Introduction to Local Level Model and Kalman Filter

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U.K. Yearly Inflation : signal extraction 0.3 0.2 0.1 0.0 −0.1 −0.2 1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000
Dow Jones 15000 10000 5000 0.25 0.00 −0.25 Dow Jones (Industrial Avg, Monthly Closures) 1930 1940 1950 1960 1970 1980 1990 2000 2010 LogReturn 1930 1940 1950 1960 1970 1980 1990 2000 2010 0 −5 LSqrLReturn −10 −15 1930 1940 1950 1960 1970 1980 1990 2000 2010
Page 1: Introduction to Local Level Model a
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 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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