Some topics in cointegration and buffered models

Abstract

In recent decades, cointegration has been one of the substantial and important topics in time series analysis. It is well-known that cointegration among two or more variables can be found in many economic or financial data. The so-called buffered autoregressive (BAR) model, a new type of threshold autoregressive model, has been recently developed, and successfully applied to many data sets. In this thesis, we study four interesting problems related to cointegration and buffered models in both theoretical and empirical perspectives. One of typical applications of cointegration is to form statistical arbitrage portfolios in a set of financial assets. However, some high-net worth investors may find that these portfolios are too risky, particularly during a bear market, and they hence lose interest in adopting them in their trading strategies. A plausible method to relieve such burden to the investors is to construct a cointegrated portfolio which is also market-neutral. We name such cointegrated market-neutral portfolio as COINMAN portfolio. In this thesis, we consider the low-dimensional and high-dimensional COINMAN portfolios. Particularly, the former is constructed by vector error correction model (VECM) with a prespecified linear constraint, while the latter is formed by VECM with adaptive Lasso. We apply the proposed COINMAN and sparse COINMAN portfolios to the constituent stocks of Hang Seng Index (HSI) and the 30 composite stocks of Dow Jones Industrial Average (DJIA), respectively. Our empirical results demonstrate that the trading strategies based on COINMAN-type portfolios are more profitable and less sensitive to the market than their cointegrated counterparts. Furthermore, we consider two extensions of the BAR model: the buffered VECM and the smooth buffered autoregressive (SBA) model. For the first buffer-type model, a least squares estimation and reduced-rank estimation are discussed, and the consistency of the estimators on the delay parameter and threshold parameters is derived. We propose a supWald test for the presence of buffer-type threshold effect. A bootstrap method is used to obtain the p-value for the supWald test. We apply the buffered VECM to study the monthly Federal bond rates of United States. Turning to the second bu er-type model, we give a sufficient condition for geometric ergodicity for SBA. A conditional least squares (CLS) estimation procedure is discussed, and the consistency and asymptotic normality of the estimators are derived. We apply the SBA model to annual sunspot numbers and industrial production of Japan. The empirical results show that the SBA model outperforms other competing time series models.