Volume 2, Issue 3

Linear asset-pricing relations, with macroeconomic factors as state variables, have found wide usein empirical finance. Applications of such relations range from academic studies of market efficiency andmarket anomalies to practical uses such as risk management and estimation of the cost of capital. Theseapplications make two key assumptions: that the relationship is exclusively linear, and that the macroeconomicfactors are exogenous to returns. For the set of macrofactors commonly used in these applications, bothassumptions run counter to economic intuition. We set out to demonstrate that they are also counter toempirical evidence.We carry out this task using tests for linear and nonlinear Granger causality. We find linear and nonlinearfeedback between stock returns and commonly used macroeconomic pricing factors. We also find linear andnonlinear feedback between residuals from linear pricing relations and returns. In addition, there is littleevidence to suggest that neglected autoregressive or autoregressive conditionally heteroskedastic dynamics areresponsible for these findings, implying that the underlying dynamics are complicated. Thus, linearasset-pricing relations omit interesting and potentially useful aspects of the relationship between stock returnsand the macroeconomy.

Econometric estimation using simulation techniques, such as the efficient method of moments, may be time consuming. The use of ordinary matrix-programming languages such as GAUSS, MATLAB, Ox, or S-PLUS will often cause extra delays. For the efficient method of moments implemented to estimate stochastic volatility models, this will surely be the case; therefore, the author made a C/C++ library containing the bulk of the procedures needed in the implemention of the efficient method of moments technique for a broad range of univariate stochastic volatility models. As a side effect of the efficient method of moments, EGARCH models with a variety of non-normal distributions can be estimated with this package. Implementations have been made for the Intel Pentium platform linked under Windows and for the IBM RS/6000 platform under AIX. The library is dynamically linked to Ox under Windows and statically linked under AIX. The speed improvements are considerable compared with pure Ox code. This paper serves as a manual for this library. It describes the efficient method of moments for this specific case of stochastic volatility models, and it describes the program. Some examples are given from other work of the author. Technicalities are given in the appendices.