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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 computationThu, 22 Nov 2007 08:26:01 -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/Nov/22/t1195745737c64q38achtzrfvb.htm/, Retrieved Fri, 03 May 2024 02:35:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6056, Retrieved Fri, 03 May 2024 02:35:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182

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] [] [2007-11-22 15:26:01] [80e26e27d8b229550cb490fed3b7813c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
102,7
103,2
105,6
103,9
107,2
100,7
92,1
90,3
93,4
98,5
100,8
102,3
104,7
101,1
101,4
99,5
98,4
96,3
100,7
101,2
100,3
97,8
97,4
98,6
99,7
99
98,1
97
98,5
103,8
114,4
124,5
134,2
131,8
125,6
119,9
114,9
115,5
112,5
111,4
115,3
110,8
103,7
111,1
113
111,2
117,6
121,7
127,3
129,8
137,1
141,4
137,4
130,7
117,2
110,8
111,4
108,2
108,8
110,2
109,5
109,5
116
111,2
112,1
114
119,1
114,1
115,1
115,4
110,8
116
119,2
126,5
127,8
131,3
140,3
137,3
143
134,5
139,9
159,3
170,4
175
175,8
180,9
180,3
169,6
172,3
184,8
177,7
184,6
211,4

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=6056&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=6056&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6056&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
019.64370
10.9025918.70430
20.8296238.00060
30.767257.39910
40.6855896.61160
50.6267016.04370
60.5795895.58940
70.5194025.00891e-06
80.452044.35931.7e-05
90.3893223.75450.000151
100.3274343.15770.001072
110.2666772.57170.005852
120.2161772.08470.019917
130.1947611.87820.031743
140.1816281.75160.041573
150.1543021.4880.070062
160.1342841.2950.099265
170.0991150.95580.170818
180.074590.71930.236873

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.6437 & 0 \tabularnewline
1 & 0.902591 & 8.7043 & 0 \tabularnewline
2 & 0.829623 & 8.0006 & 0 \tabularnewline
3 & 0.76725 & 7.3991 & 0 \tabularnewline
4 & 0.685589 & 6.6116 & 0 \tabularnewline
5 & 0.626701 & 6.0437 & 0 \tabularnewline
6 & 0.579589 & 5.5894 & 0 \tabularnewline
7 & 0.519402 & 5.0089 & 1e-06 \tabularnewline
8 & 0.45204 & 4.3593 & 1.7e-05 \tabularnewline
9 & 0.389322 & 3.7545 & 0.000151 \tabularnewline
10 & 0.327434 & 3.1577 & 0.001072 \tabularnewline
11 & 0.266677 & 2.5717 & 0.005852 \tabularnewline
12 & 0.216177 & 2.0847 & 0.019917 \tabularnewline
13 & 0.194761 & 1.8782 & 0.031743 \tabularnewline
14 & 0.181628 & 1.7516 & 0.041573 \tabularnewline
15 & 0.154302 & 1.488 & 0.070062 \tabularnewline
16 & 0.134284 & 1.295 & 0.099265 \tabularnewline
17 & 0.099115 & 0.9558 & 0.170818 \tabularnewline
18 & 0.07459 & 0.7193 & 0.236873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6056&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]9.6437[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.902591[/C][C]8.7043[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.829623[/C][C]8.0006[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.76725[/C][C]7.3991[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.685589[/C][C]6.6116[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.626701[/C][C]6.0437[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.579589[/C][C]5.5894[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.519402[/C][C]5.0089[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.45204[/C][C]4.3593[/C][C]1.7e-05[/C][/ROW]
[ROW][C]9[/C][C]0.389322[/C][C]3.7545[/C][C]0.000151[/C][/ROW]
[ROW][C]10[/C][C]0.327434[/C][C]3.1577[/C][C]0.001072[/C][/ROW]
[ROW][C]11[/C][C]0.266677[/C][C]2.5717[/C][C]0.005852[/C][/ROW]
[ROW][C]12[/C][C]0.216177[/C][C]2.0847[/C][C]0.019917[/C][/ROW]
[ROW][C]13[/C][C]0.194761[/C][C]1.8782[/C][C]0.031743[/C][/ROW]
[ROW][C]14[/C][C]0.181628[/C][C]1.7516[/C][C]0.041573[/C][/ROW]
[ROW][C]15[/C][C]0.154302[/C][C]1.488[/C][C]0.070062[/C][/ROW]
[ROW][C]16[/C][C]0.134284[/C][C]1.295[/C][C]0.099265[/C][/ROW]
[ROW][C]17[/C][C]0.099115[/C][C]0.9558[/C][C]0.170818[/C][/ROW]
[ROW][C]18[/C][C]0.07459[/C][C]0.7193[/C][C]0.236873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6056&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6056&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
019.64370
10.9025918.70430
20.8296238.00060
30.767257.39910
40.6855896.61160
50.6267016.04370
60.5795895.58940
70.5194025.00891e-06
80.452044.35931.7e-05
90.3893223.75450.000151
100.3274343.15770.001072
110.2666772.57170.005852
120.2161772.08470.019917
130.1947611.87820.031743
140.1816281.75160.041573
150.1543021.4880.070062
160.1342841.2950.099265
170.0991150.95580.170818
180.074590.71930.236873






