Quantile

international econometric journal
in Russian language

no. 10

december 2012

 

This jubilee issue is dedicated to the 20th anniversary

of the New Economic School

 

Econometric literacy: time series asymptotics

 

Hill, Jonathan. Dependence and stochastic limit theory

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.

Marmer, Vadim. Linear processes: properties and asymptotic results

This essay surveys results for linear time series including Wold decomposition, properties of spectral density functions and lag operators, autoregressive moving average models, BeveridgeNelson decomposition, and PhillipsSolo device for deriving asymptotics.

Anatolyev, Stanislav; Gospodinov, Nikolay. Asymptotics of near unit roots

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.

 

Articles: finance

 

Lapinova, Svetlana; Saichev, Alexander; Tarakanova, Maria. Volatility estimation based on extremes of the bridge

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 GarmanClass estimators. We also discuss possible usages of the estimators for estimation of integrated volatility.

 

Articles: financial econometrics

 

Rafalson, Andrey. Bootstrap inference about integrated volatility

We 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 Monte Carlo simulations we show that the block bootstrap is more accurate for a low intraday frequency, more robust and valid. Another result is that the GARCH bootstrap outperforms others when the data imply strong persistence in conditional heteroskedasticity. It also demonstrates good inference on simulated data along the baseline model with a high frequency. However, the GARCH bootstrap is more computationally costly and less robust than the others.

 

 International econometric journal in Russian language Quantile, 20062013
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