TSF Cheat Sheet

Core Definitions

Time series

Same variable observed in time order, usually at equal intervals.

Forecast

Estimated future value based on past observations and assumptions.

Trend

Long-term direction: increasing, decreasing, or roughly constant.

Seasonality

Fixed-period repeated movement, such as monthly or quarterly pattern.

Irregular component

Random leftover variation after systematic parts are explained.

De-seasonalize

Remove seasonal effect to study the underlying trend more clearly.

Component Models

Additive: Yt = Tt + St + It

Multiplicative: Yt = Tt x St x It

Forecast error: et = yt - y_hat_t

Straight trend: y = a + bx

Parabolic trend: y = a + bx + cx^2

Unit 2 Formulas

Naive: y_hat_(t+1) = yt

Average: y_hat_(t+1) = (y1 + ... + yt) / t

Moving average: y_hat_(t+1) = sum(last n observations) / n

Centered even MA: (MA_i + MA_(i+1)) / 2

SES: y_hat_(t+1) = y_hat_t + alpha(yt - y_hat_t)

Holt forecast: F_(t+h) = Lt + hBt

Decision Table

Question asks about	Write or do this	Do not forget
Forecasting methods	Compare qualitative and quantitative.	Give examples for each.
Time series components	Trend, seasonal, cyclical, irregular.	Seasonality repeats at fixed intervals.
Decomposition	State additive and multiplicative models.	Additive constant amplitude, multiplicative proportional amplitude.
i-yearly moving average	Calculate rolling means for window i.	Center even-period averages.
Exponential smoothing	Explain weights decline exponentially.	Alpha, beta, gamma are between 0 and 1.
Model performance	Compare actual and forecast.	Use same test period for fair comparison.

Fast Answer Templates

Types of exponential smoothing

Define exponential smoothing. Then write: SES is used for no trend/no seasonality; Holt or double exponential smoothing is used for trend/no seasonality; Holt-Winters or triple exponential smoothing is used for trend with seasonality. Mention level, trend, and seasonal components.

Moving-average numerical

Write the data row, mention the window size, compute consecutive totals, divide by the window size, align values to the center period, and center again if the window size is even.

Forecast validation

State that time series test data must be the latest part of the series. Do not randomly shuffle. If seasonality exists, keep at least one complete season for validation.

Common Mistakes

Using random train-test split for time series.
Forgetting to center a 4-year moving average.
Calling a cyclical movement seasonal even when the period is not fixed.
Using SES when a clear trend is visible.
Writing multiplicative decomposition for data whose seasonal swing is constant.
Comparing RMSE from different test windows.