FUZZY-INFERRED PCA AND HIERARCHICAL HMM PATTERN RECOGNITION FRAMEWORK FOR REGIME DETECTION AND INFLATION FORECASTING

Date

2025-7-14

Author

Koç, Oğuz

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

9104
views

0
downloads

Cite This

Precise inflation forecasting is critical for sound economic decision-making across various sectors, including policy development, budget allocation, and financial planning. Traditional theoretical models, while valuable, often rely on assumptions that may not consistently hold true across diverse economic environments. Given the multiple complex factors influencing inflation, a dynamic multinomial approach is necessary to capture the interactions of economic variables. Our methodology employs two novel dimension reduction techniques Fuzzy-Inferred Principal Component Analysis (FIPCA) and Fuzzy with Noise-Inferred PCA (FNIPCA). FIPCA clusters the time series into fuzzy subsets, allowing any point in the time series to be a member of multiple subsets, and then applies dimension reduction within these subsets. With this approach, we aim to increase variance explainability of PCA. An extension of this approach, FNIPCA incorporates an additional noise clustering component within the Fuzzy C-Means (FCM) framework, further improving the inference of jump points. These techniques are applied to macroeconomic time series related to inflation, including interest rates, the exchange rate of the dollar, and the fuel, electricity, and gas price index (FEG index). We anticipate that the resulting dimensionally reduced time series will more effectively retain the essential information. The obtained time series is then used as a coarse-scale variable in the Hierarchical Hidden Markov Model (HHMM), to capture long-term economic trends and inflation regimes. The state probabilities derived from the HHMM are employed to identify the regimes in which the Geometric Brownian Motion (GBM) paths will evolve at each step. The parameters of the GBM are estimated using the data subsets corresponding to the HHMM state decomposition. To further evaluate the effectiveness of the proposed approaches in enhancing forecasting reliability, these predicted regimes are also used as exogenous variables in Gated Recurrent Unit (GRU) and Bidirectional Long Short-Term Memory (BiLSTM) models. The study uses datasets from two countries representing different stages of economic development: Türkiye (emerging) and Austria (developed). The findings suggest that the proposed approaches offer notable improvements over traditional models GBM, GRU, and BiLSTM. Furthermore, FNIPCA demonstrates additional advantages over FIPCA, highlighting the benefit of incorporating noise clustering within the dimension reduction framework for enhanced predictive performance.

Subject Keywords

Fuzzy Inference, Clustering, Hierarchic Hidden Markov Model, Geometric Brownian Motion, Inflation, PCA, GRU, BiLSTM

URI

https://hdl.handle.net/11511/115494

Collections

Graduate School of Applied Mathematics, Thesis