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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationThu, 23 Oct 2008 04:32:19 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/23/t1224758070yyze3527xk3lkph.htm/, Retrieved Fri, 17 May 2024 03:43:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18451, Retrieved Fri, 17 May 2024 03:43:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact247

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Explorative Data Analysis] [Investigation Dis...] [2007-10-21 17:06:37] [b9964c45117f7aac638ab9056d451faa]
F RMPD    [(Partial) Autocorrelation Function] [] [2008-10-23 10:32:19] [75a00449045803b2332dacf227dc78d5] [Current]
-   P       [(Partial) Autocorrelation Function] [q2 autocorrelatio...] [2008-10-23 12:14:19] [7173087adebe3e3a714c80ea2417b3eb]
-   P         [(Partial) Autocorrelation Function] [Q2 Autocorrelatio...] [2008-10-24 14:00:13] [7d3039e6253bb5fb3b26df1537d500b4]
-   P         [(Partial) Autocorrelation Function] [Autocorrelatie ve...] [2008-10-24 14:28:29] [b635de6fc42b001d22cbe6e730fec936]
-   PD        [(Partial) Autocorrelation Function] [assumtion 1 autoc...] [2008-10-25 12:57:58] [7173087adebe3e3a714c80ea2417b3eb]
F   P         [(Partial) Autocorrelation Function] [q2 autocorrolations] [2008-10-27 10:28:50] [e43247bc0ab243a5af99ac7f55ba0b41]
-   P         [(Partial) Autocorrelation Function] [Autocorrelatie] [2008-10-30 21:59:14] [005293453b571dbccb80b45226e44173]
- RMPD      [Pearson Correlation] [correlation] [2008-10-26 13:18:41] [4ddbf81f78ea7c738951638c7e93f6ee]
F           [(Partial) Autocorrelation Function] [autocorrelation] [2008-10-26 13:22:17] [4ddbf81f78ea7c738951638c7e93f6ee]
- RMP         [Univariate Explorative Data Analysis] [Oplossing Q2 inve...] [2008-10-31 09:41:17] [e5d91604aae608e98a8ea24759233f66]
F           [(Partial) Autocorrelation Function] [] [2008-10-26 15:08:41] [db72903d7941c8279d5ce0e4e873d517]
-           [(Partial) Autocorrelation Function] [] [2008-10-27 17:19:11] [29747f79f5beb5b2516e1271770ecb47]
-           [(Partial) Autocorrelation Function] [] [2008-10-27 17:19:11] [29747f79f5beb5b2516e1271770ecb47]
-           [(Partial) Autocorrelation Function] [] [2008-10-27 17:19:11] [29747f79f5beb5b2516e1271770ecb47]
F           [(Partial) Autocorrelation Function] [] [2008-10-27 17:27:37] [af90f76a5211a482a7c35f2c76d2fd61]
F           [(Partial) Autocorrelation Function] [Investigation Dis...] [2008-10-27 18:34:33] [79c17183721a40a589db5f9f561947d8]
F           [(Partial) Autocorrelation Function] [investigating dis...] [2008-10-27 20:26:48] [4ad596f10399a71ad29b7d76e6ab90ac]
Feedback Forum
2008-11-01 19:55:54 [Steffi Van Isveldt] [reply] 
Om de 4 assumpties te kunnen controleren kan je best met de tool Univariate explorative data analysis werken. Van hieruit kan je de verschillende assumpties nagaan en krijg je een beter overzicht.
Zo kan je zien dat het om een normaal verdeling gaat, maar dat we hier toch met een positieve seizonale autocorrelatie zitten, daardoor is het model niet geldig.
Zie link:
http://www.freestatistics.org/blog/date/2008/Nov/01/t12255515665j9whbwaj66jspq.htm
2008-11-02 18:34:10 [Annelies Michiels] [reply] 
Ik ben het eens met de vorige student.
Ge zou hier beter de 4-plot kunnen gebruiken waardoor je alle 4 de assumpties tegelijk kunt onderzoeken. Het is wel positief dat de student weet dat de autocorrelatie niet met de run sequency plot moet worden berekent maar via een lag plot.
2008-11-03 09:18:31 [Dorien Peeters] [reply] 
Ik ben het eens met de student, namelijk dat hoe dichter de correlatie bij 1 is, hoe normaler de data verdeeld is.
Bij deze taak mis ik echter nog wat meer uitleg.Ik heb gewerkt met de correlatie a.d.h.v.de verdeling van Lambda. De best symmetrische verdeling voor de totale productie is ongeveer normaal. De correlatie bij een verdeling van Lambda 0.14 is het hoogst.Deze is namelijk :0.989505916159088, en ligt dus het dichste bij 1.

