Volume 3, Issue 1

Our paper uses simulation methods to examine the size and power of regime-switching tests for bubbles. We find that even with several hundred observations, the tests show sometimes considerable size distortion. This distortion makes the tests conservative; they understate the significance of the evidence of bubbles. Despite this, the tests display considerable power to detect bubbles even when using the conservative asymptotic critical values. We also find that the frequency with which bubbles collapse has an important influence on the tests' power. An application to monthly Canadian and American stock-price data provides mixed evidence of bubbles.

Economists have long known that time scale matters, in that the structure of decisions as to the relevant time horizon, degree of time aggregation, strength of relationship, and even the relevant variables differ by time scale. Unfortunately, until recently it was difficult to decompose economic time series into orthogonal time-scale components except for the short and long run, in which the former is dominated by noise. This paper uses wavelets to produce an orthogonal decomposition of some economic variables by time scale over six different time scales. The relationship of interest is the permanent income hypothesis. We confirm that time-scale decomposition is very important for analyzing economic relationships and that a number of anomalies previously noted in the literature are explained by these means. The analysis indicates the importance of recognizing variations in phase between variables when investigating the economic relationships.

The aim of this paper is to assess whether the data-generation process of the GDP can be interpreted by means of a nonlinear model instead of a linear one. We model the first differences of logarithmic real GDP data with constant parameters for those European countries (France, Germany, Italy, U.K., Denmark, Sweden, and Norway) which have long-term time series. Since the linear autoregressive model is rejected, an alternative nonlinear model has been specified: it turns out that the annual European GDPs can adequately be described by means of a nonlinear model with constant parameters.