# 代寫essay：基於GARCH模型構建財務模型

t =μ+∅rt-1

t2 =ω+αt-12 +βt-12

rt = t + t

t = tzt

rt =回報

t =殘差

t= rt的條件均值

t2= rt的條件方差

∅= < 1

ω> 0

α,β≥0

α+β> 1

Methodology: Build the financial model based on the GARCH model
This is one of the important part of this study to formulate the required and best model that is capable of handling this much data and is able to do the time series analysis. With help of the various methods as discussed above, the GARCH model was finalized. This was finalized because it is one of the best method or model to analyse or regress the financial time series data and characterize (Gurarda et al., 2016). This model is also applied because in the collected data above for 50 Chinese listed companies, there are lot number data points which were there in a series such that the variance for the error term or the innovation it actually the function which is related to the overall size of the error taken during the previous time periods.

This was the reason for choosing GARCH model as the best suitable method with three different models for this study to provide the required results or outputs form the given data. In GARCH model the volatility is given as:
t=μ+∅rt-1
t2=ω+αt-12+βt-12
rt=t+t
t=tzt
Where,
zt= independent and identically distributed process
rt=returns
t=residuals
t= conditional mean of rt
t2= conditional variance of rt
With given conditions as
∅=<1 ω>0
α,β≥0
α+β>1

These conditions are suitable for GARCH model to adopt in the process for analysing the leverage effect. The leverage effect is normally caused with the fact that negative returns have a greater influence on future volatility than do positive returns.