Page 145 - Contributed Paper Session (CPS) - Volume 1

CPS1216 Teppei O.

Parameter estimation for misspecified
diffusion processes with noisy,
nonsynchronous observations
Teppei Ogihara
The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo

Abstract
Forecasting variances of stocks and covariances of stock pairs is an important
task to control the loss from stock assets for many financial institutions which
hold a huge amount of stocks. Statistical analysis of stock price data and data
of financial statements is useful for this purpose. Nowadays, we can easily get
intraday stock prices data such as all transactions of a stock in a day. Then, the
study of highfrequency data becomes more important because huge
information of highfrequency data enable us to forecast stock variances and
covariances more accurately. However, there are two problems on statistical
analysis of highfrequency data. The first one is market microstructure noise:
when we model stock prices by using diffusion processes, some empirical facts
suggest the existence of additional noise. The second one is nonsynchronous
observations: We observe stock prices when transactions occur. So
observation times must be different for different stocks.
In this talk, we study parametric inference under the existence of market
microstructure noise and nonsynchronous observations. We study
maximumlikelihood-type estimation for parametric diffusion processes with
noisy, nonsynchronous observations, assuming that the true model is
contained in the parametric family. We further study the case that this
assumption is not satisfied. Such a model is called a misspecified model.
Ogihara (2018) studied maximum-likelihood-type and Bayes-type estimation
for a model of parametric diffusion processes with noisy, nonsynchronous
observations, and showed asymptotic mixed normality of the estimators with
the convergence rate $n^{-1/4}$. In this model, we assume that the true model
is contained in the parametric family.
In practice for high-frequency data, to satisfy the assumption that the true
model is contained in the parametric family, we need to choose the parametric
family carefully so that it accurately captures microstructure of stock prices.
This is a difficult task because several empirical facts of a stock market (intra-
day seasonality, volatility clustering, complicated dependence structure of
stocks, and so on) make it difficult to capture the stock microstructure. On the
other hand, high-frequency data contains huge information and therefore
machine learning methods such as neural network or support vector machine
are useful to identify the structure of the diffusion coefficient. In this approach,
we need to consider a theory of misspecified model.

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