Forecasting Ambient O3 Concentration Using Singular Spectrum Analysis

Abstract:

The time series given by daily maximum ambient O3 concentration has a strong seasonal component and correlated errors. Use of singular spectrum analysis (SSA) combined with an autoregressive (AR) model (SSA+AR hereafter) captures such features and performs well in multiple-day point forecasts. On the other hand, after SSA+AR is fitted to the O3 concentration data at various monitoring stations in the United States, the residuals from the model also appear to exhibit seasonality in volatility. That is, interval forecasts (prediction intervals) based on the common assumption of homoskedastic residuals may not properly address the changes in future volatility. Additionally, both the point and interval forecasts generated by SSA+AR may include negative numbers, a physical impossibility.

We discuss methods that provide non-negative competitive one- to five-day point and interval forecasts. Our methods include forecasting the logarithm of the O3 concentration and symmetrizing the resultant time series. We apply SSA+AR to our transformed time series to derive point forecasts. As the residuals from the SSA+AR fit exhibit seasonality in volatility, we apply the same methods to forecast the logarithm of the absolute residuals: First symmetrize the data and apply SSA+AR. We combine these two types of forecasts to derive our interval forecasts. We then compare our interval forecast performance in terms of sharpness and resolution against those based on the original SSA+AR that assumes homoskedastic residuals.