Four Bachelor's Degree Project Presentations in Mathematics: Rebeka Bajo, Subash K C, Sylvia Njoki Nuguna and Pimanchok Wennberg

09:15 Rebeka Bajo

Title: Modelling and Forecasting Unemployment with Nonlinear Time Series Models

Abstract: Accurate forecasting of unemployment rates is important for economic policy, labour market planning, and macroeconomic analysis. However, unemployment time series often show characteristics such as persistence, asymmetry, structural changes, and regime-dependent behaviour that may not be adequately described by traditional linear models. The aim of this thesis is to investigate whether nonlinear time series models can improve unemployment forecasting performance relative to linear approaches.

Monthly unemployment data from the United States, the United Kingdom, and Sweden were analysed. Following seasonal adjustment and preliminary data exploration, stationarity and nonlinearity tests were conducted to assess the suitability of nonlinear modelling techniques. Forecasting performance was then evaluated using Seasonal Autoregressive Integrated Moving Average (SARIMA), Self-Exciting Threshold Autoregressive (SETAR), Smooth Transition Autoregressive (STAR), and Markov Switching (MS) models. Forecasts were generated over three horizons: one-step-ahead, one year ahead, and a period corresponding to the final 10\% of each dataset.

The nonlinearity tests provided strong evidence of nonlinear dynamics in all three unemployment series, supporting the use of nonlinear modelling techniques. The forecasting results showed that nonlinear models can improve forecast accuracy, although their performance varied across countries and forecast horizons. SETAR models achieved the strongest overall performance for the longest forecast horizon, STAR models performed best for one-step-ahead forecasting, while Markov Switching models generally provided the most accurate one-year-ahead forecasts and produced strong results for the Swedish unemployment series. Nevertheless, the SARIMA benchmark remained competitive and often performed comparably to the nonlinear alternatives.

Overall, the results suggest that nonlinear models can improve forecasting performance. However, no single model consistently outperformed all others across countries and horizons. The findings therefore indicate that unemployment forecasting benefits from a flexible modelling strategy in which both linear and nonlinear models are considered and evaluated according to the characteristics of the data and the forecasting length.

Opponent: Subash K C

09:45 Subash K C

Title: Optimal stopping for sequential hiring with Brownian signals

Abstract: Sequential hiring under uncertainty involves a trade-off between the value of additional information and the cost of continued observation. This thesis studies a time extended variant of the classical secretary problem in which candidate quality is not observed directly, but is instead inferred from a Brownian signal. For a single candidate, the value function is characterised by a free-boundary problem with two optimal stopping thresholds: a lower threshold for rejection and an upper threshold for hiring. An explicit form of the value function is derived, and the optimality of the candidate solution is established through a verification argument. The analysis is then extended to finitely many sequential candidates, where rejection values are determined recursively by the value of continuing the search with the remaining candidates. The thesis further examines the case of infinitely many identical candidates, where the problem becomes stationary and can be interpreted as an optimal stopping problem for a diffusion reflected at the initial prior. Finally, the thesis considers the problem of optimally ordering candidates when they differ only in their initial prior probabilities. It is shown that, under identical model parameters, candidates should be interviewed in decreasing order of prior probability. Overall, the thesis combines Bayesian filtering, stochastic control, and optimal stopping techniques to analyse sequential hiribng decisions under uncertainty.

Opponent: Rebeka Bajo

10.25 Sylvia Njoki Nuguna

Title: Anomaly Detection in Financial Time Series. A Comparative Study of Intervention Analysis and Hidden Markov Models.

Abstract: This thesis looks into detecting anomalies in financial time series by comparing the results of the performance of two statistical models: Intervention Analysis (IA) and Hidden Markov Models (HMMs). This thesis compares how well the two models perform when applied to weekly log returns for the S&P 500 from 1995-2026 in terms of detecting and defining the abnormal behavior of the market. IA models an anomaly as a deviation from an ARIMA model while also incorporating identified market shocks. HMMs model the market as a multi-state system with different volatilities and analyze anomalies through the use of likelihood, residual-based, and regime transition diagnostics. The two models behave significantly differently. Both models are successful in detecting major market shocks, such as COVID-19, but do not define structural change and other non-crisis anomalies in the same way. This reveals that anomaly detection of the market is itself dependent on how you choose to model the time series, and two methods such as these may serve as potentially complementary models that will each capture different types of anomalies.

Opponent: Pimanchok Wennberg

10.55 Pimanchok Wennberg

Title: Evaluation of Software Automation with AI

Abstract: Software testing is an important stage in software development where the process is mainly manual, but it may be possible to automate parts of the process by generative artificial intelligence. This thesis evaluates the efficiency of AI implementation in software testing at Volvo Construction Equipment, using a linear regression model with random effects to analyze 3,715 observations from two software projects to investigate the relationship between participant-level factors and task completion time, to compare human and AI performance, and to estimate the potential cost saving associated with AI implementation. The results indicate that high stress levels in one project is associated with longer task completion time, while workload is a significant factor within the top 33rd percentile of task completion time. Analysis of the full dataset shows no statistically significant relationship between the participant-level factors and task completion time. The comparison between human and AI performance indicates a significant decrease in task completion time when using AI-based tools. Based on estimates from the regression model, integrating AI into the software testing workflow may contribute to potential cost savings. Although these findings suggest that generative AI improves efficiency in software testing, it is an assisting tool for the software testers since AI-generated outputs need to be supervised, validated, and debugged by human. Further research on testing quality, requirement coverage, and the time required for human review of AI-generated outputs in order to improve the estimation of efficiency.

Opponent: Sylvia Njoki Nuguna