Nonlinear dynamics of the Nikkei Stock Average Futures

This paper analyzes the conditional distribution of the Nikkei Stock Average Futures prices traded in the Singapore International Monetary Exchange (SIMEX). It is found that the conditional mean of the logarithmic price ratios is zero and the conditional variance is adequately described by the exponential generalized autoregressive conditional heteroscedasticity model (witht errors) suggested by Nelson (1991) and the autoregressive volatility model suggested by Hsieh (1993). The Brock, Dechert and Scheinkman (1987) statistic cannot reject the hypothesis that the standardized residuals are independently and identically distributed. The results are applied to calculate the maintenance margin and the long-term capital requirements of the contract given an assumed maximum failure rate. The margin requirements set by the SIMEX appear to be adequate compared to our estimates.     

Nonlinearity and Low Deterministic Chaotic Behavior in Insurance Portfolio Stock Returns

This article presents new empirical evidence indicating a deterministic component in the portfolio return dynamics of life‐health and property‐liability insurance company stocks. Our research is motivated by the fact that nonlinearities are a fact of economic life for many financial applications the source of which is logically apparent, yet empirical evidence of their existence is at best weak. The primary reason attributed to the weak findings of nonlinearities reported in previous research is the use of aggregate data that can hide nonlinearities at the micro level. Insurance sector stock returns are analyzed because unique institutional characteristics indicate the possibility of identifying nonlinear dynamics. Tests based on the correlation dimension partially confirm the presence of nonlinearity. However, the more powerful Brock, Dechert, and Scheinkman (BDS) statistic strongly suggests the presence of nonlinearities in the insurance stock portfolio data. The BDS statistic applied to the standardized residuals of exponential generalized auto regressive conditional heteroskedasticity (EGARCH) models strongly rejects the null of independent and identically distributed, indicating that conditional heteroskedasticity is not responsible for the presence of the nonlinear structures in the data. In addition, tests for chaos based on locally weighted regressions indicate that insurance stock portfolio returns indicate low‐complexity chaotic behavior. This is an important result since most previous research has failed to report evidence of chaotic behavior in the time series of stock returns. Important contributions of this article are the application of tests of nonlinearities and chaos to more desegregated data sets and the findings of statistically significant evidence indicating nonlinearities and low‐deterministic chaotic behavior in insurance stock portfolio returns.     

Emerging Markets and Stock Market Bubbles: Nonlinear Speculation?

Daily returns of stock markets in emerging markets in Asia, Africa, South America, and Eastern Europe from the early 1990s through 2006 are analyzed for the possible presence of nonlinear speculative bubbles. The absence of these is tested for by studying residuals of vector autoregressive-based fundamentals, using the Hamilton regimeswitching model and the rescaled range analysis of Hurst. For the first test, absence of bubbles is rejected for twenty-four countries (except Mexico, Sri Lanka, and Taiwan); for the second test, it is rejected for twenty-six countries (except Malaysia). BDS testing on these residuals after autoregressive conditional heteroskedasticity (ARCH) effects are removed fails to reject further nonlinearity (except for Israel). Policy issues are discussed, noting that what is appropriate varies from country to country and time period to time period.     

On the asymptotic distribution of weighted least squares estimators

Abstract

In the ELB (Empirical Linear Bayes)-approach to credibility, the unknown structural parameters are substituted by a set of parameter estimates. The weighted least squares estimators are known to be asymptotically normally distributed when the design variables are independent and identically distributed random variables. It is demonstrated that, with probability one, the conditional asymptotic distribution, given the design, is the same as the unconditional distribution. Estimation of the asymptotic covariance matrix will also be considered.     

Nonlinearity in investment grade Credit Default Swap (CDS) Indices of US and Europe: Evidence from BDS and close-returns tests

This paper is aimed at testing for nonlinearity and chaos in Investment Grade CDS indices of US and Europe. For this exercise, the author has chosen the two most liquid indices, namely CDX.NA.IG (US) and iTraxx.Europe (Europe). BDS test (Brock, Dechert, & Scheinkman, 1987) is employed to test for prevalence of nonlinearity in the US and European datasets. The author then subjects both the US and European datasets to the close-returns test (Gilmore, 1993, 1996, 2001) to examine whether the close-returns plots pertaining to these datasets exhibit any chaotic patterns. The CDS datasets were prepared differently for BDS and close-returns test. Since the BDS test cannot differentiate between linear and non-linear dependency, a best-fitting AR model was fitted to the transformed CDS datasets to remove linear-dependency in the data. The BDS test was then applied to the stationary, linearly-independent AR residuals pertaining to transformed US and European datasets. BDS test outcomes revealed rejection of null hypothesis (i.i.d.) with regard to US and European investment-grade CDS indices. The close-returns test outcomes revealed prevalence of an underlying structure that is neither random nor chaotic in nature. In short, the study's findings reveal prevalence of non-chaotic nonlinearity in the US and European CDS indices. These findings not only augment existing literature on nonlinearity of different asset classes, but also reflect the need for researchers and practitioners to accommodate and appropriately account for nonlinearity while modeling CDS indices spread movements.     

