Historically, traditional methods such as Autoregressive Integrated Moving Average (ARIMA) have played an important role for researchers studying time series data. Recently, as advances in computer science and machine learning have gained widespread attention, researchers of time series analysis have brought new techniques to the table. In this paper, we examine the performance difference between ARIMA and a relatively recent development in the machine learning community called Long-Short Term Memory Networks (LSTM). Whereas many traditional methods assume the existence of an underlying stochastic model, these algorithmic approaches make no claims about the generation process. Our primary measure of performance is how well each model forecasts out-of-sample data. We find that data with strong seasonal structure are forecast comparatively well by either method. On the other hand, without strong seasonality, there is very little information that can be extracted and both methods tend to perform poorly in forecasting.