I have data of an orbital parameter of a satellite for 456 days. I am treating this data as univariate time series data and wish to use time series models to forecast future values. However, this data seems quite complex. This data appears as sinusoidal oscillating within a sinusoidal function.

I tried using 2nd order differential to make the series weak stationary but still my ACF and PACF plots give a lot of values that exceed the confidence interval. Using all those values would give a very poor model. I wish to ask that whether my data can be treated as time series data and whether classical algorithms such as ARIMA etc can be used for forecasting.

I have uploaded the plot of original data, its 2nd differential and PACF of 2nd differential:

enter image description here

  • $\begingroup$ The first picture titled as "Raw Data" is the original data. $\endgroup$ Apr 5, 2020 at 22:34
  • 2
    $\begingroup$ That is a picture .. I requested the actual data in detail showing the observed values in a csv file format .. $\endgroup$
    – IrishStat
    Apr 6, 2020 at 0:18
  • $\begingroup$ ARMA + two deterministic sinusoids should be a good start. The methods you've used (like differencing) are designed for stochastic seasonalities and trends but deterministic seasonalities and trends require a different approach. They can be treated as exogenous predictors. $\endgroup$
    – stans
    Jan 2, 2023 at 1:51

1 Answer 1


Given the regularity of the data, I would start by simply drawing a collection of straight-line segments through the oscillating data. This presumes that you have some understanding of what is causing the sinusoidal trend (and, after talking to the right people, there may be an explanation that also lends itself to modeling).

Compute the linear coefficients of the straight line segments via regression. Using these results, you can now detrended series (or an approximation to it). Then, apply time series modeling to determine the order and nature (autoregressive, moving average,...), etc. to the detrended series.

Having accomplished this, do work on explaining the sinusoidal pattern. Based on any improved sinusoidal trend, detrend and re-examining your time series analysis.

Check your model based on the accuracy of new data point forecasts.


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