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In this paper, a heteroscedastic functional regression model with martingale difference errors is considered. We are interested in real-time estimation of the regression as well as the conditional variance operators when the response is a real-valued random variable and the covariate belongs to an infinite-dimensional space. A Robbins–Monro-type estimator of the conditional variance is introduced when a sample is collected from an underlying stationary and ergodic process. First, a local uniform L q -consistency (for q ≥ 2) rate of the recursive estimator of the regression operator is established. Then, a pointwise mean-square consistency rate of the conditional variance is given when the regression function is supposed to be known and when it is estimated recursively. Simulation studies are conducted to assess the proposed estimator's performance, in terms of reducing the computational time without affecting significantly the accuracy, compared to its natural competitor. An application to real environmental data is also carried out to illustrate the real-time on day ahead prediction of the maximum ozone concentration in Mexico city as well as its volatility. [ABSTRACT FROM AUTHOR]

This paper introduces a multivariate long-memory model with structural breaks. In the proposed framework, the time series exhibits possibly fractional orders of integration which are allowed to be different in each subsample. The break date is endogenously determined using a procedure that minimizes the residual sum of squares (RSS). Monte Carlo experiments show that this method for detecting breaks performs well in large samples. As an illustration, we estimate a trivariate VAR including prices, employment and GDP in both the US and Mexico. For the subsample preceding the break, our findings are similar to those of earlier studies based on a standard VAR approach in both the countries, such that the variables exhibit integer degrees of integration. On the contrary, the series is found to be fractionally integrated after the break, with the fractional differencing parameters being higher than one in the case of Mexico. [ABSTRACT FROM AUTHOR]