C][C]0.223167[/C][/ROW]
[ROW][C]13[/C][C]0.087334[/C][C]0.6651[/C][C]0.254305[/C][/ROW]
[ROW][C]14[/C][C]0.131594[/C][C]1.0022[/C][C]0.160208[/C][/ROW]
[ROW][C]15[/C][C]-0.110447[/C][C]-0.8411[/C][C]0.798137[/C][/ROW]
[ROW][C]16[/C][C]-0.045371[/C][C]-0.3455[/C][C]0.634528[/C][/ROW]
[ROW][C]17[/C][C]-0.030175[/C][C]-0.2298[/C][C]0.590474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2800&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2800&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
00.7349745.59740
10.0271680.20690.418405
20.1284240.9780.166056
30.1683791.28230.102413
40.0580820.44230.329944
5-0.217264-1.65460.948299
6-0.083257-0.63410.735736
7-0.206411-1.5720.939302
80.1364581.03920.151505
90.0655270.4990.30982
10-0.161134-1.22720.887639
11-0.374365-2.85110.996987
120.1006810.76680.223167
130.0873340.66510.254305
140.1315941.00220.160208
15-0.110447-0.84110.798137
16-0.045371-0.34550.634528
17-0.030175-0.22980.590474


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 0.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 0.0 ; par3 = 0 ; par4 = 1 ; 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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')