CUET · MATHS · PYQ PAPER 2025
If \(\left(t_1, y_1\right),\left(t_2, y_2\right)\),...,\(\left(t_n, y_n\right)\) denote the time series and \(y_t\) are the trend values of the variables \(y\), then
- A \(\sum_{i=1}^n\left(y_i-y_t\right)=0\)
- B \(\sum_{i=1}^n\left(y_i-y_t\right)=1\)
- C \(\sum_{i=1}^n\left(y_i-y_t\right)=\infty\)
- D \(\sum_{i=1}^n\left(y_i-y_t\right) \neq 0\)
Answer & Solution
Correct Answer
(A) \(\sum_{i=1}^n\left(y_i-y_t\right)=0\)
Step-by-step Solution
Detailed explanation
In the context of time series analysis, when we calculate the trend component \(\left(y_t\right)\) using methods like moving averages or regression, the sum of the deviations (observed values minus trend values) is typically zero. This is because the trend is the best-fitting…
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