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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 computationMon, 18 Dec 2017 13:57:57 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/18/t1513601911wmf6tgrdkemq2dx.htm/, Retrieved Tue, 14 May 2024 09:40:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310155, Retrieved Tue, 14 May 2024 09:40:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact39

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] [Autocorrelatie (D...] [2017-12-18 12:57:57] [0687db01a969247b131332e81d79dad3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
63.2
68.6
77.7
68.1
75.1
73.3
60.5
65.9
77.7
77.1
77.7
71.3
76
75.3
81.7
72.5
77.4
81.1
65.1
68.7
75.6
79.7
75.3
67.7
73.2
72.2
79.3
77.5
75.6
77.4
69.2
67.1
77.9
82.7
75.7
70.1
76.4
74.3
80.5
78
73.5
78.8
71.2
66.2
82.7
83.8
75
80.4
74.6
77.7
89.8
82.4
77
89.6
75.7
75.1
89.9
88.8
86.5
90
84
82.7
91.7
87.5
82
92.2
73.1
75.6
91.6
87.5
90.1
91.3
87.6
88.4
100.7
85.3
92
96.8
77.9
80.9
95.3
99.3
96.1
92.5
93.7
92.1
103.6
92.5
95.7
103.4
89
89.1
98.7
109.4
101.1
95.4
101.4
102.1
103.6
106
98.4
106.6
95.8
87.2
108.5
107
92
94.9
84.4
85
94
84.5
88.2
92.1
81.1
81.2
96.1
95.3
92.1
91.7
90.3
96.1
108.7
95.9
95.1
109.4
91.2
91.4
107.4
105.6
105.3
103.7
99.5
103.2
123.1
102.2
110
106.2
91.3
99.3
111.8
104.4
102.4
101
100.6
104.5
117.4
97.4
99.5
106.4
95.2
94
104.1
105.8
101.1
93.5
97.9
96.8
108.4
103.5
101.3
107.4
100.7
91.1
105
112.8
105.6
101
101.9
103.5
109.5
105
102.9
108.5
96.9
88.4
112.4
111.3
101.6
101.2
101.8
98.8
114.4
104.5
97.6
109.1
94.5
90.4
111.8
110.5
106.8
101.8
103.7
107.4
117.5
109.6
102.8
115.5
97.8
100.2
112.9
108.7
109
113.9
106.9
109.6
124.5
104.2
110.8
118.7
102.1
105.1

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310155&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310155&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310155&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.7846211.42420
20.70511310.26660
30.7896111.49690
40.71586610.42320
50.73443810.69360
60.78349411.40790
70.674389.81910
80.6512029.48160
90.6699519.75460
100.5641958.21480
110.6367449.27110
120.75895511.05060
130.5937088.64450
140.529137.70430
150.5856588.52730
160.5396477.85740
170.5591568.14140
180.5983278.71180
190.5094317.41740
200.5001927.28290
210.5088037.40830
220.421926.14320
230.4997667.27670

