(a) Exponential smoothing is a time series forecasting technique that generates forecasts by applying a weighted average to past observations, where the weights decrease exponentially over time—the most recent data receives the highest weight, and older data progressively less. In the context of the mango demand data, which exhibits a sudden shift from low to high demand levels around month 7, exponential smoothing helps in producing short-term forecasts by smoothing out random fluctuations while adapting to changes based on the chosen smoothing constant (alpha). This method is particularly practical in banking for forecasting variables like cash flows or customer deposits, where quick adaptation to market shifts (e.g., post-2022 DDEP impacts on liquidity) is essential for compliance with BoG’s Liquidity Risk Management Guidelines.

(b) Using the initial forecast value of 500, the exponential smoothing forecasts (smoothed values) for each month are calculated as follows:
New forecast = α × Actual demand + (1 – α) × Previous forecast

The computed smoothed values for α = 0.1 and α = 0.4 are presented in the tables below:

For α = 0.1:

For α = 0.4:

Comparison: For α = 0.1, the forecasts adjust slowly to the demand shift at month 7, lagging behind the actual high demands (e.g., by month 15, forecast is 1109 vs. actual 1500). For α = 0.4, the adjustment is quicker, with forecasts catching up more rapidly to the new demand level (e.g., by month 15, forecast is 1488, much closer to 1500). This highlights how higher α emphasizes recent data more.

(c) The plot would feature the x-axis as months (1 to 15) and y-axis as demand values (ranging from 0 to 1600 for visibility).

• The actual demand line (e.g., in blue) shows stable low values around 460-520 from months 1-6, then a sharp increase to 1450-1550 from months 7-15, indicating a possible level shift or trend change.
• Superimposed forecast for α = 0.1 (e.g., in green dashed line): Starts near 500, fluctuates slightly in early months, then rises gradually after month 7 but remains below actuals, ending at ~1109 by month 15—demonstrating slow responsiveness.
• Superimposed forecast for α = 0.4 (e.g., in red dotted line): Similar early behavior but jumps more aggressively post-month 7, closely tracking the high demands by month 9 onward, ending at ~1488 by month 15—showing better alignment with the shift.

In practice, such plots aid bankers in visualizing forecast accuracy for operational risks, like predicting loan defaults under Basel III-adapted standards in Ghana, ensuring BoG-compliant risk models.

(d) The forecast with α = 0.4 is more suitable for this dataset due to its faster adaptation to the abrupt demand increase after month 6, resulting in forecasts closer to actual values in the later periods (e.g., minimal lag). In contrast, α = 0.1 is less suitable as it underestimates the new demand level significantly, due to over-reliance on historical low values. For business applications like inventory management in agribusiness or liquidity forecasting in rural banks (post-2017-2019 cleanup), a higher α like 0.4 enhances resilience by responding to market volatilities, aligning with BoG’s emphasis on dynamic risk assessment.