We explore mixed data sampling (henceforth MIDAS) regression models. The regressions involve time series data sampled at different frequencies. Volatility and related processes are our prime focus, though the regression method has wider applications in macroeconomics and finance, among other areas. The regressions combine recent developments regarding estimation of volatility and a not-so-recent literature on distributed lag models. We study various lag structures to parameterize parsimoniously the regressions and relate them to existing models. We also propose several new extensions of the MIDAS framework. The paper concludes with an empirical section where we provide further evidence and new results on the risk-return trade-off. We also report empirical evidence on microstructure noise and volatility forecasting.Microstructure noise, Nonlinear MIDAS, Risk, Tick-by-tick applications, Volatility,

We explore Mixed Data Sampling (henceforth MIDAS) regression models. The regressions involve time series data sampled at different frequencies. Volatility and related processes are our prime focus, though the regression method has wider applications in macroeconomics and finance, among other areas. The regressions combine recent developments regarding estimation of volatility and a not so recent literature on distributed lag models. We study various lag structures to parameterize parsimoniously the regressions and relate them to existing models. We also propose several new extensions of the MIDAS framework. The paper concludes with an empirical section where we provide further evidence and new results on the risk-return tradeoff. We also report empirical evidence on microstructure noise and volatility forecasting. * We thank two Referees and an Associate Editor, Alberto Plazzi, Pedro Santa-Clara as well as seminar participants at

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The level and distribution of patient waiting times for elective treatment is a major concern in publicly funded health care systems. Strict targets, which have specified maximum waiting times, have been introduced in the NHS over the last decade and have been criticised for distorting existing clinical priorities in scheduling hospital treatment. We demonstrate the usefulness of Conditional Density Estimation (CDE) in the evaluation of the reform using data for Scotland for 2002 and 2007. We develop a modified goodness of fit test to discriminate between models with different numbers of bins. We document a change in prioritisation between different patient groups with longer waiting patients benefiting at the expense of those who previously waited less. Our results contribute to understanding the response of publicly funded health systems to enforced targets for maximum waiting times.

In this paper, we develop an info-metric framework for testing hypotheses about structural instability in nonlinear, dynamic models estimated from the information in population moment conditions. Our methods are designed to distinguish between three states of the world: (i) the model is structurally stable in the sense that the population moment condition holds at the same parameter value throughout the sample; (ii) the model parameters change at some point in the sample but otherwise the model is correctly specified; and (iii) the model exhibits more general forms of instability than a single shift in the parameters. An advantage of the info-metric approach is that the null hypotheses concerned are formulated in terms of distances between various choices of probability measures constrained to satisfy (i) and (ii), and the empirical measure of the sample. Under the alternative hypotheses considered, the model is assumed to exhibit structural instability at a single point in the sample, referred to as the break point; our analysis allows for the break point to be either fixed a priori or treated as occuring at some unknown point within a certain fraction of the sample. We propose various test statistics that can be thought of as sample analogs of the distances described above, and derive their limiting distributions under the appropriate null hypothesis. The limiting distributions of our statistics are nonstandard but coincide with various distributions that arise in the literature on structural instability testing within the Generalized Method of Moments framework. A small simulation study illustrates the finite sample performance of our test statistics.