We propose a Bayesian procedure for exploiting small, possibly long-lag linear predictability in the innovations of a finite order autoregression. We model the innovations as having a log-spectral density that is a continuous mean-zero Gaussian process of order 1/√T. This local embedding makes...

An appropriate metric for the success of an algorithm to forecast the variance of the rate of return on a capital asset could be the incremental profit from substituting it for the next best alternative. We propose a framework to assess incremental profits for competing algorithms to forecast...

Over the postwar, the U.S., Europe and Japan have experienced what may be thought of as medium frequency oscillations between persistent periods of robust growth and persistent periods of relative stagnation. These medium frequency movements, further, appear to bear some relation to the high...

This paper derives relationships between frequency-domain and standard time-domain distributed-lag and autoregessive moving-average models. These relations are well known in the literature but are presented here in a pedogogic form in order to facilitate interpretation of spectral and...

I translate familiar concepts of discrete-time time-series to contnuous-time equivalent. I cover lag operators, ARMA models, the relation between levels and differences, integration and cointegration, and the Hansen-Sargent prediction formulas

This paper develops a vector autoregression (VAR) for time series which are observed at mixed frequencies - quarterly and monthly. The model is cast in state-space form and estimated with Bayesian methods under a Minnesota-style prior. We show how to evaluate the marginal data density to...

This paper exploits a data rich environment to provide direct econometric estimates of time-varying macroeconomic uncertainty, defined as the common volatility in the unforecastable component of a large number of economic indicators. Our estimates display significant independent variations from...

This paper uses simulations to explore the properties of the HP filter of Hodrick and Prescott (1997), the BK filter of Baxter and King (1999), and the H filter of Hamilton (2018) that are designed to decompose a univariate time series into trend and cyclical components. Each simulated time...

Measuring the integration of world capital markets is notoriously difficult. For example, regulatory changes which appear comprehensive may have little impact on the functioning of the capital market if they fail to lead to foreign portfolio inflows. In contrast to the usual practice of...

Volatility permeates modern financial theories and decision making processes. As such, accurate measures and good forecasts of future volatility are critical for the implementation and evaluation of asset pricing theories. In response to this, a voluminous literature has emerged for modeling the...