Question

Using appropriate algebra and diagrams critically analyse the concept of ARCH:

Discuss why ARCH models are particularly useful to a financial analyst.

Answer 1

(Q) Discuss why ARCH models are particularly useful to a financial analyst.

(Ans) Autoregressive conditional heteroskedasticity (ARCH) is a time-series statistical model used to analyze effects left unexplained by econometric models. In these models, the error term is the residual result left unexplained by the model. The assumption of econometric models is that the variance of this term will be uniform. ARCH and GARCH models have become important tools in the analysis of time series data, particularly in financial applications. These models are especially useful when the goal of the study is to analyze and forecast volatility. ARCH/GARCH model are extensively used to measure volatility and are considered as risk management tools, especially used for portfolio optimization.  GARCH has been used with timeseries data for forecasting purposes, such as stock prices and rates, and models the financial time-series data to detect the clusters of prices or losses in a short time-span. Once the temporal clusters are detected, the model can be used to forecast a "value-at-risk" that should be avoided (ideally).

  ARCH models attempt to model the variance of these error terms, and in the process correct for the problems resulting from heteroskedasticity. The goal of ARCH models is to provide a measure of volatility that can be used in financial decision-making.In financial markets, analysts observe something called volatility clustering in which periods of low volatility are followed by periods of high volatility and vice versa.