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When forecasting intermittent demand the method derived by Croston (1972) is often cited. Previous research favorably compared Croston's forecasting method for demand with simple exponential smoothing assuming a nonzero demand occurs as a Bernoulli process with a constant probability. In practice, however, the assumption of a constant probability for the occurrence of nonzero demand is often violated. This research investigates Croston's method under violation of the assumption of a constant probability of nonzero demand. In a simulation study, forecasts derived using single exponential smoothing (SES) are compared to forecasts using a modification of Croston's method utilizing double exponential smoothing to forecast the time between nonzero demands assuming a normal distribution for demand size with different standard deviation levels. This methodology may be applicable to forecasting intermittent demand at the beginning or end of a product's life cycle.

There is a growing literature in nonparametric econometrics in the recent two decades. Given the space limitation, it is impossible to survey all the important recent developments in nonparametric econometrics. Therefore, we choose to limit our focus on the following areas. In Section 2, we review the recent developments of nonparametric estimation and testing of regression functions with mixed discrete and continuous covariates. We discuss nonparametric estimation and testing of econometric models for nonstationary data in Section 3. Section 4 is devoted to surveying the literature of nonparametric instrumental variable (IV) models. We review nonparametric estimation of quantile regression models in Section 5. In Sections 2–5, we also point out some open research problems, which might be useful for graduate students to review the important research papers in this field and to search for their own research interests, particularly dissertation topics for doctoral students. Finally, in Section 6 we highlight some important research areas that are not covered in this paper due to space limitation. We plan to write a separate survey paper to discuss some of the omitted topics.

New asymptotic approximations are established for the Wald and t statistics in the presence of unknown but strong autocorrelation. The asymptotic theory extends the usual fixed-smoothing asymptotics under weak dependence to allow for near-unit-root and weak-unit-root processes. As the locality parameter that characterizes the neighborhood of the autoregressive root increases from zero to infinity, the new fixed-smoothing asymptotic distribution changes smoothly from the unit-root fixed-smoothing asymptotics to the usual fixed-smoothing asymptotics under weak dependence. Simulations show that the new approximation is more accurate than the usual fixed-smoothing approximation.

We investigate whether smooth robust methods for forecasting can help mitigate pronounced and persistent failure across multiple forecast horizons. We demonstrate that naive predictors are interpretable as local estimators of the long-run relationship with the advantage of adapting quickly after a break, but at a cost of additional forecast error variance. Smoothing over naive estimates helps retain these advantages while reducing the costs, especially for longer forecast horizons. We derive the performance of these predictors after a location shift, and confirm the results using simulations. We apply smooth methods to forecasts of UK productivity and US 10-year Treasury yields and show that they can dramatically reduce persistent forecast failure exhibited by forecasts from macroeconomic models and professional forecasters.

Demand forecasting has long been an imperative tenet in production planning especially in a make-to-order environment where a typical manufacturer has to balance the issues of holding excessive safety stocks and experiencing possible stockout. Many studies provide pragmatic paradigms to generate demand forecasts (mainly based on smoothing forecasting models.) At the same time, artificial neural networks (ANNs) have been emerging as alternatives. In this chapter, we propose a two-stage forecasting approach, which combines the strengths of a neural network with a more conventional exponential smoothing model. In the first stage of this approach, a smoothing model estimates the series of demand forecasts. In the second stage, general regression neural network (GRNN) is applied to learn and then correct the errors of estimates. Our empirical study evaluates the use of different static and dynamic smoothing models and calibrates their synergies with GRNN. Various statistical tests are performed to compare the performances of the two-stage models (with error correction by neural network) and those of the original single-stage models (without error-correction by neural network). Comparisons with the single-stage GRNN are also included. Statistical results show that neural network correction leads to improvements to the forecasts made by all examined smoothing models and can outperform the single-stage GRNN in most cases. Relative performances at different levels of demand lumpiness are also examined.

I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.

Recently, star variables and the post-crisis nature of cyclical fluctuations have attracted a great deal of interest. In this chapter, the authors investigate different methods of assessing business cycles (BCs) for the European Union in general and the euro area in particular. First, the authors conduct a Monte Carlo (MC) experiment using a broad spectrum of univariate trend-cycle decomposition methods. The simulation aims to examine the ability of the analysed methods to find the observed simulated cycle with structural properties similar to actual macroeconomic data. For the simulation, the authors used the structural model’s parameters calibrated to the euro area’s real gross domestic product (GDP) and unemployment rate. The simulation outcomes indicate the sufficient composition of the suite of models (SoM) consisting of popular Hodrick–Prescott, Christiano–Fitzgerald and structural trend-cycle-seasonal filters, then used for the real application. The authors find that: (i) there is a high level of model uncertainty in comparing the estimates; (ii) growth rate (acceleration) cycles have often the worst performances, but they could be useful as early-warning predictors of turning points in growth and BCs; and (iii) the best-performing MC approaches provide a reasonable combination as the SoM. When swings last less time and/or are smaller, it is easier to pick a good alternative method to the suite to capture the BC for real GDP. Second, the authors estimate the BCs for real GDP and unemployment data varying from 1995Q1 to 2020Q4 (GDP) or 2020Q3 (unemployment), ending up with 28 cycles per country. This analysis also confirms that the BCs of euro area members are quite synchronized with the aggregate euro area. Some major differences can be found, however, especially in the case of periphery and new member states, with the latter improving in terms of coherency after the global financial crisis. The German cycles are among the cyclical movements least synchronized with the aggregate euro area.

In this paper we construct a nonparametric kernel estimator to estimate the joint multivariate cumulative distribution function (CDF) of mixed discrete and continuous variables. We use a data-driven cross-validation method to choose optimal smoothing parameters which asymptotically minimize the mean integrated squared error (MISE). The asymptotic theory of the proposed estimator is derived, and the validity of the cross-validation method is proved. We provide sufficient and necessary conditions for the uniqueness of optimal smoothing parameters when the estimation of CDF degenerates to the case with only continuous variables, and provide a sufficient condition for the general mixed variables case.