Introduction to Local Level Model and Kalman Filter

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Kalman filter for Nile Data: (i) at; (ii) Pt; (iii) vt and (iv) Ft. 1250 1000 750 500 250 0 −250 (i) 1880 1900 1920 1940 1960 (iii) 1880 1900 1920 1940 1960 17500 15000 12500 10000 7500 30000 27500 25000 22500 (ii) 1880 1900 1920 1940 1960 (iv) 32500 1880 1900 1920 1940 1960
Steady State Kalman Filter Kalman filter converges to a positive value, say Pt → ¯ P. We would then have Ft → ¯P + σ 2 ε, Kt → ¯P/(¯P + σ 2 ε). The state prediction variance updating leads to ¯P = ¯P 1 − which reduces to the quadratic ¯P ¯P + σ 2 ε x 2 − xq − q = 0, + σ 2 η, where x = ¯ P/σ 2 ε and q = σ 2 η/σ 2 ε, with solution ¯P = σ 2 ε q + q2 + 4q /2.
Page 1 and 2: Introduction to Local Level Model a
Page 3 and 4: Dow Jones 15000 10000 5000 0.25 0.0
Page 5 and 6: Classical Decomposition Basic Model
Page 7 and 8: Local Level Model General framework
Page 9 and 10: Simulated LL Data 6 4 2 0 −2 −4
Page 11 and 12: Simulated LL Data 5 σε 2 =0.1 σ
Page 13 and 14: Properties of the LL model ◮ The
Page 15 and 16: Nile Data: decomposition 1250 1000
Page 17 and 18: Nile Data: forecasts 1400 1300 1200
Page 19 and 20: Kalman Filter The unobserved variab
Page 21 and 22: Regression theory The proof of the
Page 23: Kalman Filter Derived ◮ Our best
Page 27 and 28: Kalman smoothing for Nile Data: (i)
Page 29 and 30: Nile Data with missing observations
Page 31 and 32: Nile Data: forecasting 1250 1000 75
Page 33 and 34: Parameter Estimation by ML The para
Page 35 and 36: Nile Data: diagnostics 2 0 −2 2 0
Page 37 and 38: Three exercises (cont.) 2. Derive a

Introduction to Local Level Model and Kalman Filter

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