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We introduce a new statistical model for analyzing financial time series data, improving parameter estimation accuracy using a novel saddlepoint method. This enhanced approach demonstrates superior performance in real-world exchange rate analysis.

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Area of Science:

  • Econometrics
  • Time Series Analysis
  • Statistical Modeling

Background:

  • Integer-valued autoregressive conditional heteroscedasticity (INARCH) models are crucial for analyzing count time series data.
  • Existing INARCH models face challenges in parameter estimation, particularly with complex data structures.
  • Financial market data, such as exchange rates, often exhibit discrete, time-dependent characteristics.

Purpose of the Study:

  • To propose a modified multiplicative thinning-based INARCH model for enhanced count time series analysis.
  • To introduce and evaluate the saddlepoint maximum likelihood estimation (SPMLE) method for parameter estimation in the modified model.
  • To demonstrate the practical utility and superiority of the proposed model and estimation technique.

Main Methods:

  • Development of a modified multiplicative thinning INARCH model.
  • Application of the saddlepoint maximum likelihood estimation (SPMLE) for parameter estimation.
  • Conducting simulation studies to assess model and estimator performance.
  • Analysis of real-world financial data (euro to British pound exchange rate).

Main Results:

  • The simulation study indicated that the SPMLE method offers better performance compared to existing estimation techniques.
  • The modified INARCH model, coupled with SPMLE, effectively captured the dynamics of the tick count data.
  • The proposed approach demonstrated superiority in analyzing the euro to British pound exchange rate data.

Conclusions:

  • The modified multiplicative thinning-based INARCH model provides a robust framework for count time series.
  • The SPMLE method is an efficient and accurate technique for parameter estimation in this context.
  • The proposed methodology offers significant advantages for analyzing financial market microstructure data.