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Introduction to Forecasting

Lecture 1

What can be forecast?

What can be forecast?

Some things are easy to forecast.
  • Tomorrow’s electricity demand follows a regular daily pattern.
  • Next month’s sales at a large retailer vary predictably with seasons.

What can be forecast?

Some things are easy to forecast.
  • Tomorrow’s electricity demand follows a regular daily pattern.
  • Next month’s sales at a large retailer vary predictably with seasons.
Some things are hard to forecast.
  • Exchange rates, stock prices, and lottery numbers resist systematic prediction.
  • Random shocks and human behavior create irreducible uncertainty.

What can be forecast?

Some things are easy to forecast.
  • Tomorrow’s electricity demand follows a regular daily pattern.
  • Next month’s sales at a large retailer vary predictably with seasons.
Some things are hard to forecast.
  • Exchange rates, stock prices, and lottery numbers resist systematic prediction.
  • Random shocks and human behavior create irreducible uncertainty.
Forecastability depends on three factors.
  • How well we understand the drivers of the variable.
  • How much relevant historical data is available.
  • Whether our forecasts themselves affect the outcome.

What is the difference between forecasting, planning, and goals?

Forecasting, planning, and goals are related but distinct.
Forecasting is a prediction about the future based on available information — it describes what is likely to happen if nothing changes.
Planning is the response to the forecast: deciding what to do given what we expect.
Goals are what we want to happen — desirable outcomes that may or may not align with forecasts.
A forecast that says “sales will fall 10%” is not a goal; it is information that should trigger a plan.
Forecast horizons vary with the decision at hand.
Horizon Typical length Example
Short-term Days – weeks Staffing, inventory ordering
Medium-term Months – 1–2 years Production planning, budgets
Long-term Years – decades Capital investment, infrastructure
Accuracy generally falls as the horizon lengthens — uncertainty compounds over time.

Before building a model, what decisions must you make?

Determining what to forecast

Identify the right variable and level of aggregation.
  • Total company sales vs. sales by product line vs. sales by store.
  • Finer detail is harder to forecast but more actionable for operations.
Choose the forecast horizon.
  • How far ahead does the decision require a forecast?
  • A short horizon allows use of more recent data; a long horizon requires robust models.
Decide how often forecasts will be updated.
  • Weekly, monthly, or quarterly — depends on data frequency and operational needs.

What are the two broad classes of forecasting methods?

Qualitative and quantitative methods

Qualitative methods use expert judgment, not historical data.
  • Used when little or no numerical history exists (new product launches, rare events).
  • Examples: Delphi method, market research, expert panels.
Quantitative methods use numerical data and statistical models.
  • Require sufficient historical data and an assumption that past patterns persist.
  • Two main types: time series models and explanatory models.
This course focuses on quantitative methods.
  • We will use R and the fpp3 framework throughout.
Two types of quantitative forecasting models.
Time series models use only the variable’s own past values to predict the future. The pattern in the data — trend, seasonality, cycles — is projected forward.
Explanatory models use other variables (predictors) to explain and forecast. A model of electricity demand might include temperature, day of week, and economic activity.
In practice, forecasters often combine both approaches. We will study them in sequence.

What are the basic steps in a forecasting task?

The basic steps in a forecasting task

1. Problem definition.
  • What exactly needs to be forecast, and who will use the forecasts?
2. Gather information.
  • Statistical data (historical observations) and expert domain knowledge.
3. Preliminary (exploratory) analysis.
  • Plot the data. Look for trends, seasonality, outliers, and structural breaks.
4. Choose and fit models.
  • Select candidate models based on the data’s features. Estimate parameters.
5. Evaluate and use.
  • Assess accuracy on held-out data. Deploy the best model; update regularly.

What does it mean to take a statistical perspective on forecasting?

A forecast is a probability distribution, not just a number.
Let yt be the value of the variable at time t. Given information I available at time T, the forecast for horizon h is the conditional distribution:
yT+h | I
The point forecast is typically the mean (or sometimes median) of this distribution.
A prediction interval captures uncertainty: an 80% interval contains the true value 80% of the time in repeated forecasting.

Why prediction intervals matter

A point forecast is never exactly right.
  • Even a perfect model cannot eliminate randomness — the future has an irreducible stochastic component.
Decision-making requires knowing the range of outcomes.
  • A retailer ordering inventory needs to know the low and high demand scenarios, not just the average.
  • Overconfidence in point forecasts leads to systematically poor planning.
Intervals widen with the horizon.
  • Uncertainty compounds: a 1-day ahead forecast is much tighter than a 1-year ahead forecast.
Forecast accuracy is measured by forecast errors.
The forecast error for period t is: et = yt − ŷt, where ŷt is the forecast.
Common accuracy measures:
  • MAE (Mean Absolute Error) — average of |et|; easy to interpret in the original units.
  • RMSE (Root Mean Squared Error) — penalizes large errors more heavily than MAE.
  • MAPE (Mean Absolute Percentage Error) — scale-free; useful for comparing across series.
A good model has small, randomly distributed errors with no systematic pattern (bias).
Most business time series can be decomposed into components.
Trend (T) — the long-run direction of the series. Sales that grow year over year have an upward trend.
Seasonality (S) — regular, calendar-driven fluctuations. Retail sales spike every December; ice cream sales peak every summer.
Cycle (C) — longer irregular waves driven by the business or economic cycle. Unlike seasonality, cycles do not have a fixed period.
Remainder (R) — the leftover variation after removing trend, seasonality, and cycles. Ideally small and random.
This course builds a complete forecasting toolkit.
We will move from simple benchmarks to state-of-the-art models, always asking: does additional complexity pay off in accuracy?
  • Time series graphics and decomposition
  • Exponential smoothing (ETS) models
  • ARIMA models
  • Regression with time series errors
  • Dynamic regression and advanced topics
All forecasting will be done in R using the fpp3 package suite. No prior R experience is assumed.
Practice Questions
Question 1 of 4

Key Terms