Forecast Calculation Rationale
Introduction
The forecast aims to project future costs based on historical data, adjusting projections based on factors such as seasonality, organic growth and specific events (whether or not they occur). In addition, it incorporates a measure of uncertainty (represented by a confidence band) that reflects the variability of historical data and increases for more distant projections.
Process Overview
The forecast calculation is carried out in two main steps:
Preparation and Enrichment of Historical Data:
Processing of historical cost data.
Calculation of indicators such as daily cost, seasonality and weighted daily cost.
Forecast Projection:
Calculation of projections using enriched data.
Adjustments for organic growth, seasonality and events.
Calculation and adjustment of the confidence band to reflect uncertainty, especially in future months.
Calculation Details
Preparation of Historical Data and Lags
Historical Data:
Historical costs are used, disregarding values influenced by specific events that have already occurred. This data serves as a basis for future projections.
Cost Lag:
Previous months' costs are considered (for example, using data from periods preceding the current reference). This lag allows for comparing current costs with historical data and identifying trends or variations.
Seasonality Calculation:
Seasonality is determined by comparing the cost of a reference month with the costs of previous months. To do this, the percentage variation between the cost of the reference month and the costs of three selected previous months is calculated.
⇒ Average of variations: The average of these percentage variations provides an index of seasonality.
⇒ Limitation of Values: To avoid distortions, this index is limited to a maximum of 20% positive or negative variation.
Daily Cost Estimate
Daily Cost:
For each month, the daily cost is estimated by dividing the accumulated cost (excluding amounts influenced by one-time events already completed) by the number of days elapsed until the reference date. This measure allows you to monitor the pace of spending throughout the month.
Weighted Daily Cost Calculation
Selection of Historical Months:
A certain number of historical months are considered (limiting the quantity to maintain data relevance). This set represents the recent cost history.
Weight Assignment:
To value the relative importance of historical months, a numerical sequence inspired by the Fibonacci sequence is used. Each month receives a weight that reflects its influence on the weighted average.
Weighted Calculation:
The daily cost of each historical month is multiplied by its respective weight. The sum of these weighted values is then divided by the total sum of the weights, resulting in a weighted daily cost. This indicator provides an adjusted average, taking into account the importance of each historical period.
Calculation of "Hard" and "Soft" Forecasts
Hard Forecast:
This forecast is designed to reflect a robust estimate of future cost and is calculated as follows:
Multiply the weighted daily cost by the total number of days in the projection month.
A multiplicative adjustment is applied that incorporates organic growth and identified seasonality, that is, a percentage corresponding to the sum of growth and seasonal variation is added.
Adjustments resulting from specific events (both those that occurred and those that were planned but did not happen) are also added.
Summarized Formula:
Hard Forecast = (Weighted Daily Cost x Total Days in Month) x (1 + Organic Growth + Seasonality) + Event Adjustments
Soft Forecast:
Unlike the Hard forecast, the Soft forecast is calculated based on the simple daily cost (without weighting) and includes the same adjustments related to events.
Multiply the daily cost by the total number of days in the month.
Event adjustments are added.
Summarized Formula:
Soft Forecast = (Daily Cost * Total Days in Month) + Event Adjustments
Confidence Band Calculation
Definition:
The confidence band represents the margin of uncertainty of the projection, that is, how much the projected values can vary based on the variability of historical data.
Standard Deviation Calculation
The most recent historical costs (e.g., from the last six months) are analyzed. The standard deviation of these values is calculated to quantify the dispersion of the data.
Application of the Trust Factor:
The standard deviation is then multiplied by a factor (Z-value) that corresponds to the desired degree of confidence (e.g., 1.96 for 95% confidence).
Summarized Formula:
Confidence Band = Z-Value x Standard Deviation of Historical Costs
Adjustment for Future Months:
As uncertainty increases the further the projection extends, the confidence band is progressively widened for future months by a growing factor, reflecting the higher degree of uncertainty in distant periods.
Final Considerations
The forecast approach described in this documentation integrates historical data and adjustable parameters to project future costs in a robust and flexible manner. The main points of the method are:
Weighted Average with Weights Inspired by the Fibonacci Sequence: Allows you to give different importance to historical months, adjusting the average in a non-linear way.
Adjustment for Organic Growth and Seasonality: Considers natural variations and growth trends, refining the monthly cost estimate.
Incorporation of One-Time Events: Ensures that extraordinary factors (realized or predicted) are reflected in the projections.
Confidence Band: Provides a measure of uncertainty, essential for decision making, especially in longer projections.
This modular and parameterized methodology enables the adaptation of the forecast to different scenarios while maintaining consistency and robustness in cost projections.
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