Parameter identification in time series models
Vimalajeewa, Horahenage Dixon (2015)
Diplomityö
Vimalajeewa, Horahenage Dixon
2015
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe201504222783
https://urn.fi/URN:NBN:fi-fe201504222783
Tiivistelmä
Time series analysis can be categorized into three different approaches: classical,
Box-Jenkins, and State space. Classical approach makes a basement for the analysis
and Box-Jenkins approach is an improvement of the classical approach and deals
with stationary time series. State space approach allows time variant factors and
covers up a broader area of time series analysis.
This thesis focuses on parameter identifiablity of different parameter estimation
methods such as LSQ, Yule-Walker, MLE which are used in the above time series
analysis approaches. Also the Kalman filter method and smoothing techniques are
integrated with the state space approach and MLE method to estimate parameters
allowing them to change over time.
Parameter estimation is carried out by repeating estimation and integrating with
MCMC and inspect how well different estimation methods can identify the optimal
model parameters. Identification is performed in probabilistic and general senses and
compare the results in order to study and represent identifiability more informative
way.
Box-Jenkins, and State space. Classical approach makes a basement for the analysis
and Box-Jenkins approach is an improvement of the classical approach and deals
with stationary time series. State space approach allows time variant factors and
covers up a broader area of time series analysis.
This thesis focuses on parameter identifiablity of different parameter estimation
methods such as LSQ, Yule-Walker, MLE which are used in the above time series
analysis approaches. Also the Kalman filter method and smoothing techniques are
integrated with the state space approach and MLE method to estimate parameters
allowing them to change over time.
Parameter estimation is carried out by repeating estimation and integrating with
MCMC and inspect how well different estimation methods can identify the optimal
model parameters. Identification is performed in probabilistic and general senses and
compare the results in order to study and represent identifiability more informative
way.