a (i) Index numbers are relative measures showing changes in variables (e.g., prices) over time or space, expressed as percentages relative to a base. Construction: Select base period (100), collect data, apply formula like Laspeyres (weighted by base quantities) or Paasche. Uses: Measure inflation (e.g., Ghana’s CPI), track economic trends; in banking, for adjusting loan rates amid BoG-monitored inflation.

a (ii) An expenditure index measures changes in total spending on a basket of goods/services, incorporating both price and quantity changes. Construction: (Current expenditure / Base expenditure) × 100. Useful for budgeting; e.g., banks track client expenditure patterns post-DDEP for credit risk.

a (iii) A price index tracks average price changes for a fixed basket over time. Construction: Weighted average, e.g., CPI = (Σ current prices × base quantities / Σ base prices × base quantities) × 100. In Ghana, BoG uses it for monetary policy, affecting interest rates.

a (iv) The base period is the reference time (set to 100) against which changes are measured, chosen for stability. E.g., Ghana rebased CPI to 2018; crucial for accurate comparisons in bank forecasting.

(Note: Marks allocated based on exam, assuming distribution to total 13 for (a) as per sum, but explained four.)

b i) Key elements of a time series:

• Trend: Long-term movement (up/down), e.g., rising deposits.
• Seasonal variation: Regular patterns within a year, e.g., end-year spikes.
• Cyclical variation: Longer fluctuations tied to business cycles.
• Random/irregular: Unpredictable shocks, e.g., COVID impacts.

Decomposition: Y = T × S × C × I (multiplicative model).

b ii) Uses in forecasting:

• Predict future values: Extrapolate trend/seasonals, e.g., forecast loan defaults.
• Identify patterns: For budgeting, like seasonal cash flows in Ghana’s agriculture-linked banking.
• Policy decisions: BoG uses for economic projections.
• Evaluate interventions: Post-policy changes, e.g., after recapitalization.
• Limitations: Assumes past patterns continue; in volatile Ghana (e.g., cedi depreciation), combine with other methods.