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.78462 & 11.4242 & 0 \tabularnewline
2 & 0.705113 & 10.2666 & 0 \tabularnewline
3 & 0.78961 & 11.4969 & 0 \tabularnewline
4 & 0.715866 & 10.4232 & 0 \tabularnewline
5 & 0.734438 & 10.6936 & 0 \tabularnewline
6 & 0.783494 & 11.4079 & 0 \tabularnewline
7 & 0.67438 & 9.8191 & 0 \tabularnewline
8 & 0.651202 & 9.4816 & 0 \tabularnewline
9 & 0.669951 & 9.7546 & 0 \tabularnewline
10 & 0.564195 & 8.2148 & 0 \tabularnewline
11 & 0.636744 & 9.2711 & 0 \tabularnewline
12 & 0.758955 & 11.0506 & 0 \tabularnewline
13 & 0.593708 & 8.6445 & 0 \tabularnewline
14 & 0.52913 & 7.7043 & 0 \tabularnewline
15 & 0.585658 & 8.5273 & 0 \tabularnewline
16 & 0.539647 & 7.8574 & 0 \tabularnewline
17 & 0.559156 & 8.1414 & 0 \tabularnewline
18 & 0.598327 & 8.7118 & 0 \tabularnewline
19 & 0.509431 & 7.4174 & 0 \tabularnewline
20 & 0.500192 & 7.2829 & 0 \tabularnewline
21 & 0.508803 & 7.4083 & 0 \tabularnewline
22 & 0.42192 & 6.1432 & 0 \tabularnewline
23 & 0.499766 & 7.2767 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310155&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]0.78462[/C][C]11.4242[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.705113[/C][C]10.2666[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.78961[/C][C]11.4969[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.715866[/C][C]10.4232[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.734438[/C][C]10.6936[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.783494[/C][C]11.4079[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.67438[/C][C]9.8191[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.651202[/C][C]9.4816[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.669951[/C][C]9.7546[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.564195[/C][C]8.2148[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.636744[/C][C]9.2711[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.758955[/C][C]11.0506[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.593708[/C][C]8.6445[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.52913[/C][C]7.7043[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.585658[/C][C]8.5273[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.539647[/C][C]7.8574[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.559156[/C][C]8.1414[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.598327[/C][C]8.7118[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.509431[/C][C]7.4174[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.500192[/C][C]7.2829[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.508803[/C][C]7.4083[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.42192[/C][C]6.1432[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.499766[/C][C]7.2767[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310155&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310155&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
10.7846211.42420
20.70511310.26660
30.7896111.49690
40.71586610.42320
50.73443810.69360
60.78349411.40790
70.674389.81910
80.6512029.48160
90.6699519.75460
100.5641958.21480
110.6367449.27110
120.75895511.05060
130.5937088.64450
140.529137.70430
150.5856588.52730
160.5396477.85740
170.5591568.14140
180.5983278.71180
190.5094317.41740
200.5001927.28290
210.5088037.40830
220.421926.14320
230.4997667.27670






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.7846211.42420
20.2328093.38980.000417
30.5020047.30930
4-0.044592-0.64930.258433
50.346915.05110
60.131581.91580.028366
7-0.114821-1.67180.048017
8-0.040703-0.59260.277025
9-0.094674-1.37850.084756
10-0.262168-3.81728.9e-05
110.2848834.1482.4e-05
120.4383736.38280
13-0.210716-3.06810.001218
14-0.229134-3.33620.000501
15-0.100808-1.46780.071822
160.0834361.21480.112889
17-0.058397-0.85030.198066
180.072011.04850.147806
190.0650620.94730.172276
200.054330.79110.214897
21-0.02869-0.41770.338282
22-0.033254-0.48420.314375
230.0497590.72450.234777

