Time series prediction has wide applications ranging from stock price prediction, product demand estimation to economic forecasting. In this article, we treat the taxi and Uber demand in each location as a time series, and reduce the taxi and Uber demand prediction problem to a time series prediction problem. We answer two key questions in this area. First, time series have different temporal regularity. Some are easy to be predicted and others are not. Given a predictive algorithm such as LSTM (deep learning) or ARIMA (time series), what is the maximum prediction accuracy that it can reach if it captures all the temporal patterns of that time series? Second, given the maximum predictability, which algorithm could approach the upper bound in terms of prediction accuracy? To answer these two question, we use temporal-correlated entropy to measure the time series regularity and obtain the maximum predictability. Testing with 14 million data samples, we find that the deep learning algorithm is not always the best algorithm for prediction. When the time series has a high predictability a simple Markov prediction algorithm (training time 0.5s) could outperform a deep learning algorithm (training time 6 hours). The predictability can help determine which predictor to use in terms of the accuracy and computational costs. We also find that the Uber demand is easier to be predicted compared the taxi demand due to different cruising strategies as the former is demand driven with higher temporal regularity.
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