An ARMA Representation of Unobserved Component Models under Generalized Random Walk Specifications: New Algorithms and Examples

Among the alternative Unobserved Components formulations within the stochastic state space setting, the Dynamic Harmonic Regression (DHR) has proved particularly useful for adaptive seasonal adjustment signal extraction, forecasting and back-casting of time series. Here, we show first how to obtain ARMA representations for the Dynamic Harmonic Regression (DHR) components under several random walk specifications. Later, we uses these theoretical results to derive an alternative algorithm based on the frequency domain for the identification and estimation of DHR models. The main advantages of this algorithm are linearity, fast computing, avoidance of some numerical issues, and automatic identification of the DHR model. To compare it with other alternatives, empirical applications are provided.