Econometric analysis of time series data is frequently preceded by regression on time to remove a trent component in the date. The resulting residuals are then treated as a stationary series to which procedures requiring stationarity, such as spectral analysis, can be applied. The objective is often to investigate the dynamics of transitory movements in the systems, for example, in econometric models of the business cycle. When the data does consist of a deterministic function of time plus a stationary error then regression residuals will clearly be unbiased estimates of the stationary component. However, if the data is generated by (possibly repeated) summation of a satisfactory and inevitable process then the series cannot be expressed as a deterministic function of time plus a stationary deviation, even though a least squares trend line and the associated residuals can always be calculated for any given finite sample. In a recent paper, Chan, Hayya, and Ord (1977) hereafter CHO) were able to show that a residuals from linear regression of a realization of a random walk (the summation of a purely random series) on time have autocovariances which for given lag are a function of time and thereafter that the residuals are not stationary. Further, CHO established that the expected sample autocovariance function (the expected autocovariances for given lag averaged over the time interval of the sample) is a function of sample size as well as lag and therefore an artifact of the detrending procedure. This function is characterized by CHO in their figure 1 as being effectively linear in lag (although the exact function is a fifth degree polynomial) with the rate of decay from unity at the origin depending inversely on sample size.

We hope to answer three questions: Has there been a structural break in postwar U.S. real GDP growth towards stabilization? If so, when? What is the nature of this structural break?We employ a Bayesian approach to identify a structural break at an unknown changepoint in a Markov-switching model of the business cycle. Empirical results suggest a break in GDP growth toward stabilization, with the posterior mode of the break date at 1984:1. Furthermore, we find a narrowing gap between growth rates during recessions and booms that is at least as important as any decline in the volatility of shocks.

The synthesis of the dynamic factor model of Stock and Watson (1989) and the regime-switching model of Hamilton (1989) proposed by Diebold and Rudebusch (1996) potentially encompasses both features of the business cycle identified by Burns and Mitchell (1946): (1) comovement among economic variables through the cycle and (2) nonlinearity in its evolution. However, maximum-likelihood estimation has required approximation. Recent advances in multimove Gibbs sampling methodology open the way to approximation-free inference in such non-Gaussian, nonlinear models. This paper estimates the model for U.S. data and attempts to address three questions: Are both features of the business cycle empirically relevant? Might the implied new index of coincident indicators be a useful one in practice? Do the resulting estimates of regime switches show evidence of duration dependence? The answers to all three would appear to be yes.

This paper reexamines the empirical evidence for mean-reverting behavior in stock prices. Comparison of data before and after World War II shows that mean reversion is entirely a prewar phenomenon. Using randomization methods to calculate significance levels, the authors find that the full sample evidence for mean reversion is weaker than previously indicated by Monte Carlo methods under a normal assumption. Further, the switch to mean-averting behavior after the war is about to be too strong to be compatible with sampling variation. The authors interpret these findings as evidence of a fundamental change in the stock returns process.

We examine a variety of models in which the variance of a portfolio's excess return depends on a state variable generated by a first-order Markov process. A model in which the state is known to economic agents is estimated. It suggests that the mean excess return moves inversely with the level of risk. We then estimate a model in which agents are uncertain of the state. The estimates indicate that agents are consistently surprised by high-variance periods, so there is a negative correlation between movements in volatility and in excess returns.

Introduction to modern corporate finance economic foundations the economic system and contracting the time value of money the valuation of financial securities the techniques of capital budgeting risk and diversification the capital asset pricing model an introduction to options financial leverage financing in imperfect markets the dividend decision corporate ethics and shareholder wealth maximization estimating project cash flows advanced topics in capital budgeting financial analysis and planning working capital and management international finance mergers and reorganizations.

This paper reconciles two widely used decompositions of GDP into trend and cycle that yield starkly different results. The Beveridge-Nelson (BN) decomposition implies that a stochastic trend accounts for most of the variation in output, whereas the unobserved-components (UC) implies cyclical variation is dominant. Which is correct has broad implications for the relative importance of real versus nominal shocks. We show the difference arises from the restriction imposed in UC that trend and cycle innovations are uncorrelated. When this restriction is relaxed, the UC decomposition is identical to the BN decomposition. Furthermore, the zero-correlation restriction can be rejected for U.S. quarterly GDP, with the estimated correlation being -0.9.