Abstract: This article establishes a functional coefficient moving average model (FMA) that allows the coefficient of the classical moving average model to adapt with a covariate. The functional coefficient is identified as a ratio of two conditional moments. A local linear estimation technique is used for estimation and the asymptotic properties of the resulting estimator are investigated. Its convergence rate depends on whether the underlying function reaches its boundary or not, and the asymptotic distribution can be nonstandard. A model specification test in the spirit of Härdle-Mammen (1993) is developed to check the stability of the functional coefficient. Simulations have been conducted to study the finite sample performance of our proposed estimator, and the size and the power of the test. Application is made to CPI data from the China Mainland and to German egg prices to show the efficacy of FMA.

Key words and phrases: Consumer price index, forecasting, functional coefficient model, moving average model.