Determination of the effective cointegration rank in high-dimensional time-series predictive regressions

Puyi Fang, Zhaoxing Gao and Ruey S. Tsay

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Abstract: This paper proposes a new approach to identifying the effective cointegration rank in high-dimensional unit-root (HDUR) time series from a prediction perspective using reduced-rank regression. For a HDUR process $\mathbf{x}_t\in \mathbb{R}^N$ and a stationary series $\mathbf{y}_t\in \mathbb{R}^p$ of interest, our goal is to predict future values of $\mathbf{y}_t$ using $\mathbf{x}_t$ and lagged values of $\mathbf{y}_t$. The proposed framework consists of a two-step estimation procedure. First, the Principal Component Analysis is used to identify all cointegrating vectors of $\mathbf{x}_t$. Second, the co-integrated stationary series are used as regressors, together with some lagged variables of $\mathbf{y}_t$, to predict $\mathbf{y}_t$. The estimated reduced rank is then defined as the effective cointegration rank of $\mathbf{x}_t$. Under the scenario that the autoregressive coefficient matrices are sparse (or of low-rank), we apply the Least Absolute Shrinkage and Selection Operator (or the reduced-rank techniques) to estimate the autoregressive coefficients when the dimension involved is high. Theoretical properties of the estimators are established under the assumptions that the dimensions $p$ and $N$ and the sample size $T \to \infty$. Both simulated and real examples are used to illustrate the proposed framework, and the empirical application suggests that the proposed procedure fares well in predicting stock returns.

Date: 2023-04, Revised 2023-04
New Economics Papers: this item is included in nep-ecm and nep-ets
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