A nonparametric least squares regression method for forecasting building energy performance

The Convex Nonparametric Least Squares (CNLS) method assumes that the regression function is either concave or convex to forecast building energy performance. However, there may be instances where the regression function exhibits both concave and convex patterns, rendering this assumption invalid. This paper aims to address this drawback and to derive a new method called Monotone Nonparametric Least Squares (MNLS), which incorporates both concavity and convexity constraints in CNLS. It is proved that MNLS has a better goodness-of-fit performance compared to CNLS. Since MNLS contains both concave and convex portions, it is not sufficient to rely solely on the concavity assumption (or convexity assumption) during the forecasting process of building energy performance. To tackle this issue, using both concave and convex portions separately and then combining the resulting forecasts is suggested. An illustrative example is provided, and the energy performance of Hong Kong secondary schools is used as an application to demonstrate the goodness-of-fit of MNLS.