Why the Forecast Horizon Matters
A prediction is not fully specified by saying what outcome is of interest. It also needs to say when the future outcome will be measured. A prediction about whether a repair will be needed soon is different from one about whether a repair will be needed at any time during the next year. The cases being predicted may be the same, but the period covered—and therefore the target—has changed.
The forecast horizon should be chosen with the intended decision in mind. A short horizon may help a service team plan next month’s appointments. A longer horizon may be more useful for annual staffing or budgeting. Neither is universally better. The useful horizon is the one that matches the timing and purpose of the decision.
The open left endpoint means the outcome at the prediction time itself is not treated as a future outcome. The closed right endpoint means an outcome exactly at the stated endpoint is included. Other endpoint conventions are possible, but they must be specified consistently. For calendar periods, the endpoint might instead be the end of a named month, quarter, or year.
A prediction time and a horizon answer different questions. The prediction time says when the prediction is made; the horizon says how far ahead it looks. Holding the prediction time fixed while changing the horizon changes the future period being summarized. In general, represent the target for case \(i\) at horizon \(H\) as:
Here, \(g\) describes how the outcomes in that period are summarized. It might identify whether an event occurred, count events, or total a quantity. The horizon must be specified before the target can be interpreted: “total over the next three months” and “total over the next year” are different targets even if both are measured in dollars.
Why Changing the Horizon Changes the Target
A short horizon includes a narrower slice of the future than a longer horizon. For an illustrative event that can occur at most once, define \(E(H)\) to mean that it occurs during the chosen period. If the periods share the same prediction time and the shorter period is contained in the longer one, then:
This follows because an event occurring within the shorter period also occurs within the longer period. The reverse need not hold: an event can occur after \(H_1\) but by \(H_2\). Thus, the label or measured outcome for a case can depend on the horizon, not just on the case’s characteristics. This set relationship assumes the same starting time, consistent endpoint rules, and complete observation of the relevant periods.
For a cumulative target, a similar idea applies when the quantity being added is nonnegative. A longer period can include additional amounts that were not part of the shorter-period total. But not every target must increase with horizon: a net change, a rate, or an average can rise or fall as the period extends. State what is being measured rather than assuming that a longer horizon simply means a larger value.
Worked Examples
Worked Example: Choosing a Horizon for Equipment Service
A hypothetical equipment-support team makes a prediction for each machine on January 1, 2026. A planning team wants to compare a 30-day horizon with a 180-day horizon. One machine in a historical record needed repairs on January 20, March 15, and May 20, 2026. Assume the repair dates are recorded accurately, the prediction time is January 1, and the interval convention is \((t_i,t_i+H]\). Which repair dates fall within each horizon, and what planning question does each horizon support?
Method. Calculate each endpoint from the prediction time, then include repair dates after January 1 and on or before that endpoint.
30-day endpoint. January 1 plus 30 elapsed days is January 31, 2026. The January 20 repair is after January 1 and no later than January 31, so it is included. The March 15 and May 20 repairs are after January 31, so they are excluded. There is 1 repair in the 30-day period.
180-day endpoint. January 1 plus 180 elapsed days is June 30, 2026. All three repair dates—January 20, March 15, and May 20—fall after January 1 and no later than June 30. There are 3 repairs in the 180-day period.
The 30-day horizon can inform near-term appointment planning; the 180-day horizon includes a broader period and can inform longer-range service planning. The repair on March 15 is outside the first target period but inside the second. The method avoids treating “needs repair” as a horizon-free outcome. The common mistake is to count all future repairs for both horizons; the corrected counts are 1 and 3.
Worked Example: Matching a Revenue Horizon to a Planning Decision
A hypothetical analyst makes a prediction at the close of March 31, 2026, for one account. A finance team is considering whether it needs an estimate for the next quarter or for the next year. The account’s recorded receipts are $400 on April 15, $600 on June 30, $500 on September 30, and $300 on March 31, 2027. For this example, define the target as the sum of receipts after the prediction time and on or before the horizon endpoint. Calculate both targets.
Method. Set each endpoint, select only receipts within its period, and add the selected amounts.
Next-quarter horizon. The three calendar months after March 31 are April 1 through June 30, 2026. The receipts in this period are $400 and $600. Therefore:
Next-year horizon. The 12 calendar months after March 31, 2026 run from April 1, 2026, through March 31, 2027. All four listed receipts fall within this period. Therefore:
The next-quarter target is $1,000; the next-year target is $1,800. The first supports near-term cash planning, while the second supports an annual view. The method avoids adding receipts outside the stated window. A common mistake is to use the full $1,800 as the next-quarter target simply because all four receipts occur in the next year. That is incorrect: the September and March receipts are outside the quarter.
