Abstract
In this work we study a variant of the GARCH model when we consider the arrival of heterogeneous information in high-frequency data. This model is known as HARCH(n). We modify the HARCH(n) model when taking into consideration some market components that we consider important to the modeling process. This model, called parsimonious HARCH(m,p), takes into account the heterogeneous information present in the financial market and the long memory of volatility. Some theoretical properties of this model are studied. We used maximum likelihood and Griddy-Gibbs sampling to estimate the parameters of the proposed model and apply it to model the Euro-Dollar exchange rate series.
Highlights
High frequency data are those measured in small time intervals
This model incorporates heterogeneous characteristics of high frequency financial time series and it is given by rt = σtεt, σt2 = c0 + ∑nj=1 cj where c0 > 0, cn > 0, cj ≥ 0 ∀j = 1, . . . , n − 1 and εt are identically and independent distributed (i.i.d.) random variables with zero expectation and unit variance
We propose a new model known as the parsimonious heterogeneous autoregressive conditional heteroscedastic model, in short-form PHARCH, as an extension of the HARCH model
Summary
High frequency data are those measured in small time intervals. This kind of data is important to study the micro structure of financial markets and because their use is becoming feasible due to the increase of computational power and data storage. The HARCH(n) model was introduced by Müller et al (1997) to try to solve this problem This model incorporates heterogeneous characteristics of high frequency financial time series and it is given by rt = σtεt, σt2 = c0 + ∑nj=1 cj. N − 1 and εt are identically and independent distributed (i.i.d.) random variables with zero expectation and unit variance This model has a high computational cost to fit when compared with GARCH models, due to the long memory of volatility, so the number of parameters to be estimated is usually large. HARCH models are important because they take account the natural behavior of the traders in the market They have some problems, mainly because they need to include several aggregations, so the number of parameters to estimate is large, because of the large memory feature of financial time series.
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