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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 computationTue, 08 Dec 2015 19:56:53 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/08/t14496073773j20dipaizd7p2n.htm/, Retrieved Thu, 16 May 2024 20:11:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285565, Retrieved Thu, 16 May 2024 20:11:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51

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] [] [2015-12-08 19:56:53] [5fd2fca6b664199b2dd86155c5786748] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.132
1.964
2.209
1.965
2.631
2.583
2.714
2.248
2.364
3.042
2.316
2.735
2.493
2.136
2.467
2.414
2.556
2.768
2.998
2.573
3.005
3.469
2.540
3.187
2.689
2.154
3.065
2.397
2.787
3.579
2.915
3.025
3.245
3.328
2.840
3.342
2.261
2.590
2.624
1.860
2.577
2.646
2.639
2.807
2.350
3.053
2.203
2.471
1.967
2.473
2.397
1.904
2.732
2.297
2.734
2.719
2.296
3.243
2.166
2.261
2.408
2.536
2.324
2.178
2.803
2.604
2.782
2.656
2.801
3.122
2.393
2.233
2.451
2.596
2.467
2.210
2.948
2.507
3.019
2.401
2.818
3.305
2.101
2.582
2.407
2.416
2.463
2.228
2.616
2.934
2.668
2.808
2.664
3.112
2.321
2.718
2.297
2.534
2.647
2.064
2.642
2.702
2.348
2.734
2.709
3.206
2.214
2.531
2.119
2.369
2.682
1.840
2.622
2.570
2.447
2.871
2.485
2.957
2.102
2.250
2.051
2.260
2.327
1.781
2.631
2.180
2.150
2.837
1.976
2.836
2.203
1.770

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'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285565&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285565&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285565&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'George Udny Yule' @ yule.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.0891921.02470.153681
20.2926333.36210.000506
30.2915683.34990.000527
4-0.07178-0.82470.205517
50.1957072.24850.013101
6-0.195394-2.24490.013219
70.0482370.55420.290188
80.0550370.63230.264134
90.1152621.32430.093853
100.124041.42510.078243
110.0862010.99040.161901
120.5839186.70870
13-0.074043-0.85070.19824
140.151871.74490.041669
150.008260.09490.462271
16-0.223275-2.56520.005714
170.0471160.54130.2946
18-0.462452-5.31320
19-0.090532-1.04010.150089
20-0.071575-0.82230.206184
21-0.134995-1.5510.061651