2008-11-03 09:53:56 [Dorien Peeters] [reply] 
Hoe moet je de assumpties nu testen? Je doet dit door te onderzoeken of de tijdreeks autocorrelatie heeft.Dit had de student van vorig jaar dus verkeerd gedaan.De auto correlatie moet dicht bij 0 liggen, naar de log plot kijken. Dan vul je de lags in(gelijk aan 12 of aan max 36)Dan naar de 1e en laagste lag kijken. Er staat : wat is het verband tussen heden en verleden? De punten zijn gespreid rond rechte; auto correlatie is gelijk aan 0.Als ik de vorige ind. productie ken, kan ik GEEN voorspelling doen nr de toekomst van industriele productie.Conclusie: Tijdreeks is niet random, bevat wel degelijk auto-correlatie maar is wel een speciale, want heeft 2 correlaties.
Assumptie2:Kijken naar histogram en density plot=>histogram :min of meer normaalverdeling.Density plot: bult,maar niet erg uitgesproken dus normaalverdeling. Horizontale as: punten moeten dus zo dicht mogelijk op de rechte liggen.=>Geen auto-correlatie, maar het is niet omdat je geen normaal verdeling hebt dat je ook geen auto-correlatie hebt.
Assumptie 3: mag niet functioneren op LT. Sequence plot: kijken naar LT trend: gaat dit niveau constant blijven?
Op LT->niveau van deze reeks is geen constante. Is moeilijk=>andere manier(hoe kijken of gemiddelde constant is)Veranderen module->centrale tendency->die calculator gebruiken. Gemiddelde ligt nu bij 87.(=constant?)OUtliers hebben hier geen invloed op. Random component=moeilijk te zien, ik vermoed een dalende trend.
Assumptie 4:Kijken naar sequence plot->kijken naar spreiding van reeks over de tijd heen. Reeks in 2 kolommen:spreiding in 1e deel. Reeks 1 schommelt harder=>verandering van de spreiding.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
109.20
88.60
94.30
98.30
86.40
80.60
104.10
108.20
93.40
71.90
94.10
94.90
96.40
91.10
84.40
86.40
88.00
75.10
109.70
103.00
82.10
68.00
96.40
94.30
90.00
88.00
76.10
82.50
81.40
66.50
97.20
94.10
80.70
70.50
87.80
89.50
99.60
84.20
75.10
92.00
80.80
73.10
99.80
90.00
83.10
72.40
78.80
87.30
91.00
80.10
73.60
86.40
74.50
71.20
92.40
81.50
85.30
69.90
84.20
90.70
100.30

Tables (Output of Computation)





Summary of computational 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 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18451&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18451&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18451&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 computational 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
10.1348681.05340.148167
2-0.230388-1.79940.038452
3-0.025856-0.20190.420317
40.2268231.77150.040733
50.1893471.47880.072164
60.1969711.53840.064562
70.0967310.75550.226431
80.1573531.2290.111903
9-0.121757-0.9510.172691
10-0.273532-2.13640.018336
110.0938150.73270.233269
120.6218644.85694e-06
13-0.008279-0.06470.474327
14-0.26372-2.05970.02185
15-0.145361-1.13530.130345
160.1151760.89960.185948
170.1370871.07070.144266

