Modelling and forecasting time series using autoregressive approximation

预测未来是我们生活中最重要的活动之一。每天，库存、生产、人员和机器的调度、财务和营销决策都是根据短期、中期和长期预测做出的。一个好的预测者必须能够迅速识别现有数据和最相关的建模技术之间的桥梁，提供对未来的可靠推断，并使预测模型适应世界上的新变化。在许多实际情况下，观测的样本大小是先验未知的，并且可能无限增加，而数据分析师仍然需要实时执行预测任务。这种情况通常被称为在线建模和预测，在各种现代应用中被广泛满足，例如股票或货币兑换收益的预测、心率的心电测量过滤等。新观测的到来通常意味着当前使用的模型的阶数应该被改进，因此，所有的模型参数都需要重新计算。因此，计算成本最终会增加。如果基础模型具有复杂的结构，这一点尤为重要。

Forecasting the future is one of the most important activities in our life. Every day, inventory, production, scheduling of personnel and machinery, financial and marketing decisions are made which depend on short, medium and long-term forecasts. A good forecaster must be able to quickly identify a bridge between the available data and the most relevant modeling technique, provide the reliable inference about the future and to adapt the forecasting model to new changes in the world. In many practical situations the sample size of observations is not known a-priori and may indefinitely increase while a data analyst still needs to perform prediction tasks in real time. Such cases are typically referred to as online modelling and forecasting and are widely met in a variety of modern applications, e.g. prediction of stock or currency exchange returns, filtering electrocardiogram measurements of heart rate etc. Arrival of new observations often implies that the order of the currently utilized model should be refined and, thus, all model parameters need to be recalculated. Hence, computational costs eventually increase. This is especially important if the underlying model has a complicated structure.