City University of Department of Economics and Finance
Course EF5213 Assignment #1 ( due February 6, 2022)
1. In GARCH(1,1) model, future variance is a weighted average of its immediate past estimation, the most recent observation of squared residual of price return, and a long-run average variance. It follows an iteration equation given by
2 (1)VL (r )2 2 t1tt
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with weight factors 0, 0, and 1. The parameters and VL can be estimated based on the historical mean and variance, respectively, of a given time series {r1, … , rn} as (1/n)(r1 … rn) andVL (1/n)[(r1 )2 …(rn )2 ].
(a) Given, in file HSI.csv, historical daily closing prices for Hang Seng Index from 2001 to 2020 as {timestamp, open, high, low, close, volume}
use VBA to develop a procedure that captures the time series of price returns as
This return This close Last close Last close
(b) Determine the GARH(1,1) model for the extracted time series in (a). The parameters and should be determined by considering the notion of minimizing root-mean-square error (RMSE) defined as
RMSE√1n ∑nt1[2t (rt )2 ]2
based on the historical time series of price returns { r1 , r2 , … , rn }. For this purpose, use the enclosed
Brent’s minimizer from netlib with your own modification on functions f(), fa2(), and fb2(). Sample user interface is given below:
(40 points)