Comparison of Weighted Lag Adaptive LASSO with Autometrics for Covariate Selection and Forecasting Using Time-Series Data

Abstract

In order to reduce the dimensionality of parameter space and enhance out-of-sample forecasting performance, this research compares regularization techniques with Autometrics in time-series modeling. We mainly focus on comparing weighted lag adaptive LASSO (WLAdaLASSO) with Autometrics, but as a benchmark, we estimate other popular regularization methods LASSO, AdaLASSO, SCAD, and MCP. For analytical comparison, we implement Monte Carlo simulation and assess the performance of these techniques in terms of out-of-sample Root Mean Square Error, Gauge, and Potency. The comparison is assessed with varying autocorrelation coefficients and sample sizes. The simulation experiment indicates that, compared to Autometrics and other regularization approaches, the WLAdaLASSO outperforms the others in covariate selection and forecasting, especially when there is a greater linear dependency between predictors. In contrast, the computational efficiency of Autometrics decreases with a strong linear dependency between predictors. However, under the large sample and weak linear dependency between predictors, the Autometrics potency ⟶ 1 and gauge ⟶ α. In contrast, LASSO, AdaLASSO, SCAD, and MCP select more covariates and possess higher RMSE than Autometrics and WLAdaLASSO. To compare the considered techniques, we made the Generalized Unidentified Model for covariate selection and out-of-sample forecasting for the trade balance of Pakistan. We train the model on 1985–2015 observations and 2016–2020 observations as test data for the out-of-sample forecast.