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Threshold Autoregressive (TAR) Models

Threshold Autoregressive (TAR) Models. Movements between regimes governed by an observed variable. TAR model: Where s t-k is the state determining variable. The integer k determines with how many lags does the state-determining variable influences the regime in time t .

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Threshold Autoregressive (TAR) Models

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  1. Threshold Autoregressive (TAR) Models • Movements between regimes governed by an observed variable. • TAR model: • Where st-k is the state determining variable. • The integer k determines with how many lags does the state-determining variable influences the regime in time t. • When st-k = yt-k we have a self-exciting TAR (SETAR) model: • There are many possible variations of this simple model.

  2. Threshold Autoregressive (TAR) Models • Example: when st-k = yt-k we have a self-exciting TAR (SETAR) model: • Consider k = 1. Parameters to be estimated: • 1, 2, 1, 2, • r • Estimation method: least squares with r estimated by a grid search. • There are many possible variations of this simple model: • Switching in only some of the parameters • More than 2 regimes • Different threshold variables • Alternative dynamic specifications Can use AIC or other information criteria to select models

  3. EXAMPLE: Threshold error correction (cointegration) model

  4. EXAMPLE: Threshold error correction (cointegration) model

  5. EXAMPLE: Threshold error correction (cointegration) model EVIEWS program: series y = d(r120) series x = d(r3) series spread = r120 - r3 scalar th = 3.22 series _d = ( spread(-1) < th ) equation tar.ls y c y(-1) y(-2) x(-1) x(-2) _d*spread(-1) (1-_d)*spread(-1)

  6. EXAMPLE: Threshold error correction (cointegration) model

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