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Abstract.  Fisher's equation for the determination of the real rate of interest is studied from a fresh econometric perspective. Some new methods of data description for nonstationary time series are introduced. The methods provide a nonparametric mechanism for modelling the spatial densities of a time series that displays random wandering characteristics, like interest rates and inflation. Hazard rate functionals are also constructed, an asymptotic theory is given, and the techniques are illustrated in some empirical applications to real interest rates for the United States. The paper ends by calculating semiparametric estimates of long‐range dependence in U.S. real interest rates, using a new estimation procedure called modified log periodogram regression and new asymptotics that covers the nonstationary case. The empirical results indicate that the real rate of interest in the United States is (fractionally) nonstationary over 1934–1997 and over the more recent subperiods 1961–1985 and 1961–1997. Unit root nonstationarity and short memory stationarity are both strongly rejected for all these periods.

AbstractAustralian housing markets experienced widespread and, in some cases, extraordinary growth in prices between 2020 and 2023. Using recently developed methodology that accounts for fundamental economic drivers, we assess the existence and degree of speculative behaviour, as well as the timing of exuberance and downturns in these markets. Our findings indicate that speculative behaviour was indeed present in six of the eight capital cities at some time over the period studied. The sequence of events in this nation‐wide housing bubble began in the Brisbane market and concluded in Melbourne, Canberra, and Hobart following the interest rate rise implemented by the Reserve Bank of Australia in May 2022. As of March 2023, the housing markets in Sydney, Canberra and Hobart had broadly regained stability, while Melbourne's return to its normal state is more gradual. In addition, over‐corrections against fundamentals are evident in the housing markets of Brisbane, Adelaide, Darwin and Perth. For regular updates on the housing markets, readers may visit the authors' website at https://www.housing-fever.com.