Normally Distributed Seasonal Unit Root Tests

• Activity Number: 480
• Type: Invited
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): David Alan Dickey*+
• Companies: North Carolina State University
• Keywords: Nonstationary ; Seasonality ; Unit Roots

Abstract

One approach to modeling seasonality is to fit deterministic functions such as seasonal dummy variables or sine-cosine pairs and another is to difference the data at the seasonal lag. The decision as to which approach is more appropriate arises and this paper deals with a hypothesis test that helps with making that decision. In early work along these lines, distributions of seasonal unit root tests were developed for common seasonal periods such as 4 (quarters) and 12 (months) using asymptotics based on increasing the number of years m of quarterly (s=4) or monthly (s=12) data. These distributions are nonstandard even in the limit. When the period s increases, some moment adjustments described in this paper allow a central limit theorem (in s) do be developed which appears to work quite well even for reasonably small s values. The limit results and theory leading to them for a fixed number of sinusoids are quite different than those for s seasonal dummy variables. The distinction between these cases is a point of emphasis in this paper.