# 英国贝尔法斯特论文代写：异方差模型

ARMA模型是自回归滑动平均模型。这是AR和MA模型在一个方程的组合。在自回归模型中，自变量是因变量的一个或多个滞后项。

This essay tries to determine the volatility of a financial time series data. The volatility of time series data is empirically determined by the ARCH/GARCH models. ARCH or Autoregressive Conditional Heteroskedascticity is a model developed to regress the residuals on their lagged squares. This means that the dependent variable is the data which is to be forecasted at time and the independent variable is the square of the residual of the ARIMA model at time t-1. This model is called ARCH(1) owing to one lag. This simplified model can also be extended to ARCH(p) where p lag terms are used.

This essay tries to implement the use of the ARCH model to forecast volatility of a certain stock. Volatility in the price is determined by the error term of the ARIMA model. ARCH or its generalized version called GARCH are popular in the analysis of financial time series data because they do not use a separate independent variable but the error term itself which reduces certain problems in regression. When a separate explanatory variable is used, it may lead to the problems of wrongful estimation, as one is never sure of the extent of causality between the two variables. Sometimes when a proxy explanatory variable is used, it even leads to biased estimation. The coefficients thus estimated may not be BLUE (Best Linear Unbiased Estimators).

Thus, the ARCH estimation takes statistical analysis of the financial time series a step further. Furthermore, conditional forecasts done in the ARCH model are far superior to their unconditional counterparts. The vast application for an ARCH model comes from the fact that the residuals in the model can come from an autoregressive model, ARMA model or any other standard regression model.

This essay tries to apply the ARCH/GARCH model to the daily IBM stock returns taken from January 2, 1980 to September 13, 2013.

Empirical Framework

The essay intends to use GARCH model using the residuals of an ARMA model. The different models are compared by using Schwarz Information Criteria (SIC).

ARMA model is Autoregressive Moving Average Model. It is a combination of AR and MA models in one equation. In an autoregressive model, the independent variable is one or more lagged terms of the dependent variable.