Knowledge about the nature of the dynamics can help improve the model quality and thus the forecasting accuracy. If you have prior knowledge of the system dynamics, you can fit the estimation data using a nonlinear grey-box model. Note that to reduce the number of regressors, you can pick an optimal subset of (transformed) variables using principal component analysis (see pca) or feature selection (see sequentialfs) in the Statistics and Machine Learning Toolbox™. Nonlinear black-box modeling did not require prior knowledge about the equations governing the data. The plots show that forecasting using a nonlinear ARX model gave better forecasting results than using a linear model. Legend( 'Measured', 'Predicted', 'Forecasted') Ylabel( 'Predator population (thousands)') A linear-in-regressor form of Nonlinear ARX model will be estimated.Ĭreate a nonlinear ARX model with 2 outputs and no inputs. You do not require prior knowledge about the equations governing the estimation data. Estimate a Nonlinear Black-Box Modelįit a nonlinear black-box model to the estimation data. This indicates that the population change dynamics might be nonlinear. The plots show that forecasting using a linear ARMA model (with added handling of offsets) worked somewhat and the results showed high uncertainty compared to the actual populations over the 12-20 years time span. Ylabel( 'Prey population, in thousands') Ylabel( 'Predator population, in thousands') įig.Position = Since the data was detrended for estimation, you need to specify those offsets for meaningful predictions. Use "polydata", "getpvec", "getcov" for parameters and their uncertainties.Įstimated using ARMAX on time domain data "zed".įit to estimation data: % (prediction focus)Ĭompute a 10-step-ahead (1 year) predicted output to validate the model over the time span of the estimation data.