Topics for master's theses

In structural time series models, the time series is modeled as a sum of different random components (trend, seasonality, cyclical component).  Structural time series models have been briefly reviewed in the course on time series analysis. In the master's thesis, in the theoretical part, it is planned to give a comprehensive overview of structural time series models. In the practical part of the work, the plan is to forecast various macroeconomic indicators with structural time series models and compare this forecasting method with other methods. The advantage of structural time series models in medium-term forecasting of macroeconomic indicators is pointed out in the literature.

Struktuursete aegridade mudelite korral modelleeritakse aegrida erinevate juhuslike komponentide (trend, sesoonsus, tsükliline komponent) summana.  Põgusalt on struktuurseid aegridade mudeleid vaadeldud aegridade analüüsi kursuses. Magistritöös teoreetilises osas on kavas anda põhjalik ülevaade struktuursetest aegridade mudelitest. Töö praktilises osas on kavas  erinevate makromajandusnäitajate prognoosimine struktuursete aegridade mudelitega ning prognooside võrdlus teiste prognoosimeetoditega saadud prognoosidega. Kirjanduses on välja toodud struktuursete aegridade mudelite eelis makromajandusnäitajate keskpika perioodi prognoosimisel.

In the case of an Asian option, the payout associated with the option depends on the average price of the underlying asset over the life of the option. Average price can be found as both geometric and arithmetic mean. In the master's thesis, it is planned to study the pricing  of the Asian option with both the Monte-Carlo method and the lattice method, and to compare the effectiveness of different methods during numerical experiments.

Aasia optsiooni korral sõltub optsiooniga seotud väljamakse alusvara keskmisest hinnast optsiooni eluea jooksul. Keskmist hinda võib leida nii geomeetrilise kui aritmeetilise keskmisena. Magistritöös on kavas uurida Aasia optsiooni hindamist nii Monte-Carlo meetodiga kui ka võremeetodiga ning numbriliste eksperimentide käigus võrrelda erinevate meetodite efektiivsust.

Multistate models are widely used stochastic models in many areas including (among many others) insurance and finance.
The core of these models is a finite state Markov chain where transitions are allowed in one direction, only. This means that when a transition from state A to state B is allowed (with some positive probability),
then going back from B to A is impossible. Sometimes such Markov chains are referred also as left-right Markov chains. Typically a state represent a situation/position/property/status of an individual
(customer/policyholder/patient). Then a multistate model describes the (random) evolution/dynamic of an individual. The individuals are typically  assumed to be independent and so the data consists of iid
realizations of a multistate model. Often the realizations are not observed until the terminal state, i.e. the data are censored. Moreover, often states are not exactly observed, so that the data are
sampled from a hidden Markov process.

In the theses, some fairly simple basic discrete time partially hidden multistate models are studied. MLE estimates and its (asymptotic) properties are derived and some fast iterative parameter estimation algorithms
are derived. Also some elementary Bayesian inference is possible.

Intraday energy prices offer 24 products for each day which are very short lived (up to 36h) and as the hour nears they become more and more liquid. From Jan, Baltic system will connect to Europe trading system which will expand the number of products to 96. Systematically understanding what is the correct hour price level and how much liquidity that hour will have is really important to make sure balancing costs for renewables is minimised. Ideally we would have different price levels with probabilistic estimates continuously until the product closes.

When desynchronizing from the RU system into the Central EU system local TSO's will have a bigger responsibility/challenge to keep the system frequency in required range. This means that TSO's have created multiple new markets/instruments in order to acquire different power and volumes from the flexible asset owners. Now this means that BESS (Battery Energy Storage System) operators need to solve a complex optimisation thorugh multiple markets, time periods and products while still maintaining the "battery state" under certain criteria (for example can't go negative). Markets are consecutive in their nature, meaning that decisions in previous market influence what kind of offers/positions you can have in the next markets as well as time periods (for example when Battery is full, you can't anymore buy energy in following hour).

Recent years have seen a big rise in Foundational ML models (very much talked about GPT models and LLM's) but there has been also a recent revolution in time-series with big players producing zero-shot (aka no training) time-series models. For energy markets this could provide highly valuable to forecast consumptions, renewable trends and generation from different countries without high volumes of historical data.