Modeling the time varying volatility of housing returns: Further evidence from the U.S. metropolitan condominium markets

This study extends the literature on modeling the volatility of housing returns to the case of condominium returns for five major U.S. metropolitan areas (Boston, Chicago, Los Angeles, New York, and San Francisco). Through the estimation of ARMA models for the respective condominium returns, we find volatility clustering of the residuals. The results from an ARMA‐TGARCH‐M model reveal the absence of asymmetry in the conditional variance. Dummy variables associated with the housing market collapse unique to each metropolitan area were statistically insignificant in the conditional variance equation, but negative and statistically significant in the mean equation. Condominium markets in Los Angeles and San Francisco exhibit the greatest persistence to volatility shocks.     

Are stock markets really efficient? Evidence of the adaptive market hypothesis

This study examines the adaptive market hypothesis in the S&P500, FTSE100, NIKKEI225 and EURO STOXX 50 by testing for stock return predictability using daily data from January 1990 to May 2014. We apply three bootstrapped versions of the variance ratio test to the raw stock returns and also whiten the returns through an AR-GARCH process to study the nonlinear predictability after accounting for conditional heteroscedasticity through the BDS test. We evaluate the time-varying return predictability by applying these tests to fixed-length moving subsample windows and also examine whether there is a relationship between the level of predictability in stock returns and market conditions. The results show that there are periods of statistically significant return predictability, but also episodes of no statistically significant predictability in stock returns. We also find that certain market conditions are statistically significantly related to predictability in certain markets but each market interacts differently with the different market conditions. Therefore our findings suggest that return predictability in stock markets does vary over time in a manner consistent with the adaptive market hypothesis and that each market adapts differently to certain market conditions. Consequently our findings suggest that investors should view each market independently since different markets experience contrasting levels of predictability, which are related to market conditions.     

Testing For Threshold Nonlinearity in Short-Term Interest Rates

This article addresses some empirical problems in the term structureof interest rates using a threshold autoregressive frameworkwith GARCH errors. This framework provides a parsimonious representationof some stylized features of interest rate data and facilitatesstatistical inference in the presence of high persistence andconditional heteroskedasticity. We propose a bootstrap-basedLM test for linearity in the conditional mean and variance functions.The empirical results indicate a presence of threshold nonlinearitiesin the AR and GARCH representations of the conditional momentsof short-term rate. The explicit modeling of these nonlinearitiesappears to improve the stability properties of the process forspot rate. The article also reports that allowing for thresholdnonlinearities in conditional mean and variance leads to significantforecast improvements. The economic significance of these findingsis evaluated by the term structure implications of the estimatedTAR-GARCH model.     

ALTERNATIVE TESTS OF THE ZERO‐BETA CAPM

In this paper I develop an analytical Wald test of the zero‐beta capital asset pricing model (CAPM) in a simple iid (independent and identically distributed) setting and extend the Wald test to the generalized method of moments (GMM) framework that allows for a general form of serial correlation and conditional heteroskedasticity. The size and power of these tests, along with some existing tests, are investigated under normal errors and other alternative distributional specifications. The results show that, under alternative distributional assumptions for the error terms, the proposed Wald and GMM tests have reliable sizes for medium‐size samples, whereas the likelihood ratio test (LRT) rejects the efficiency too often, especially when the error terms significantly deviate from normality. However, the LRT is more powerful than both the Wald and GMM tests. JEL classification: C13, C53, G14.     

On a conjecture related to the ruin probability for nonhomogeneous exponentially distributed claims

Recently, some recursive formulas have been obtained for the ruin probability evaluated at or before claim instants for a surplus process under the assumptions that the claim sizes are independent, nonhomogeneous Erlang distributed, and independent of the inter-claim revenues, which are assumed to be independent, identically distributed, following an arbitrary distribution. Based on numerical examples, a conjecture has also been stated relating the order in which the claims arrive to the magnitude of the corresponding ruin probability. In this paper, we prove this conjecture in the particular case when the claims are all exponentially distributed with different parameters.     

Forecasting Surrender Rates Using Elliptical Copulas and Financial Variables

A multistage stochastic model to forecast surrender rates for life insurance and pension plans is proposed. Surrender rates are forecasted by means of Monte Carlo simulation after a sequence of GLM, ARMA-GARCH, and copula fitting is executed. The model is illustrated by applying it to age-specific time series of surrender rates derived from pension plans with annuity payments of a Brazilian insurer. In the GLM process, the only macroeconomic variable used as an explanatory variable is the Brazilian real short-term interest rate. The advantage of such a variable is that we can take future market expectation through the current term structure of interest rates. The GLM residuals of each age/gender group are then modeled by ARMA-GARCH processes to generate i.i.d. residuals. The dependence among these residuals is then modeled by multivariate Gaussian and Student's t copulas. To produce a conditional forecast on a stock market index, in our application we used the residuals of an ARMA-GARCH model fitted to the Brazilian stock market index (Ibovespa) returns, which generates one of the marginal distributions used in the dependence modeling through copulas. This strategy is adopted to explain the high and uncommon surrender rates observed during the recent economic crisis. After applying known simulation methods for elliptical copulas, we proceeded backwards to obtain the forecasted distributions of surrender rates by application, in the sequel, of ARMA-GARCH and GLM models. Additionally, our approach produced an algorithm able to simulate multivariate elliptical copulas conditioned on a marginal distribution. Using this algorithm, surrender rates can be simulated conditioned on stock index residuals (in our case, the residuals of the Ibovespa returns), which allows insurers and pension funds to simulate future surrender rates assuming a financial stress scenario with no need to predict the stock market index.     

