### 3.1 Linear regression

Linear (auto)regression means representing the value of a time series at time by a linear combination
of values at times , , , . Admitting some random error , the value of R
in point n is
where is the order of the autoregression and the ’s are weight parameters. A further twist on the
model admits a propagation of errors from the previous points:

This is known as the ARMA (AutoRegressive Moving Average) model.

Linear regression techniques have been widely used for solar activity prediction during the course of an
ongoing cycle. Their application for cycle-to-cycle prediction has been less common and successful (Lomb
and Andersen, 1980; Box et al., 2008; Wei, 2005).

Brajša et al. (2009) applied an ARMA model to the series of annual values of R. A successful
fit was found for , . Using this fit, the next solar maximum was predicted to
take place around 2012.0 with an amplitude 90 ± 27, and the following minimum occurring in
2017.

Instead of applying an autoregression model directly to SSN data, Hiremath (2008) applied it to a
forced and damped harmonic oscillator model claimed to well represent the SSN series. This resulted in a
predicted amplitude of 110 ± 10 for solar cycle 24, with the cycle starting in mid-2008 and lasting 9.34
years.