Given more than one locally stationary (LS) time series, this article describes a method to discover time-varying linear combinations of the LS series that are stationary. Systems for which this can occur are called costationary, and the associated time-varying linear combinations are called...

We outline a range of criteria for evaluating model selection approaches that have been used in the literature. Focusing on three key criteria, we evaluate automatically selecting the relevant variables in an econometric model from a large candidate set. General-to-specific selection is outlined...

Standard cointegration analysis yields spurious results when relevant I(1) variables are omitted from the model. As an alternative, an unobserved components approach is proposed where the error term is modelled as the sum of a transitory and a random walk component. The latter should capture...

Campbell and Shiller (1987) proposed a graphical technique for the present value model, which consists of plotting estimates of the spread and theoretical spread as calculated from the cointegrated vector autoregressive model without imposing the restrictions implied by the present value model....

In this paper, a new GARCH-M type model, denoted as GARCH-AR, is proposed. In particular, it is shown that it is possible to generate a volatility-return trade-off in a regression model simply by introducing dynamics in the standardized disturbance process. Importantly, the volatility in the...

In an important generalization of zero frequency autoregressive unit root tests, Hylleberg, Engle, Granger, and Yoo (1990) developed regression-based tests for unit roots at the seasonal frequencies in quarterly time series. We develop likelihood ratio tests for seasonal unit roots and show that...

Even though the trend components of economic time series were among the first to be distinguished, even today the trend remains relatively little understood. As Phillips (2005) notes, no one understands trends, but everyone sees them in the data. Economists and econometricians can give plenty of...

Whilst the existence of a unit root implies that current shocks have permanent effects, in the long run, the simultaneous presence of a deterministic trend obliterates that consequence. As such, the long-run level of macroeconomic series depends upon the existence of a deterministic trend. This...

This paper investigates whether using natural logarithms (logs) of price indices for forecasting inflation rates is preferable to employing the original series. Univariate forecasts for annual inflation rates for a number of European countries and the USA based on monthly seasonal consumer price...