# Forecasting Methods > Forecasting theory and computation for the MGT4897 DXB report — moving averages, weighted moving averages, single and trend-adjusted exponential smoothing, least-squares trend, and associative regression; the CFE, MAD, MSE, MAPE and tracking-signal metrics the brief names; how to choose and defend a model; and how to handle the 2020–2022 COVID structural break. Use for task 3 and for any number that feeds the capacity gap analysis. - Skill: `faaz17/forecasting-methods` (Agent Skill, multi-file: 2 files) - Install (CLI): `npx skillmds@latest add faaz17/forecasting-methods` - Raw SKILL.md: https://api.skillmd.com/api/skills/faaz17/forecasting-methods/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: AI & ML - Author: Faaz17 (https://skillmd.com/u/faaz17) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/faaz17/forecasting-methods --- # Forecasting — methods, metrics, and model choice Task 3 carries **35 of 100 marks**. This skill covers the arithmetic and, more importantly, the judgement the marks actually reward. ## Run the engine, do not hand-calculate py .claude/skills/forecasting-methods/scripts/forecast.py --markdown Every method, every error metric, the 2026 forecast, the long-run projection and the associative regression come out of one command. Useful variants: | Command | Purpose | |---|---| | `--series passengers` | One series only | | `--from 2013 --to 2019` | Pre-COVID fitting basis | | `--from 2022` | Post-COVID fitting basis | | `--long-to 2036` | Projection horizon (default 2036) | | `--associative` | Only the passengers-on-movements regression | | `--at 500000,550000,600000` | Movement levels for the associative forecast | | `--alpha 0.1,0.2,0.3,0.5` | Smoothing constants to compare | | `--plain` | Console-friendly output instead of markdown tables | Numbers typed by hand into prose drift from the workbook and get caught. Generate, then quote. ## The methods ### Naive F(t+1) = A(t). Zero parameters. Its only role is as a **benchmark** — a sophisticated model that cannot beat naive is not earning its complexity. Reporting that comparison is a mark of a careful analyst. ### Simple moving average F(t+1) = mean of the last *n* actuals. Smooths noise; **lags a trend**, and the lag grows with *n*. On a rising series it under-forecasts systematically, which shows up as a positive CFE and a rising tracking signal. ### Weighted moving average Same, with declining weights on older periods — e.g. 0.5 / 0.3 / 0.2 with the largest weight on the most recent year. Weights must sum to 1 (the script normalises). Responds faster than a simple MA, still lags a trend. **Justify the weights**; arbitrary weights invite the question "why those?". ### Single exponential smoothing F(t+1) = F(t) + α(A(t) − F(t)), with 0 < α < 1. α is the responsiveness dial: high α tracks recent movement and reacts to noise; low α is stable and slow. Compare at least two or three values. **Single exponential smoothing has no trend term** — on a series with a persistent trend it lags permanently, which is exactly what the DXB data shows. ### Trend-adjusted (Holt's) exponential smoothing Smooths level and trend separately: L(t) = α·A(t) + (1−α)·(L(t−1) + T(t−1)) T(t) = β·(L(t) − L(t−1)) + (1−β)·T(t−1) F(t+1) = L(t) + T(t) Appropriate where a trend is present and the analyst wants recent trend weighted more heavily than a straight line does. On the short post-COVID window it extrapolates recovery momentum aggressively — note that rather than quoting it flat. ### Least-squares linear trend y = a + b·x fitted on the year index. Uses the whole window, gives an interpretable slope ("about b additional passengers per year"), and reports **r²** — the share of variation explained. It is also the only method here that is straightforwardly extendable to 2036. ### Associative (causal) regression — task 3(c) Passengers regressed on flight movements, not on time: passengers = a + b · movements This is a **different kind of model** from everything above, and the report must say so. Time-series methods project the past forward; an associative model predicts one variable from another. The brief asks for expected passenger traffic at 500,000, 550,000 and 600,000 movements — that is this model, not the trend line. The slope has a physical meaning: **passengers per aircraft movement**, a function of average aircraft size and load factor. Interpreting it that way, and asking whether it can hold at higher movement volumes, is the analysis the marks are for. ## The error metrics — what each one actually detects Let e(t) = A(t) − F(t), over the *n* periods where a forecast exists. | Metric | Formula | Detects | Watch for | |---|---|---|---| | **CFE** | Σ e(t) | Cumulative bias | Large positive = persistent under-forecasting. On a capacity decision, that is the dangerous direction | | **MAD** | Σ\|e(t)\| / n | Average error size, in original units | Same units as the data, so it is the one to quote to a COO | | **MSE** | Σ e(t)² / n | Average squared error | Penalises large misses heavily — the right lens when one bad year is costlier than several small ones | | **MAPE** | (Σ \|e(t)/A(t)\| / n) × 100 | Average error as a percentage | Unit-free, so it compares across the two series. Distorted by small denominators — the 2020 collapse inflates it | | **TS** | CFE / MAD | Bias relative to typical error | **Outside ±4 = the model is out of control.