FRM Part I · FRM Exam Part I · Nonstationary Time Series
Quarterly sales of a firm are modeled as Y_t = 100 + 2t + S_q, where S_q is a seasonal dummy effect measured relative to Q4 (the base). The estimated effects are Q1 = +10, Q2 = -5, Q3 = -15, Q4 = 0. Time t = 1 corresponds to Q1 of year 1. What is the forecast for Q2 of year 3 (t = 10)?
The forecast is 115. Quarter 2 of year 3 is t = 10, so the trend component is 100 + 20 = 120, and adding the Q2 seasonal effect of -5 gives 115. Ignoring the seasonal term would overstate the forecast.
- A115Correct
- B120
- C125
- D105
Explanation
Q2 of year 3 is t = 2 + 8 = 10. Trend gives 100 + 2(10) = 120. Adding the Q2 effect of -5 gives 115. Omitting the seasonal term gives 120, and using the Q1 effect would give 130.
Did you get it right without looking?
One question tells you little. A timed set on Nonstationary Time Series shows your real accuracy, how long you take and where you lose marks.
More Nonstationary Time Series questions
- An analyst runs an augmented Dickey-Fuller test on the level of a series and obtains a statistic of -1.50 against a 5% critical value of -2.…
- An analyst models monthly log sales of a firm as ln(Y_t) = 2.50 + 0.012 t + e_t, where t = 1 for the first month and e_t is a stationary, me…
- A researcher regresses one random walk on an independent random walk and finds R² = 0.85 and a t-statistic of 14 on the slope, with a Durbin…
- An AR(1) process Y_t = 0.9 Y_{t-1} + e_t and a random walk Y_t = Y_{t-1} + e_t both have shock variance 1. Which statement correctly contras…
- Which statement best describes the effect of ignoring a structural break in the mean of a stationary series when applying a Dickey-Fuller te…
- An analyst fits the regression Y_t = δ·Y_{t-1} + ε_t to a monthly series of a bond spread and wants to test for a unit root using the Dickey…