Question:easy

The patterns and behavior of the data in any time series are based on which of the following components.
A. Seasonal component
B. Secular trend component
C. Irregular component
D. Cyclical component
Choose the correct answer from the options given below:

Show Hint

A time series has four components: trend, seasonal, cyclical and irregular.
Updated On: Oct 1, 2026
  • A and B only
  • B and C only
  • B, C and D only
  • A, B, C and D
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Idea:
Recall the classical decomposition of a time series and count the parts.

Step 2: Write the model.
The value at time $t$ is built from $T_t$ (trend), $S_t$ (seasonal), $C_t$ (cyclical) and $I_t$ (irregular). For example, in the multiplicative model: \[ Y_t = T_t \times S_t \times C_t \times I_t \]

Step 3: Match each statement.
A is $S_t$, B is $T_t$, C is $I_t$ and D is $C_t$. Every statement names one of the four terms.

Step 4: Rule out shorter lists.
If we drop any term, the model cannot explain all patterns. For example, without $S_t$ we cannot explain repeating yearly peaks, and without $C_t$ we cannot explain multi-year booms and slumps.

Step 5: Select the option.
The list that has all four is A, B, C and D, which is option 4.

Final Answer:
All four components shape a time series. \[ \boxed{\text{A, B, C and D}} \]
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