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.

We present a new measure of dependence suitable for time series forecasting: Partial Monotone Correlation (PMC) that generalizes Monotone Correlation. Unlike the Monotone Correlation, the new measure of dependence uses piecewise strictly monotone transformations that increase the value of the correlation coefficient. We explore its properties, its relationship with Monotone and Maximal Correlation, and present an algorithm that calculates it based on the Simultaneous Perturbation Stochastic Approximation method. We also demonstrate how to apply Partial Monotone Correlation for time series analysis and forecasting introducing Partial Monotone Autoregressive model (PMAR) of order 1. Its performance is then evaluated against the baseline of linear and nonlinear autoregressive models (AR, LSTAR) on 150 time series produced from 3 datasets: Yellow Taxi pickups, Citi Bike pickups, and Cellular Network hits. Overall, PMAR model outperforms the baseline with the average sMAPE of about 1.7-4% lower.

Most humans today have mobile phones. According to the GSMA, there are almost 10 billion mobile connections in the world every day. These devices automatically capture behavioral data from human society and store it in databases around the world. However, data capture has several challenges to deal with, especially if it comes from old sources. Obsolete technologies such as 2G and 3G represent two-thirds of the total devices. To the best of our knowledge, all previous work only eliminates obvious problems in the data or use well-curated data. Eliminating traces in a time series can lead to deviations and biases in further analyses, especially when we are studying small areas or groups of peoples in the city. In this work, we present two algorithms to solve the problem of the Neighboring Network Hit (NNH) and calculate the distributions of trips and traveled distances with greater precision in small areas or groups of peoples. The problem of NNH arises when a mobile device connects to cellular sites other than those defined in the network design, which complicates the analysis of space-time mobility. We use cellular device data from three cities in Chile, obtained from the mobile phone operator and duly anonymized. We compare our results with the Government's Origin and Destination Surveys and use a novel method to generate synthetic data to which errors are added in a controlled manner to evaluate the performance of our solution. We conclude that our algorithms improve results compared to naive methods, increasing the accuracy in the count of trips and, mainly, in the distance distributions.

In big cities, taxi service is imbalanced. In some areas, passengers wait too long for a taxi, while in others, many taxis roam without passengers. Knowledge of where a taxi will become available can help us solve the taxi demand imbalance problem. In this paper, we employ a holistic approach to predict taxi demand at high spatial resolution. We showcase our techniques using two real-world data sets, yellow cabs and Uber trips in New York City, and perform an evaluation over 9,940 building blocks in Manhattan. Our approach consists of two key steps. First, we use entropy and the temporal correlation of human mobility to measure the demand uncertainty at the building block level. Second, to identify which predictive algorithm can approach the theoretical maximum predictability, we implement and compare three predictors: the Markov predictor (a probability-based predictive algorithm), the Lempel-Ziv-Welch predictor (a sequence-based predictive algorithm), and the Neural Network predictor (a predictive algorithm that uses machine learning). The results show that predictability varies by building block and, on average, the theoretical maximum predictability can be as high as 83%. The performance of the predictors also vary: the Neural Network predictor provides better accuracy for blocks with low predictability, and the Markov predictor provides better accuracy for blocks with high predictability. In blocks with high maximum predictability, the Markov predictor is able to predict the taxi demand with an 89% accuracy, 11% better than the Neural Network predictor, while requiring only 0.03% computation time. These findings indicate that the maximum predictability can be a good metric for selecting prediction algorithms.