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.089192 & 1.0247 & 0.153681 \tabularnewline
2 & 0.292633 & 3.3621 & 0.000506 \tabularnewline
3 & 0.291568 & 3.3499 & 0.000527 \tabularnewline
4 & -0.07178 & -0.8247 & 0.205517 \tabularnewline
5 & 0.195707 & 2.2485 & 0.013101 \tabularnewline
6 & -0.195394 & -2.2449 & 0.013219 \tabularnewline
7 & 0.048237 & 0.5542 & 0.290188 \tabularnewline
8 & 0.055037 & 0.6323 & 0.264134 \tabularnewline
9 & 0.115262 & 1.3243 & 0.093853 \tabularnewline
10 & 0.12404 & 1.4251 & 0.078243 \tabularnewline
11 & 0.086201 & 0.9904 & 0.161901 \tabularnewline
12 & 0.583918 & 6.7087 & 0 \tabularnewline
13 & -0.074043 & -0.8507 & 0.19824 \tabularnewline
14 & 0.15187 & 1.7449 & 0.041669 \tabularnewline
15 & 0.00826 & 0.0949 & 0.462271 \tabularnewline
16 & -0.223275 & -2.5652 & 0.005714 \tabularnewline
17 & 0.047116 & 0.5413 & 0.2946 \tabularnewline
18 & -0.462452 & -5.3132 & 0 \tabularnewline
19 & -0.090532 & -1.0401 & 0.150089 \tabularnewline
20 & -0.071575 & -0.8223 & 0.206184 \tabularnewline
21 & -0.134995 & -1.551 & 0.061651 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285565&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]0.089192[/C][C]1.0247[/C][C]0.153681[/C][/ROW]
[ROW][C]2[/C][C]0.292633[/C][C]3.3621[/C][C]0.000506[/C][/ROW]
[ROW][C]3[/C][C]0.291568[/C][C]3.3499[/C][C]0.000527[/C][/ROW]
[ROW][C]4[/C][C]-0.07178[/C][C]-0.8247[/C][C]0.205517[/C][/ROW]
[ROW][C]5[/C][C]0.195707[/C][C]2.2485[/C][C]0.013101[/C][/ROW]
[ROW][C]6[/C][C]-0.195394[/C][C]-2.2449[/C][C]0.013219[/C][/ROW]
[ROW][C]7[/C][C]0.048237[/C][C]0.5542[/C][C]0.290188[/C][/ROW]
[ROW][C]8[/C][C]0.055037[/C][C]0.6323[/C][C]0.264134[/C][/ROW]
[ROW][C]9[/C][C]0.115262[/C][C]1.3243[/C][C]0.093853[/C][/ROW]
[ROW][C]10[/C][C]0.12404[/C][C]1.4251[/C][C]0.078243[/C][/ROW]
[ROW][C]11[/C][C]0.086201[/C][C]0.9904[/C][C]0.161901[/C][/ROW]
[ROW][C]12[/C][C]0.583918[/C][C]6.7087[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.074043[/C][C]-0.8507[/C][C]0.19824[/C][/ROW]
[ROW][C]14[/C][C]0.15187[/C][C]1.7449[/C][C]0.041669[/C][/ROW]
[ROW][C]15[/C][C]0.00826[/C][C]0.0949[/C][C]0.462271[/C][/ROW]
[ROW][C]16[/C][C]-0.223275[/C][C]-2.5652[/C][C]0.005714[/C][/ROW]
[ROW][C]17[/C][C]0.047116[/C][C]0.5413[/C][C]0.2946[/C][/ROW]
[ROW][C]18[/C][C]-0.462452[/C][C]-5.3132[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.090532[/C][C]-1.0401[/C][C]0.150089[/C][/ROW]
[ROW][C]20[/C][C]-0.071575[/C][C]-0.8223[/C][C]0.206184[/C][/ROW]
[ROW][C]21[/C][C]-0.134995[/C][C]-1.551[/C][C]0.061651[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285565&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285565&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
10.0891921.02470.153681
20.2926333.36210.000506
30.2915683.34990.000527
4-0.07178-0.82470.205517
50.1957072.24850.013101
6-0.195394-2.24490.013219
70.0482370.55420.290188
80.0550370.63230.264134
90.1152621.32430.093853
100.124041.42510.078243
110.0862010.99040.161901
120.5839186.70870
13-0.074043-0.85070.19824
140.151871.74490.041669
150.008260.09490.462271
16-0.223275-2.56520.005714
170.0471160.54130.2946
18-0.462452-5.31320
19-0.090532-1.04010.150089
20-0.071575-0.82230.206184
21-0.134995-1.5510.061651






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.0891921.02470.153681
20.2869613.29690.000628
30.2717223.12180.001104
4-0.202506-2.32660.010754
50.0537620.61770.268925
6-0.24984-2.87040.002388
70.0962411.10570.135429
80.1055341.21250.113744
90.3187753.66240.00018
10-0.048225-0.55410.290235
110.0097870.11240.455319
120.5310326.10110
13-0.308619-3.54580.000271
14-0.258366-2.96840.001778
15-0.287582-3.30410.000613
160.0110750.12720.449472
17-0.074882-0.86030.195585
18-0.197053-2.2640.012604
19-0.024985-0.28710.387262
200.0171340.19690.422122
210.0427670.49140.311995

