Introduction to Local Level Model and Kalman Filter

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LogSqr LogReturns Dow Jones : signal extraction −5 −10 −15 −5 −10 −15 1940 1960 1980 2000 1950 1960 1970 1980 1990 2000 2010 2 1 0 0.1 0.0 −0.1 −0.2 1940 1960 1980 2000 1950 1960 1970 1980 1990 2000 2010
Classical Decomposition Basic Model A basic model for representing a time series is the additive model yt = µt + γt + εt, t = 1, . . . , n, also known as the Classical Decomposition. yt = observation, µt = slowly changing component (trend), γt = periodic component (seasonal), εt = irregular component (disturbance). Unobserved Components Time Series Model In a Structural Time Series Model (STSM) or Unobserved Components Model (UCM), the various components are modelled explicitly as stochastic processes.
Page 1 and 2: Introduction to Local Level Model a
Page 3: Dow Jones 15000 10000 5000 0.25 0.0
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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