Frequency Domain Tests of Semiparametric Hypotheses for Locally Stationary Processes

Abstract.  Many time series in applied sciences obey a time-varying spectral structure. In this article, we focus on locally stationary processes and develop tests of the hypothesis that the time-varying spectral density has a semiparametric structure, including the interesting case of a time-varying autoregressive moving-average (tvARMA) model. The test introduced is based on a L ₂ -distance measure of a kernel smoothed version of the local periodogram rescaled by the time-varying spectral density of the estimated semiparametric model. The asymptotic distribution of the test statistic under the null hypothesis is derived. As an interesting special case, we focus on the problem of testing for the presence of a tvAR model. A semiparametric bootstrap procedure to approximate more accurately the distribution of the test statistic under the null hypothesis is proposed. Some simulations illustrate the behaviour of our testing methodology in finite sample situations.     

THE IMPORTANCE OF TRADE COSTS IN DEVIATIONS FROM THE LAW‐OF‐ONE‐PRICE: ESTIMATES BASED ON THE DIRECTION OF TRADE

The full impact of trade costs in segmenting product markets cannot be captured by considering aggregate prices or in the absence of information on the direction of trade. We address this problem by utilizing product‐specific prices, cross‐sectional productivity indices, and bilateral trade flows, allowing us to identify the probable source of any one product. We show that trade costs in the form of transportation and distribution costs are important in determining international price differences and segmenting international markets. Physical distance relative to the origin has a precisely estimated positive impact on international deviations from the Law‐of‐One‐Price that is larger than estimates that do not account for the origin of each product. Based on our benchmark estimates, the price elasticity of distance was around 10% in 1990. (JEL F4)