Local Adaptive Multiplicative Error Models For High-Frequency Forecasts

Abstract

We propose a local adaptive multiplicative error model (MEM) accommodating time-varying 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. Analysing 1-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.We apply the LPA to seasonally adjusted 1-minute aggregated trading volumes for all five stocks at each minute from 22 February to 31 December 2008 (215 trading days; 77,400 trading minutes). We use the EACD and WACD models as the two (local) specifications, two risk levels (modest, r D 0:5;

Forecasting limit order book liquidity supply–demand curves with functional autoregressive dynamics

“…Huberman and Halka (2001) evidenced the serial dependence of bid-ask spread and depth in the AutoRegressive model. Härdle, Hautsch and Mihoci (2015) proposed a local adaptive multiplicative error model to forecast the high-frequency series of one-minute cumulative trading volumes of several NASDAQ blue chip stocks. Serial dependence also exists in limit order demand and supply, see Dierker, Kim, Lee and Morck (2014).…”