Modeling time-series of noisy two-cycle ecological oscillators

In this work, we investigate how time-series of an ecological oscillator can be modeled and predicted when the true dynamics of oscillator is unknown.  Two-cycle ecological oscillators have two phases of oscillations: high values at even times or high values at odd times.  In the presence of noise, exact high and low values vary from cycle to cycle, and the two-cycles at times may change their phase of oscillation.  We develop two discrete-state models and a continuous-state model to study their predictive ability given the noisy time-series data.  For discrete-state models, we have a two-state system with two phases of oscillation as two states and a three-state system with an additional third state to incorporate transition dynamics between the phases of oscillations.  We will present forecast skill results for the three developed models (two-state, three-state and continuous-state) and a machine learning forecasting tool.  We will also discuss maximum likelihood inference methods for the developed models and the comparison of obtained forecast skill with mutual information between the data used for models and the time-series data.