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We present a unified and up-to-date overview of temporal aggregation techniques for univariate and multivariate time series models explaining in detail, although intuitively, the technical machinery behind the results. Some empirical applications illustrate the main issues.

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Realized volatilities measured on several assets exhibit a common secular trend and some idiosyncratic pattern. We accommodate such an empirical regularity extending the class of Multiplicative Error Models (MEMs) to a model where the common trend is estimated nonparametrically while the idiosyncratic dynamics are assumed to follow univariate MEMs. Estimation theory based on seminonparametric methods is developed for this class of models for large cross-sections and large time dimensions. The methodology is illustrated using two panels of realized volatility measures between 2001 and 2008: the SPDR Sectoral Indices of the S&P500 and the constituents of the S&P100. Results show that the shape of the common volatility trend captures the overall level of risk in the market and that the idiosyncratic dynamics have an heterogeneous degree of persistence around the trend. An out-of-sample forecasting exercise shows that the proposed methodology improves volatility prediction over a number of benchmark specifications.