﻿ Page 17 - Contributed Paper Session (CPS) - Volume 7
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``````CPS2014 Ma. S.B.P. et al.
results, 200 bootstrap replicates are considered in the estimation procedure
and applied to 100 data replicates generated for each scenario. Simulation
results are assessed according to the bias of estimates in the autocorrelation
11   12
coefficient   = [  21   22 ]  and  the  MAPE  on  each  scenario.  The  output

autocorrelation  to  be  estimated  in  the  simulation  studies  is  set  to   =
0.10 0.15
[           ].
0.95 0.20
The MAPE is computed for each of the 100 data replicates as in . The
MAPE  per  scenario  is  also  computed  as  in    to  measure  the  predictive
performance of the postulated procedure. MAPE 1 and MAPE 2 represents the
MAPE of the first and second column vector of the bivariate output series,
respectively.

1      ℎ,  −  ̂
ℎ,
,  = ( ∑ |    |) × 100, ℎ = 1,2  

=1    ℎ,

100
1
,  =  100  ∑   ,ℎ  
=1

Instead  of  the  actual  bias,  the  Absolute  Percentage  of  Bias  (APB)  is
computed for each estimate to simplify the presentation of over estimation or
under  estimation  of  the  output  autocorrelation.  Given  the  actual  output
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autocorrelation  = [  21   22 ], we have
,  − ̂
,
̂ = |   ,  | × 100,  ,  = 1,2 
,
The  VAR(1)  estimation on  the  bivariate output  series  will  be  used  as  a
benchmark in assessing the bias of estimates of the output autocorrelation
matrix ρ. The MAPE under VAR(1) is also computed to compare the predictive
performance of the proposed estimation procedure.
Each of the specified length of time series (t) has corresponding pairs of
number of input time series (p) of (m) lags. The covariate matrix − ,  = 1, …
,  considered for each scenario comes from one of the following sets of t,p,
and m values:  = 20, (, ) = (5, 6), (8, 4); for  = 30, (, ) = (6, 13), (13, 6),
(14, 5); and for  = 50, (, ) = (5, 16), (6, 12), (13, 6), (16, 5).

3.  Result
It  is  observed  that  APB  of  the  estimates  of  the  proposed  estimation
procedure is larger when  = 30,50 compared for cases when  = 20. Most of
the APB of estimates of the proposed procedure is less compared with the
APB of estimates of VAR(1) over the different series lengths. The procedure
consistently produces low MAPE across all the varying length of time series

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