Modelling high-frequency FX rate dynamics: A zero-delay multi-dimensional HMM-based approach

We develop a zero-delay hidden Markov model (HMM) to capture the evolution of multivariate foreign exchange (FX) rate data under a frequent trading environment. Recursive filters for the Markov chain and pertinent quantities are derived, and subsequently employed to obtain estimates for model parameters. The rationale of zero-delay HMM hinges on the idea that with fast trading, available information must be incorporated immediately in the evolution equations of the financial variables being modelled. Our proposed model is compared with the usual one-step delay HMM, GARCH and random walk models using likelihood-based criteria and error-type metrics. Parameter estimation both under the static and dynamic settings are carried out as well as in the models used as benchmarks in a comparative analysis. Implementation details are provided. We include a numerical illustration of the methodology applied to the currency data on UK sterling pounds and US dollars both against the Japanese yen. Our empirical results demonstrate greater fitting capacity and forecasting power of the zero-delay HMM over the comparators included in our analysis.