An Improved Approach To Modelling and Evaluation of Economic data with Irregular Benchmarks

Abstract

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 IV a 1 1 1 1 1 1 ' ' ' ' ˆ ' ' var ˆ ' ' var ˆ                 R  R J V JV J IV a V J V JR  R J V JV J IV 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