Band‐Pass Filtering With High‐Dimensional Time Series. A Synthetic Indicator of the Medium‐to‐Long Run Component of Growth

ABSTRACT The paper deals with the construction of a synthetic indicator of economic growth, obtained by projecting a quarterly measure of aggregate economic activity, namely gross domestic product (GDP), into the space spanned by a finite number of smooth principal components, representative of the medium‐to‐long‐run component of economic growth of a high‐dimensional time series, available at the monthly frequency. The smooth principal components result from applying a cross‐sectional filter distilling the low‐pass component of growth in real time. The outcome of the projection is a monthly nowcast of the medium‐to‐long‐run component of GDP growth. After discussing the theoretical properties of the indicator, we deal with the assessment of its reliability and predictive validity with reference to a panel of macroeconomic US time series.