Question

In time series analysis of forecasting technique, which of the source variation can be estimated by ratio to trend method?

• A. Cyclical
• B. Irregular
• C. Trend
• D. Seasonal

Hint:

The Ratio-to-Trend method divides out the baseline trend vector from time series data to calculate precise Seasonal Indices.

Answer 1

The Correct Option is D

Concept: A time series data model contains four distinct components of variation:

• Trend ($T$): Long-term upward or downward directional shifts over years.

• Seasonal ($S$): Variations that repeat regularly within a fixed period of one year or less (e.g., higher ice cream sales in summer).

• Cyclical ($C$): Long-term oscillations around the trend line driven by multi-year economic business cycles.

• Irregular ($I$): Unpredictable random shocks or noise.
The Ratio-to-Trend Method assumes a multiplicative relationship among these time series components: \[ Y = T \times S \times C \times I \]

Step 1: Explain the operational steps of the Ratio-to-Trend method. 1. The long-term trend value (\( T \)) is calculated for each period using a linear regression model. 2. The actual observed data value (\( Y \)) is divided by its calculated trend value (\( T \)): \[ \frac{Y}{T} = \frac{T \times S \times C \times I}{T} = S \times C \times I \] 3. By averaging these ratios across multiple years for identical calendar periods (e.g., averaging all past month-of-July values), the cyclical and irregular variations smooth out toward baseline averages. This isolates the Seasonal Index ($S$). Therefore, this method is primarily used to isolate and estimate seasonal variations.