This paper examines a poignant but essentially generic problem that plagues the world of financial analysis -the extent to which visual or analytical interpretation of relationships between accumulating (and therefore auto-correlated or serially dependent) series -are demonstrably fallacious by means of standard statistical techniques that assume stationarity. The problem, despite being age-old, continues to be ignored by an appreciable proportion of tertiary educated financial professionals the world over, and is imputed to contribute, in no small part, to broad market inefficiency. The problem persists from high-frequency pairstrading strategies in hedge funds through to top-down macro-economic inferences by institutional strategists. We examine the mechanism for the error in accessible non-mathematical prose, and demonstrate by way of several common examples how easily well-used inferences fall foul of the requisite statistical rigour and correct interpretation. We further note that there is a well developed, although less frequently utilised, suite of econometric tools, termed cointegration, that considers relationships between two or more non-stationary price series. Cointegration techniques are cast at the unit of the non-stationary price series, rather than the unit of the stationary differences.

Contemporary actuarial and accounting practices (APN 110 in the South African context) require the use of market-consistent models for the valuation of embedded investment derivatives. These models have to be calibrated with accurate and up-to-date market data. Arguably, the most important variable in the valuation of embedded equity derivatives is implied volatility. However, accurate long-term volatility estimation is difficult because of a general lack of tradable, liquid medium-and long-term derivative instruments, be they exchange-traded or over the counter. In South Africa, given the relatively short-term nature of the local derivatives market, this is of particular concern. This paper attempts to address this concern by: -providing a comprehensive, critical evaluation of the long-term volatility models most commonly used in practice, encompassing simple historical volatility estimation and econometric, deterministic and stochastic volatility models; and -introducing several fairly recent nonparametric alternative methods for estimating long-term volatility, namely break-even volatility and canonical option valuation.The authors apply these various models and methodologies to South African market data, thus providing practical, long-term volatility estimates under each modelling framework whilst accounting for real-world difficulties and constraints. In so doing, they identify those models and methodologies they consider to be most suited to long-term volatility estimation and propose best estimation practices within each identified area. Thus, while application is restricted to the South African market, the general discussion, as well as the suggestion of best practice, in each of the evaluated modelling areas remains relevant for all long-term volatility estimation.