Sinusoidal model
In statistics, signal processing, and time series analysis, a sinusoidal model is used to approximate a sequence y i {\displaystyle y_{i}} to a sine function: y i = c + α sin ( ω t i + φ ) + ε i {\displaystyle y_{i}=c+\alpha \sin(\omega t_{i}+\varphi )+\varepsilon _{i}} where c {\displaystyle c} is constant defining a mean level, α {\displaystyle \alpha } is an amplitude for the sine, ω {\displaystyle \omega } is the angular frequency, t i {\displaystyle t_{i}} is a time variable, φ {\displaystyle \varphi } is the phase-shift, and ε i {\displaystyle \varepsilon _{i}} is the error sequence. This sinusoidal model can be fit using nonlinear least squares; to obtain a good fit, routines may require good starting values for the unknown parameters.