Lesson 10 — Time Series for Business/Economics

(trend, seasonality, forecasting baselines, and honest evaluation)

Why this matters (motivation)¶

Business and economics are full of time-indexed questions:

• How will sales evolve next month?

• Is inflation accelerating or stabilizing?

• Are customer visits seasonal?

• Did a policy change coincide with a shift in a trend?

Time series analysis gives a disciplined way to:

• describe patterns over time,

• and forecast future values with transparent assumptions.

Time series mindset: time is not just another variable¶

Unit of observation (again)¶

Be explicit:

• daily sales (store-day),

• monthly inflation (country-month),

• quarterly GDP (country-quarter).

This determines what “seasonality” means and what forecasts are useful.

Describing time series: the three components¶

A useful conceptual decomposition: [ y_t = \text{trend}_t + \text{seasonality}_t + \text{noise}_t ] (or multiplicative forms when growth is proportional).

Trend¶

Long-run movement (growth/decline).

Seasonality¶

Regular cycles (day-of-week, monthly, quarterly).

Noise (irregular component)¶

Random shocks, measurement noise, one-off events.

Forecasting as a benchmark game¶

Baseline 1: naïve¶

[ \hat{y}_{t+1} = y_t ]

Baseline 2: seasonal naïve¶

[ \hat{y}{t+h} = y{t+h-s} ] where (s) is seasonal period (e.g., 12 for monthly with yearly seasonality).

Baseline 3: moving average¶

Forecast using recent average: [ \hat{y}{t+1} = \frac{1}{k}\sum{i=0}^{k-1} y_{t-i} ]

How to evaluate forecasts (practically)¶

Time-based splitting¶

• Train on early period

• Test on later period (“future”)

Example:

• Train: 2010–2019

• Test: 2020–2023

Metrics (choose one or two and interpret)¶

• MAE (mean absolute error): easy to interpret in units

• RMSE (root mean squared error): penalizes large errors more

• MAPE (percentage error): intuitive but unstable when values near zero

Visual communication for time series¶

Minimum set of plots that actually helps:

1. Line plot of the series (with clear time axis)

2. Rolling average (optional) to show trend

3. Seasonality view (e.g., month-of-year average or day-of-week average)

4. Forecast plot: actual vs predicted for the test window

Mini case options (choose one)¶

Option A (business): sales forecasting¶

• Weekly or monthly sales

• Forecast next month/quarter

• Use seasonal naïve if clear seasonality

Option B (economics): OWID time series¶

Use an OWID dataset that is time-indexed (country-year, country-month, etc.). Examples:

• CO₂ emissions per capita

• GDP per capita

• energy consumption

• inflation (if available in your chosen dataset)

Focus: describe trend/seasonality and create a baseline forecast.

Mini-lab (Google Colab)¶

In-class checkpoints (data preparation)¶

1. Load a time series dataset with a clear time column.

2. Sort by time and set the time column correctly (datetime or integer year).

3. Plot the full time series and write one sentence describing the main pattern.

In-class checkpoints (decomposition / pattern checks)¶

4. Compute a rolling average (choose a window and justify).

5. If seasonal frequency exists (e.g., monthly), compute a seasonal profile:

   • average by month-of-year or day-of-week.

In-class checkpoints (forecast baselines)¶

6. Create a train/test split by time (e.g., last 20% as test).

7. Implement at least two baselines:

   • naïve

   • moving average OR seasonal naïve

8. Plot predictions vs actual in the test window.

In-class checkpoints (evaluation)¶

9. Compute MAE and RMSE for each baseline on the test window.

10. Choose the “best” baseline and justify using both:

• metric evidence, and

• business reasoning (what errors matter?).

Submission (after class)¶

• Colab link (view permission) or PDF export.

• Include:

  • your forecast plot,

  • metric table,

  • and a short “forecast memo” (headline + caveat + what could break it).

AI check (responsible use for time series)¶

Good prompt examples

• “Write Python code to split a time series into train/test by date and compute MAE.”

• “Implement a seasonal naïve forecast for monthly data with period 12.”

• “Suggest a clear plot to compare forecasts vs actual in the test period.”

Bad prompt example

• “Pick the best model and guarantee the forecast is accurate.”

Review questions (quiz / reflection)¶

1. Why should train/test splits be done by time for forecasting?

2. What is a naïve forecast, and why is it a strong baseline?

3. When might MAPE be misleading?

4. Give one factor that could cause a forecast to fail (structural break).