The Shortest Duration Constrained Hidden Markov Model: Data denoise and forecast optimization on the country-product matrix for the Fitness-Complexity Algorithm.

The Economic Fitness Index describes industrial completeness and comprehensively reflects product diversification with competitiveness and product complexity in production globalization. The Fitness-Complexity Algorithm offers a scientific approach to predicting GDP and obtains fruitful results. As a recursion algorithm, the non-linear iteration processes give novel insights into product complexity and country fitness without noise data. However, the Country-Product Matrix and Revealed Comparative Advantage data have abnormal noises which contradict the relative stability of product diversity and the transformation of global production. The data noise entering the iteration algorithm, combined with positively related Fitness and Complexity, will be amplified in each recursion step. We introduce the Shortest Duration Constrained Hidden Markov Model (SDC-HMM) to denoise the Country-Product Matrix for the first time. After the country-product matrix test, the country case test, the noise estimation test and the panel regression test of national economic fitness indicators to predict GDP growth, we show that the SDC-HMM could reduce abnormal noise by about 25% and identify change points. This article provides intra-sample predictions that theoretically confirm that the SDC-HMM can improve the effectiveness of economic fitness indicators in interpreting economic growth.