In this paper, we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (1962-1985) and for all sub-periods for a variety of...

We study the use of a misspecified overdifferenced model to forecast the level of a stationary scalar time series. Let x(t) be the series, and let bias be the sample average of a series of forecast errors. Then, the bias of forecasts of x(t) generated by a misspecified overdifferenced ARMA model...

In a model where a variable Y[sub t] is proportional to the present value, with constant discount rate, of expected future values of a variable y[sub t] the "spread" S[sub t]= Y[sub t] - [theta sub t] will be stationary for some [theta] whether or not y[sub t]must be differenced to induce...

We study the usefulness of root tests as diagnostic tools for selecting forecasting models. Difference stationary and trend stationary models of economic and financial time series often imply very different predictions, so deciding which model to use is tremendously important for applied...

This paper investigates the possibility, raised by Perron (1989, 1990a), that aggregate economic time series can be characterized as being stationary around broken trend lines. Unlike Perron, we treat the break date as unknown a priori. Asymptotic distributions are developed for recursive,...

It is often argued that the presence of a unit root in aggregate output implies that there is no "business cycle": the economy does not return to trend following a disturbance. This paper makes this notion precise, but then develops a simple aggregative model where this relation is contradicted....

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...

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...