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This paper gives a selective review on some recent developments of nonparametric methods in both continuous and discrete time finance, particularly in the areas of nonparametric estimation and testing of diffusion processes, nonparametric testing of parametric diffusion models, nonparametric pricing of derivatives, nonparametric estimation and hypothesis testing for nonlinear pricing kernel, and nonparametric predictability of asset returns. For each financial context, the paper discusses the suitable statistical concepts, models, and modeling procedures, as well as some of their applications to financial data. Their relative strengths and weaknesses are discussed. Much theoretical and empirical research is needed in this area, and more importantly, the paper points to several aspects that deserve further investigation.

We derive marginal conditions of optimality (i.e., Euler equations) for a general class of Dynamic Discrete Choice (DDC) structural models. These conditions can be used to estimate structural parameters in these models without having to solve for approximate value functions. This result extends to discrete choice models the GMM-Euler equation approach proposed by Hansen and Singleton (1982) for the estimation of dynamic continuous decision models. We first show that DDC models can be represented as models of continuous choice where the decision variable is a vector of choice probabilities. We then prove that the marginal conditions of optimality and the envelope conditions required to construct Euler equations are also satisfied in DDC models. The GMM estimation of these Euler equations avoids the curse of dimensionality associated to the computation of value functions and the explicit integration over the space of state variables. We present an empirical application and compare estimates using the GMM-Euler equations method with those from maximum likelihood and two-step methods.

The global slack hypothesis is central to the discussion of the trade-offs that monetary policy faces in an increasingly more integrated world. The workhorse New Open Economy Macro (NOEM) model of Martínez-García and Wynne (2010), which fleshes out this hypothesis, shows how expected future local inflation and global slack affect current local inflation. In this chapter, I propose the use of the orthogonalization method of Aoki (1981) and Fukuda (1993) on the workhorse NOEM model to further decompose local inflation into a global component and an inflation differential component. I find that the log-linearized rational expectations model of Martínez-García and Wynne (2010) can be solved with two separate subsystems to describe each of these two components of inflation.

I estimate the full NOEM model with Bayesian techniques using data for the United States and an aggregate of its 38 largest trading partners from 1980Q1 until 2011Q4. The Bayesian estimation recognizes the parameter uncertainty surrounding the model and calls on the data (inflation and output) to discipline the parameterization. My findings show that the strength of the international spillovers through trade – even in the absence of common shocks – is reflected in the response of global inflation and is incorporated into local inflation dynamics. Furthermore, I find that key features of the economy can have different impacts on global and local inflation – in particular, I show that the parameters that determine the import share and the price-elasticity of trade matter in explaining the inflation differential component but not the global component of inflation.

We compare methods to measure comovement in business cycle data using multi-level dynamic factor models. To do so, we employ a Monte Carlo procedure to evaluate model performance for different specifications of factor models across three different estimation procedures. We consider three general factor model specifications used in applied work. The first is a single-factor model, the second a two-level factor model, and the third a three-level factor model. Our estimation procedures are the Bayesian approach of Otrok and Whiteman (1998), the Bayesian state-space approach of Kim and Nelson (1998) and a frequentist principal components approach. The latter serves as a benchmark to measure any potential gains from the more computationally intensive Bayesian procedures. We then apply the three methods to a novel new dataset on house prices in advanced and emerging markets from Cesa-Bianchi, Cespedes, and Rebucci (2015) and interpret the empirical results in light of the Monte Carlo results.

Since the seminal works by Granger and Joyeux (1980) and Hosking (1981), estimations of long-memory time series models have been receiving considerable attention and a number of parameter estimation procedures have been proposed. This paper gives an overview of this plethora of methodologies with special focus on likelihood-based techniques. Broadly speaking, likelihood-based techniques can be classified into the following categories: the exact maximum likelihood (ML) estimation (Sowell, 1992; Dahlhaus, 1989), ML estimates based on autoregressive approximations (Granger & Joyeux, 1980; Li & McLeod, 1986), Whittle estimates (Fox & Taqqu, 1986; Giraitis & Surgailis, 1990), Whittle estimates with autoregressive truncation (Beran, 1994a), approximate estimates based on the Durbin–Levinson algorithm (Haslett & Raftery, 1989), state-space-based maximum likelihood estimates for ARFIMA models (Chan & Palma, 1998), and estimation of stochastic volatility models (Ghysels, Harvey, & Renault, 1996; Breidt, Crato, & de Lima, 1998; Chan & Petris, 2000) among others. Given the diversified applications of these techniques in different areas, this review aims at providing a succinct survey of these methodologies as well as an overview of important related problems such as the ML estimation with missing data (Palma & Chan, 1997), influence of subsets of observations on estimates and the estimation of seasonal long-memory models (Palma & Chan, 2005). Performances and asymptotic properties of these techniques are compared and examined. Inter-connections and finite sample performances among these procedures are studied. Finally, applications to financial time series of these methodologies are discussed.

