Analyze a time series to predict a value I have about 50 observations where every observation is composed of a time series of an index and a value Y. Is it possible to use the time series to predict the value Y? What do I need to study to work on that data?
Adding information about my data:
I'm studying in the agriculture sector. My time series are composed of NDVI values taken every 5 days (the NDVI is an index that measures the vigor of a plant). At the end of the season, every plant produces Y kg of fruit which is the yield. My objective is trying to forecast the yield based on the time series of NDVI.
I have tried to do a regression with the sum of NDVI (for example the sum of 4 acquisitions), single acquisition in some key moments, the sum of all the period analyzed... against the yield. I have done these tests because I have only basic statistical skills but I would like to deepen further in this subject.
If needed, I can work with R and Python.
 A: There are a few approaches you can use for this type of regression model using time series data. I'll mention a couple that are commonly used in earth/environmental science applications. The first is to simply treat the time steps as independent attributes and use them to train a standard regression algorithm. Random Forest and Support Vector Regression are frequently used. The second approach is to use deep learning methods such as 1-d Convolutional neural networks (CNNs) and Recurrent neural networks (RNNs). Both these methods take into account the ordering in the time series, so are often more effective than standard regression algorithms.
This type of time series problem is one focus of my research group, so here are some references to some of our papers that you may find useful.
This paper: Temporal Convolutional Neural Network for the Classification of Satellite Image Time Series firstly reviews methods of land cover classification from remote sensing time series data and discusses the advantages of using a specialised time series algorithm. It also presents a temporal CNN classification algorithm, which has been adapted for a regression task in the paper Live fuel moisture content estimation from MODIS: A deep learning approach.
This paper: Time series extrinsic regression (you can also access a preprint on ArXiv if you don't have access to the public version) reviews a wide range of algorithms for this type of regression problem (here called "extrinsic regression" to distinguish it from forecasting).
