Chapter 6 · Section 4 practice

Kalman Filters and Regime Switching

0 of 3 answered

These questions review the examples in the companion slides. Choose an answer, then check the explanation.

Question 1

Observations become much noisier (\(R\) ↑). The Kalman gain \(K_t\)…

  • falls — trust the model more, the data less
  • rises — noisy data needs bigger corrections
  • is unchanged — \(K\) depends only on \(Q\)
  • becomes negative

Question 2

Set \(Q = 0\). What does the filtered \(\beta_t\) become?

  • Zero — no signal means no beta
  • The rolling 60-day OLS beta
  • Recursive least squares: it converges to the full-sample OLS beta and stops moving
  • Undefined — the gain divides by zero

Question 3

If the staying probabilities are \(p_{00} = 0.98\) (calm) and \(p_{11} = 0.96\) (stormy), the expected durations are…

  • 98 and 96 days
  • 50 and 25 days — \(1/(1-p_{ii})\)
  • 2 and 4 days
  • Equal — a Markov chain has no memory