In statistics, signal processing, and time series analysis, a sinusoidal model is used to approximate a sequence Yi to a sine function: where C is constant defining a mean level, α is an amplitude for the sine, ω is the angular frequency, Ti is a time variable, φ is the phase-shift, and Ei is the error sequence.
If the data show a trend, i.e., the assumption of constant location is violated, one can replace C with a linear or quadratic least squares fit.
If the plot is essentially flat, i.e., zero slope, then it is reasonable to assume a constant amplitude in the non-linear model.
However, if the slope varies over the range of the plot, one may need to adjust the model to be: That is, one may replace α with a function of time.
For example, a run sequence plot to check for significant shifts in location, scale, start-up effects and outliers.