Volatility reflects the degree of deviation between actual value and price, and can also be used to measure the degree of market response to external information. Volatility is closely related to market operation efficiency, and its size will change with the change of market operation efficiency, while financial time series data generally have the characteristics of peak, thick tail, fluctuation aggregation and long memory.

In order to find out the time-varying characteristics and connotation of volatility in conditional variance, Engle first proposed ARCH model. Its basic idea is that the conditional variance of the disturbance term is a quantity that changes with time and is a linear combination of its finite square of the previous value.

The standard ARCH(p) model is:

Yt=βxt+μt (formula 1)

μt|φt- 1~N(0，σ2)

var(μt)=σ2t =ω+α 1μ2t- 1+α2μ2t-2+……+αpμ2t-p

(Formula 2)

Where φt- 1 is the information set, and the constraint ω >; 0，αi≥0(i= 1，2……p).

The ARCH(p) model consists of the following two parts:

First, the formula (1) is a mean equation;

Second, in formula (2), σ2 is the conditional variance, μ2t- 1(t= 1, 2...p) is the lag residual square, also called the ARCH term. However, in practice, it is easy for μt to lag behind the order, and this model with more parameters will affect the accuracy of its parameter estimation.