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Open Theses

On this page you find open theses to be supervised by the Chair of Economic and Social Statistics.

The modelling of real-valued (univariate or multivariate) time series data with autoregressive (AR) models is a classical approach and has been used for decades. However, the use of autoregressive models is still favoured in practice, because AR models are flexible, they allow for a nice interpretation and the AR coefficients are easy and explicitly estimable. In contrast, when dealing with serially dependent integer-valued data (i.e. count data), an autoregressive modelling is not straightforward as classical AR models do not respect the integer-valued range. To remedy this, for (non-negative) integer-valued data, i.e. count data, so called integer-valued AR (INAR) models are often used, which are still of autoregressive nature, but respect the integer-valued range by incorporating a so-called thinning operation. These models are still easy to estimate and nicely interpretable, but the parameter range is more restrictive in comparison to the AR model. Whereas the literature that investigates both models separately is huge, the literature lacks a unified approach to model jointly real-valued and integer-valued time series in an autoregressive way.

In this thesis, the goal is to investigate how real-valued and integer-valued time series can be jointly modelled using an autoregressive way such that

  1. The corresponding ranges, i.e. the real line and the integers, respectively, are respected by the modelling approach.
  2. The famous Yule-Walker equations hold, which leads to simple and explicit estimators for the autoregressive coefficients.
  3. The range of the AR model parameters is not restricted and ideally coincides with that of a classical vector autoregressive model.

Literature:

  • Brockwell, P.J. and Davis, R.A. (1991). Time Series: Theory and Methods. Springer, New York.
  • Jentsch, C. und C. H. Weiß (2019). Bootstrapping INAR models. Bernoulli 25(3), 2359-2408.
  • Kim, H.Y. and Park, Y. (2008). A non-stationary integer-valued autoregressive model. Statistical Papers 49(3):485-502.
  • Weiß, C.H. (2018). An Introduction to Discrete-Valued Time Series, 1st edn. Wiley

If you are interested in writing this thesis, please contact Prof. Dr. Carsten Jentsch.

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Location & approach

The campus of TU Dort­mund Uni­ver­sity is located close to interstate junction Dort­mund West, where the Sauerlandlinie A45 (Frankfurt-Dort­mund) crosses the Ruhrschnellweg B1 / A40. The best interstate exit to take from A45 is “Dort­mund-Eichlinghofen” (closer to South Cam­pus), and from B1 / A40 “Dort­mund-Dorstfeld” (closer to North Cam­pus). Signs for the uni­ver­si­ty are located at both exits. Also, there is a new exit before you pass over the B1-bridge leading into Dort­mund.

For travelling to the Department of Statistics, convenient parking places can be found at Vogelpothsweg (Gates 21 / 24) or alternatively at the Otto-Hahn-Straße (Gates 28 / 30 / 35).

TU Dort­mund Uni­ver­sity has its own train station (“Dort­mund Uni­ver­si­tät”). From there, suburban trains (S-Bahn) leave for Dort­mund main station (“Dort­mund Hauptbahnhof”) and Düsseldorf main station via the “Düsseldorf Airport Train Station” (take S-Bahn number 1, which leaves every 15 or 30 minutes). The uni­ver­si­ty is easily reached from Bo­chum, Essen, Mülheim an der Ruhr and Duis­burg.

You can also take the bus or subway train from Dort­mund city to the uni­ver­si­ty: From Dort­mund main station, you can take any train bound for the Station “Stadtgarten”, usually lines U41, U45, U 47 and U49. At “Stadtgarten” you switch trains and get on line U42 towards “Hombruch”. Look out for the Station “An der Palmweide”. From the bus stop just across the road, busses bound for TU Dort­mund Uni­ver­sity leave every ten minutes (445, 447 and 462). Another option is to take the subway routes U41, U45, U47 and U49 from Dort­mund main station to the stop “Dort­mund Kampstraße”. From there, take U43 or U44 to the stop “Dort­mund Wittener Straße”. Switch to bus line 447 and get off at “Dort­mund Uni­ver­si­tät S”.

The H-Bahn is one of the hallmarks of TU Dort­mund Uni­ver­sity. There are two stations on North Cam­pus. One (“Dort­mund Uni­ver­si­tät S”) is directly located at the suburban train stop, which connects the uni­ver­si­ty directly with the city of Dort­mund and the rest of the Ruhr Area. Also from this station, there are connections to the “Technologiepark” and (via South Cam­pus) Eichlinghofen. The other station is located at the dining hall at North Cam­pus and offers a direct connection to South Cam­pus every five minutes.

The AirportExpress is a fast and convenient means of transport from Dort­mund Airport (DTM) to Dort­mund Central Station, taking you there in little more than 20 minutes. From Dort­mund Central Station, you can continue to the uni­ver­si­ty campus by interurban railway (S-Bahn). A larger range of in­ter­na­tio­nal flight connections is offered at Düsseldorf Airport (DUS), which is about 60 kilometres away and can be directly reached by S-Bahn from the uni­ver­si­ty station.

Interactive map

The facilities of TU Dortmund University are spread over two campuses, the larger Campus North and the smaller Campus South. Additionally, some areas of the university are located in the adjacent "Technologiepark".

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