# Markov-Switching Multifractal and FX Rates

Is there a better model than Markov-Switching Multifractal (MSM) for detecting regime shifts in FX rates across multiple time horizons? I am especially interested in the different aspects of the question that have been covered in Multifractal Volatility: Theory, Forecasting, and Pricing:

### Multifrequency Equilibrium

Ability to detect regime switches across multiple time horizons, from seconds to years, and to "imitate one of the defining features of long memory, a hyperbolic decline of the autocovariogram." The combination of long-memory behavior with sudden volatility movements is one of the qualities that make MSM very attractive.

### Volatility persistence

Ability to deal with volatility persistence components that have different degrees of persistence.

### Persistence skewness

“We observe that investors may learn quickly about volatility increases, because a single extreme fluctuation is highly improbable with low volatility. By contrast, learning about reduced risk takes time because observations near the mean are a relatively likely outcome regardless of the true state. Thus bad news about volatility is incorporated into prices quickly, while good news is assimilated slowly.” The MSM model takes this skewness into account.

### Information quality

“Skewness increases and kurtosis falls as information quality deteriorates.”

### Daily seasonality

High-frequency data for FX rates show strong patterns of daily seasonality.

### Parsimony

Ability to model the process with very few variables. For example, MSM can model $2^k$ states where $k$ is the number of time horizons with just 4 parameters. This is a direct result of the observation that volatility shocks have the same magnitude at all time scales.

### Closed-form parameters estimation

Ability to estimate parameters by maximixing the closed-form likelihood of the return series. Alternatively, return moments can be used to quickly calibrate or estimate the model.

### Discrete and continuous-time versions

Ability to easily switch between discrete and continuous-time versions of the model.

### Good performance

Ability to provide good forecasts of volatility and generate reliable estimates of the value-at-risk in a position or portfolio of assets.

Multifractal Volatility was written in 2008. Have there been more recent developments that should be taken into account? Do significantly-different models provide much better results along the lines outlined above, especially when dealing with real-time data?