Introduction to Local Level Model and Kalman Filter

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Forecasting Forecasting requires no extra theory: just treat future observations as missing: ◮ put vj = 0, Kj = 0 <strong>and</strong> Fj = ∞ for j = n + 1, . . . , n + k ◮ proceed further calculations as normal ◮ forecast for yj is aj
Nile Data: forecasting 1250 1000 750 500 1200 1100 1000 900 800 (i) (iii) 1900 1950 2000 1900 1950 2000 50000 40000 30000 20000 10000 60000 50000 40000 30000 (ii) (iv) 1900 1950 2000 1900 1950 2000
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 and 24: Kalman Filter Derived ◮ Our best
Page 25 and 26: Steady State Kalman Filter Kalman f
Page 27 and 28: Kalman smoothing for Nile Data: (i)
Page 29: Nile Data with missing observations
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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