Urban flows prediction from spatial-temporal data using machine learning: A survey <s> Statistics-based methods <s> SUMMARY Recently, methods for detecting unit roots in autoregressive and autoregressivemoving average time series have been proposed. The presence of a unit root indicates that the time series is not stationary but that differencing will reduce it to stationarity. The tests proposed to date require specification of the number of autoregressive and moving average coefficients in the model. In this paper we develop a test for unit roots which is based on an approximation of an autoregressive-moving average model by an autoregression. The test statistic is standard output from most regression programs and has a limit distribution whose percentiles have been tabulated. An example is provided. <s> BIB001 </s> Urban flows prediction from spatial-temporal data using machine learning: A survey <s> Statistics-based methods <s> The application of seasonal time series models to the single-interval traffic flow forecasting problem for urban freeways is addressed. Seasonal time series approaches have not been used in previous forecasting research. However, time series of traffic flow data are characterized by definite periodic cycles. Seasonal autoregressive integrated moving average (ARIMA) and Winters exponential smoothing models were developed and tested on data sets belonging to two sites: Telegraph Road and the Woodrow Wilson Bridge on the inner and outer loops of the Capital Beltway in northern Virginia. Data were 15-min flow rates and were the same as used in prior forecasting research by B. Smith. Direct comparisons with the Smith report findings were made and it was found that ARIMA (2, 0, 1)(0, 1, 1)96 and ARIMA (1, 0, 1)(0, 1, 1)96 were the best-fit models for the Telegraph Road and Wilson Bridge sites, respectively. Best-fit Winters exponential smoothing models were also developed for each site. The single-step forecast... <s> BIB002 </s> Urban flows prediction from spatial-temporal data using machine learning: A survey <s> Statistics-based methods <s> Automatic forecasts of large numbers of univariate time series are often needed in business and other contexts. We describe two automatic forecasting algorithms that have been implemented in the forecast package for R. The first is based on innovations state space models that underly exponential smoothing methods. The second is a step-wise algorithm for forecasting with ARIMA models. The algorithms are applicable to both seasonal and non-seasonal data, and are compared and illustrated using four real time series. We also briefly describe some of the other functionality available in the forecast package. <s> BIB003 </s> Urban flows prediction from spatial-temporal data using machine learning: A survey <s> Statistics-based methods <s> Predictions of short-term traffic volume support proactive transportation management and traveler information services. To address the periodicity, nonlinearity, uncertainty, and complexity of short-term traffic forecasting, seasonal autoregressive integrated moving average (SARIMA) and support vector machine (SVM) models are often used separately to forecast the time series of traffic flow. SARIMA can discover intrinsic relations (correlations) in time series data, especially fit for modeling seasonal, stochastic time series. In contrast, SVM has a strong nonlinear mapping ability for input and output, appropriate for solving complex, nonlinear problems. The few combined schemes that have been presented previously tend to be complicated. A simple and effective novel hybrid methodology that combines the SARIMA and SVM models is proposed to take advantage of the individual strengths of the two models. Two key issues in building a hybrid model process are discussed: identification of SVM input dimensions vi... <s> BIB004
In statistics-based methods, ARMA (Autoregressive Moving Average) BIB001 is a fundamental time series prediction methods, and the variant method is ARIMA (Autoregressive Integrated Moving Average) BIB002 . An integrated version of ARMA model is also very popular in time-series prediction problems. You can use the Hyndman-Khandakar algorithm for automatic ARIMA modelling in R BIB003 . The default procedure contains two steps  : (i) The number of differences (0 ≤ d ≤ 2) is determined using repeated KPSS tests; (ii) The value of p and q are then chosen by minimising the AICc (AICc is AIC (Akaike Information Criterion) with a correction for small sample sizes) after differencing the data d times. Rather than considering every possible combination of p and q, the algorithm uses a stepwise search to traverse the model space. And the process for forecasting is summarized in Figure 5 . As an another extension of the ARMA method, Seasonal Auto-Regressive Integrated Moving Average(SARIMA) method BIB004 can catch intrinsic correlations in time series data, especially fit for modeling seasonal, stochastic time series that always occur in traffic flow data. Although these classical time-series methods can capture temporal dependencies in time series data, they can't depict the spatial influence in urban flows prediction problems.