Which of the following statements are correct?

A. If $x_1,x_2,x_3,\dots,x_n$ is the given annual time series, then 3-yearly moving averages are $\dfrac{x_1+x_2+x_3}{3},\dfrac{x_2+x_3+x_4}{3},\dots\dots$

B. In the method of the least squares, if $(t_1,y_1),(t_2,y_2),\dots(t_n,y_n)$ denote the time series and $y_t$ are trend values of $y$, then $\sum(y-y_t)=0$

C. In the method of the least squares, the sum of squares of the deviations of the values of $y$ from their corresponding trend values is least.

D. The rise in prices before Diwali is an example of a cyclical trend.

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Match List-I with List-II

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Let $y = 138.86 + 7.64(x - 2021)$ be a straight line of best fit by using least square method to the following data:

Then the trend value for the year 2024 is:

Consider the following data

Then for the above data the equation of straight line trend by method of least square is given by:

For the given 9 values, 4,5,5,6,7,8,9,8,10, the three years moving averages are

Due to which of the following, the irregular variations in a time series are caused:

(A) Floods

(B) Rise in prices before festivals

(C) A fire in a factory

(D) Epidemics

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Consider the following data:

Using method of least squares, the trend value for year 2004 will be