Nestálosti a strukturální změny v stochastických modelech
| Název práce v češtině: | Nestálosti a strukturální změny v stochastických modelech |
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| Název v anglickém jazyce: | Instabilities and structural changes in stochastic models |
| Klíčová slova: | bod změny|strukturální změna|stochastická nestabilita|testování hypotézy|odhadování parametru|technika resamplingu |
| Klíčová slova anglicky: | change point|structural change|stochastic instability|hypothesis testing|parameter estimation|resampling technique |
| Akademický rok vypsání: | 2024/2025 |
| Typ práce: | disertační práce |
| Jazyk práce: | |
| Ústav: | Katedra pravděpodobnosti a matematické statistiky (32-KPMS) |
| Vedoucí / školitel: | doc. RNDr. Michal Pešta, Ph.D. |
| Řešitel: |
| Zásady pro vypracování |
| To know whether a change has happened is a task that not only interesting, but also desirable for many scientific fields, e.g., in econometrics, biology, or climatology. We deal with sequences of observations that are naturally ordered in time and assume various underlying stochastic models. These models are predominantly parametric and some of the parameters are possibly subject to change at some unknown time point. There can be at most one change point or even more than one change points present. The main goal is to detect whether such an unknown change has occurred or not. Furthermore, a secondary aim is to estimate the change point.
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| Seznam odborné literatury |
| [1] Bai J (2010) Common Breaks in Means and Variances for Panel Data. Journal of Econometrics 157:78–92
[2] Baltagi BH, Feng Q, Kao C (2016) Estimation of heterogeneous panels with structural breaks. Journal of Econometrics 191:176–195 [3] Cho H, Fryzlewicz P (2015) Multiple change-point detection for high-dimensional time series via Sparsified Binary Segmentation. Journal of the Royal Statistical Society Series B 77:475-507 [4] Csörgo ̋ M, Horváth L (1997) Limit theorems in change-point analysis. Wiley, Chichester [5] Fryzlewicz P (2014) Wild Binary Segmentation for multiple change-point detection. Annals of Statistics 42:2243-2281 [6] Horváth L, Hušková, M (2012) Change-point Detection in Panel Data. Journal of Time Series Analysis 33:631–648 [7] Horváth L, Horváth Z, Hušková M (2008) Ratio tests for change point detection. In: Balakrishnan N, Peña EA, Silvapulle MJ (eds) Beyond parametrics in interdisciplinary research: Festschrift in Honor of Professor Pranab K. Sen, IMS Collections, Beachwood, Ohio, vol 1, pp 293–304 [8] Hušková M, Kirch C, Prášková Z, Steinebach J (2008) On the detection of changes in autoregressive time series, II. Resampling procedures. Journal of Statistical Planning and Inference 138:1697–1721 [9] Peštová B, Pešta M (2015) Testing structural changes in panel data with small fixed panel size and bootstrap. Metrika 78(6):665–689 [10] Peštová B, Pešta M (2018) Abrupt change in mean using block bootstrap and avoiding variance estimation. Computational Statistics 33(1):413-441 [11] Peštová B, Pešta M (2017) Change point estimation in panel data without boundary issue. Risks 5(1):7 |