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Given the recent explosion of interest in streaming data and online algorithms, clustering of time series subsequences has received much attention. In this work we make a surprising claim. Clustering of time series subsequences is completely meaningless. More concretely, clusters extracted from these time series are forced to obey a certain constraint that is pathologically unlikely to be satisfied by any dataset, and because of this, the clusters extracted by any clustering algorithm are essentially random. While this constraint can be intuitively demonstrated with a simple illustration and is simple to prove, it has never appeared in the literature. We can justify calling our claim surprising, since it invalidates the contribution of dozens of previously published papers. We will justify our claim with a theorem, illustrative examples, and a comprehensive set of experiments on reimplementations of previous work.

In the last few decades, there has been growing interest in forecasting with computer intelligence, and both fuzzy time series (FTS) and artificial neural networks (ANNs) have gained particular popularity, among others. Rather than the conventional methods (e.g., econometrics), FTS and ANN are usually thought to be immune to fundamental concepts such as stationarity, theoretical causality, post-sample control, among others. On the other hand, a number of studies significantly indicated that these fundamental controls are required in terms of the theory of forecasting, and even application of such essential procedures substantially improves the forecasting accuracy. The aim of this paper is to fill the existing gap on modeling and forecasting in the FTS and ANN methods and figure out the fundamental concepts in a comprehensive work through merits and common failures in the literature. In addition to these merits, this paper may also be a guideline for eliminating unethical empirical settings in the forecasting studies.

One crucial but sometimes overlooked fact regarding the difference between observation in the cross-section and observation over time must be stated before proceeding further. Tempting though it is to draw conclusions about the dynamics of a process from cross-sectional observations taken as a snapshot of that process, it is a fallacious practice except under a very precise condition that is highly unlikely to obtain in processes of interest to the social scientist. That condition is known as ergodicity.

The time series of the federal funds rate has recently been extended back to 1928, now including several episodes during which interest rates remained near the lower bound of zero. This series is analyzed, using the method of indirect inference, by applying recent research on bounded time series to estimate a set of bounded parametric diffusion models. This combination uncouples the specification of the bounds from the law of motion. Although Louis Bachelier was the first to use arithmetic Brownian motion to model financial time series, he has often been criticized for this proposal, since the process can take on negative values. Most researchers favor processes such as geometric Brownian motion (GBM), which remains positive. Under this framework, Bachelier's proposal remains valid when specified with bounds and is shown to compare favorably when modeling the federal funds rate.

We develop a theoretical model to compare forecast uncertainty estimated from time-series models to those available from survey density forecasts. The sum of the average variance of individual densities and the disagreement is shown to approximate the predictive uncertainty from well-specified time-series models when the variance of the aggregate shocks is relatively small compared to that of the idiosyncratic shocks. Due to grouping error problems and compositional heterogeneity in the panel, individual densities are used to estimate aggregate forecast uncertainty. During periods of regime change and structural break, ARCH estimates tend to diverge from survey measures.

Volume 20 of Advances in Econometrics is dedicated to Rob Engle and Sir Clive Granger, winners of the 2003 Nobel Prize in Economics, for their many valuable contributions to the econometrics profession. The Royal Swedish Academy of Sciences cited Rob “for methods of analyzing economic time series with time-varying volatility (ARCH),” while Clive was cited “for methods of analyzing economic time series with common trends (cointegration).” Of course, these citations are meant for public consumption but we specialists in time-series analysis know their contributions go far beyond these brief citations. Consider some of Rob's other contributions to our literature: Aggregation of Time Series, Band Spectrum Regression, Dynamic Factor Models, Exogeneity, Forecasting in the Presence of Cointegration, Seasonal Cointegration, Common Features, ARCH-M, Multivariate GARCH, Analysis of High Frequency Data, and CAViaR. Some of Sir Clive's additional contributions include Spectral Analysis of Economic Time Series, Bilinear Time Series Models, Combination Forecasting, Spurious Regression, Forecasting Transformed Time Series, Causality, Aggregation of Time Series, Long Memory, Extreme Bounds, Multi-Cointegration, and Non-linear Cointegration. No doubt, their Nobel Prizes are richly deserved. And the 48 authors of the two parts of this volume think likewise. They have authored some very fine papers that contribute nicely to the same literature that Rob's and Clive's research helped build.