As JQ Veenstra has pointed out your method of evaluation depends a lot on the particular type of time series model that you are estimating. Have a look at the following points.

Usually you should have a set of residuals in your model that are uncorrelated. You can test that.
You can test the forecasting ability of your model by starting with a subset of the data recursively estimate the model and look at the errors when forecasting each re-estimated model.
For general guidance on forecasting I would recommend Granger, Clive W. J. and Paul Newbold (1986) -Forecasting Economic Time Series - Academic Press 1986 which is a bit dated but covers well many aspects of forecast evaluation. Elliott, G. and Timmermann, A (2016). Economic Forecasting, Princeton University Press is, perhaps a little mathematical but provides a comprehensive coverage of forecasting. The references to specific areas in this may give you more guidance on the evaluation of specific forecalting methods.

2your testPred plot doesn't start at zero. Are you sure you're plotting it right? – Mohammad Athar – 2017-03-02T16:11:41.743

@MohammadAthar, testPred is the forecast. There needs to be some amount of data before making a prediction, which is why testPred does not start at 0. – Hobbes – 2017-05-01T15:22:17.397

@Horacet not sure why you're singling me out for this info, since I just asked if the data are plotted right – Mohammad Athar – 2017-05-01T20:00:51.320

1@MohammadAthar I meant to address the author of the post. Sorry. – horaceT – 2017-05-01T20:09:25.220

@Mustafa You have to provide a lot more details about your

modelanddatabefore anyone could help you. First, is the response just an univariate time series? what's your predictors that got fed into the LSTM? is it just $y_t$ lagged by a few time steps? what's the LSTM arch? – horaceT – 2017-05-01T20:11:25.827