[This paper investigates the degree to which a "leading" time series improves the prediction of coincident series. The theory of covariance-stationary processes is used as the theoretical framework and empirical tests dealing with the predictive ability of "leading" series are supplied.]

It has long been argued that major cyclical variables such as the unemployment rate display an asymmetric behavior over various phases of the business cycle. The paper provides a statistical test for this hypothesis. Using the framework of finite state Markov processes I implement a test to see if the behavior of the unemployment rate is characterized by sudden jumps and slower drops. It is argued that the framework provided in the paper can also be used to test other sample path properties of economic time series.

It has long been argued that major cyclical variables such as the unemployment rate display an asymmetric behavior over various phases of the business cycle. The paper provides a statistical test for this hypothesis. Using the framework of finite state Markov processes I implement a test to see if the behavior of the unemployment rate is characterized by sudden jumps and slower drops. It is argued that the framework provided in the paper can also be used to test other sample path properties of economic time series.

In this paper, the theory of covariance-stationary stochastic processes is used in order to investigate the sign and the significance of the relationship between employment and real wages. It is shown that when appropriate distributed lags are estimated the data suggest that employment and real wages are negatively correlated. The response appears to be non-contemporaneous and statistically significant.

In this paper, the theory of covariance-stationary stochastic processes is used in order to investigate the sign and the significance of the relationship between employment and real wages. It is shown that when appropriate distributed lags are estimated the data suggest that employment and real wages are negatively correlated. The response appears to be non-contemporaneous and statistically significant.

T HE purpose of this paper is to evaluate the policy option of controlling cyclicality in housing and briefly review its policy-related implications. This subject has recently returned to the forefront of public concern,' because it is feared that housing cyclicality contributes to the high cost of housing (HUD, 1979) and has a detrimental effect on the continuity of urban change (as patterns of neighborhood development are affected (HUD, 1978)). The importance of housing derives from its dual role in the economy (Federal Home Loan Bank Board, 1969; Goldsmith and Lipsey, 1963). At the micro level it is a large component of both the consumer budget and asset portfolio (Artle and Varaiya, 1978). It also affects the quality of urban neighborhoods spatially. At the macro level, it accounts for 25% to 30% of gross domestic investment. Since the marked cycles in housing construction lead the business cycle, countercyclical monetary policy has relied on housing as a policy instrument (Harberger, 1970). Two arguments plead in favor of greater control of housing cyclicality: (i) the high and rising cost of housing causes housing unaffordability,2 raising questions of consumer welfare and equity: which socio-economic groups suffer most and deserve compensation; (ii) cyclicality destabilizes the macro economy, generating unemployment (hence the loss of urban jobs) while at the same time compounding the high cost of housing by creating inefficiency in the housing construction industry. These combined effects limit the redevelopment of urban neighborhoods called for under the 1974 Housing and Community Development Act and thus conflict with the aims of this Act. In section II we investigate the existence of significant cyclicality and characterize it. Problems of statistical methodology are discussed in section III. We conclude in section IV with an outline of the policy-related implications of our analysis, leaving the details of the statistical formulae and data sources to appendices A and B. The main highlights of the paper are (i) New Housing construction exhibits significant cyclicality. The length of the dominant cycle varies depending on which estimate of the spectral density is used. The smoothed periodogram shows a powerful cycle around 128 months' length. The unaveraged periodogram, on the other hand, is dominated by a shorter cycle of 70 to 80 months' length. These estimates of the spectral density are shown diagramatically. The difference in the length of the dominant cycles is attributed to the well-known problem of resolution when two peaks are near each other, the smoothed periodogram will be unable to distinguish between the two. The KolmoReceived for publication October 15, 1979. Revision accepted for publication December 9, 1980. * Cornell University and Boston College, respectively. This paper was developed while the first author was a Visiting Research Scholar with the Division of Policy and Research Development at the U.S. Department of Housing and Urban Development (HUD), Washington, D.C. A preliminary version of this paper was presented at the Annual Allied Social Sciences Meeting of the American Real Estate and Urban Economics Association, Atlanta, December 1979. The authors are grateful to Craig Swan and an anonymous referee for useful comments. Ibrahim Levent helped with the calculations. 1 The U.S. Department of Housing and Urban Development (HUD), the White House, the Council on Wage and Price Control, various Congressional committees, the Office of Budget Management, etc., are all now interested in housing cyclicality and its policy implications. 2 Housing costs increased faster than most components of the consumer price index (U.S. Department of Labor, 1978), and threaten to make housing unaffordable (Data Resources, Inc., 1978; Jacobe and Parliment, 1979; Weicher, 1977). Some studies deny this, pointing to several important elements which offset the cost of housing, especially during periods of high inflation. These include tax advantages accruing to homeowners and capital gains on houses (Diamond, 1979; Hendershott and Hu, 1979; Van Order, 1979; Villani, 1978). These studies, however, neglect the equity problem resulting from the income distribution welfare effect. In a recent study using a production function analysis, Clemhout (1979) found that fluctuations in residential housing starts (or expenditures) create a range of inefficiencies in production, thereby increasing costs. Additional increases can be attributed to government regulation (Seidel, 1978), but many costs could be reduced if fluctuations in construction were moderated.

This paper develops a time-series model for continuous time asset prices and then uses tick-by-tick data from Treasury bill futures to develop both a definition and test for efficiency in the continuous time case. The results suggest that intra-day data on futures prices do not behave like a Markov Renewal process; rather, lagged values of futures prices do have some predictive power. In addition, trading times are not useful in predicting futures prices. Finally, we estimate the bid-ask spread and show that even after adjusting for this spread, the serial dependence between current and lagged returns remains. The multitude of studies concerning efficiency in futures markets support the proposition that a Martingale approximation is reasonable for most commodity and capital asset markets, while the same data reject Gaussian processes as an appropriate model.1 All of these studies, however, use either close to close prices or open to open prices in the estimation process. The choice of daily data is arbitrary; a natural question concerns whether, based on continuous time data, futures prices can be shown to be realizations of continuous time Markov processes and whether they can be represented as stochastically linear processes. In this paper, we use intra-day, tick-by-tick, data on Treasury bills futures and develop both a definition and a test for efficiency in the continuous time case. Observations on continuous time prices yield two separate time series: the trading prices and times. As a result, we claim that the standard procedures for tests of market efficiency must be replaced by two separate necessary conditions; the first is the usual condition that successive price changes are independent; the second requires that the recurrence times between trades obey a Poisson process. We apply the above definitions to intra-day futures prices for Treasury bills for a 57 day period in 1983. The results indicate that the Markov model does not hold for intra-day futures prices but the trading times do seem to behave approximately as a Poisson process. Received for publication January 29, 1988. Revision accepted for publication July 19, 1989. * City University of New York and State University of New York at Stony Brook, respectively. We gratefully acknowledge financial support for this research from the Center for the Study of Futures Markets at Columbia University. Stephanie Dieringer provided invaluable help as a research assistant for this project. 1 Several studies have examined the martingale property. For a summary of these results see, for example, Kamara (1982). 2 See, for example, Fama (1965), Mandlebrot (1963), Stevenson and Bear (1970), and Neftci and Policano (1984). Some studies that do analyze intraday data include Feinstone (1985) and Hinich and Patterson (1985).

Paul D. McNelis, , Policy-Dependent Parameters in the Presence of Optimal Learning: An Application of Kalman Filtering to the Fair and Sargent Supply-Side Equations, The Review of Economics and Statistics, Vol. 64, No. 2 (May, 1982), pp. 296-306