Introduction to Local Level Model and Kalman Filter

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Diagnostics ◮ Null hypothesis: standardised residuals vt/ √ F t ∼ N ID(0, 1) ◮ Apply standard test for Normality, heteroskedasticity, serial correlation; ◮ A recursive algorithm is available to calculate smoothed disturbances (auxilliary residuals), which can be used to detect breaks and outliers; ◮ Model comparison and parameter restrictions: use likelihood based procedures (LR test, AIC, BIC).
Nile Data: diagnostics 2 0 −2 2 0 −2 (i) 1880 1900 1920 1940 1960 (iii) −2 −1 0 1 2 0.5 0.4 0.3 0.2 0.1 0.5 0.0 −0.5 (ii) −3 −2 −1 0 1 2 3 (iv) 1.0 0 5 10
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 and 30: Nile Data with missing observations
Page 31 and 32: Nile Data: forecasting 1250 1000 75
Page 33: Parameter Estimation by ML The para
Page 37 and 38: Three exercises (cont.) 2. Derive a

Introduction to Local Level Model and Kalman Filter

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