China is one of the world’s largest tea-producing countries, and its fluctuations in production affect the international market and domestic economic stability. Existing research often uses limited predictive models at the local scale and lacks systematic national analysis. This study evaluated five models—autoregressive integrated moving average model (ARIMA), grey model (GM (1,1)), Markov chain grey model (Markov-GM (1,1)), particle swarm optimization Markov chain grey model (PSO-Markov-GM), and dynamic rolling update grey model (DRUGM (1,1))—using three stages of annual tea production data from China (2004–2023). The results indicate that DRUGM (1,1) has the lowest prediction error, demonstrating superior ability to capture production trends. The dynamic update mechanism of this model enhances its adaptability, providing an efficient and scalable framework for predicting the production level of tea and other crops. Accurate predictions are crucial for improving agricultural planning, optimizing resource allocation, and providing information for trade policy design. This study provides practical tools for sustainable agricultural decision-making, helping to strengthen rural economic stability and resilient food systems.

The Bregman divergence of two probability vectors is a stronger form of the f-divergence introduced by Csiszar. Two versions of the Bregman universal portfolio are presented by exploiting the mean-value theorem. The explicit form of the Bregman universal portfolio generated by a function of a convex polynomial is derived and studied empirically. This portfolio can be regarded as another generalized of the well-known Helmbold portfolio. By running the portfolios on selected stock-price data sets from the local stock exchange, it is shown that it is possible to increase the wealth of the investor by using the portfolios in investment.

The universal portfolio is an important investment strategy in a stock market where no stochastic model is assumed for the stock prices. The zero-gradient set of the objective function estimating the next-day portfolio which contains the reverse Kullback-Leibler order-alpha divergence is considered. From the zero-gradient set, the explicit, reverse Helmbold universal portfolio is obtained. The performance of the explicit, reverse Helmbold universal portfolio is studied by running them on some stock-price data sets from the local stock exchange. It is possible to increase the wealth of the investor by using these portfolios in investment.

The f -divergence of Csiszar is defined for a non-negative convex function on the positive axis. A pseudo f -divergence can be defined for a convex function not satisfying the usual requirements. A rational function where both the numerator and the denominator are non-integer polynomials will be used to generate universal portfolios. Five stock-price data sets from the local stock exchange are selected for the empirical study. Empirical results are obtained by running the generated portfolios on these data sets. The empirical results demonstrate that it is possible for the investors to increase their wealth by using the portfolios in investment.

The logarithm of the estimated next-day wealth return is approximated by k terms of its Taylor series. The resulting Type k universal portfolio generated by the f -divergence is obtained. An implicit form of the portfolio is also obtained by exploiting the mean-value theorem. An empirical study of the performance of the portfolio is focused on the Type 2 Helmbold universal portfolio. A few generalizations of the Helmbold universal portfolio have recently been studied, namely the reverse Helmbold and the parametric Helmbold portfolios. This new type of portfolio can be regarded a contribution to the inventory of Helmbold related universal portfolios. It is verified experimentally that an investor’s wealth can be significantly increased by using the Type 2 Helmbold portfolio in investment.