英国贝尔法斯特论文代写：异方差模型

英国贝尔法斯特论文代写：异方差模型

本文试图确定金融时间序列数据的波动性。时间序列数据的波动性经验确定的ARCH / GARCH模型。拱或自回归条件异方差性开发回归残差对滞后最小二乘模型。这意味着，因变量是数据是可预测的时间和独立变量是ARIMA模型的残差的平方在时间t-1。这种模式被称为拱（1）由于一个滞后。这种简化模型也可以扩展到拱（P）P滞后项使用。

本文试图利用ARCH模型预测某一股票的波动性。价格的波动取决于ARIMA模型的误差项。ARCH或它的广义版本称为GARCH是流行的金融时间序列数据的分析，因为他们不使用一个单独的独立变量，但误差项本身，减少了某些问题的回归。当一个单独的解释变量被使用时，它可能会导致错误估计的问题，因为一个是从来没有把握两个变量之间的因果关系的程度。有时，当使用代理解释变量，它甚至导致有偏估计。因此，估计的系数可能不是蓝色（最佳线性无偏估计）。

因此，ARCH估计的金融时间序列的统计分析进一步。此外，ARCH模型的条件预测远远优于他们的无条件同行。ARCH模型的巨大应用来自模型中的残差可以来自自回归模型，ARMA模型或任何其他标准回归模型的事实。

本文尝试应用ARCH / GARCH模型，从1980年1月2日至2013年9月13日的每日IBM股票回报率。

实证框架

本文利用ARMA模型残差的GARCH模型。不同的模型进行比较，使用施瓦茨信息标准（SIC）。

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。

英国贝尔法斯特论文代写：异方差模型

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.