Additive modeling of realized variance: tests for parametric specifications and structural breaks

For an additive autoregression model, we study two types of testing problems. First, a parametric specification of a component function is compared against a nonparametric fit. Second, two nonparametric fits of two different time periods are tested for equality. We apply the theory to a nonparametric extension of the linear heterogeneous autoregressive (HAR) model. The linear HAR model is widely employed to describe realized variance data. We find that the linearity assumption is often rejected, in particular on equity, fixed income, and currency futures data; in the presence of a structural break, nonlinearity appears to prevail on the sample before the outbreak of the financial crisis in mid-2007.