Partial Monotone Dependence

We present a new measure of dependence suitable for time series forecasting: Partial Monotone Correlation (PMC) that generalizes Monotone Correlation. Unlike the Monotone Correlation, the new measure of dependence uses piecewise strictly monotone transformations that increase the value of the correlation coefficient. We explore its properties, its relationship with Monotone and Maximal Correlation, and present an algorithm that calculates it based on the Simultaneous Perturbation Stochastic Approximation method. We also demonstrate how to apply Partial Monotone Correlation for time series analysis and forecasting introducing Partial Monotone Autoregressive model (PMAR) of order 1. Its performance is then evaluated against the baseline of linear and nonlinear autoregressive models (AR, LSTAR) on 150 time series produced from 3 datasets: Yellow Taxi pickups, Citi Bike pickups, and Cellular Network hits. Overall, PMAR model outperforms the baseline with the average sMAPE of about 1.7-4% lower.