Nonstationary Nonlinearity: An Outlook for New Opportunities

In this paper, we look for new opportunities that can be exploited using some of the recent developments on the theory of nonlinear models with integrated time series. Heuristic introductions on the basic tools and asymptotics are followed by the opportunities in three different directions: in data generation, in mean and in volatility. In the direction of data generation, we investigate the nonlinear transformations of random walks. It is shown in particular that they can generate stationary long memory as well as bounded nonstationarity and leptokurticity, which we commonly observe in many of economic and financial data. We then discuss how the nonlinear mean relationships between integrated processes can be appropriately formulated, interpreted and estimated within the regression framework. Both the nonlinear least squares regression and the nonparametric kernel regression are considered. Such formulations allow us to explore the nonlinear and nonparametric cointegration, which may be used in modelling the nonlinear and nonparametric longrun relationships among various economic and financial time series. Finally, a stochastic volatility model with the conditional variance specified as a nonlnear function of a random walk is examined. Established are various time series properties of the model, which are shown to be largely consistent with the observed characteristics of many time series data.

Bootstrap Unit Root Tests

We consider the bootstrap unit root tests based on finite order autoregressive integrated models driven by iid innovations, with or without deterministic time trends. A general methodology is developed to approximate asymptotic distributions for the models driven by integrated time series, and used to obtain asymptotic expansions for the Dickey-Fuller unit root tests. The second-order terms in their expansions are of stochastic orders Op(n-1/4) and Op(n-1/2), and involve functionals of Brownian motions and normal random variates. The asymptotic expansions for the bootstrap tests are also derived and compared with those of the Dickey-Fuller tests. We show in particular that the bootstrap offers asymptotic refinements for the Dickey-Fuller tests, i.e., it corrects their second-order errors. More precisely, it is shown that the critical values obtained by the bootstrap resampling are correct up to the second-order terms, and the errors in rejection probabilities are of order o(n-1/2) if the tests are based upon the bootstrap critical values. Through simulations, we investigate how effective is the bootstrap correction in small samples.

Strong Approximations for Nonlinear Transformations of Integrated Time Series

In this paper we establish the strong approximations for the nonlinear transformations of integrated time series. Both the asymptotically homogeneous and integrable transformations are considered, and the explicit rates for the convergence to their limit distributions are obtained under mild regularity conditions that are satisfied by virtually all nonlinear models used in practical applications. The first order asymptotics are also derived under the conditions that are significantly weaker than those required by earlier works.

A Bootstrap Theory for Weakly Integrated Processes

This paper develops a bootstrap theory for models including autoregressive time series with roots approaching to unity as the sample size increases. In particular, we consider the processes with roots converging to unity with rates slower than n?1. We call such processes weakly integrated processes. It is established that the bootstrap relying on the estimated autoregressive model is generally consistent for the weakly integrated processes. Both the sample and bootstrap statistics of the weakly integrated processes are shown to yield the same normal asymptotics. Moreover, for the asymptotically pivotal statistics of the weakly integrated processes, the bootstrap is expected to provide an asymptotic refinement and give better approximations for the finite sample distributions than the first order asymptotic theory. For the weakly integrated processes, the magnitudes of potential refinements by the bootstrap are shown to be proportional to the rate at which the root of the underlying process converges to unity. The order of boostrap refinement can be as large as o(n-1/2+_) for any espial > 0. Our theory helps to explain the actual improvements observed by many practitioners, which are made by the use of the bootstrap in analyzing the models with roots close to unity.

Bootstrap Unit Root Tests

We consider the bootstrap unit root tests based on autoregressive integrated models, with or without deterministic time trends. A general methodology is developed to approximate asymptotic distributions for the models driven by integrated time series, and used to obtain asymptotic expansions for the Dickey-Fuller unit root tests. The second-order terms in their expansions are of stochastic orders Op($n^{-1/4}$) and Op($n^{-1/2}$), and involve functionals of Brownian motions and normal random variates. The asymptotic expansions for the bootstrap tests are also derived and compared with those of the Dickey-Fuller tests. We show in particular that the usual nonparametric bootstrap offers asymptotic refinements for the Dickey-Fuller tests, i.e., it corrects their second-order errors. More precisely, it is shown that the critical values obtained by the bootstrap resampling are correct up to the second-order terms, and the errors in rejection probabilities are of order o($n^{-1/2}$) if the tests are based upon the bootstrap critical values. Through simulation, we investigate how effective is the bootstrap correction in small samples.