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.089192 & 1.0247 & 0.153681 \tabularnewline
2 & 0.286961 & 3.2969 & 0.000628 \tabularnewline
3 & 0.271722 & 3.1218 & 0.001104 \tabularnewline
4 & -0.202506 & -2.3266 & 0.010754 \tabularnewline
5 & 0.053762 & 0.6177 & 0.268925 \tabularnewline
6 & -0.24984 & -2.8704 & 0.002388 \tabularnewline
7 & 0.096241 & 1.1057 & 0.135429 \tabularnewline
8 & 0.105534 & 1.2125 & 0.113744 \tabularnewline
9 & 0.318775 & 3.6624 & 0.00018 \tabularnewline
10 & -0.048225 & -0.5541 & 0.290235 \tabularnewline
11 & 0.009787 & 0.1124 & 0.455319 \tabularnewline
12 & 0.531032 & 6.1011 & 0 \tabularnewline
13 & -0.308619 & -3.5458 & 0.000271 \tabularnewline
14 & -0.258366 & -2.9684 & 0.001778 \tabularnewline
15 & -0.287582 & -3.3041 & 0.000613 \tabularnewline
16 & 0.011075 & 0.1272 & 0.449472 \tabularnewline
17 & -0.074882 & -0.8603 & 0.195585 \tabularnewline
18 & -0.197053 & -2.264 & 0.012604 \tabularnewline
19 & -0.024985 & -0.2871 & 0.387262 \tabularnewline
20 & 0.017134 & 0.1969 & 0.422122 \tabularnewline
21 & 0.042767 & 0.4914 & 0.311995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285565&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]0.089192[/C][C]1.0247[/C][C]0.153681[/C][/ROW]
[ROW][C]2[/C][C]0.286961[/C][C]3.2969[/C][C]0.000628[/C][/ROW]
[ROW][C]3[/C][C]0.271722[/C][C]3.1218[/C][C]0.001104[/C][/ROW]
[ROW][C]4[/C][C]-0.202506[/C][C]-2.3266[/C][C]0.010754[/C][/ROW]
[ROW][C]5[/C][C]0.053762[/C][C]0.6177[/C][C]0.268925[/C][/ROW]
[ROW][C]6[/C][C]-0.24984[/C][C]-2.8704[/C][C]0.002388[/C][/ROW]
[ROW][C]7[/C][C]0.096241[/C][C]1.1057[/C][C]0.135429[/C][/ROW]
[ROW][C]8[/C][C]0.105534[/C][C]1.2125[/C][C]0.113744[/C][/ROW]
[ROW][C]9[/C][C]0.318775[/C][C]3.6624[/C][C]0.00018[/C][/ROW]
[ROW][C]10[/C][C]-0.048225[/C][C]-0.5541[/C][C]0.290235[/C][/ROW]
[ROW][C]11[/C][C]0.009787[/C][C]0.1124[/C][C]0.455319[/C][/ROW]
[ROW][C]12[/C][C]0.531032[/C][C]6.1011[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.308619[/C][C]-3.5458[/C][C]0.000271[/C][/ROW]
[ROW][C]14[/C][C]-0.258366[/C][C]-2.9684[/C][C]0.001778[/C][/ROW]
[ROW][C]15[/C][C]-0.287582[/C][C]-3.3041[/C][C]0.000613[/C][/ROW]
[ROW][C]16[/C][C]0.011075[/C][C]0.1272[/C][C]0.449472[/C][/ROW]
[ROW][C]17[/C][C]-0.074882[/C][C]-0.8603[/C][C]0.195585[/C][/ROW]
[ROW][C]18[/C][C]-0.197053[/C][C]-2.264[/C][C]0.012604[/C][/ROW]
[ROW][C]19[/C][C]-0.024985[/C][C]-0.2871[/C][C]0.387262[/C][/ROW]
[ROW][C]20[/C][C]0.017134[/C][C]0.1969[/C][C]0.422122[/C][/ROW]
[ROW][C]21[/C][C]0.042767[/C][C]0.4914[/C][C]0.311995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285565&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285565&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
10.0891921.02470.153681
20.2869613.29690.000628
30.2717223.12180.001104
4-0.202506-2.32660.010754
50.0537620.61770.268925
6-0.24984-2.87040.002388
70.0962411.10570.135429
80.1055341.21250.113744
90.3187753.66240.00018
10-0.048225-0.55410.290235
110.0097870.11240.455319
120.5310326.10110
13-0.308619-3.54580.000271
14-0.258366-2.96840.001778
15-0.287582-3.30410.000613
160.0110750.12720.449472
17-0.074882-0.86030.195585
18-0.197053-2.2640.012604
19-0.024985-0.28710.387262
200.0171340.19690.422122
210.0427670.49140.311995


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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)
x <- na.omit(x)
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')