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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
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Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
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Statistical Inference for Periodic Self-Exciting Threshold Integer-Valued Autoregressive Processes.

Congmin Liu1, Jianhua Cheng1, Dehui Wang2

  • 1School of Mathematics, Jilin University, 2699 Qianjin Street, Changchun 130012, China.

Entropy (Basel, Switzerland)
|July 2, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces periodic self-exciting threshold integer-valued autoregressive processes with finite second moments. Quasi-likelihood methods demonstrate superior performance for parameter estimation and forecasting in real-world count data applications.

Keywords:
integer-valued threshold modelsparameter estimationperiodic autoregression

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Area of Science:

  • Time Series Analysis
  • Statistical Modeling
  • Econometrics

Background:

  • Integer-valued time series models are crucial for count data analysis.
  • Existing models often require strong assumptions on innovation distributions.
  • Periodic autoregressive models capture seasonality in data.

Purpose of the Study:

  • To investigate periodic self-exciting threshold integer-valued autoregressive (SETIAR) processes under weaker conditions.
  • To develop and evaluate quasi-likelihood inference methods for parameter estimation.
  • To apply the model to real-world count data for forecasting.

Main Methods:

  • Development of SETIAR models with finite second moments.
  • Quasi-likelihood inference for parameter estimation.
  • Asymptotic analysis of estimators.
  • Comparison with least squares and maximum likelihood methods.
  • Application to monthly disability benefits claimant data.

Main Results:

  • The statistical properties of the proposed SETIAR model are established.
  • Quasi-likelihood estimators exhibit desirable asymptotic behavior.
  • Simulation studies indicate quasi-likelihood methods outperform least squares and maximum likelihood for realistic sample sizes.
  • The model is effectively applied to analyze and forecast disability benefits data.

Conclusions:

  • The developed quasi-likelihood approach provides a robust method for analyzing periodic count time series.
  • The SETIAR model with weaker conditions offers a flexible alternative for count data modeling.
  • The findings have implications for statistical modeling in fields with seasonal count data.