Page 17 - Contributed Paper Session (CPS) - Volume 7

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
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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 [4]. The
MAPE per scenario is also computed as in [5] 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 [4]

=1 ℎ,

100
1
, = 100 ∑ ,ℎ [5]
=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 [6]
,
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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