Andrija Mihoci

Local Adaptive Multiplicative Error Models For High-Frequency Forecasts

We propose a local adaptive multiplicative error model (MEM) accommodating timevarying parameters. MEM parameters are adaptively estimated based on a sequential testing procedure. A data-driven optimal length of local windows is selected, yielding adaptive forecasts at each point in time. Analyzing one-minute cumulative trading volumes of five large NASDAQ stocks in 2008, we show that local windows of approximately 3 to 4 hours are reasonable to capture parameter variations while balancing modelling bias and estimation (in)efficiency. In forecasting, the proposed adaptive approach significantly outperforms a MEM where local estimation windows are fixed on an ad hoc basis.

Modelling and forecasting liquidity supply using semiparametric factor dynamics

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 modelled jointly with best bid and best ask quotes using a vector error correction specification. 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. We find spill-over effects between both sides of the market and provide evidence for short-term quote predictability. 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 models forecasting power can be used to improve optimal order execution strategies.

lCARE - localizing conditional autoregressive expectiles

We account for time-varying parameters in the conditional expectile-based value at risk (EVaR) model. The EVaR downside risk is more sensitive to the magnitude of portfolio losses compared to the quantile-based value at risk (QVaR). Rather than fitting the expectile models over ad-hoc fixed data windows, this study focuses on parameter instability of tail risk dynamics by utilizing a local parametric approach. Our framework yields a data-driven optimal interval length at each time point by a sequential test. Empirical evidence at three stock markets from 2005–2016 shows that the selected lengths account for approximately 4–6 months of daily observations. This method performs favourable compared to the models with one-year fixed intervals, as well as quantile based candidates while employing a time invariant portfolio protection (TIPP) strategy for the DAX, FTSE 100 and S&P 500 portfolios. The tail risk measure implied by our model finally provides valuable insights for asset allocation and portfolio insurance.

Modelling Limit Order Book Volume Covariance Structures

Limit order volume data have been here analysed using key multivariate techniques: principal components, factor and discriminant analysis. The focus lies on understanding of the covariance structure of posted quantities of the asset to be potentially sold or bought at the market. Employing the methods to data of 20 blue chip companies traded at the NASDAQ stock market in June 2016, one observes that two principal components account for approximately 85–95% of order book variation. The most important factor related to order book data variation has furthermore been the demand side (variability). The order book data variation, moreover, successfully classifies stock price movements. Potential applications include improving order execution strategies, designing trading algorithms and understanding price formation.

LCARE - Localizing Conditional Autoregressive Expectiles

We account for time-varying parameters in the conditional expectile based value at risk (EVaR) model. EVaR appears more sensitive to the magnitude of portfolio losses compared to the quantile-based Value at Risk (QVaR), nevertheless, by fitting the models over relatively long ad-hoc fixed time intervals, research ignores the potential time-varying parameter properties. Our work focuses on this issue by exploiting the local parametric approach in quantifying tail risk dynamics. By achieving a balance between parameter variability and modelling bias, one can safely fit a parametric expectile model over a stable interval of homogeneity. Empirical evidence at three stock markets from 2005- 2014 shows that the parameter homogeneity interval lengths account for approximately 1-6 months of daily observations. Our method outperforms models with one-year fixed intervals, as well as quantile based candidates while employing a time invariant portfolio protection (TIPP) strategy for the DAX portfolio. The tail risk measure implied by our model finally provides valuable insights for asset allocation and portfolio insurance.

Structural adaptive models in financial econometrics

Modern methods in statistics and econometrics successfully deal with stylized facts observed on financial markets. The presented techniques aim to understand the dynamics of financial market data more accurate than traditional approaches. Economic and financial benefits are achievable. The results are here evaluated in practical examples that mainly focus on forecasting of financial data. Our applications include: (i) modelling and forecasting of liquidity supply, (ii) localizing multiplicative error models and (iii) providing evidence for the empirical pricing kernel paradox across countries.