Abstract
This paper introduces Quasi-Maximum Likelihood Estimation for Long Memory Stock Transaction Data of unknown underlying distribution. The moments with conditional heteroscedasticity have been discussed. In a Monte Carlo experiment, it was found that the QML estimator performs as well as CLS and FGLS in terms of eliminating serial correlations, but the estimator can be sensitive to start value. Hence, two-stage QML has been suggested. In empirical estimation on two stock transaction data for Ericsson and AstraZeneca, the 2SQML turns out relatively more efficient than CLS and FGLS. The empirical results suggest that both of the series have long memory properties that imply that the impact of macroeconomic news or rumors in one point of time has a persistence impact on future transactions.
Highlights
Classical economic theory of price determination is a function of demand and supply
Drost et al (2009) investigate finite sample behavior of semiparametric integer-valued AR(p) models, while Brännäs and Quoreshi (2010) study finite lag misspecification when the data is generated according to an infinite-lag INMA model. In this Monte Carlo experiment we study the bias, mean square error (MSE), Ljung–Box statistics, Akaike Information Criteria (AIC), and Schwarz Bayesian Information Criterion (SBIC) properties of the Feasible Generalized Least Square (FGLS) and 2SQML estimators for finite-lag specifications when data is generated according to INARFIMA (0, d, 0).The data generating process is as in (1), with dj = Γ( j + d)/[Γ( j + 1)Γ(d)], j = 0, 1, 2, . . . where d0 = 1 and where ut is drawn according to Equation (2)
It is to be noted that the AIC and SBIC criteria are not applicable in the context of long memory (Brännäs and Quoreshi 2010; Quoreshi 2014), which is supported by the Monte Carlo Experiment
Summary
Classical economic theory of price determination is a function of demand and supply. For example, in the Walrasian auctioneer approach, demands and supplies of a good are aggregated to find a market-clearing price. Quoreshi (2006, 2008, 2014, 2017) advances further the INMA model into bivariate, multivariate and long memory (INARFIMA) framework These papers consider Conditional Least Square (CLS), Feasible Generalized Least Square (FGLS), and Generalized Methods of Moments (GMM). Ristic et al (2018) introduces a new bivariate integer-valued moving average of the first order (BINMA(1)) process with independent Negative Binomial (NB) innovations under nonstationary moment conditions They employed a generalized quasi-likelihood (GQL) method of estimation. We propose a quasi-maximum likelihood (QML) estimator for nonstationary integer-valued long memory model for unknown underlying distribution and compare this estimator with CLS and FGLS that have performed better than GMM in the previous studies.
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