Point forecasting of intraday volume using Bayesian autoregressive conditional volume models

• DOI: http://doi.org/10.1002/for.2555
• Author: Roman Huptas
• Date: 01 July 2019
• Published date: 01 July 2019

SPECIAL ISSUE ARTICLE

Point forecasting of intraday volume using Bayesian

autoregressive conditional volume models

Roman Huptas

Department of Statistics, Cracow

University of Economics, Cracow, Poland

Correspondence

Roman Huptas, Department of Statistics,

Cracow University of Economics, 27

Rakowicka St., Cracow 31‐510, Poland.

Email: huptasr@uek.krakow.pl

Funding information

Ministry of Science and Higher Education

(MNiSW, Poland), Grant/Award Number:

044/WZ‐KS/03/2016/S/6044

Abstract

In this paper, we apply Bayesian inference to model and forecast intraday trad-

ing volume, using autoregressive conditional volume (ACV) models, and we

evaluate the quality of volume point forecasts. In the empirical application,

we focus on the analysis of both in‐and out‐of‐sample performance of Bayesian

ACV models estimated for 2‐minute trading volume data for stocks quoted on

the Warsaw Stock Exchange in Poland. We calculate two types of point fore-

casts, using either expected values or medians of predictive distributions. We

conclude that, in general, all considered models generate significantly biased

forecasts. We also observe that the considered models significantly outperform

such benchmarks as the naïve or rolling means forecasts. Moreover, in terms of

root mean squared forecast errors, point predictions obtained within the ACV

model with exponential distribution emerge superior compared to those

calculated in structures with more general innovation distributions, although

in many cases this characteristic turns out to be statistically insignificant. On

the other hand, when comparing mean absolute forecast errors, the median

forecasts obtained within the ACV models with Burr and generalized gamma

distribution are found to be statistically better than other forecasts.

KEYWORDS

autoregressive conditional volume model, Bayesian inference, forecasting, intraday volume, market

microstructu re

1|INTRODUCTION

Modeling and forecasting of trading volume have become

crucial for many international financial institutions, pro-

fessionals, and—especially—traders. The reason for this

is that trading volume plays a significant role in the trad-

ing process, and is one of the key measures of liquidity on

stock markets. Therefore, the ability of producing accu-

rate volume forecasts can facilitate trading algorithms,

many of which, indeed, depend on the quantity consid-

ered, particularly volume‐weighted average price (VWAP)

trading strategy. The goal of the VWAP trading strategy is

to split large orders into smaller‐size orders and to execute

them during the trading day to achieve an average price

that is close to the VWAP (Brownlees, Cipollini, & Gallo,

2011). Hence accurate intraday volume predictions are

crucial to accomplish that goal. Other examples of the

importance of intraday volume forecasting are enumer-

ated in Satish, Saxena, and Palmer (2014).

In this paper, we concentrate on analyzing and point

forecasting of intraday volume time series. In the existing

financial market literature, volume has often been ana-

lyzed in the context of dependencies between trade size

and other financial variables, such as price or volatility

(see,e.g., Andersen, 1996; Darrat, Rahman, & Zhong,

2003; Easley & O'Hara, 1987; Foster & Viswanathan,

Received: 7 December 2015 Revised: 6 June 2018 Accepted: 6 September 2018

DOI: 10.1002/for.2555

Journal of Forecasting. 2019;38:293–310. © 2018 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/for 293

