Time Series • Statistics Background for Forecasting
Time Series / General Approach to Time Series Modelling and Forecasting

General Approach to Time Series Modelling and Forecasting

Notes 3 Statistics Background for Forecasting

The general approach to time series modelling and forecasting is a planned sequence of steps: define the task, prepare data, study pattern, choose and fit a method, evaluate it, produce a forecast, and then watch how well it performs.

Notes

General Approach to Time Series Modelling and Forecasting

Definition

The general approach to time series modelling and forecasting is a planned sequence of steps: define the task, prepare data, study pattern, choose and fit a method, evaluate it, produce a forecast, and then watch how well it performs.

Example

A shop wants a forecast of monthly packet sales for the next three months. It collects past monthly sales, plots them, notes a gentle rise, fits a simple method on earlier months, checks the method on later months, then forecasts and later compares the forecast with actual sales.

Standard Workflow

1. Define forecasting objective ↓ 2. Collect data ↓ 3. Inspect and clean data ↓ 4. Visualize data ↓ 5. Identify structure ↓ 6. Transform/adjust if required ↓ 7. Select candidate model ↓ 8. Fit model ↓ 9. Evaluate model ↓ 10. Generate forecast ↓ 11. Monitor performance

Meaning of Each Step

  1. Define the objective: state what will be forecast, for which dates, and for what decision (for example, next three months of sales for stock planning).
  2. Collect data: gather a long enough history at the right frequency (here, monthly sales).
  3. Inspect and clean: check missing values, typing errors and impossible figures.
  4. Visualize: draw a time series plot before choosing a method.
  5. Identify structure: note trend, seasonality, unusual points or a change in behaviour.
  6. Transform or adjust if required: use a log, a difference or another simple change only when the plot suggests it. Detailed ARIMA order selection belongs to Unit 3.
  7. Select a candidate model: start with a method that matches the visible structure (for example a simple trend summary, not an advanced seasonal ARIMA at this stage).
  8. Fit the model: estimate the method using historical data set aside for fitting.
  9. Evaluate: compare forecasts with observations that were not used in fitting.
  10. Generate the forecast: produce future values and, where possible, a sense of uncertainty.
  11. Monitor: when new actual sales arrive, compare them with the forecast and revise the method if performance worsens.

Training Data, Test Data and a Simple Sales Example

Training Data and Test Data

Training data (also called fitting data) are the earlier observations used to build the method. Test data (evaluation data) are later observations held back to check how well the method forecasts new time points.

Example

Use January–September sales to fit a simple method. Keep October–December to evaluate it. Do not judge the method only on the months that were used to fit it.

The split must respect time: test months come after training months. Randomly mixing months would destroy chronological order.

End-to-End Illustration: Monthly Sales

Objective: forecast the next quarter of packet sales. Data: two years of monthly sales, cleaned for missing months. Plot: a gentle rise and a December peak. Structure: trend plus yearly seasonality is suspected. Adjustment: none required at first if variation looks stable. Candidate method at Unit 2 level: a simple combination of a trend idea and a seasonal comparison of Decembers — not a full SARIMA. Fit on the first 21 months, evaluate on the last 3 months, then forecast the next 3 months and later monitor them against actuals.

Exam Note

Unit 2 teaches the workflow. Choosing ARIMA or SARIMA orders is a Unit 3 task.

Exam-Oriented Key Points

  1. Forecasting follows a sequence from objective and data through plot, structure, optional transform, fit, evaluate, forecast and monitor.
  2. Always plot before selecting a method.
  3. Training data are used to fit; test data are later dates used to evaluate.
  4. A good in-sample fit is not enough; later performance must be checked.