Semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices

We consider a new class of semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a type of sparse structure in order to include as many panels as possible. We apply the local linear method and least squares method for Yule-Walker equation to estimate trend function and spatio-temporal autoregressive coefficient matrices respectively. We also balance the over-determined and under-determined phenomena in part by adjusting the order of extracting sample information. Both the asymptotic normality and convergence rates of the proposed estimators are established. The proposed methods are further illustrated using both simulation and case studies, the results also show that our estimator is stable among different sample size, and it performs better than the traditional method with known spatial weight matrices.

Conditional violation of weak-form market efficiency

PurposeMany prior tests of market efficiency, which occurred decades ago, were limited by data and did not employ methodology to correct for leptokurtosis in the stock return distribution. Furthermore, these studies did not test many aspects of conditional market efficiency. One aspect of a potential conditional violation of market efficiency is whether stock markets are efficient conditional on the level of stock return.Design/methodology/approachThis paper uses quantile regressions to control for leptokurtosis in the stock return distribution and simultaneous quantile regressions to test whether markets are efficient conditional on the level of the market return. This paper uses market-level stock return data to bias against finding significant results in the efficiency tests. Furthermore, the author uses data from 1926 through 2018, providing the longest time period to date under which market efficiency is tested.FindingsThis paper presents evidence that the autoregressive coefficient decreases across return levels in stock market indices. The autoregressive coefficient is positive around highly negative returns and negative or insignificant around highly positive returns, which suggests that when stock returns are low they are more likely to continue lower, and when stock returns are high they are more likely to reverse. Results additionally suggest that market efficiency is not time-invariant and that stock markets have become more efficient over the sample period.Originality/valueThis paper extends the literature by finding evidence of a violation of weak-form market efficiency conditional on the level of stock returns. It further extends the literature by finding evidence that the stock market has become more efficient between 1926 and 2018.

Probabilistic forecasting of bubbles and flash crashes

Summary We propose a near-explosive random coefficient autoregressive model (NERC) to obtain predictive probabilities of the apparition and devolution of bubbles. The distribution of the autoregressive coefficient of this model is allowed to be centred at an O(T−α) distance of unity, with α ∈ (0, 1). When the expectation of the autoregressive coefficient lies on the explosive side of unity, the NERC helps to model the temporary explosiveness of time series and obtain related predictive probabilities. We study the asymptotic properties of the NERC and provide a procedure for inference on the parameters. In empirical illustrations, we estimate predictive probabilities of bubbles or flash crashes in financial asset prices.

SECOND ORDER EXPANSION OF THE T-STATISTIC IN AR(1) MODELS

The purpose of this paper is to differentiate between several asymptotically valid methods for confidence set construction for the autoregressive coefficient in AR(1) models. We show that the nonparametric grid bootstrap procedure suggested by Hansen (1999, Review of Economics and Statistics 81, 594–607) achieves a second order refinement in the local-to-unity asymptotic approach when compared with a modified version of Stock’s (1991, Journal of Monetary Economics 28, 435–459) and Andrews’ (1993, Econometrica 61, 139–165) grid testing procedures. We establish a second order expansion of the t-statistic in an AR(1) model in the local-to-unity asymptotic approach, which differs drastically from the usual Edgeworth-type expansions by approximating the statistic around a nonstandard and nonpivotal limit.

MODELING THE IMPACT OF PARTIAL INFORMATION SHARING IN A THREE-ECHELON SUPPLY CHAIN

This paper investigates the impact of partial information sharing in a three-echelon supply chain. Partial information sharing means that information sharing occurs only between the distributor and the retailer, but not between the distributor and the manufacturer. This paper contributes to the literature by summarizing the circumstances in which information sharing between the retailer and the distributor benefits the manufacturer. In addition, our study points out that such information sharing does not always bring benefits to the manufacturer and that in some cases the information sharing may harm the manufacturer. We explain the reasons why this can happen and give managerial intuition for our results. Using numerical analysis, we illustrate the impact of partial information sharing on the agents in the supply chain with the change of the autoregressive coefficient in the demand process.

Nonstationary INAR(1) Process with th-Order Autocorrelation Innovation

This paper is concerned with an integer-valued random walk process withqth-order autocorrelation. Some limit distributions of sums about the nonstationary process are obtained. The limit distribution of conditional least squares estimators of the autoregressive coefficient in an auxiliary regression process is derived. The performance of the autoregressive coefficient estimators is assessed through the Monte Carlo simulations.