A Consistent Nonparametric Test of Ergodicity for Time Series with Applications.

We propose a set of algorithms for testing the ergodicity of empirical time series, without reliance on a specific parametric framework. It is shown that the resulting test asymptotically obtains the correct size for stationary and nonstationary processes, and maximal power against non-ergodic but stationary alternatives. The test will not reject in the presence of nonstationarity that does not lead to ergodic failure. The work is linked to recent research on reformulations of the concept of integrated processes of order zero, and we demonstrate the means to operationalize new concepts of "short memory" for economic time series. Limited Monte Carlo evidence is provided with respect to power against the non-stationary and non-ergodic alternative of unit root processes. The method is used to investigate debates over stability of monetary aggregates relative to GDP, and the mean reversion hypothesis with respect to high frequency data on exchange rates.TESTS ; TIME SERIES

Financial Market Structure and the Ergocicity of Prices.

The properties of prices, especially with respect to initial conditions related to market startup and unusual shocks to the market environment, are of concern to regulators assessing alternative financial market structures. A natural way to investigate the importance of initial conditions is to evaluate the ergodicity of the price process. A consistent nonparametric test for ergodic failure is introduced for this purpose. We compare the ergodic properties of prices across (i) a computerized market, characterized by an electronic limit order book and a separate batch opening protocol; and (ii) a traditional open-outcry floor market. The work is enabled in part by unusual matched high-frequency trading data on identical financial instruments traded in both markets over the same 24-hour period.AUCTIONS ; FINANCIAL MARKET

A quantitative model of trading and price formation in financial markets

We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of a market, such as the diffusion rate of prices, which is the standard measure of financial risk, and the spread and price impact functions, which are the main determinants of transaction cost. Guided by dimensional analysis, simulation, and mean field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.Comment: 5 pages, 4 figure

The position profiles of order cancellations in an emerging stock market

Order submission and cancellation are two constituent actions of stock trading behaviors in order-driven markets. Order submission dynamics has been extensively studied for different markets, while order cancellation dynamics is less understood. There are two positions associated with a cancellation, that is, the price level in the limit-order book (LOB) and the position in the queue at each price level. We study the profiles of these two order cancellation positions through rebuilding the limit-order book using the order flow data of 23 liquid stocks traded on the Shenzhen Stock Exchange in the year 2003. We find that the profiles of relative price levels where cancellations occur obey a log-normal distribution. After normalizing the relative price level by removing the factor of order numbers stored at the price level, we find that the profiles exhibit a power-law scaling behavior on the right tails for both buy and sell orders. When focusing on the order cancellation positions in the queue at each price level, we find that the profiles increase rapidly in the front of the queue, and then fluctuate around a constant value till the end of the queue. These profiles are similar for different stocks. In addition, the profiles of cancellation positions can be fitted by an exponent function for both buy and sell orders. These two kinds of cancellation profiles seem universal for different stocks investigated and exhibit minor asymmetry between buy and sell orders. Our empirical findings shed new light on the order cancellation dynamics and pose constraints on the construction of order-driven stock market models.Comment: 17 pages, 6 figures and 6 table

Firm-size distribution and price-cost margins in Dutch manufacturing

Industrial economists surmise a relation between the size distribution of firms and performance. Usually, attention is focused on the high end of the size distribution. The widely used 4-firm seller concentration, C4, ignores what happens at the low end of the size distribution. An investigation is presented of the extent to which the level and the growth of small business presence influence price-cost margins in Dutch manufacturing. A large data set of 66 industries for a 13-year period is used. This allows the investigation of both small business influences within a framework in which that of many other market structure variables is also studied. Evidence is shown that price-cost margins are influenced by large firm dominance, growth in small business presence, capital intensity, business cycle, international trade, and buyer concentration