I have created this homepage to keep track of our progress for the Fall 2023 Directed Reading Program (DRP) run
by the Berkeley math department. Below you will find summaries of our weekly readings. If you are interested in joining or being part
of a future directed reading program feel free to reach out for me.
This semester we are covering Time Series Analysis by State Space Methods by Durbin and Koopman [DK].
- September 14,
Filtering and Smoothing in the Local Level Model, DK Chapter 2.1-2.6
- In this meeting we introduced the idea of time series analysis and the special case of the (gaussian) local level model. We discussed how the Kalman filter for
this model can be derived from basic properties of the conditional distributions of mulivariate normals, and how it has an alternate interpretation from a Bayesian perspective
and through minimum variance linear unbiased estimation. Lastly, we discussed the idea of state space smoothing in the local level model and again derived the relevant update rules.
- September 21,
Missing observations, Initilization, and Parameter Estimation in the Local Level Model, DK Chapter 2.7-2.12
- In this meeting we discussed how to adjust the updates of the Kalman filter to account for missing data in the time series, and how a special case of this allows us to use the
local level model to forecast future values of the time series. We also discussed how to replace the standard gaussian prior distribution of the first state alpha1 with
a diffusive prior in the case the initial state distibution is unknown. Lastly, we discussed how we could use MLE to estimate the variance parameters sigma_eta and sigma_epsilon
of the local level model in case they too are unknown.
- September 28,
The General Linear Model, DK Chapter 3.1-3.6
- In this meeting we discussed the general linear (gaussian) model, a more general framework for time series analysis. This framework encapsulates
the local level model we have studied previously as well as other more advanced models like the ARMA/ARIMA models, exponential smoothing models, or
models with seasonal and/or trend components.