|
Abstract:
|
The Vector AutoRegressive Moving Average (VARMA) model is a fundamental tool for modeling multivariate time series. Recently, a growing interest has arisen in high-dimensional models, where the number of marginal time series is increasingly large. However, as the number of time series increases, the VARMA model becomes heavily overparameterized. For such high-dimensional VARMA models, estimation is generally intractable. In this setting, the high-dimensional Vector AutoRegression (VAR) model has been favored, in both theory and practice. We propose adapting modern regularization methods to estimate high-dimensional VARMA models. Our estimation method is sparse, meaning many model parameters are estimated as exactly zero. The proposed framework has good estimation and forecast accuracy under numerous simulation settings. We illustrate the forecast performance of the sparse VARMA models for several application domains, including macro-economic forecasting, demand forecasting and volatility forecasting. The sparse VARMA estimator gives parsimonious forecast models that lead to important gains in relative forecast accuracy.
|
