Time Series Seasonal Adjustment Using Regularized Singular Value Decomposition

We propose a new seasonal adjustment method based on the Regularized Singular Value Decomposition (RSVD) of the matrix obtained by reshaping the seasonal time series data. The method is flexible enough to capture two kinds of seasonality: the fixed seasonality that does not change over time and the time-varying seasonality that varies from one season to another. RSVD represents the time-varying seasonality by a linear combination of several seasonal patterns. The right singular vectors capture multiple seasonal patterns, and the corresponding left singular vectors capture the magnitudes of those seasonal patterns and how they change over time. By assuming the time-varying seasonal patterns change smoothly over time, the RSVD uses penalized least squares with a roughness penalty to effectively extract the left singular vectors. The proposed method applies to seasonal time-series data with a stationary or nonstationary nonseasonal component. The method also has a variant that can handle the case that an abrupt change (i.e., break) may occur in the magnitudes of seasonal patterns. Our proposed method compares favorably with the state-of-art X-13ARIMA-SEATS program on both simulated and real data examples.