Course 4: Time Series and Sequential Decisions

Time Series and Sequential Decisions covers multivariate econometrics, continuous time stochatic processes, and optimal sequential decisions making.

In particular, Time Series and Sequential Decisions covers the following topics:

Multivariate econometrics, with focus on the most relevant discrete time processes: random walk, vector autoregression, linear state space models, markov chains, GARCH
Continuous time processes: Brownian motion, Poisson, Levy, Ornstein-Uhlenbeck, stochastic volatility
Markov decision processes with partially observable states

After the course you will obtain a Statement of Completion. Furthermore, you can choose to complete an optional code-based project that will count as one of the two Practical Projects towards the ARPM Certification.

Syllabus

The course covers in depth the Time Series and Sequential Decisions topics in the Lab.

Stochastic processes

• Main definitions

• Stationarity

• Prediction

Random walk

• Random walk

• Lévy processes

Autoregressive processes

• Introduction

• Autoregression of order one

• Vector autoregression of order one

• Ornstein-Uhlenbeck process

• Multivariate Ornstein-Uhlenbeck

Advanced mean-covariance models

• ARMA processes

• Linear state-space models

• Harmonic processes

• Integrated processes

Covariance stationary theory

• Introduction

• Spectral analysis

• Filtering

• Wold decomposition

• Wiener-Kolmogorov forecasting

Probabilistic models

• Markov processes

• Markov chains

• State-space processes

• GARCH

• Stochastic volatility

• Probabilistic forecasting

• Markov processes forecasting

Sequential decisions theory

• Markov decision processes

• Linear-quadratic Gaussian control

• Relevant special cases