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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.

In their seminal papers on ARCH and GARCH models, Engle (1982) and Bollerslev (1986) specified parametric inequality constraints that were sufficient for non-negativity and weak stationarity of the estimated conditional variance function. This paper uses Bayesian methodology to impose these constraints on the parameters of an ARCH(3) and a GARCH(1,1) model. The two models are used to explain volatility in the London Metals Exchange Index. Model uncertainty is resolved using Bayesian model averaging. Results include estimated posterior pdfs for one-step-ahead conditional variance forecasts.

This chapter analyzes the properties of an alternative least-squares based estimator for linear panel data models with general predetermined regressors. This approach uses backward means of regressors to approximate individual specific fixed effects (FE). The author analyzes sufficient conditions for this estimator to be asymptotically efficient, and argue that, in comparison with the FE estimator, the use of backward means leads to a non-trivial bias-variance tradeoff. The author complements theoretical analysis with an extensive Monte Carlo study, where the author finds that some of the currently available results for restricted AR(1) model cannot be easily generalized, and should be extrapolated with caution.

Several stationarity tests in heterogeneous panel data models are proposed in this chapter. By allowing maximum degree of heterogeneity in the panel, two different ways of pooling information from independent tests, the group mean and the Fisher tests, are used to develop the panel stationarity tests. We consider the case of serially correlated errors in the level and trend stationary models. The small sample performances of the tests are investigated via Monte Carlo simulations. The simulation experiments reveal good small sample performances. In the presence of serial correlation, either the group mean or the Fisher tests based on individual KPSS tests with l2 and LMC tests with p = 1 are recommended for use in empirical work due to their good small sample performances.

The authors propose a family of tests for stationarity against a local unit root. It builds on the Karhunen–Loève (KL) expansions of the limiting CUSUM process under the null hypothesis and a local alternative. The variance ratio type statistic VRq is a ratio of quadratic forms of q weighted Gaussian sums such that the nuisance long-run variance cancels asymptotically without having to be estimated. Asymptotic critical values and local power functions can be calculated by standard numerical means, and power grows with q. However, Monte Carlo experiments show that q may not be too large in finite samples to obtain tests with correct size under the null. Balancing size and power results in a superior performance compared to the classic KPSS test.

We examine the roles of sample initial conditions and unobserved individual effects in consistent estimation of the dynamic binary response panel data model. Different specifications of the model are estimated using female welfare and labor force participation data from the Survey of Income and Program Participation. These include alternative random effects (RE) models, in which the conditional distributions of both the unobserved heterogeneity and the initial conditions are specified, and fixed effects (FE) conditional logit models that make no assumptions on either distribution. There are several findings. First, the hypothesis that the sample initial conditions are exogenous is rejected by both samples. Misspecification of the initial conditions results in drastically overstated estimates of the state dependence and understated estimates of the short- and long-run effects of children on labor force participation. The FE conditional logit estimates are similar to the estimates from the RE model that is flexible with respect to both the initial conditions and the correlation between the unobserved heterogeneity and the covariates. For female labor force participation, there is evidence that fertility choices are correlated with both unobserved heterogeneity and pre-sample participation histories.

Statistical inference (estimation and testing) for the stochastic volatility (SV) model Taylor (1982, 1986) is challenging, especially likelihood-based methods which are difficult to apply due to the presence of latent variables. The existing methods are either computationally costly and/or inefficient. In this paper, we propose computationally simple estimators for the SV model, which are at the same time highly efficient. The proposed class of estimators uses a small number of moment equations derived from an ARMA representation associated with the SV model, along with the possibility of using “winsorization” to improve stability and efficiency. We call these ARMA-SV estimators. Closed-form expressions for ARMA-SV estimators are obtained, and no numerical optimization procedure or choice of initial parameter values is required. The asymptotic distributional theory of the proposed estimators is studied. Due to their computational simplicity, the ARMA-SV estimators allow one to make reliable – even exact – simulation-based inference, through the application of Monte Carlo (MC) test or bootstrap methods. We compare them in a simulation experiment with a wide array of alternative estimation methods, in terms of bias, root mean square error and computation time. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that ARMA-SV estimators match (or exceed) alternative estimators in terms of precision, including the widely used Bayesian estimator. The proposed methods are applied to daily observations on the returns for three major stock prices (Coca-Cola, Walmart, Ford) and the S&P Composite Price Index (2000–2017). The results confirm the presence of stochastic volatility with strong persistence.

Purpose – The purpose of this study is to examine the impact of foreign direct investment (FDI) on the performance of manufacturing firms in Nigeria.

Methodology – Annual data of aggregate foreign direct investment, manufacturing foreign direct investment, manufacturing index, manufacturing capacity utilization, manufacturing value added, and manufacturing turnovers were used. In the analysis, we tested for stationarity using augmented Dickey–Fuller test, and the test for long-run relationship was conducted using Johansen cointegration test. Vector error correction model was used for causality test.

Findings – The data satisfied the stationarity test and that there is a long-run relationship between FDI and the performance of manufacturing firms in Nigeria. The study also found that causality runs from FDI to the performance of manufacturing firms.

Practical implications – Since there is a long-run relationship among the variables, policies to attract FDI into the manufacturing sector should have a long range view and should be sustainable. The policy direction should focus on improving productivity and innovative capabilities of the manufacturing sectors and strengthening the supporting industries and institutions. Specifically, policies like provision of tax relief to manufacturers on importation of new technology and expatriate that will bring about efficiency and effectiveness in productions.

Originality/Value of paper – This is one of the few attempts at studying the impact of FDI on manufacturing firms. The study draws attention of policy makers in Nigeria to the fact that diversification of the economy can be achieved through a viable manufacturing sector.

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.

A univariate GARCH(p,q) process is quickly transformed to a univariate autoregressive moving-average process in squares of an underlying variable. For positive integer m, eigenvalue restrictions have been proposed as necessary and sufficient restrictions for existence of a unique mth moment of the output of a univariate GARCH process or, equivalently, the 2mth moment of the underlying variable. However, proofs in the literature that an eigenvalue restriction is necessary and sufficient for existence of unique 4th or higher even moments of the underlying variable, are either incorrect, incomplete, or unnecessarily long. Thus, the paper contains a short and general proof that an eigenvalue restriction is necessary and sufficient for existence of a unique 4th moment of the underlying variable of a univariate GARCH process. The paper also derives an expression for computing the 4th moment in terms of the GARCH parameters, which immediately implies a necessary and sufficient inequality restriction for existence of the 4th moment. Because the inequality restriction is easily computed in a finite number of basic arithmetic operations on the GARCH parameters and does not require computing eigenvalues, it provides an easy means for computing “by hand” the 4th moment and for checking its existence for low-dimensional GARCH processes. Finally, the paper illustrates the computations with some GARCH(1,1) processes reported in the literature.