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.134868 & 1.0534 & 0.148167 \tabularnewline
2 & -0.230388 & -1.7994 & 0.038452 \tabularnewline
3 & -0.025856 & -0.2019 & 0.420317 \tabularnewline
4 & 0.226823 & 1.7715 & 0.040733 \tabularnewline
5 & 0.189347 & 1.4788 & 0.072164 \tabularnewline
6 & 0.196971 & 1.5384 & 0.064562 \tabularnewline
7 & 0.096731 & 0.7555 & 0.226431 \tabularnewline
8 & 0.157353 & 1.229 & 0.111903 \tabularnewline
9 & -0.121757 & -0.951 & 0.172691 \tabularnewline
10 & -0.273532 & -2.1364 & 0.018336 \tabularnewline
11 & 0.093815 & 0.7327 & 0.233269 \tabularnewline
12 & 0.621864 & 4.8569 & 4e-06 \tabularnewline
13 & -0.008279 & -0.0647 & 0.474327 \tabularnewline
14 & -0.26372 & -2.0597 & 0.02185 \tabularnewline
15 & -0.145361 & -1.1353 & 0.130345 \tabularnewline
16 & 0.115176 & 0.8996 & 0.185948 \tabularnewline
17 & 0.137087 & 1.0707 & 0.144266 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18451&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]0.134868[/C][C]1.0534[/C][C]0.148167[/C][/ROW]
[ROW][C]2[/C][C]-0.230388[/C][C]-1.7994[/C][C]0.038452[/C][/ROW]
[ROW][C]3[/C][C]-0.025856[/C][C]-0.2019[/C][C]0.420317[/C][/ROW]
[ROW][C]4[/C][C]0.226823[/C][C]1.7715[/C][C]0.040733[/C][/ROW]
[ROW][C]5[/C][C]0.189347[/C][C]1.4788[/C][C]0.072164[/C][/ROW]
[ROW][C]6[/C][C]0.196971[/C][C]1.5384[/C][C]0.064562[/C][/ROW]
[ROW][C]7[/C][C]0.096731[/C][C]0.7555[/C][C]0.226431[/C][/ROW]
[ROW][C]8[/C][C]0.157353[/C][C]1.229[/C][C]0.111903[/C][/ROW]
[ROW][C]9[/C][C]-0.121757[/C][C]-0.951[/C][C]0.172691[/C][/ROW]
[ROW][C]10[/C][C]-0.273532[/C][C]-2.1364[/C][C]0.018336[/C][/ROW]
[ROW][C]11[/C][C]0.093815[/C][C]0.7327[/C][C]0.233269[/C][/ROW]
[ROW][C]12[/C][C]0.621864[/C][C]4.8569[/C][C]4e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.008279[/C][C]-0.0647[/C][C]0.474327[/C][/ROW]
[ROW][C]14[/C][C]-0.26372[/C][C]-2.0597[/C][C]0.02185[/C][/ROW]
[ROW][C]15[/C][C]-0.145361[/C][C]-1.1353[/C][C]0.130345[/C][/ROW]
[ROW][C]16[/C][C]0.115176[/C][C]0.8996[/C][C]0.185948[/C][/ROW]
[ROW][C]17[/C][C]0.137087[/C][C]1.0707[/C][C]0.144266[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18451&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18451&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
10.1348681.05340.148167
2-0.230388-1.79940.038452
3-0.025856-0.20190.420317
40.2268231.77150.040733
50.1893471.47880.072164
60.1969711.53840.064562
70.0967310.75550.226431
80.1573531.2290.111903
9-0.121757-0.9510.172691
10-0.273532-2.13640.018336
110.0938150.73270.233269
120.6218644.85694e-06
13-0.008279-0.06470.474327
14-0.26372-2.05970.02185
15-0.145361-1.13530.130345
160.1151760.89960.185948
170.1370871.07070.144266






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.1348681.05340.148167
2-0.253183-1.97740.026259
30.0513990.40140.344751
40.1792421.39990.083301
50.1406331.09840.138178
60.2718562.12330.018899
70.1344911.05040.148838
80.2529031.97520.026385
9-0.200811-1.56840.060983
10-0.378002-2.95230.002236
11-0.137616-1.07480.143345
120.4737473.70010.000232
13-0.089353-0.69790.243955
140.0727080.56790.286104
15-0.09552-0.7460.229255
16-0.014972-0.11690.453649
17-0.008653-0.06760.473169

