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The resulting model average estimator is proved to be asymptotically optimal. It is shown that the Kullback\u2013Leibler model averaging (KLMA) estimator asymptotically minimizes the in\u2010sample Kullback\u2013Leibler divergence and improves the forecast accuracy of out\u2010of\u2010sample even under different loss functions. In simulations, we show that the KLMA estimator compares favorably with smooth\u2010AIC estimator (SAIC), smooth\u2010BIC estimator (SBIC), and Mallows model averaging estimator (MMA), especially when some nonlinear noise is added to the data generation process. The empirical applications in the daily range of S&amp;P500 and price duration of IBM show that the out\u2010of\u2010sample forecasting capacity of the KLMA estimator is better than that of other methods.<\/jats:p>","DOI":"10.1155\/2022\/7706992","type":"journal-article","created":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T19:05:19Z","timestamp":1651086319000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Model Averaging Estimation Method by Kullback\u2013Leibler Divergence for Multiplicative Error 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