international econometric journal
in Russian language
This jubilee issue is dedicated to the 20th anniversary
of the New Economic School
In this essay we provide the basic asymptotic theory that serves as background theory for estimators in time series. We outline concepts of dependence used for stochastic limit theory, covering mixing, mixingale and near epoch dependence properties. We then detail some of the most general probability and distribution limit theorems for these processes popularly employed for time series theory and applications.
This essay surveys results for linear time series including Wold decomposition, properties of spectral density functions and lag operators, autoregressive moving average models, Beveridge–Nelson decomposition, and Phillips–Solo device for deriving asymptotics.
Sometimes the conventional asymptotic theory yields that the limiting distribution changes discontinuously, or that the asymptotic distribution does not approximate accurately the actual finite-sample distribution. In such situations one finds useful an asymptotic tool of drifting parameterizations where certain parameters are allowed to depend explicitly on the sample size. It proves useful, among other things, for impulse response analysis and forecasting of strongly dependent processes at long horizons. This essay provides a review of these alternative asymptotic approximations in the context of time series models.
We investigate properties of the volatility estimator, which is proportional to the square of oscillations of the bridge formed by the logarithm of the incremental price of a financial instrument at a specified time interval. In the framework of the geometric Brownian motion model for price increments we show by analytical computations and statistical simulations that the proposed volatility estimator by the bridge is much more efficient than the well-known Parkinson and Garman–Class estimators. We also discuss possible usages of the estimators for estimation of integrated volatility.
extend the work of Gonçalves & Meddahi (2009) who suggest using the
iid and wild bootstrap for realized volatility instead of the asymptotic
approach in order to estimate integrated volatility. We propose the block
bootstrap and GARCH residual bootstrap approaches motivated by the persistence
of the intraday term structure of returns. Using