C32 Time-Series Models; Dynamic Quantile Regressions (Updated!)
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We extend the classical ”martingale-plus-noise” model for high-frequency prices by an error correction mechanism originating from prevailing mispricing. The speed of price reversal is a natural measure for informational efficiency. The strength of the price reversal relative to the signal-to-noise ratio determines the signs of the return serial correlation and the bias in standard realized variance estimates. We derive the model’s properties and locally estimate it based on mid-quote returns of the NASDAQ 100 constituents. There is evidence of mildly persistent local regimes of positive and negative serial correlation, arising from lagged feedback effects and sluggish price adjustments. The model performance is decidedly superior to existing stylized microstructure models. Finally, we document intraday periodicities in the speed of price reversion and noise-to-signal ratios.
We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced by Bibinger et al. (2014). We extend the LMM estimator to allow for autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. We prove the consistency and asymptotic normality of the proposed spot covariance estimator. Based on extensive simulations we provide empirical guidance on the optimal implementation of the estimator and apply it to high-frequency data of a cross-section of NASDAQ blue chip stocks. Employing the estimator to estimate spot covariances, correlations and betas in normal but also extreme-event periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, (iii) are strongly serially correlated, and (iv) can increase strongly and nearly instantaneously if new information arrives.
We propose an iterative procedure to efficiently estimate models with complex log-likelihood functions and the number of parameters relative to the observations being potentially high. Given consistent but inefficient estimates of sub-vectors of the parameter vector, the procedure yields computationally tractable, consistent and asymptotic efficient estimates of all parameters. We show the asymptotic normality and derive the estimator's asymptotic covariance in dependence of the number of iteration steps. To mitigate the curse of dimensionality in high-parameterized models, we combine the procedure with a penalization approach yielding sparsity and reducing model complexity. Small sample properties of the estimator are illustrated for two time series models in a simulation study. In an empirical application, we use the proposed method to estimate the connectedness between companies by extending the approach by Diebold and Yilmaz (2014) to a high-dimensional non-Gaussian setting.
We introduce a copula-based dynamic model for multivariate processes of (non-negative) high-frequency trading variables revealing time-varying conditional variances and correlations. Modeling the variables’ conditional mean processes using a multiplicative error model we map the resulting residuals into a Gaussian domain using a Gaussian copula. Based on high-frequency volatility, cumulative trading volumes, trade counts and market depth of various stocks traded at the NYSE, we show that the proposed copula-based transformation is supported by the data and allows capturing (multivariate) dynamics in higher order moments. The latter are modeled using a DCC-GARCH specification. We suggest estimating the model by composite maximum likelihood which is sufficiently flexible to be applicable in high dimensions. Strong empirical evidence for time-varying conditional (co-)variances in trading processes supports the usefulness of the approach. Taking these higher-order dynamics explicitly into account significantly improves the goodness-of-fit of the multiplicative error model and allows capturing time-varying liquidity risks.
Despite their importance in modern electronic trading, virtually no systematic empirical evidence on the market impact of incoming orders is existing. We quantify the short-run and long-run price effect of posting a limit order by proposing a high-frequency cointegrated VAR model for ask and bid quotes and several levels of order book depth. Price impacts are estimated by means of appropriate impulse response functions. Analyzing order book data of 30 stocks traded at Euronext Amsterdam, we show that limit orders have significant market impacts and cause a dynamic (and typically asymmetric) rebalancing of the book. The strength and direction of quote and spread responses depend on the incoming orders’ aggressiveness, their size and the state of the book. We show that the effects are qualitatively quite stable across the market. Cross-sectional variations in the magnitudes of price impacts are well explained by the underlying trading frequency and relative tick size.
We model the dynamics of ask and bid curves in a limit order book market using a dynamic semiparametric factor model. The shape of the curves is captured by a factor structure which is estimated nonparametrically. Corresponding factor loadings are assumed to follow multivariate dynamics and are modelled using a vector autoregressive model. Applying the framework to four stocks traded at the Australian Stock Exchange (ASX) in 2002, we show that the suggested model captures the spatial and temporal dependencies of the limit order book. Relating the shape of the curves to variables reflecting the current state of the market, we show that the recent liquidity demand has the strongest impact. In an extensive forecasting analysis we show that the model is successful in forecasting the liquidity supply over various time horizons during a trading day. Moreover, it is shown that the model’s forecasting power can be used to improve optimal order execution strategies.