A Hill Climbing Algorithm for Maximum Likelihood Estimation of the Gamma Distributed-lag Model with Multiple Explanatory Variables

Linear regression with distributed-lags is a consolidated methodology in time series analysis to assess the impact of several explanatory variables on an outcome that may persist over periods.Finite polynomial have long tradition due good flexibility accompanied by advantage linear representation, which allows parameter estimation through Ordinary Least Squares (OLS).However, they require specify degree and lag length, entail loss some initial observations.Gamma overcome these problems represents compromise between number parameters, however not representation parameters currently available methods, like OLS-based grid search non-linear least squares, are unsatisfactory case multiple variables.For reasons, Gamma distribution has been able replace finite lags applied analysis, it mostly employed single variable.In this paper, we propose hill climbing algorithm for maximum likelihood distributed-lags.The proposed dynamic relationship Bitcoin's price three composite indices US stock market.