Date of Publication :28th July 2023

Abstract: This paper chooses two correlated (Y(t), X(t)) stock prices observed at t = 1, 2..., N and develops algorithms to locate best profitable positions for future trading. We divide the past N1 pairs as training set, say TR and the remaining (N-N1) pairs as future series, say TE, to be used for testing tasks and fixing a trading strategy. Assuming the response variables as Y=Y(t) and the predictor as X=X(t) in the paired dataset TR. We fit a simple linear model (LM) of the response variable Y of TR with the predictor X using the statistical command "lm()" and then a non-linear model (NLM) using the command "neuralnet()' of the neural net package in R. The stationary property of the residuals is then checked by the "Augmented Dickey-Fuller" (ADF) test. We then develop a trading strategy to maximize profits over trading period of TE and thus a positional chart to show profitable positions using co-integrated stationary spread obtained from TE based on the estimated results by both the LM and NLM cases. Only real data sets are used for illustration and optimal performance is determined. Finally, the total profit of pairs trading is calculated on a case-by-case basis and compared. Finally, the NLM is shown to perform better than the LM approach.

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