i) If a time series data is expressed by a growth model Y_t = beta_0 (beta^t_1)
ID: 3182921 • Letter: I
Question
i) If a time series data is expressed by a growth model Y_t = beta_0 (beta^t_1) elementof _t show that Y_t = (Y_t - 1) beta_1 elementof_t. ii) For a certain growth model based on 10 years observations collected quarterly the prediction equation is given by: lnY = 3.118 + 0.2555 t a) Use the regression equation to estimate the following three periods. b) Estimate the growth rate of the data. c) Use the fact in (i) above "growth rate technique" to forecast Y_41 given that Y_40 = 620935, compare the result with (a)Explanation / Answer
Q.4 (i) Yt = 0 (t1) t...............(i)
Yt-1 = 0 (t-11) t-1............(ii)
by doing (i)/(ii)
Yt /Yt-1 = 1 t
Yt = Yt-1 1 t
(ii) lnY = 3.118 + 0.2555t
a) for following three periods t = 41,42,43 quarters
b) average growth rate r = exp ((ln(pn/p1))/n) - 1
where pn and p1 are the last and first observations in the period, n is the number of years in the period, and ln is the natural logarithm operator. This growth rate is based on a model of continuous, exponential growth between two points in time.
pn = p40 = exp(3.118 + 0.2555 * 40) = 620325
pn = p0= exp(3.118 ) = 29
r = exp ((ln(620325/29))/40) - 1 = 0.2830
c) Yt = exp ( 3.118 + 0.2555t) = e3.118 * e0.2555t = 22.60 * (1.2904)t
so 1= 1.2904
Y41 = Yt-1 1 t = Y40 * (1.29) = 620935 * 1.29 = 801000
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