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Estimation of the Physical Quantities

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...

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GARTFIMA process and its empirical spectral density based estimation.

Niharika Bhootna¹, Arun Kumar¹

¹Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, India.

Journal of Applied Statistics

|July 29, 2024

Summary

This summary is machine-generated.

This study introduces a new time series model, the Gegenbauer autoregressive tempered fractionally integrated moving average (GARTFIMA) process. GARTFIMA demonstrates superior performance in modeling real-world data compared to existing time series methods.

Keywords:

62M10 Fractional ARIMA processes Gegenbauer processes parameter estimation spectral density tempered fractional ARIMA processes

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Area of Science:

Time Series Analysis
Stochastic Processes
Econometrics

Background:

Fractionally integrated time series models are widely used in various fields.
Existing models may not capture complex temporal dependencies effectively.
The need for advanced models with enhanced flexibility is evident.

Purpose of the Study:

Introduce a novel Gegenbauer autoregressive tempered fractionally integrated moving average (GARTFIMA) process.
Analyze the theoretical properties, including spectral density and autocovariance function.
Evaluate parameter estimation techniques and model performance.

Main Methods:

Developed the GARTFIMA process and derived its spectral density and autocovariance functions.
Employed nonlinear least squares and Whittle likelihood estimation for parameter estimation.
Assessed model performance using simulated data.

Main Results:

The spectral density and autocovariance functions for the GARTFIMA process were derived.
Parameter estimation techniques were successfully applied to simulated data.
The GARTFIMA process showed improved modeling capabilities for real-world datasets.

Conclusions:

The proposed GARTFIMA process offers a flexible and effective tool for time series modeling.
The developed estimation methods are suitable for practical application.
GARTFIMA outperforms traditional models in capturing real-world data dynamics.