Probability of Default (PD) is a crucial credit risk parameter. International accords have motivated banks and credit institutions to adopt objective systems of evaluating and monitoring the PD. This study examines retail unsecured loans of a major Greek bank during the period of the financial crisis. It focusses on the stochastic behaviour of the financial states of the loans. It is tested whether a first-order Markov chain (MC) model describes sufficiently the transitions from one state to another. Moreover, Poisson regression models are estimated in order to calculate the limiting transition matrix, the limiting state probabilities and the PD. It is proved that the MC of the financial states of loans is non-homogeneous suggesting that the transition probabilities from one financial state to another are not constant across time. From the Poisson regression models, the transition probability matrix is estimated from one state to another in alternative time periods. From the limiting transition matrix, it is shown that if a loan is delayed then it is very likely to move towards the next worst case. The findings of this research could be useful for bank management.

The objective of this study is to investigate the simultaneity between farm couples’ decisions on labor allocation and production efficiency. Using an unbalanced panel data set of Norwegian farm households (1989–2008), we estimate off-farm labor supply of married farm couples and farm efficiency in a three-equation system of jointly determined endogenous variables. We address the issue of latent heterogeneity between households. We solve the problem by two-stage OLS and GLS estimation where state dependence is accounted for in the reduced form equations. We compare the results against simpler model specifications where we suppress censoring of off-farm labor hours and endogeneity of regressors, respectively. In the reduced form specification, a considerably large number of parameters are statistically significant. Davidson–McKinnon test of exogeneity confirms that both operator and spouse's off-farm labor supply should be treated as endogenous in estimating farming efficiency. The parameter estimates seem robust across model specifications. Off-farm labor supply of farm operators and spouses is jointly determined. Off-farm work by farm operator and spouses positively affects farming efficiency. Farming efficiency increases with operator's age, farm size, agricultural subsidises, and share of current investment to total farm capital stock.

This chapter investigates the impact of different state correlation assumptions for out-of-sample performance of unobserved components (UC) models with stochastic volatility. Using several measures of US inflation the author finds that allowing for correlation between inflation’s trend and cyclical (or gap) components is a useful feature to predict inflation in the short run. In contrast, orthogonality between such components improves the out-of-sample performance as the forecasting horizon widens. Accordingly, trend inflation from orthogonal trend-gap UC models closely tracks survey-based measures of long-run inflation expectations. Trend dynamics in the correlated-component case behave similarly to survey-based nowcasts. To carry out estimation, an efficient algorithm which builds upon properties of Toeplitz matrices and recent advances in precision-based samplers is provided.

The Bureau of Economic Analysis provides data from 1969 to 2016 regarding state-level and county-level unemployment costs. These data are used to construct least-squares estimations including linear growth, the persistence of business cycles, and the unique anomaly of the Great Recession. Each of these models is constructed for North Carolina data, including the state as a whole and each individual county in the state. The state and county models are compared for differences and insights.

This chapter proposes a vector autoregressive VAR model with structural shocks (SVAR) that are identified using sign restrictions, and whose distribution is subject to time varying skewness. The authors also present an efficient Bayesian algorithm to estimate the model. The model allows tracking joint asymmetric risks to macroeconomic variables included in the SVAR, and provides a structural narrative to the evolution of those risks. When faced with euro area data, our estimation suggests that there has been a significant variation in the skewness of demand, supply and monetary policy shocks. Such variation can explain a significant proportion of the joint dynamics of real GDP growth and inflation, and also generates important asymmetric tail risks in those macroeconomic variables. Finally, compared to the literature on growth- and inflation-at-risk, the authors find that financial stress indicators are not enough to explain all the macroeconomic tail risks.