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Unit 3: Time Series Points to Remember Year 1 2 3 In case of 3 yearly moving averages Data In case of 4 yearly moving averages 4 yearly sums 2 item Sums Trend Start Here In case of 5 yearly moving averages Year Data 1 2 3 Trend Start Here Year Data 1 2 3 4 3 yearly sums 5 yearly sums Trend Start Here In case of 2 yearly moving averages Year Data 1 2 2 yearly sums 2 item Sums Trend Start Here Year For equation y=a+bx y ∑y x2 x ∑x ∑x2 xy ∑xy For equation y =a+bx+cx 2 Remember the following na+b∑x+c∑ x2 =∑y a∑x +b∑x2+c∑ x3=∑xy a∑x2 +b∑x3+c∑ x4=∑x2y Here ‘n’ is the number of values. Year y ∑y x2 x ∑x ∑x2 x3 ∑x3 x4 ∑x4 xy ∑xy x2 y ∑x2y For questions in the equation format, substitute the values of x in the equation once you arrive at the solution to get the trend values. Exponential Trend This is given as: y=abx Where ‘y’ denotes time series data, x denotes time, a and b are constants log y = log a + x log b log 𝑎 = log 𝑏 = ∑ log 𝑦 𝑛 ∑ 𝑥 log 𝑦 ∑ 𝑥2 𝑎 = 𝑎𝑛𝑡𝑖𝑙𝑜𝑔 [ 𝑏 = 𝑎𝑛𝑡𝑖𝑙𝑜𝑔 [ Year y x x2 log y ∑ 𝑙𝑜𝑔 𝑦 ] 𝑛 ∑ 𝑥 𝑙𝑜𝑔 𝑦 ] ∑ 𝑥2 x log y When they ask you to find trend, solve the equation for log y by taking antilog of the answer.