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# Presentation_1375280857464

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### Presentation_1375280857464

1. 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.    ≥++ <++ = −− −− rsifuy rsifuy y kttt kttt t 2122 1111 φµ φµ    ≥++ <++ = −− −− ryifuy ryifuy y kttt kttt t 2122 1111 φµ φµ
2. 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: µ1, µ2,σ1,σ2, – 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    ≥++ <++ = −− −− ryifuy ryifuy y kttt kttt t 2122 1111 φµ φµ
3. 3. EXAMPLE: Threshold error correction (cointegration) model 2 4 6 8 10 12 14 16 18 1960 1965 1970 1975 1980 1985 1990 R3 R120
4. 4. EXAMPLE: Threshold error correction (cointegration) model -3 -2 -1 0 1 2 3 4 5 1960 1965 1970 1975 1980 1985 1990 SPREAD
5. 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. 6. EXAMPLE: Threshold error correction (cointegration) model
7. 7. EXAMPLE: Threshold error correction (cointegration) model