The idea of fractional differencing is introduced in terms of the infinite filter that corresponds to the expansion of (1 -B)d. When the filter is applied to white noise, a class of time series is generated with distinctive properties, particularly in the very low frequencies and provides potentially useful long-memory forecasting properties. Such models are shown to possibly arise from aggregation of independent components. Generation and estimation of these models are considered and applications on generated and real data presented.

This paper aims to explain changes in real house prices in Australia from 1970 to 2003. We develop and estimate a long‐run equilibrium model that shows the real long‐run economic determinants of house prices and a short‐run asymmetric error correction model to represent house price changes in the short run. We find that, in the long run, real house prices are determined significantly and positively by real disposable income and the consumer price index. They are also determined significantly and negatively by the unemployment rate, real mortgage rates, equity prices and the housing stock. Employing our short‐run asymmetric error correction model, we find that there are significant lags in adjustment to equilibrium. When real house prices are rising at more than 2 per cent per annum, the housing market adjusts to equilibrium in approximately four quarters. When real house prices are static or falling, the adjustment process takes six quarters.

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