Standard Linear Tests Research Articles

Mean Reversion Properties in Real Effective Exchange Rates

In recent years, advances in the field of unit root tests helped to partially solve the first purchasing power parity puzzle. Non-linear mean-reversion tests with real exchange rates were able to reject the null of a unit root (indicating mean reversion) in significantly more cases than the standard linear tests. These papers suffer from two problems: small samples and sensitivity of numeraire currency. This study investigates the mean reversion property of real effective exchange rates, which are robust to the choice of numeraire. In a large sample of 96 countries, we show that mean reversion is present in approximately 60 % of all countries depending on the underlying timeseries model.

Long- and Short-Run Relationships between House and Stock Prices in South Africa: A Nonparametric Approach

This paper provides empirical evidence on the long- and short-run relationships between real house and stock prices of South Africa. Standard linear tests may not detect the existence of these relationships between time series especially in the presence of structural shifts or regime changes, which, in turn, may cause nonlinearities in the observed series. Thus, in this study, both linear and nonparametric cointegration and Granger causality tests were conducted. Results from the linear cointegration test showed no long-run relationship between house and stock prices. The linear Granger causality test produced no evidence of causality either. In contrast, the nonparametric cointegration test revealed a long-run one-to-one relationship between the two series, with the nonparametric Granger causality test indicating a bi-directional causality. Therefore, stability in the housing market drives stability in the equity market and vice versa.

‘Ripple’ Effects in South African House Prices

This paper analyses the ‘ripple’ effect of house prices in large-, medium- and small-sized houses of five major metropolitan areas of South Africa—namely, Cape Town, Durban Unicity, Greater Johannesburg, Port Elizabeth/Uitenhage and Pretoria—based on available quarterly data covering the period of 1966:Q1 to 2010:Q1. Following the extant literature, the issue is contextualised as a unit root problem, with one expecting the ratios of metropolitan house price to national house price to exhibit stationarity to an underlying trend value, if there is diffusion in house prices. Using Bayesian and non-linear unit root tests, besides the standard linear tests of stationarity with and without structural break, overwhelming support is found for the existence of robust ripple effects. Also factor analysis conducted suggested that ripple effects originate in Cape Town for the large housing segment and in Durban for the medium- and small-sized houses.

On the mean-reverting properties of target zone exchange rates: a cautionary note

We estimate a franc–mark target zone model and find a very limited ‘honeymoon effect’. Monte Carlo experiments calibrated with the estimates caution against the use of standard linear tests for non-mean reversion as indirect tests of the target zone model.

A higher‐order accurate Petrov–Galerkin finite‐element method for elliptic boundary‐value problems

AbstractWe formulate a higher‐order (superconvergent) Petrov–Galerkin method by determining, using a finite‐difference approximation, the optimal selection of quadratic and cubic modifications to the standard linear test function for bilinear elements. Application of this method to linear elliptic problems results in improved accuracy and higher rates of convergence for problems with constant coefficients and improved accuracy for problems with variable coefficients. Supporting numerical examples are given.

Limits of parallelism in explicit ODE methods

Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are easiest to implement. For these reasons there has been considerable research activity devoted to generating methods of this class which utilize independent function evaluations that can be performed in parallel. Each such group of concurrent function evaluations can be regarded as a stage of the method. However, it turns out that parallelism affords only limited opportunity for reducing the computing time with such methods. This is most evident for the simple linear homogeneous constant-coefficient test problem, whose solution is essentially a matter of approximating the exponential by an algebraic function. For a given number of stages and a given number of saved values, parallelism offers a somewhat enlarged set of algebraic functions from which to choose. However, there is absolutely no benefit in having the degree of parallelism (number of processors) exceed the number of saved values of the method. Thus, in particular, parallel one-step methods offer no speedup over serial one-step methods for the standard linear test problem. Although the implication of this result for general nonlinear problems is unclear, there are indications that dramatic speedups are not possible in general. Also given are some results relevant to the construction of methods.