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.134868 & 1.0534 & 0.148167 \tabularnewline
2 & -0.253183 & -1.9774 & 0.026259 \tabularnewline
3 & 0.051399 & 0.4014 & 0.344751 \tabularnewline
4 & 0.179242 & 1.3999 & 0.083301 \tabularnewline
5 & 0.140633 & 1.0984 & 0.138178 \tabularnewline
6 & 0.271856 & 2.1233 & 0.018899 \tabularnewline
7 & 0.134491 & 1.0504 & 0.148838 \tabularnewline
8 & 0.252903 & 1.9752 & 0.026385 \tabularnewline
9 & -0.200811 & -1.5684 & 0.060983 \tabularnewline
10 & -0.378002 & -2.9523 & 0.002236 \tabularnewline
11 & -0.137616 & -1.0748 & 0.143345 \tabularnewline
12 & 0.473747 & 3.7001 & 0.000232 \tabularnewline
13 & -0.089353 & -0.6979 & 0.243955 \tabularnewline
14 & 0.072708 & 0.5679 & 0.286104 \tabularnewline
15 & -0.09552 & -0.746 & 0.229255 \tabularnewline
16 & -0.014972 & -0.1169 & 0.453649 \tabularnewline
17 & -0.008653 & -0.0676 & 0.473169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18451&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]0.134868[/C][C]1.0534[/C][C]0.148167[/C][/ROW]
[ROW][C]2[/C][C]-0.253183[/C][C]-1.9774[/C][C]0.026259[/C][/ROW]
[ROW][C]3[/C][C]0.051399[/C][C]0.4014[/C][C]0.344751[/C][/ROW]
[ROW][C]4[/C][C]0.179242[/C][C]1.3999[/C][C]0.083301[/C][/ROW]
[ROW][C]5[/C][C]0.140633[/C][C]1.0984[/C][C]0.138178[/C][/ROW]
[ROW][C]6[/C][C]0.271856[/C][C]2.1233[/C][C]0.018899[/C][/ROW]
[ROW][C]7[/C][C]0.134491[/C][C]1.0504[/C][C]0.148838[/C][/ROW]
[ROW][C]8[/C][C]0.252903[/C][C]1.9752[/C][C]0.026385[/C][/ROW]
[ROW][C]9[/C][C]-0.200811[/C][C]-1.5684[/C][C]0.060983[/C][/ROW]
[ROW][C]10[/C][C]-0.378002[/C][C]-2.9523[/C][C]0.002236[/C][/ROW]
[ROW][C]11[/C][C]-0.137616[/C][C]-1.0748[/C][C]0.143345[/C][/ROW]
[ROW][C]12[/C][C]0.473747[/C][C]3.7001[/C][C]0.000232[/C][/ROW]
[ROW][C]13[/C][C]-0.089353[/C][C]-0.6979[/C][C]0.243955[/C][/ROW]
[ROW][C]14[/C][C]0.072708[/C][C]0.5679[/C][C]0.286104[/C][/ROW]
[ROW][C]15[/C][C]-0.09552[/C][C]-0.746[/C][C]0.229255[/C][/ROW]
[ROW][C]16[/C][C]-0.014972[/C][C]-0.1169[/C][C]0.453649[/C][/ROW]
[ROW][C]17[/C][C]-0.008653[/C][C]-0.0676[/C][C]0.473169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18451&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18451&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
10.1348681.05340.148167
2-0.253183-1.97740.026259
30.0513990.40140.344751
40.1792421.39990.083301
50.1406331.09840.138178
60.2718562.12330.018899
70.1344911.05040.148838
80.2529031.97520.026385
9-0.200811-1.56840.060983
10-0.378002-2.95230.002236
11-0.137616-1.07480.143345
120.4737473.70010.000232
13-0.089353-0.69790.243955
140.0727080.56790.286104
15-0.09552-0.7460.229255
16-0.014972-0.11690.453649
17-0.008653-0.06760.473169


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; 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')