Forecasting the intra-day effective bid ask spread by combining density forecasts

ABSTRACT

The bid-ask spread refers to the tightness dimension of liquidity and can be used as a proxy for transaction costs. Despite the importance of the bid-ask spread in the financial literature, few studies have investigated its forecastability. We propose a new methodology to predict the bid ask spread by combining density forecasts of two types of models: Multiplicative Errors Models and ARMA-GARCH models. Our method is employed to predict the effective intra-day bid-ask spread series of all shares pertaining to the CAC40 index. Using a one-step-ahead out-of-sample framework, we resort on the Model Confidence Set procedure to classify models and we found that the proposed model appears to beat all the benchmark specifications.

KEYWORDS:

• Effective bid-ask spread
• high-frequency
• multiplicative errors models
• forecasting

Disclosure of potential conflicts of interest

No potential conflict of interest was reported by the author(s).

Notes

¹ Autoregressive Moving Average – Generalized Autoregressive Conditional Heteroscedastic models.

² These stocks are actively traded, henceforth a trade-based liquidity metric as the effective spread appears relevant.

³ see footnote 10 of Lee and Ready (1991).

⁴ See Giot and Laurent (2004); Lambert and Laurent (2002) for details.

⁵ We follow the procedure proposed by Mccarthy, Disario, and Saraoglu (2003) to fractionnaly difference time series data.

⁶ Originally this final set was called the ‘ Model Confidence Set’ by Hansen, Lunde, and Nason (2004), we change this name to avoid confusion with the procedure which has the same terminology.

⁷ Put in simple terms: a dataset with few variations in the data will lead to a large SSM and a dataset with large variation will lead to a smaller number of models in the SSM.

⁸ Only for estimation based on out-of-sample forecasts.

⁹ for instance, the FIACD (MEM type) versus the ARMA-GJR (ARMA type) model.

¹⁰ that is to say that we aggregate the series over two time scales: 5 and 10 minutes.

¹¹ To ease computation, when evaluating the combined density forecast type of model, we only employ a combination of models for the 5 min grid forecast, 10 min forecasts are based on GARCH density forecasts. This is not a concern since we expect the trading profit to increase if we had use the full combined scheme, thus keeping the direction of our results.

¹² Between time $t$ and $t+10$ we observe 2 one-step-ahead forecasts on the 5-minute grid; only the first point is considered.