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
00.9025918.70430
10.0806820.77810.219253
20.0327650.3160.376367
3-0.124923-1.20470.884314
40.0580230.55960.288563
50.0433450.4180.338453
6-0.066969-0.64580.740009
7-0.103268-0.99590.839053
8-0.037416-0.36080.640478
9-0.017468-0.16850.566705
10-0.032709-0.31540.623431
11-0.008504-0.0820.532592
120.1286821.2410.10887
130.0748130.72150.236216
14-0.073941-0.71310.761202
15-0.018618-0.17950.571051
16-0.08361-0.80630.788938
170.052540.50670.306789
18-0.039949-0.38530.649535

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.902591 & 8.7043 & 0 \tabularnewline
1 & 0.080682 & 0.7781 & 0.219253 \tabularnewline
2 & 0.032765 & 0.316 & 0.376367 \tabularnewline
3 & -0.124923 & -1.2047 & 0.884314 \tabularnewline
4 & 0.058023 & 0.5596 & 0.288563 \tabularnewline
5 & 0.043345 & 0.418 & 0.338453 \tabularnewline
6 & -0.066969 & -0.6458 & 0.740009 \tabularnewline
7 & -0.103268 & -0.9959 & 0.839053 \tabularnewline
8 & -0.037416 & -0.3608 & 0.640478 \tabularnewline
9 & -0.017468 & -0.1685 & 0.566705 \tabularnewline
10 & -0.032709 & -0.3154 & 0.623431 \tabularnewline
11 & -0.008504 & -0.082 & 0.532592 \tabularnewline
12 & 0.128682 & 1.241 & 0.10887 \tabularnewline
13 & 0.074813 & 0.7215 & 0.236216 \tabularnewline
14 & -0.073941 & -0.7131 & 0.761202 \tabularnewline
15 & -0.018618 & -0.1795 & 0.571051 \tabularnewline
16 & -0.08361 & -0.8063 & 0.788938 \tabularnewline
17 & 0.05254 & 0.5067 & 0.306789 \tabularnewline
18 & -0.039949 & -0.3853 & 0.649535 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6056&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]0.902591[/C][C]8.7043[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.080682[/C][C]0.7781[/C][C]0.219253[/C][/ROW]
[ROW][C]2[/C][C]0.032765[/C][C]0.316[/C][C]0.376367[/C][/ROW]
[ROW][C]3[/C][C]-0.124923[/C][C]-1.2047[/C][C]0.884314[/C][/ROW]
[ROW][C]4[/C][C]0.058023[/C][C]0.5596[/C][C]0.288563[/C][/ROW]
[ROW][C]5[/C][C]0.043345[/C][C]0.418[/C][C]0.338453[/C][/ROW]
[ROW][C]6[/C][C]-0.066969[/C][C]-0.6458[/C][C]0.740009[/C][/ROW]
[ROW][C]7[/C][C]-0.103268[/C][C]-0.9959[/C][C]0.839053[/C][/ROW]
[ROW][C]8[/C][C]-0.037416[/C][C]-0.3608[/C][C]0.640478[/C][/ROW]
[ROW][C]9[/C][C]-0.017468[/C][C]-0.1685[/C][C]0.566705[/C][/ROW]
[ROW][C]10[/C][C]-0.032709[/C][C]-0.3154[/C][C]0.623431[/C][/ROW]
[ROW][C]11[/C][C]-0.008504[/C][C]-0.082[/C][C]0.532592[/C][/ROW]
[ROW][C]12[/C][C]0.128682[/C][C]1.241[/C][C]0.10887[/C][/ROW]
[ROW][C]13[/C][C]0.074813[/C][C]0.7215[/C][C]0.236216[/C][/ROW]
[ROW][C]14[/C][C]-0.073941[/C][C]-0.7131[/C][C]0.761202[/C][/ROW]
[ROW][C]15[/C][C]-0.018618[/C][C]-0.1795[/C][C]0.571051[/C][/ROW]
[ROW][C]16[/C][C]-0.08361[/C][C]-0.8063[/C][C]0.788938[/C][/ROW]
[ROW][C]17[/C][C]0.05254[/C][C]0.5067[/C][C]0.306789[/C][/ROW]
[ROW][C]18[/C][C]-0.039949[/C][C]-0.3853[/C][C]0.649535[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6056&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6056&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
00.9025918.70430
10.0806820.77810.219253
20.0327650.3160.376367
3-0.124923-1.20470.884314
40.0580230.55960.288563
50.0433450.4180.338453
6-0.066969-0.64580.740009
7-0.103268-0.99590.839053
8-0.037416-0.36080.640478
9-0.017468-0.16850.566705
10-0.032709-0.31540.623431
11-0.008504-0.0820.532592
120.1286821.2410.10887
130.0748130.72150.236216
14-0.073941-0.71310.761202
15-0.018618-0.17950.571051
16-0.08361-0.80630.788938
170.052540.50670.306789
18-0.039949-0.38530.649535


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 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')