If the trend of the data is cyclic and wave-like on yearly basis we normally use Fourier Series to model it, but if the data is cyclic, wave-like, and possesses increasing trend per wave packet what type of mathematics would be better to model it?
Possibly in time series theory, data sets possessing cyclic also maintain seasonal property along the time axis. You would try AR(p), ARMA ... models to guess the seasonal trend then.
Thanks Nguyen but Auto-Regressive Moving Average Models are not useful for the purpose.
In fact, in this case, the variations are occurring not around a zero level, but around a straight line which is not parallel to the time axis.
see Cuestas and GilAlana 2016. The attached paper. Prof Gil-Alana is my friend. We have applied Fractional Integration with nonlinear deterministic terms in our papers...see Yaya and Gil-alana...
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