Abstract
The exponentially weighted moving average (EWMA) model is a particular modelling scheme used by RiskMetrics for predicting the current level of volatility of financial time series. It is designed to track changes in volatility by assigning exponentially decreasing weights to the observed historical squared financial returns.
The applied weighting factors are conventionally prescribed by experts (users), or they are estimated employing standard statistical inference procedures, e.g. the maximum likelihood method. However, it is also possible to consider recursive (sequential or on-line) estimation techniques, which represent numerically effective alternatives to the already established approaches.
The aim of this paper is to introduce and study a one-stage self-weighted on-line estimation algorithm appropriate for calibrating the EWMA model. Firstly, its derivation and theoretical properties are briefly outlined and summarized.
Secondly, its practical performance is investigated by various Monte Carlo simulations. Lastly, the suggested calibration scheme is examined in the context of empirical financial data.
In particular, volatility of the central index of Prague Stock Exchange (PX index) is monitored using the suggested estimation technique to reflect (eventual) structural changes of the EWMA parameter.