Chandra Gulati

Loss protection in pairs trading through minimum profit bounds: a cointegration approach

Pairs trading is a comparative-value form of statistical arbitrage designed to exploit temporary random departures from equilibrium pricing between two shares. However, the strategy is not riskless. Market events as well as poor statistical modeling and parameter estimation may all erode potential profits. Since conventional loss limiting trading strategies are costly, a preferable situation is to integrate loss limitation within the statistical modeling itself. This paper uses cointegration principles to develop a procedure that embeds a minimum profit condition within a pairs trading strategy. We derive the necessary conditions for such a procedure and then use them to define and implement a five-step procedure for identifying eligible trades. The statistical validity of the procedure is verified through simulation data. Practicality is tested through actual data. The results show that, at reasonable minimum profit levels, the protocol does not greatly reduce trade numbers or absolute profits relative to an unprotected trading strategy.

Strong approximation for long memory processes with applications

In this paper we inverstigate the strong approximation of a linear process with long memory to a Gaussian process. The results are then applied to derive the law of the iterated logarithm and Darling–Erdős type theorem for long memory processes under ideal conditions.

Asymptotics for general fractionally integrated processes with applications to unit root tests

In this paper, functional limit theorems for general fractional processes are established under quite weak conditions. The results are then used to derive weak convergence of general nonstationary fractionally integrated processes and to characterize unit root distribution in a model with error being a fractional autoregressive moving average process or a nonstationary fractionally integrated process. The authors thank three referees and an associate editor for their detailed reading of this paper and valuable comments, which have led to this much improved version of the paper.

The invariance principle for linear processes with applications

Let Xt be a linear process defined by Xt 5 (k50 ‘ cket2k, where

Finding the Optimal Pre-set Boundaries for Pairs Trading Strategy Based on Cointegration Technique

ck,k

Asymptotics for moving average processes with dependent innovations

0% is a sequence of real numbers and

Asymptotics for general nonstationary fractionally integrated processes without prehistoric influence

ek,k 5 0,61,62,+++ % is a sequence of random variables+ Two basic results, on the invariance principle of the partial sum process of the Xt converging to a standard Wiener process on @0,1#, are presented in this paper+ In the first result, we assume that the innovations ek are independent and identically distributed random variables but do not restrict (k50 ‘ 6ck6 , ‘+ We note that, for the partial sum process of the Xt converging to a standard Wiener process, the condition (k50 ‘ 6ck6 , ‘ or stronger conditions are commonly used in previous research+ The second result is for the situation where the innovations ek form a martingale difference sequence+ For this result, the commonly used assumption of equal variance of the innovations ek is weakened+ We apply these general results to unit root testing+ It turns out that the limit distributions of the Dickey‐Fuller test statistic and Kwiatkowski, Phillips, Schmidt, and Shin ~KPSS! test statistic still hold for the more general models under very weak conditions+

Cointegration between exchange rates: a generalized linear cointegration model

Pairs trading is one of the arbitrage strategies that can be used in trading stocks on the stock market. This paper incorporates pairs trading with the use of cointegration technique to exploit stocks that are temporarily out of equilibrium. In determining which two stocks can be a pair, Banerjee, Dolado, Galbraith and Hendry (1993) and Vidyamurthy (2004) showed that the cointegration technique is more effective than correlation criterion for extracting profit potential in temporary pricing anomalies between two stock prices driven by common underlying factors. By using stationary properties of cointegration errors following an AR(1) process, this paper explores the ways in which the pre-set boundaries chosen to open a trade can influence the minimum total profit over a specified trading horizon. The minimum total profit relates to the pre-set minimum profit per trade and the number of trades during the trading horizon. The higher the pre-set boundaries for opening trades, the higher the profit per trade but the lower the trade numbers. The number of trades over a specified trading horizon is estimated by using the average trade duration and the average inter-trade interval. For any pre-set boundaries, both of these values are estimated by making an analogy to the mean first-passage time. The aims of this paper are to develop numerical algorithm to estimate the average trade duration, the average inter-trade interval, and the average number of trades and to use these to find optimal pre-set boundaries that maximize the minimum total profit.

Unit Root Tests for ESTAR Models

Let Xt be a moving average process defined by Xt=[summation operator]k=0[infinity][psi]k[var epsilon]t-k, t=1,2,... , where the innovation {[var epsilon]k} is a centered sequence of random variables and {[psi]k} is a sequence of real numbers. Under conditions on {[psi]k} which entail that {Xt} is either a long memory process or a linear process, we study asymptotics of the partial sum process [summation operator]t=0[ns]Xt. For a long memory process with innovations forming a martingale difference sequence, the functional limit theorems of [summation operator]t=0[ns]Xt (properly normalized) are derived. For a linear process, we give sufficient conditions so that [summation operator]t=1[ns]Xt (properly normalized) converges weakly to a standard Brownian motion if the corresponding [summation operator]k=1[ns][var epsilon]k is true. The applications to fractional processes and other mixing innovations are also discussed.

The Probability of an Out of Control Signal from Nelson’s Supplementary Zig-Zag Test

This paper derives a functional limit theorem for general nonstationary fractionally integrated processes having no influence from prehistory. Asymptotic distributions of sample autocovariances and sample autocorrelations based on these processes are also investigated. The problem arises naturally in discussing fractionally integrated processes when the processes starts at a given initial date.