Forecasting

Predicting the future based on past data. Essential for inventory, sales, and budgeting.

Components of a Time Series

  • Trend (T): Long-term upward or downward movement.
  • Seasonality (S): Regular, repeating patterns (e.g., holiday sales).
  • Cyclical (C): Long-term wave-like patterns (e.g., business cycles).
  • Random (R): Unpredictable noise.

Smoothing Methods

Used to remove random noise to see the trend.

Moving Average (MA)

Average of the last $k$ periods.

$$ MA_t = \frac{\sum \text{last } k \text{ values}}{k} $$

Exponential Smoothing

Gives more weight to recent data.

$$ F_{t+1} = \alpha Y_t + (1-\alpha)F_t $$
$\alpha$ = Smoothing constant (0 to 1)

Trend Projection

Using linear regression where $X$ is time ($t$).

$$ \hat{Y} = b_0 + b_1t $$

Test Yourself

Q1: Which component represents regular, repeating patterns within a year?

  • Trend
  • Seasonality
  • Cyclical