1990; Gouriéroux, Jasiak, & Le Fol, 1999; Karpoff & Boyd,

1987; Manganelli, 2005; Tauchen & Pitts, 1983). However,

in several studies the focus has been placed exclusively on

modeling and predicting volume on stock exchanges. For

instance, Białkowski, Darolles, and Le Fol (2008) pre-

sented a new methodology for modeling intraday volume,

the main idea of which resided in a decomposition of

traded volume into a market component and a stock‐

specific component. The dynamics of the intraday specific

volume part was modeled by autoregressive moving aver-

age (ARMA) or self‐exciting threshold autoregressive

(SETAR) models. In turn, Brownlees et al. (2011) con-

structed a component multiplicative error model for intra-

day volumes so as to capture salient features of the series,

such as time series dependence, intraday periodicity, and

volume asymmetry. The conditional expected volume

was the product of a daily component, an intraday periodic

component, and an intraday dynamic non‐periodic com-

ponent. The authors did not assume any specific distribu-

tion for the error term in order to work within a

semiparametric setting, estimating the model by the gen-

eralized method of moments. Next, Humphery‐Jenner

(2011) predicted volume percentage using an approach

called a “dynamic VWAP.”Satish et al. (2014) proposed

a raw volume forecast model, which consisted of four com-

ponents and exploited interday as well as intraday infor-

mation. The final component of the model, minimizing

the error on the in‐sample data, was a dynamic weighted

average of rolling historical component and interday and

intraday components, which were modeled by ARMA

structures. In turn, Li and Ye (2013) developed a model

for decomposing a volume series based on the fast Fourier

transform algorithm, whereas Ye, Yan, and Li (2014) com-

bined the autoregressive fractionally integrated moving

average (ARFIMA) model with the PC‐VWAP method

(principal component analysis used to decompose trading

volume and combined with the VWAP) to predict volume

in the Chinese stock market. The spline‐DCS model

(spline‐dynamic conditional score model) was introduced

and applied to forecasting the high‐frequency trade vol-

ume of selected equity and foreign currency exchange

pairs in a paper by Ito (2016). Liu and Lai (2017) presented

a dynamic support vector machine (SVM)‐based model to

forecast intraday volume percentages by decomposing the

trade volume into two parts: the average part as the intra-

day volume pattern and the residual term as the abnormal

changes. Finally, Szűcs (2017) compared the model of

Białkowski et al. (2008) to that of Brownlees et al. (2011)

using intraday data of selected NYSE and NASDAQ

shares. Other relevant papers, published before 2008,

include Kaastra and Boyd (1995), Lo and Wang (2000),

Konishi (2002), Darolles and Le Fol (2003), McCulloch

(2004), and Hobson (2006), among others. Nevertheless,

it is not an exaggeration to claim that the number of

articles providing well‐established econometric tools for

volume forecasting is still limited, leaving open the issue

of how to forecast trading volume effectively.

The aim of this paper is to apply Bayesian inference to

modeling and point forecasting of intraday volume data

using a linear autoregressive conditional volume (ACV)

model introduced by Manganelli (2005), and to evaluate

the quality of the obtained predictions. In the empirical

study, we undertake modeling and forecasting intraday

volume data of representative, widely traded stocks

quoted on the Warsaw Stock Exchange in Poland. In par-

ticular, a rolling window prediction exercise is performed

for 2‐minute volume data. We consider two types of point

forecasts, using expected values and medians of predictive

distributions. Evaluation of the point forecasts reveals

that, in general, all considered models generate signifi-

cantly biased forecasts. Additionally, Bayesian ACV

models significantly outperform such benchmarks as the

naїve and rolling means techniques. Moreover, in terms

of the root mean squared forecast errors, the ACV model

with exponential error term performs better than its

counterparts with more general innovation distributions,

but in many cases this characteristic turns out to be statis-

tically insignificant. On the other hand, in most cases,

with respect to the mean absolute forecast errors, the

median forecasts obtained within the ACV model with

the Burr and generalized gamma (GG) distributions are

found to be statistically superior to other forecasts.

This paper contributes to the recent literature on high‐

frequency volume forecasting. First, a Bayesian approach

to modeling and forecasting intraday volume data with

the use of ACV models has not been covered in the liter-

ature so far, except for the recent study of Huptas

(2018). In fact, the current study may be regarded as com-

plementary to the cited work. Second, in this study we

consider and compare two types of point forecasts, based

either on expected values or medians of predictive distri-

butions. Moreover, it also still contributes to the line of

research focused on the microstructure of the Polish stock

market, the latter being currently one of the most impor-

tant and rapidly growing markets in Central and Eastern

Europe. As compared with developed financial markets,

for which, admittedly, analyses of trading volume are

quite abundant, modeling trading volume in emerging

markets, such as Poland, has been somehow out of focus.

Filling this gap to some extent justifies our focus on that

particular region of the global financial market.

The remainder of the paper is organized as follows. In

Section 2 we provide the specifics of the ACV model, for

which the Bayesian estimation along with relevant

Markov chain Monte Carlo (MCMC) techniques is dealt

with in Section 3. Section 4 briefly describes the

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