This paper studies how a retailer decides the length of product line in a vertically related industry. We study a market with two product varieties. Each retailer decides the number of varieties it procures from an upstream manufacturer. The manufacturer may open an online store and encroach on...

This paper discusses brand firms' endogenous timing problem when facing nonbrand firms under quantity competition. We study a market comprising brand and nonbrand products. There exist heterogeneous consumer groups-one group buys only brand products while the other one cares little about the...

I revisit supplier encroachment under the framework of a two-part tariff contract. When a monopoly manufacturer supplies competing retailers and each retailer's contracting process is unobservable to the rival, the retailer's lack of knowledge vis-à-vis its rival's contract may undermine the...

We consider a bilateral monopoly in which a manufacturer can open its direct channel that is less efficient than the existing retailer. We find the following results. The manufacturer opens its direct channel if its bargaining power over the existing retailer is weak. Opening the direct channel...

This paper provides a review of some recent theoretical results for time series models with GARCH errors, and is directed towards practitioners. Starting with the simple ARCH model and proceeding to the GARCH model, some results for stationary and nonstationary ARMA-GARCH are summarized. Various...

Least squares (LS) and maximum likelihood (ML) estimation are considered for unit root processes with GARCH (1, 1) errors. The asymptotic distributions of LS and ML estimators are derived under the condition alpha + beta 1. The former has the usual unit root distribution and the latter is a...

This paper examines stationary and nonstationary time series by formally testing for the presence of unit roots and seasonal unit roots prior to estimation, model selection and forecasting. Various Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) models are estimated over the period...

This paper investigates some structural properties of a family of GARCH processes. A simple sufficient condition for the existence of the αδ-order stationary solution of the processes is derived, where α ∈ (0, 1] and δ 0. The solution is strictly stationary and ergodic, and the causal...