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.78462 & 11.4242 & 0 \tabularnewline
2 & 0.232809 & 3.3898 & 0.000417 \tabularnewline
3 & 0.502004 & 7.3093 & 0 \tabularnewline
4 & -0.044592 & -0.6493 & 0.258433 \tabularnewline
5 & 0.34691 & 5.0511 & 0 \tabularnewline
6 & 0.13158 & 1.9158 & 0.028366 \tabularnewline
7 & -0.114821 & -1.6718 & 0.048017 \tabularnewline
8 & -0.040703 & -0.5926 & 0.277025 \tabularnewline
9 & -0.094674 & -1.3785 & 0.084756 \tabularnewline
10 & -0.262168 & -3.8172 & 8.9e-05 \tabularnewline
11 & 0.284883 & 4.148 & 2.4e-05 \tabularnewline
12 & 0.438373 & 6.3828 & 0 \tabularnewline
13 & -0.210716 & -3.0681 & 0.001218 \tabularnewline
14 & -0.229134 & -3.3362 & 0.000501 \tabularnewline
15 & -0.100808 & -1.4678 & 0.071822 \tabularnewline
16 & 0.083436 & 1.2148 & 0.112889 \tabularnewline
17 & -0.058397 & -0.8503 & 0.198066 \tabularnewline
18 & 0.07201 & 1.0485 & 0.147806 \tabularnewline
19 & 0.065062 & 0.9473 & 0.172276 \tabularnewline
20 & 0.05433 & 0.7911 & 0.214897 \tabularnewline
21 & -0.02869 & -0.4177 & 0.338282 \tabularnewline
22 & -0.033254 & -0.4842 & 0.314375 \tabularnewline
23 & 0.049759 & 0.7245 & 0.234777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310155&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]0.78462[/C][C]11.4242[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.232809[/C][C]3.3898[/C][C]0.000417[/C][/ROW]
[ROW][C]3[/C][C]0.502004[/C][C]7.3093[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.044592[/C][C]-0.6493[/C][C]0.258433[/C][/ROW]
[ROW][C]5[/C][C]0.34691[/C][C]5.0511[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.13158[/C][C]1.9158[/C][C]0.028366[/C][/ROW]
[ROW][C]7[/C][C]-0.114821[/C][C]-1.6718[/C][C]0.048017[/C][/ROW]
[ROW][C]8[/C][C]-0.040703[/C][C]-0.5926[/C][C]0.277025[/C][/ROW]
[ROW][C]9[/C][C]-0.094674[/C][C]-1.3785[/C][C]0.084756[/C][/ROW]
[ROW][C]10[/C][C]-0.262168[/C][C]-3.8172[/C][C]8.9e-05[/C][/ROW]
[ROW][C]11[/C][C]0.284883[/C][C]4.148[/C][C]2.4e-05[/C][/ROW]
[ROW][C]12[/C][C]0.438373[/C][C]6.3828[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.210716[/C][C]-3.0681[/C][C]0.001218[/C][/ROW]
[ROW][C]14[/C][C]-0.229134[/C][C]-3.3362[/C][C]0.000501[/C][/ROW]
[ROW][C]15[/C][C]-0.100808[/C][C]-1.4678[/C][C]0.071822[/C][/ROW]
[ROW][C]16[/C][C]0.083436[/C][C]1.2148[/C][C]0.112889[/C][/ROW]
[ROW][C]17[/C][C]-0.058397[/C][C]-0.8503[/C][C]0.198066[/C][/ROW]
[ROW][C]18[/C][C]0.07201[/C][C]1.0485[/C][C]0.147806[/C][/ROW]
[ROW][C]19[/C][C]0.065062[/C][C]0.9473[/C][C]0.172276[/C][/ROW]
[ROW][C]20[/C][C]0.05433[/C][C]0.7911[/C][C]0.214897[/C][/ROW]
[ROW][C]21[/C][C]-0.02869[/C][C]-0.4177[/C][C]0.338282[/C][/ROW]
[ROW][C]22[/C][C]-0.033254[/C][C]-0.4842[/C][C]0.314375[/C][/ROW]
[ROW][C]23[/C][C]0.049759[/C][C]0.7245[/C][C]0.234777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310155&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310155&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
10.7846211.42420
20.2328093.38980.000417
30.5020047.30930
4-0.044592-0.64930.258433
50.346915.05110
60.131581.91580.028366
7-0.114821-1.67180.048017
8-0.040703-0.59260.277025
9-0.094674-1.37850.084756
10-0.262168-3.81728.9e-05
110.2848834.1482.4e-05
120.4383736.38280
13-0.210716-3.06810.001218
14-0.229134-3.33620.000501
15-0.100808-1.46780.071822
160.0834361.21480.112889
17-0.058397-0.85030.198066
180.072011.04850.147806
190.0650620.94730.172276
200.054330.79110.214897
21-0.02869-0.41770.338282
22-0.033254-0.48420.314375
230.0497590.72450.234777


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,'ACF(k)',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,'PACF(k)',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')