On some properties of composite distributed lag models

The analysis presented in this paper is focused on basic properties of discrete distributed lag models. Such models are commonly used to model dynamic systems in various applications. In the presented considerations, time-varying distributed lags have been analyzed. Composite distributed lag models analyzed in this paper result from the summation or superposition of component distributed lag models. The analysis is restricted to models with a lag distribution, whose mean lag and variance exist. The paper presents relationships between the mean values and variances of the lag distributions of composite distributed lag models and of the component distributed lag models, as well as the relationships between the variance of the random term of composite distributed lag models and the variance of the random term of the component distributed lag models.