The Spatial Analysis of Time Series

In this paper, we propose a method of analyzing time series, called the spatial analysis. The analysis consists mainly of the statistical inference on the distribution given by the expected local time, which we define to be the spatial distribution, of a given time series. The spatial distribution is introduced primarily for the analysis of nonstationary time series whose distributions change over time. However, it is well defined for both stationary and nonstationary time series, and reduces to the time invariant stationary distribution if the underlying time series is indeed stationary. The spatial analysis may therefore be regarded as an extension of the usual inference on the distribution of a stationary time series to accommodate for nonstationary time series. In fact, we show that the concept of the spatial distribution allows us to extend many notions and ideas built upon the presumption of stationarity and make them applicable also for the analysis of nonstationary data. Our approach is nonparametric, and imposes very mild conditions on the underlying time series. In particular, we allow for the observations generated from a wide class of stochastic processes with stationary and mixing increments, or general markov processes including virtually all diffusion models used in practice. For illustration, we provide some empirical applications of our methodology to various topics such as the risk management, distributional dominance and option pricing.

What are Best Practices for Retaining Employees During Mergers and Acquisitions?

The purpose of this report is to guide decision makers at this company, by offering the most recent theories and practices regarding talent retention programs. Recently mergers and acquisitions have become a major part of global business. During the M&A, it is important to manage the organizational and human resource issues. Our team focused on gathering real business cases. Then we highlight some suggestions from the best practices to create successful M&A. It is our intent that the research findings in this report will help to enlighten and inform the company’s leaders to guide the effective human management program centered on key talent, ultimately leading to organizational success

Is There a Correlation for Companies With a Strong Employment Brand Between Employee Engagement Levels and Bottom Line Results?

The concept of employer brand was first introduced in 1996, where the authors defined “employer brand” as “the package of functional, economic and psychological benefits provided by employment, and identified with the employing company” (Amber & Barrow, 1996). Initial application of employer brand in human resource management focused heavily on attracting and recruiting talents; However, a recent survey by People in Business Co. found that 42% of the 104 survey participants (organizations that are currently developing employer brands) focus as much internal as external (People in Business, 2010). Employer brand is recognized as a powerful tool to help employees to internalize corporate values (The Conference Board, 2001), to shape corporate culture (Backhaus & Tikoo, 2004), to engage employees, and to align talent management with business strategies (Kunerth & Mosley, 2011). SHRM’s survey in 2008 found that 61% of surveyed companies have had an employer brand, and that 25% were either developing or planning to do so within the next 12 months (SHRM, 2008)

What are the Key Factors in Managing Diversity and Inclusion Successfully in Large International Organizations?

Question: What are the key factors in managing diversity and inclusion successfully in large international organizations? Which companies are best in class and what does that entail

Time series properties of ARCH processes with persistent covariates

We consider ARCH processes with persistent covariates and provide asymptotic theories that explain how such covariates affect various characteristics of volatility. Specifically, we propose and study a volatility model, named ARCH-NNH model, that is an ARCH(1) process with a nonlinear function of a persistent, integrated or nearly integrated, explanatory variable. Statistical properties of time series given by this model are investigated for various volatility functions. It is shown that our model generates time series that have two prominent characteristics: high degree of volatility persistence and leptokurtosis. Due to persistent covariates, the time series generated by our model has the long memory property in volatility that is commonly observed in high frequency speculative returns. On the other hand, the sample kurtosis of the time series generated by our model either diverges or has a well-defined limiting distribution with support truncated on the left by the kurtosis of the innovation, which successfully explains the empirical finding of leptokurtosis in financial time series. We present two empirical applications of our model. It is shown that the default premium (the yield spread between Baa and Aaa corporate bonds) predicts stock return volatility, and the interest rate differential between two countries accounts for exchange rate return volatility. The forecast evaluation shows that our model generally performs better than GARCH(1,1) and FIGARCH at relatively lower frequencies.ARCH; nonstationarity; nonlinearity; NNH; volatility persistence; leptokurtosis