A Functional Garch Model with Multiple Constant Parameters

The emergence of high-frequency time series has led to the development of research on functional methods. Recently, many studies have used functional ARCH or GARCH class models to describe intraday volatility. However, these studies use a similar mathematical structure to address the problem of which integral operator to use. In this paper, we extend the structure of the integral operator and propose a functional GARCH model with multiple constant parameters (fMCGARCH). The addition of these parameters expands the space where the conditional variance is located. This helps to include more information when calculating the conditional variance. Additionally, it helps to consider different periods of time for intraday data. We provide the theoretical results and the specific parameter estimation process for the fMCGARCH model. A simulation study is performed to evaluate the finite-sample performance. An application to real data shows that the fMCGARCH model has a better fit and stable volatility prediction in the stock market.