We propose a cointegration-based method for evaluating the long-term independence of sectoral Real Estate Investment Trusts (REITs) within a portfolio. We employ this innovative approach to construct diversified portfolios. Our argument is that sectors contributing less to cointegration provide greater risk reduction benefits to the portfolio. To gauge the level of independence, we use the reciprocal of the aggregate likelihood ratio (RAL) statistics. Based on these statistics, we introduce a novel allocation strategy that assigns a higher weight to a sector with a larger RAL. Using CRSP/Ziman REIT sector data, we demonstrate that this new strategy outperforms traditional methods and the real estate market benchmark. Our paper introduces a fresh framework for REIT portfolio management and provides guidance on sector allocation.