Forecasting and Time Series
Forecasting and time series helps management predict future values from past data. The exam tests moving averages, exponential smoothing, seasonal indices, and forecast accuracy.
Methods
- Moving average: average the last k observations. For an even k, centre the averages (average two consecutive MAs) so they align with a time point.
- Exponential smoothing: F_{t+1} = αY_t + (1−α)F_t, where α is the smoothing constant (0 < α < 1). A higher α reacts faster to recent changes.
- Seasonal index: express each season's actual as a percentage of the centred moving-average trend, then average by season. Forecast = trend × seasonal index/100.
- Accuracy: MAD = mean of |actual − forecast|; MSE = mean of squared errors.
Worked example: sales are 100, 120, 130; use α = 0.2 and F1 = 100. F2 = 0.2(100)+0.8(100)=100. F3 = 0.2(120)+0.8(100)=104. F4 = 0.2(130)+0.8(104)=109.2. The forecast for period 4 is 109.2.
Traps: applying α to the previous forecast instead of the actual; failing to centre an even-period moving average; using a simple average as a seasonal index; and comparing MAD and MSE as if they had the same units.