How to construct NDVI series?

I have long-time series of MODIS NDVI and want to construct the NDVI series.

The figure shows how MODIS NDVI changes in one year. In this figure, the triangle is true values of MODIS NDVI and the curve is the smoothed curve of the true values. By the smoothed curve, we can predict the value of NDVI in the days without MODIS satellites visiting.

My problem is that I don't know how to do smoothed curve and predict the value of NDVI at pixels.