Worked Example: Clarifying a 90-Day Versus Three-Month Horizon
A hypothetical facilities team makes a prediction on January 31, 2027, for each building. It wants to count buildings with a service disruption during either the next 90 elapsed days or the next three calendar months. Consider four buildings with disruption dates of February 2, April 30, May 1, and May 2, respectively. Assume the period starts after January 31 and includes its endpoint. Find the counts and identify why the horizon wording matters.
Method. Work out both endpoints before counting. A 90-day horizon is an elapsed-time duration; three calendar months is a calendar-period duration. They are not always the same.
Three calendar months. The period runs from February 1 through April 30, 2027. The February 2 and April 30 disruptions fall within it; May 1 and May 2 do not. The count is 2 buildings.
90 elapsed days. From January 31, February contributes 28 days, March contributes 31 more, and April contributes 30 more. That totals \(28+31+30=89\) days by April 30. The 90th day is May 1. The period therefore runs through May 1, inclusive. February 2, April 30, and May 1 fall within it, so the count is 3 buildings.
The May 1 disruption is excluded by the three-calendar-month horizon but included by the 90-day horizon. The two counts, 2 and 3, are both correct for their specified periods. The method avoids silently substituting calendar months for a stated number of elapsed days. The common mistake is to assume that “three months” always means 90 days; here the periods end on different dates.
A Practical Process for Specifying a Horizon
A horizon should be written precisely enough that two analysts would assign the same outcome period to the same prediction. The following process makes the choice explicit without confusing it with the separate decision of what information is available at prediction time.
Identify when the decision-maker needs to act and how far ahead that action can usefully be planned. A decision made next week may need a different horizon from an annual resource plan.
Specify the duration or calendar period, the starting point, and whether the endpoint is included. Use wording such as “the 90 days after the prediction time, including day 90” rather than just “near term.”
Say whether the target concerns an occurrence, a count, a total amount, or another summary. Keep the measurement tied to the stated period; do not let a longer-period outcome silently replace a shorter-period one.
Historical cases need sufficient follow-up through the entire horizon to establish the target. If a data extract ends before the horizon does, the outcome may not yet be known; absence of a recorded event is not automatically evidence that none occurred.
Record why this period is useful. A horizon that is easy to calculate but too short or too long for the action can produce a precisely defined target that does not answer the business question.
Common Horizon Errors
- Leaving the duration vague. “Future claims” does not say whether the target covers one month, one year, or the life of a policy.
- Mixing elapsed time and calendar periods. Ninety days and three calendar months can end on different dates. Specify which convention is intended.
- Counting outcomes beyond the endpoint. An event after the horizon does not belong to that period, even if it occurs soon afterward.
- Assuming a longer horizon is always better. A longer period may suit long-range planning but be less aligned with an immediate action. The target and intended use determine the appropriate horizon.
- Treating unobserved future outcomes as no outcome. If follow-up ends before the horizon endpoint, the full-period result may be unknown. The data must support the target definition.
- Comparing results without checking their periods. Two quantities with the same units can still represent different targets if one covers a quarter and the other a year.
Horizon specification is part of defining the predictive task, not a cosmetic reporting choice. It determines which future outcomes are relevant to a prediction and whether the resulting prediction can support the intended action. A well-defined horizon states its starting point, length or calendar endpoint, inclusion rule, and connection to the decision. This framing is aligned with the SOA Exam PA (Predictive Analytics) syllabus.
Check Your Understanding
For each problem, identify the period carefully before deciding which outcomes belong to the target.
- A hypothetical delivery team predicts at the end of August 31, 2026, and wants the total number of late deliveries in the next calendar month. The recorded late deliveries are September 1, September 30, and October 1. How many belong to the target, and what is the period? (Answer: September 1–30, inclusive; 2 late deliveries.)
- A hypothetical equipment operator predicts on April 1, 2027, using a 10-day horizon with the interval \((t_i,t_i+H]\). An incident occurs on April 11. Is it included? State the endpoint. (Answer: Yes; the endpoint is April 11, and the endpoint is included.)
- A hypothetical account forecast is made at the close of June 30. The target is total receipts during the next quarter. Receipts are $250 on July 1, $350 on September 30, and $100 on October 1. Calculate the target and identify the excluded receipt. (Answer: $600 for July 1–September 30; exclude the October 1 receipt.)
- A hypothetical program begins forecasting on January 31, 2028. It must choose between the next three calendar months and 90 elapsed days. Which endpoint does each convention use, and why can the targets differ? (Answer: Three calendar months ends April 30; 90 elapsed days ends April 30 in leap year 2028? Wait: February has 29 days, March 31, and April 30, totaling 90 days. Both end April 30, so those conventions do not produce different periods in this case.)
- A hypothetical maintenance team predicts on May 31, 2027. It observes service events on June 30, August 31, and September 1. Compare the count in the next three calendar months with the count in the next 90 elapsed days, using an inclusive endpoint. (Answer: Three calendar months ends August 31 and includes 2 events; 90 elapsed days ends August 29 and includes 1 event.)