In this article 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 subperiod for a variety of aggregate returns indexes and size-sorted portofolios. Although the rejections are due largely to the behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or timevarying volatilities. Moreover, the rejection of the random walk for weekly returns does not support a mean-reverting model of asset prices.

participants in seminars at the Federal Reserve Bank of Philadelphia and the University of Pennsylvania, as well as those at the Midwest Macroeconomics meetings, for their comments. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Philadelphia or of the Federal Reserve System. A REAL-TIME DATA SET FOR MACROECONOMISTS This paper presents the concept and uses of a real-time data set that can be used by economists for testing the robustness of published econometric results, for analyzing policy, and for forecasting. The data set consists of vintages, or snapshots, of the major macroeconomic data available at quarterly intervals in real time. The paper illustrates why such data may matter, explains the construction of the data set, examines the properties of several of the variables in the data set across vintages, examines key empirical papers in macroeconomics and investigates their robustness to different vintages, looks at how policy analysis may be affected by data revisions, and shows how forecasts can be affected by data revisions. A REAL-TIME DATA SET FOR MACROECONOMISTS I.

It is obvious that forecasts are of great importance and widely used in economics and finance. Quite simply, good forecasts lead to good decisions. The importance of forecast evaluation and combination techniques follows immediately-- forecast users naturally have a keen interest in monitoring and improving forecast performance. More generally, forecast evaluation figures prominently in many questions in empirical economics and finance, such as: Are expectations rational? (e.g., Keane and Runkle, 1990; Bonham and Cohen, 1995) Are financial markets efficient? (e.g., Fama, 1970, 1991) Do macroeconomic shocks cause agents to revise their forecasts at all horizons, or just at short- and medium-term horizons? (e.g., Campbell and Mankiw, 1987; Cochrane, 1988) Are observed asset returns "too volatile"? (e.g., Shiller, 1979; LeRoy and Porter, 1981) Are asset returns forecastable over long horizons? (e.g., Fama and French, 1988; Mark, 1995)

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This paper investigates the Multifractal Model of Asset Returns, a class of continuous-time processes that incorporate the thick tails and volatility persistence exhibited by many financial time series. The simplest version of the model compounds a Brownian Motion with a multifractal time-deformation process. Prices follow a semi-martingale, which precludes arbitrage in a standard two-asset economy. Volatility has long memory, and the highest finite moments of returns can take any value greater than two. The local variability of the process is highly heterogeneous, and is usefully characterized by the local Hölder exponent at every instant. In contrast with earlier processes, this exponent takes a continuum of values in any time interval. The model also predicts that the moments of returns vary as a power law of the time horizon. We confirm this property for Deutsche Mark/U.S. Dollar exchange rates and several equity series. We then develop an estimator, and infer a parsimo...

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The acceleration of productivity since 1995 has prompted a debate over whether the economy's underlying growth rate will remain high. In this paper, we draw on growth theory to identify variables other than productivity— namely consumption and labor compensation—to help estimate trend productivity growth. We treat that trend as a common factor with two "regimes " high-growth and low-growth. Our analysis picks up striking evidence of a switch in the mid-1990s to a higher long-term growth regime, as well as a switch in the early 1970s in the other direction. In addition, we find that productivity data alone provide insufficient evidence of regime changes; corroborating evidence from other data is crucial in identifying changes in trend growth. We also argue that our methodology would be effective in detecting changes in trend in real time: In the case of the 1990s, the methodology would have detected the regime switch within one quarter of its actual occurrence according to subsequent data.

We consider the use of indices of leading indicators in forecasting and macro-economic modelling. The procedures used to select the components and construct the indices are examined since the composition of indicator systems gets altered frequently. Issues of model choice and data-based restrictions are investigated. Possible biases in estimated standard errors are considered, as is cointegration within the indices and between their components and macro-economic variables. The effectiveness of indices ex-post is contrasted with evidence about their ex-ante performance. A framework is proposed for index analysis and applied to selecting indices. The role of leading indicators in macro models is discussed. Contents 1 Introduction 2 2 Current UK and US composite leading indicators 3 2.1 The United Kingdom's index of leading indicators 3 2.2 The United States' index of leading indicators 5 3 Analysis of indices of leading indicators 6 3.1 Foundations for leading indices 6 3.2 Selection pr...

An enormous amount of analytical literature has recently appeared on the topic of “unit roots ” in macroeconomic time series. Indeed, tests for the presence of unit roots and techniques for dealing with them have together comprised one of the most active areas, over the past decade, in the entire field of macroeconomics. The issues at hand have involved substantive questions about the nature of macroeconomic growth and fluctuations in developed economies and technical questions about model formulation and estimation in systems that include unit-root variables. The present paper attempts to describe several of the main issues and to evaluate alternative positions. It does not pretend to be a comprehensive survey of the literature or to provide an “even-handed ” treatment of issues, however. 1 Instead, it attempts to develop a convincing perspective on the topic, one that is consistent with the views of many active researchers in the area but that may nevertheless be somewhat idiosyncratic. The exposition that is presented below is designed to be predominantly nontechnical in nature. Indeed, it takes a rather old-fashioned approach to