Forecasting the solar modulation potential: Tests of time series models

Abstract

This study analyzes the predictability of the solar modulation potential using time series models. Recently, new data sets for the modulation potential have become available, at daily, monthly, and annual resolutions. At lower frequencies, the data show the well-known 11-22-year cycle. Both the periodicity and amplitude vary over time. At higher resolutions, the probability distribution has heavy tails, while the data show the intermittent outliers characteristic of multifractal processes. Forecasting experiments are run using regressions in levels and differences, frequency domain methods, models with sinusoidal terms and neural networks. For the daily data, all the models achieve high degrees of accuracy at proximate horizons. As the horizon extends, accuracy falls away rapidly. At 27 days, corresponding to one solar rotation, a transfer function in differences achieves a more accurate forecast than either regressions or neural nets, since it is able to replicate the range of the data. At the annual resolution, both the regression and neural net predict well at horizons of 1 year. Again, forecast accuracy deteriorates sharply as the forecast horizon extends. At the monthly resolution, forecasting is problematic. The resolution is not low enough to bring out the low frequency cycles, but there is so much short-term dependence that the data are completely dominated by serial correlation. Any model incorporating proximate lags will generate inertial forecasts. Any model using lower frequency cyclical terms will be unable to pick up on near-term patterns. The forecasting skill of time series models appears limited to short horizons. The recommendation for forecasting over longer intervals is some combination of physics and statistical models.