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Parameter Update Schemes for Hidden Markov Models applied to Financial Returns

Forsberg, Sigfrid LU (2022) In Master's Theses in Mathematical Sciences MASM02 20221
Mathematical Statistics
Abstract
This thesis was dedicated to investigating the use of different parameter update schemes for Hidden Markov models with time-varying parameters, with an emphasis on developing alternatives to the quasi-Newton step. The focus was on applications to financial returns, using data from the S\&P-500 and the Nikkei index, and for comparison, a trial using synthetic data was also performed. Different properties of the parameter update schemes were explored, with Predictor-Corrector and Trust-Region based methods showing promise in comparison to the quasi-Newton methods previously tried. The Trust-Region method proved to be a more stable alternative, whereas the Predictor-Corrector method showed a significant smoothing of parameter adaptation which... (More)
This thesis was dedicated to investigating the use of different parameter update schemes for Hidden Markov models with time-varying parameters, with an emphasis on developing alternatives to the quasi-Newton step. The focus was on applications to financial returns, using data from the S\&P-500 and the Nikkei index, and for comparison, a trial using synthetic data was also performed. Different properties of the parameter update schemes were explored, with Predictor-Corrector and Trust-Region based methods showing promise in comparison to the quasi-Newton methods previously tried. The Trust-Region method proved to be a more stable alternative, whereas the Predictor-Corrector method showed a significant smoothing of parameter adaptation which was not replicable by using the quasi-Newton method. Additionally, manipulating the norm of the Trust-Region method proved to be a versatile tool for e.g. calibrating the persistence of the hidden states without interfering with other parameter updates. (Less)
Popular Abstract
The state of the market changes constantly. Interest rates go up and down,
volatility increases and decreases and many other factors change over time, all
impacting market behavior. For this reason, it is not surprising that models
that capture the way the market behaves in one time period may fall flat when
applied on another.
In order to counteract this decrease in model performance over time, this thesis
explores different methods of updating the model adaptively as new information
becomes available. The model used is a 2 state Hidden Markov model, which
lets the market switch between 2 different states as time progresses. This means
that the model can differentiate between e.g. periods of high and low volatility,
and is able... (More)
The state of the market changes constantly. Interest rates go up and down,
volatility increases and decreases and many other factors change over time, all
impacting market behavior. For this reason, it is not surprising that models
that capture the way the market behaves in one time period may fall flat when
applied on another.
In order to counteract this decrease in model performance over time, this thesis
explores different methods of updating the model adaptively as new information
becomes available. The model used is a 2 state Hidden Markov model, which
lets the market switch between 2 different states as time progresses. This means
that the model can differentiate between e.g. periods of high and low volatility,
and is able to categorize new information as belonging to one of these 2 states.
Using different methods of updating the parameters of this Hidden Markov
model, we were able to produce methods which are far more robust than previous attempts. Additionally, we were able to find versatile methods for fine tuning the model based on Trust-Region methods for optimization and PredictorCorrector methods from solvers of ordinary differential equations.
All methods were applied to both synthetic and real data in the form of the
S&P-500 and Nikkei indices. By using such a wide range of data, the model
performance can be observed on both gradual and abrupt changes in the data.
Additionally, we observe how the model performs when faced with real life
historical events such as the global and sudden crash of 1987 called ”Black
Monday”, when the S%P-500 fell by over 20% in a single day. The results were
highly interesting, with some methods reacting strongly and suddenly to the
events while others experienced a more gradual reaction. (Less)
Please use this url to cite or link to this publication:
author
Forsberg, Sigfrid LU
supervisor
organization
course
MASM02 20221
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Markov Chain, Finance, Hidden Markov Model, Generalized Autoregressive Score Model, S&P-500, Nikkei, Adaptive Model, Volatility, Regime-switching Model, Line-Search Algorithm, Predictor-Corrector, Quasi-Newton
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMS-3115-2022
ISSN
1404-6342
other publication id
2022:E63
language
English
id
9098341
date added to LUP
2022-08-29 15:25:33
date last changed
2022-08-30 16:02:25
@misc{9098341,
  abstract     = {{This thesis was dedicated to investigating the use of different parameter update schemes for Hidden Markov models with time-varying parameters, with an emphasis on developing alternatives to the quasi-Newton step. The focus was on applications to financial returns, using data from the S\&P-500 and the Nikkei index, and for comparison, a trial using synthetic data was also performed. Different properties of the parameter update schemes were explored, with Predictor-Corrector and Trust-Region based methods showing promise in comparison to the quasi-Newton methods previously tried. The Trust-Region method proved to be a more stable alternative, whereas the Predictor-Corrector method showed a significant smoothing of parameter adaptation which was not replicable by using the quasi-Newton method. Additionally, manipulating the norm of the Trust-Region method proved to be a versatile tool for e.g. calibrating the persistence of the hidden states without interfering with other parameter updates.}},
  author       = {{Forsberg, Sigfrid}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Parameter Update Schemes for Hidden Markov Models applied to Financial Returns}},
  year         = {{2022}},
}