Discrete-Time Markov Chain Method for Predicting Probability of Crop Yield Variability

Agricultural crop yield prediction is vital for ensuring global food security and optimizing resource management amid the increasing challenges posed by climate change and extreme weather variability. This study investigates the use of discrete-time, finite-state, time-homogeneous Markov chains to model crop failure and yield fluctuation probability. Maize yields in Hungary during 1921–1960 and 1980–2023 were analyzed. Yield distribution was assumed to depend only on the yield of the previous year. The Olympic average was computed for 5-year periods, excluding the highest and lowest values. Annual yield was divided by the value of the moving average and expressed as a percentage. According to our estimates, a higher degree of yield fluctuation is associated with an increased frequency of years with yields close to the long-term average. Considering the long-time trend during 1925–1960, the probability of having average maize yield, yield failure, and high yield would be 73.5%, 11.8%, and 14.7%, respectively. For the period of 1985–2023, the probability of failure was calculated to be at least 15% higher, while that of the high yield was found to be lower than for the first period. Taking the second period’s trend into account, the probabilities of average harvest, crop failure, and high harvest would be 66%, 21%, and 13%, respectively. Our findings confirm that the probability of yield variability can be modeled using the discrete-time Markov chain method, providing a new mathematical approach for crop yield prediction.