Narrow Results

In this paper, I examine the ability of equity market illiquidity to predict Australian macroeconomic variables, between 1976 and 2010. In contrast to existing, U.S.-based, studies, I find that stock market illiquidity does not, on average, have much predictive power over economic growth. Consistent with the weak in-sample predictive power, economic growth forecasts from models that exclude stock illiquidity from the set of explanatory financial variables are statistically no worse than forecasts from models that include illiquidity. However, I find strong evidence that the predictive power of equity market illiquidity is state-contingent, with much higher predictability in states associated with economic and financial stress. The difference between the single-state and regime-switching models' results reflects the fact that, as the nonstressed states have been much more prevalent, parameter estimates from a single-state model averages over both stressed and non-stressed states thus lowering the statistical and economic significance of the estimates.

The second-order autoregressive AR(2) model is used to analyze rotational data for seismic events captured by a large ring laser gyroscope. Both the Sagnac frequency and linewidth estimates obtained from this model sense the rotational components of seismic waves. An event of magnitude M_L = 6.5 at a distance of D = 5.4° from a large ring laser gyroscope operating at its quantum limit is used to compare the AR(2) model with the previous analytical phase angle method of analysis. The frequency, linewidth and analytic phase angle data each satisfactorily estimate the rotation magnitude. The direct detection of rotational motion in the P wave coda is observed, demonstrating the conversion to transverse S wave polarizations by the local geology.

A wavelet-based forecasting method for time series is introduced. It is based on a multiple resolution decomposition of the signal, using the redundant "à trous" wavelet transform which has the advantage of being shift-invariant.

The result is a decomposition of the signal into a range of frequency scales. The prediction is based on a small number of coefficients on each of these scales. In its simplest form it is a linear prediction based on a wavelet transform of the signal. This method uses sparse modelling, but can be based on coefficients that are summaries or characteristics of large parts of the signal. The lower level of the decomposition can capture the long-range dependencies with only a few coefficients, while the higher levels capture the usual short-term dependencies.

We show the convergence of the method towards the optimal prediction in the autoregressive case. The method works well, as shown in simulation studies, and studies involving financial data.

Suppose we observe a time series that alternates between different autoregressive processes. We give conditions under which it has a stationary version, derive a characterization of efficient estimators for differentiable functionals of the model, and use it to construct efficient estimators for the autoregression parameters and the innovation distributions. We also study the cases of equal autoregression parameters and of equal innovation densities.