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SETAR models were introduced by Howell Tong in 1977 and more fully developed in the seminal paper (Tong and Lim, 1980). They can be thought of in terms of extension of autoregressive models, allowing for changes in the model parameters according to the value of weakly exogenous threshold variable z t, assumed to be past values of y, e.g. y t-d, where d is the delay parameter, triggering the ...
The Bayesian estimation of FAVAR models helps address the uncertainty in both the latent factors and model parameters, providing more robust inference. [11] Time-varying parameter FAVAR (TVP-FAVAR) further extends this framework by allowing the model parameters to evolve over time, capturing potential structural changes in the economy.
These models and extensions to include moving average spline models are described in "Univariate Time Series Modelling and Forecasting using TSMARS: A study of threshold time series autoregressive, seasonal and moving average models using TSMARS". Bayesian MARS (BMARS) uses the same model form, but builds the model using a Bayesian approach. It ...
The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation) which should not be confused with a differential equation.
The model consists of 2 autoregressive (AR) parts linked by the transition function. The model is usually referred to as the STAR(p) models proceeded by the letter describing the transition function (see below) and p is the order of the autoregressive part. Most popular transition function include exponential function and first and second-order ...
where L is the likelihood of the data, p is the order of the autoregressive part and q is the order of the moving average part. The k represents the intercept of the ARIMA model. For AIC, if k = 1 then there is an intercept in the ARIMA model (c ≠ 0) and if k = 0 then there is no intercept in the ARIMA model (c = 0).
Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method. [1] The sub-models combine to form the hierarchical model, and Bayes' theorem is used to integrate them with the observed data and account for all the ...
A threshold model used in toxicology posits that anything above a certain dose of a toxin is dangerous, and anything below it safe. This model is usually applied to non-carcinogenic health hazards. Edward J. Calabrese and Linda A. Baldwin wrote: The threshold dose-response model is widely viewed as the most dominant model in toxicology. [6]