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.
This article was originally published as Wang, Q, Lin, YX and Gulati, CM, Asymptotics for general fractionally intergrated processes with applications to unit root tests,
Let Xt be a linear process defined by [refer paper], where [refer paper] is greater than or equal to 0 is a sequence of real numbers and (ek, k = 0, plus or minus 1, plus or minus 2, ...) 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 [refer paper]. We note that, for the partial sum process of the Xt converging to a standard Wiener process, the condition [refer paper] 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. Disciplines Physical Sciences and Mathematics University of WollongongLet X t be a linear process defined by X t ϭ (kϭ0 c k e tϪk , where $c k , k Ն 0% is a sequence of real numbers and $e k , k ϭ 0,61,62, + + + % is a sequence of random variables+ Two basic results, on the invariance principle of the partial sum process of the X t converging to a standard Wiener process on @0,1#, are presented in this paper+ In the first result, we assume that the innovations e k are independent and identically distributed random variables but do not restrict (kϭ0 6c k 6 Ͻ`+We note that, for the partial sum process of the X t converging to a standard Wiener process, the condition (kϭ0 6c k 6 Ͻ`or stronger conditions are commonly used in previous research+ The second result is for the situation where the innovations e k form a martingale difference sequence+ For this result, the commonly used assumption of equal variance of the innovations e k 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+
Pairs trading is one of the arbitrage strategies that can be used in trading stocks on the stock market. It incorporates the use of a standard statistical model to exploit the stocks that are out of equilibrium for short-term time. In determining which two stocks can be a pair, Banerjee et al. (1993) shows that the cointegration technique is more effective than correlation criterion for extracting profit potential in temporary pricing anomalies for share prices driven by common underlying factors. 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 opposite applies for lowering the boundary values. The number of trades over a specified trading horizon is determined jointly by 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 then use them to find the optimal pre-set boundaries that would maximize the minimum total profit for cointegration error following an AR(1) process.
Abstract. 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.
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