An Improved Approach To Modelling and Evaluation of Economic data with Irregular Benchmarks
http://hdl.handle.net/123456789/1312
2026-04-05T04:30:26ZAn Improved Approach To Modelling and Evaluation of Economic data with Irregular Benchmarks
http://hdl.handle.net/123456789/1313
An Improved Approach To Modelling and Evaluation of Economic data with Irregular Benchmarks
AJAO, ISAAC OLUWASEYI
Benchmarking deals with problem of combining a series of high-frequency data with a series of low frequency data to form a single consistent time series. Various benchmarking methods in literature lack
some observations (necessary for development of the eventual new series), at the beginning and end of
the original series, which pose missing values challenge to the methods. Hence, there is need for an
improved approach that will better capture these missing values. Therefore, the study was designed to
develop an Autocorrelated Indicator Benchmarking Model (AIBM) that fills the value gaps without
affecting the movement and pattern of the original series.
Two equations:
t t
H
h
t th h
s r B e
1
and
m
t
t t m mt t
m
m
a j
2
1
from the generalised least squares
regression models were used to develop the new model, where
t
s
is the high-frequency series, r the
regressors, h minimum value of the regressors, H the maximum value of the regressors, and B the bias
values. The time effect is
H
h
thBh
r
1
. The benchmarked values
t
, satisfied the annual constraints. The
autocorrelated error, low-frequency series, the coverage fractions, and the non-autocorrelated error, are
t
e , m a , mt j
, and
m
, respectively. The i
th and j
th values in the high frequency series are
m
t
1
and
m
t
2
,
respectively. The model was validated with simulated data and real life data on the Nigeria’s Gross
Domestic Product (1975 to 2013) obtained from the Nigeria Bureau of Statistics annual report. The
performance of the proposed model was evaluated based on autocorrelation coefficients (𝜌) values
compared with the existing models such as, Proportional Balanced Difference (PBD), Proportional Order
One Difference (POOD), Additive Order Two Difference (AOTD), Proportional Order Two Difference
(POTD), and Bias Adjusted (BADJ), using the Coefficient of Variation (CV) of the obtained growth
rates. Minimum CV value will give a preferred model.
The developed AIBM was given as
s Ve
J Vd
Js Ve
J Vd
JR R J Vd
Js R R J Vd
Js Ve
J Vd
JVe
J IV a
1 1 1 1 1 1
' ' ' '
ˆ
' ' var
ˆ
' ' var
ˆ
R R J V JV J IV a V J V JR R J V JV J IV a d e e d d e
1 1 1 1 1
' ' '
ˆ
' ' ' ' var
ˆ
var
, where
ˆ
is the matrix of
the benchmarked estimates. The covariance matrices of the survey, low frequency, and high frequency
errors are
Ve
, Vd
, and
V
, respectively. Also the estimates of bias parameters and regressors are
ˆ
and
R , respectively. For simulated data, the CV values of growth rates from PLD, PFD, ASD, PSD, BADJ,
and AIBM at 𝜌 = 0.729 were -29.620, -14.033, -24.353, -13.160, -19.591, -29.486; at 𝜌 = 0.900 were
-29.620, -14.033, -24.353, -13.160, -19.632, -29.606; at 𝜌 = 0.990 were -4.402, -4.987, -4.371, -4.954,
-7.137, -4.402; and at 𝜌 = 0.999 were -4.402, -4.987, -4.371, -4.994, -7.309, -4.402, respectively. For
real life data, the CV values at 𝜌 = 0.729 were 3.195, 3.196, 3.198, 3.200, 1.582, 1.318; at 𝜌 = 0.900
were 3.195, 3.196, 3.198, 3.200, 1.582, 1.318; at 𝜌 = 0.990 were 3.195, 3.196, 3.198, 3.200, 1.582, 1.121;
and at 𝜌 = 0.999 were 3.195, 3.196, 3.198, 3.200, 1.582, 1.105, respectively. The AIBM has the minimum
CV in the growth rates, indicating its strength over the existing models.
The autocorrelated indicator benchmarking model captured missing values at the beginning and end of
the original series, while pre
2021-04-06T00:00:00Z