Holt's method forecasting

Question

Can someone explain how 63 was achieved for T_{t. I have an idea how all other components are achieved.}

Can you write out the entire calculation to achieve at 63. I need this answer asap .

Thank you again

alpha 0.5, beta0.3, F_t 120, T_t 60, m 1

Year X₁ F_t T_t H_t

₁ 120 120 60

2 200 190 63

3 150 202 48

Answer 1

L(t) = alpha*F(t) + (1-alpha)*(L(t-1)+T(t-1))

T(t) = beta*(L(t)-L(t-1))+(1-beta)*T(t-1)

Forecast = Level + Trend

L(t=1) = 120; T(t=1) = 60

L(t=2) = 190; T(t=2) = 0.3*(190-120)+(1-0.3)*60 = 63

Similarly:

L(t=3) = 0.5*150+(1-0.5)*(190+63) = 201.5 = 202

T(t=3) = 0.3*(201.5-190)+(1-0.3)*63 = 47.55 = 48

Hope that helps!