Essays in time series econometrics

Given the mixed signals provided by the various macroeconomic time series available, the task of accurately determining the state of the economy is a challenging one. Specifically, it is hard to determine precisely in real-time which movements in economic activity are part of a slowly evolving stochastic trend and which movements are attributable to the typical business cycle fluctuations. Given the importance of this knowledge for the policymaker, one should be able to extract the relevant information through statistically rigorous methods capable of providing a clear signal regarding current economic developments.;This dissertation aims at providing such methods. We depart from common procedures by exploring multiple sources of information. While the signal of interest in the fundamental measure of economic activity (Gross Domestic Product) can be precisely defined, the attempts to extract the relevant signal (i.e., to filter the data) in this variable using other sources of information have been inexistent.;We start by dealing with a technical difficulty in the definition of relevant signal when the time series data is not assumed to be stationary. The application of standard filtering methods (aimed at extracting the relevant signal) when this assumption fails is not always fully justified. We will show that the interpretation of the relevant extracted signal is indeed independent of this assumption.;We proceed to the development of a multivariate filter which is an optimal (in the mean squared error sense) approximation to the ideal (band-pass) filter that isolates a specified range of fluctuations in a time series, e.g., business cycle fluctuations in macroeconomic time series. We illustrate the application of the filter by constructing a business cycle indicator for the U.S. economy. The filter can additionally be used in any similar signal extraction problem demanding accurate real-time estimates.;The last chapter proposes a multivariate band-pass filter that is based on a trend plus cycle decomposition model. The underlying multivariate dynamic factor model relies on specific formulations for trend and cycle components and produces smooth business cycle indicators with band-pass filter properties. The multivariate approach leads to a business cycle indicator that is less subject to revisions than the ones produced by univariate filters and available at a frequency higher than that of the series of interest.