** MAPE will not tell you this | **Compare models on more than one metric.** The classic error is ranking by MAPE alone and recommending a model with a tracking signal of 3.5 — accurate on average, but wrong in the same direction nearly every year. Say which metric drove the recommendation and why. The metrics must be computed over a **common comparison window** where possible. A 3-year moving average produces fewer forecasts than a naive model, so their metrics are not computed over identical periods; the script reports *n* for each so the report can acknowledge it. Acknowledging it is worth more than hiding it. ## The COVID structural break — the analytical crux DXB fell from 86.4m passengers in 2019 to 25.8m in 2020, and recovered past 2019 by 2023. This is not noise. It is a **structural break**, and how it is handled separates a competent report from a distinction. Fitting a least-squares trend across the whole 2013–2025 series gives **r² ≈ 0.006** — the line explains essentially none of the variation, and projects 2035 *below* the 2025 actual. Quoting that number as a forecast would be indefensible. Run it, show it, and explain why it is rejected. Demonstrating that a model fails is evidence of judgement. Three defensible bases, each with a different answer: | Basis | Fitting window | r² | Character | |---|---|---|---| | Full series | 2013–2025 | ~0.006 | Break dominates; unusable for projection | | Pre-COVID | 2013–2019 | ~0.85 | Mature-growth trajectory, ignores the recovery | | Post-COVID | 2022–2025 | ~0.82 | Steep, but part of that slope is recovery, not growth | Run all three (`--from` / `--to`), report them, and **argue for one** — or for a blended view with a stated range. A capacity decision on a 20-year asset should not rest on a four-observation recovery trend, and saying so is the argument. Other legitimate treatments worth naming: excluding 2020–2021 as outliers; using a dummy variable for the break; forecasting from 2023 onward once recovery completed. Each has a cost. Name it. ## Choosing and defending a model — the marks are here The brief says *"recommend the most suitable model"*. A recommendation needs four things: 1. **The metric comparison**, laid out honestly 2. **The metric that decided it**, and why that metric fits this decision — MAD for operational staffing, MSE where a single large miss is costly, TS where sustained bias would compound into an infrastructure error 3. **The behaviour of the series** — trend present? break present? seasonality? (annual data hides seasonality, which is itself worth a sentence, since airport operations are acutely seasonal and the annual series conceals it) 4. **The decision the forecast serves** — a 2026 staffing plan and a 2036 capacity decision do not need the same model, and saying so explicitly is exactly the kind of judgement task 2 asks for It is entirely defensible to recommend **different models for different horizons**: a responsive short-term method for 2026, a trend model on a stated basis for 2036. That reads as an analyst thinking, not a student ticking a box. ## Sanity checks before any number reaches the report - Does the 2026 forecast sit in a plausible band against 95.2m in 2025? - Does the 2035/2036 figure imply a growth rate you would defend out loud? - Is the associative forecast an **extrapolation** beyond the observed movement range (max 454,800 in 2025)? Say so — all three of the brief's levels are. - Does passengers ÷ movements stay plausible at the forecast levels (roughly 209 in 2025)? - Do the two series stay consistent with each other? - Are the units right — passengers in millions vs absolute; movements in thousands? ## Reporting conventions - Round in prose, keep full precision in the workbook: "approximately 112.3 million", not "112,292,354" - State the fitting window every time a forecast is quoted - Give the regression equation, r and r² whenever a regression is used - Number every table and figure and refer to each in the text - Put full method-by-method workings in the **appendices**; the main text carries the comparison summary and the interpretation ## Citing the theory Forecasting method claims should carry a textbook or journal citation. Standard operations management texts covering exactly this material: - Heizer, Render and Munson — *Operations Management* - Slack, Brandon-Jones and Burgess — *Operations Management* - Krajewski, Malhotra and Ritzman — *Operations Management: Processes and Supply Chains* - Stevenson — *Operations Management* For the **five journal articles** the brief requires, air transport demand forecasting is a well-served literature — see `aviation-data-sources` for the journals to search. Verify every reference; never invent a DOI.