The ldhmm package provides the core class and functions to calculate Hidden Markov Model (HMM) using lambda distribution framework. The main goal is to provide a theoretically solid foundation to explore the return time-series in the financial market, where the normal distribution is not adequate due to the leptokurtic nature of the data. Major features in the S&P 500 index, such as regime identification, volatility clustering, and anti-correlation between return and volatility, can be extracted from HMM cleanly. Univariate symmetric lambda distribution is essentially a location-scale family of power-exponential distribution. Such distribution is suitable for describing highly leptokurtic time series obtained from the financial market.
The main change compared to a normal-distribution based HMM is to add the third paramter
lambda to describe the kurtosis level of the distribution. When
lambda is one, the model
converges back to a normal-distribution based HMM (e.g. using depmixS4 package).
The ability to optimize kurtosis brings the model output to be more consistent with the data.
In particular, for daily data, the level of kurtosis is quite high. This puts
the normal distribution in great disadvantage. This problem is solved by using the
Stephen H-T. Lihn
Walter Zucchini, Iain L. MacDonald, Roland Langrock (2016). "Hidden Markov Models for Time Series, An Introduction Using R." Second Edition. CRC Press.
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