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Say I have some data for past 5 years and I have trained my classifier (anything decision tree, svm etc.) based on that i.e. given the appropriate input feature data and correct output labeling.

Now for current year when I have to make prediction (predicting the output) I can supply the input feature data I am having for the current year and the classifier would predict the correct output labels.

So far so good.

However suppose If I dont have the current input feature data, how can I go about making predictions just based on the past data?

For an example election prediction, i.e. which party would win from each constituency. In this we have lots of past data but no current input feature data so how to go about this?

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So, first you need to find out that kind of data you have as input for your machine learning model and what kind of output you would like to get.

If you are talking about "past years", you are most likely mean the time series, e.g. (multi-)variable data distributed over time.

In the linked Wikipedia-article you already find enough information to start with your task. Just to mention some possible approaches here:

  1. If your process is stochastic, then you better stick to stochastic simulations
  2. or try regression analysis if you think you can derive a model for it.
  3. Approximation with an approriate domain function could provide results with predictive force, especially if your domain is specifica and well constrained.

And generally it might be advisable to take some advanced course in statistics where such kind of "predictions" are often covered.

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