Chapter 6 quiz

Time Series Models for Trading and Risk

0 of 10 answered

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

Question 1

Which series looks stationary β€” constant mean and variance over the day?

  • The close price β€” it stays between 108 and 111 all day
  • The minute return β€” it oscillates around zero with a stable spread
  • Both β€” the day is too short for either to drift
  • Neither β€” intraday data is never stationary

Question 2

Which metric is unusable for forecasting minute-by-minute price changes?

  • MAE β€” absolute errors are not differentiable
  • RMSE β€” it over-penalises large errors
  • MAPE β€” it divides by actual values that are near or exactly zero
  • Directional accuracy β€” the sign of a change is meaningless

Question 3

Apple 2015–24 on Dow 1985–95, 2 516 rows each. What will RΒ² and the t-statistic look like?

  • RΒ² β‰ˆ 0, t β‰ˆ 0 β€” unrelated series
  • RΒ² β‰ˆ 0.05, t β‰ˆ 2 β€” mild chance correlation
  • RΒ² β‰ˆ 0.3, t β‰ˆ 5
  • RΒ² β‰ˆ 0.8, t > 100 β€” a β€œhighly significant” fiction

Question 4

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

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

Question 5

For daily Dow Jones returns, which is more predictable from yesterday?

  • The sign (up or down)
  • The size (how big the move is)
  • Both equally
  • Neither β€” returns are i.i.d.

Question 6

For a stock index, the sign of \(\gamma\) is expected to be:

  • Negative β€” good news is more surprising
  • Positive β€” bad news raises volatility more (the leverage effect)
  • Zero β€” the square already captures size
  • Depends on the seed

Question 7

\(y_t = 0.5\,t + 3\varepsilon_t\). You difference it instead of detrending. What do you get?

  • A random walk β€” differencing creates a unit root
  • A stationary series, but with a larger variance than the detrended one (over-differenced)
  • Exactly the same residual as detrending
  • A series with a deterministic trend of slope 1

Question 8

Target is y = r (today’s return). A colleague builds X[β€œstd21”] = r.rolling(21).std() with no shift. What is wrong?

  • Nothing β€” volatility is a legitimate feature
  • The window at day \(t\) contains \(r_t\) itself: the target leaks into the feature
  • Rolling std needs at least 60 days to be stable
  • The feature is non-stationary

Question 9

You run a plain ADF on the OLS residual and get p = 0.024, but coint() reports p = 0.080. Which is right?

  • ADF β€” coint() is just ADF with more decimals
  • coint() β€” the residual’s Ξ² was estimated, so the critical values must be harsher
  • Neither β€” average them
  • ADF, because the sample is large

Question 10

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

  • Zero β€” 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 β€” the gain divides by zero