Question-bank practice
These cards are for quick drilling. For complete exam-style answers with every numerical step, open the full QP solutions page.
Write detailed notes comparing qualitative and quantitative methods of forecasting.
Define forecasting. Compare basis, data requirement, nature, examples, advantages, and limitations. Use market survey, expert opinion, Delphi under qualitative; use regression and time series models under quantitative.
Data: years 1991-1997; sales 102, 105, 114, 110, 108, 116, 112. Calculate 3, 5, and 7-year moving averages.
3-year MA: 107.00, 109.67, 110.67, 111.33, 112.00. 5-year MA: 107.80, 110.60, 112.00. 7-year MA: 109.57. For odd windows, place each answer at the middle year.
Data: years 1985-1992; y = 90, 110, 185, 200, 195, 210, 300, 450. Calculate moving averages and plot trend values.
3-year MA: 128.33, 165.00, 193.33, 201.67, 235.00, 320.00. Raw 4-year MA: 146.25, 172.50, 197.50, 226.25, 288.75. Centered 4-year MA: 159.38, 185.00, 211.88, 257.50. 5-year MA: 156.00, 180.00, 218.00, 271.00. 7-year MA: 184.29, 235.71.
Data: years 1990-1997; f = 9, 13, 11, 14, 12, 9, 3, 1. Calculate 3, 4, 5, and 7-year moving averages.
3-year MA: 11.00, 12.67, 12.33, 11.67, 8.00, 4.33. Raw 4-year MA: 11.75, 12.50, 11.50, 9.50, 6.25. Centered 4-year MA: 12.12, 12.00, 10.50, 7.88. 5-year MA: 11.80, 11.80, 9.80, 7.80. 7-year MA: 10.14, 9.00.
Fit a straight-line and parabolic trend to x = 2001-2005 and y = 5, 12, 26, 60, 97. Estimate y for 2006.
Using coded x = -2, -1, 0, 1, 2: straight-line trend y = 40 + 23.2x, so 2006 has x = 3 and estimate 109.60. Parabolic trend is approximately y = 28.57 + 23.2x + 5.71x^2, so the 2006 estimate is 149.60.
Write the steps to fit y = a + bx and y = a + bx + cx^2 by least squares.
Code time around the middle so sum x = 0. For a line, use a = sum y / n and b = sum xy / sum x^2. For a parabola, use normal equations: sum y = na + c sum x^2, sum xy = b sum x^2, and sum x^2 y = a sum x^2 + c sum x^4.
Describe the decomposition process and explain additive vs multiplicative models.
Define decomposition as separation into trend, seasonal, cyclical, and irregular components. Additive model is used when seasonal swing is roughly constant; multiplicative model is used when seasonal swing changes with the series level. Explain de-trending, estimating seasonal indices, adjusting indices, and reapplying components for forecasts.
Given two years of monthly passenger, retail, electric, or SaaS-user data, decide whether additive or multiplicative decomposition is more suitable.
Plot or inspect each month across years. If the seasonal differences are similar in absolute size, choose additive. If peaks and troughs become larger when the series level rises, choose multiplicative. State the model before calculating indices.
Explain simple, double, and triple exponential smoothing with justification.
SES uses one smoothing parameter alpha and estimates level only. Holt's double exponential smoothing uses alpha for level and beta for trend, so it handles trend. Holt-Winters uses level, trend, and seasonal components, so it handles trend plus seasonality. Mention additive and multiplicative seasonal versions.
For a given data series and alpha values 0.1, 0.2, and 0.5, calculate exponential smoothing forecasts.
Choose the initial forecast, often F2 = y1 unless the question states otherwise. Then repeatedly apply F_(t+1) = Ft + alpha(yt - Ft). Larger alpha tracks new observations faster; smaller alpha smooths more.
For yearly data and given alpha and beta values, calculate Holt forecasts.
Initialize level and trend. Update level with alpha, update trend with beta, then forecast using F_(t+h) = Lt + hBt. Show a table with columns: t, yt, Lt, Bt, and forecast.
Write briefly about the components of time series.
Define components as parts of observed variation. Trend is long-term movement; seasonality is fixed-period repetition; cyclical variation is long wave-like movement without fixed period; irregular variation is random error or noise. Add examples for at least two components.