Stock returns and the term structure

In monthly U.S. data for 1959–1979 and 1979–1983, the state of the term structure of interest rates predicts excess stock returns, as well as excess returns on bills and bonds. This paper documents this fact and uses it to examine some simple asset pricing models. In 1959–1979, the data strongly reject a single-latent-variable specification of predictable excess returns. There is considerable evidence that conditional variances of excess returns change through time, but the relationship between conditional mean and conditional variance is reliably positive only at the short end of the term structure.     

A comparison of statistical tests for the adequacy of a neural network regression model

An integral part of econometric practice is to test the adequacy of model specifications. If a model is adequately specified, it should not leave interesting features of the data-generating process in the errors. Despite the common tradition, the importance of diagnostic checking as a safeguard against mis-specification has only recently been recognized by neural network (NN) practitioners, possibly because this type of semi-parametric methodology was not originally designed for economic and financial applications. The purpose of this paper is to compare a number of analytical statistical testing procedures suitable to diagnostic checking on a neural network regression model. We present the standard Lagrange multiplier (LM) testing framework designed under the assumption of identically distributed disturbances and also examine two modifications that are robust to heteroskedasticity in errors. One modification also gives the researcher an opportunity to incorporate information concerning the volatility structure of the data-generating process in the testing procedure. By means of a Monte Carlo simulation, we investigate the performance of these tests under GARCH-type heteroskedasticity in errors and various distributional assumptions. The results show that although the primary concern of the researcher may be to design a regression model that accurately captures relations in the mean of the conditional distribution, developing a good approximation of the underlying volatility structure generally increases the efficiency of tests in detecting non-adequacy of a NN model.     

Value at risk forecasts by extreme value models in a conditional duration framework

The analysis of extremes in financial return series is often based on the assumption of independent and identically distributed observations. However, stylized facts such as clustered extremes and serial dependence typically violate the assumption of independence. This has been the main motivation to propose an approach that is able to overcome these difficulties by considering the time between extreme events as a stochastic process. One of the advantages of the method consists in its capability to capture the short-term behavior of extremes without involving an arbitrary stochastic volatility model or a prefiltration of the data, which would certainly affect the estimate. We make use of the proposed model to obtain an improved estimate for the value at risk (VaR). The model is then compared to various competing approaches such as Engle and Marianelli's CAViaR and the GARCH-EVT model. Finally, we present a comparative empirical illustration with transaction data from Bayer AG, a typical blue chip stock from the German stock market index DAX, the DAX index itself and a hypothetical portfolio of international equity indexes already used by other authors.     

The specification of conditional expectations

This paper explores different specifications of conditional expectations. The most common specification, linear least squares, is contrasted with nonparametric techniques that make no assumptions about the distribution of the data. Nonparametric regression is successful in capturing some nonlinearities in financial data, in particular, asymmetric responses of security returns to the direction and magnitude of market returns. The technique is ideally suited for empirically modeling returns of securities that have complicated embedded options. The conditional mean and variance of the NYSE market return are also examined. Forecasts of market returns are not improved with the nonparametric techniques which suggests that linear conditional expectations are a reasonable approximation in conditional asset pricing research. However, the linear model produces a disturbing number of negative expected excess returns. My results also indicate that the relation between the conditional mean and variance depends on the specification of the conditional variance. Furthermore, a linear model relating mean to variance is rejected and these tests are not sensitive to the expectation generating mechanism nor the conditioning information. Rejections are driven by the distinct countercyclical variation in the ratio of the conditional mean to variance.     

The BDS Test as a Test for the Adequacy of a GARCH(1,1) Specification: A Monte Carlo Study

In this study we examine the widely used Brock, Dechert, andScheinkman (BDS) test when applied to the logarithm of the squaredstandardized residuals of an estimated GARCH(1,1) model as atest for the adequacy of this specification. We review the conditionsderived by De Lima (1996; Econometric Reviews 15, 237–259)for the nuisance-parameter-free property to hold and addressthe issue of their necessity, using the flexible framework offeredby the GARCH(1,1) model in terms of moment, memory, and timeheterogeneity properties. By means of Monte Carlo simulations,we show that the BDS test statistic still approximates the standardnull distribution even for mildly explosive processes that violatethe majority of the conditions. Thus the test performs reasonablywell, its empirical size being rather close to the nominal one.As a by-product of this study, we also shed light on the relatedissue of the consistency of the QML estimators of the conditionalvariance parameters under various parameter configurations andalternative distributional assumptions on the innovation process.     

Asymptotic results for the risk process based on marked point processes

Abstract

In this paper asymptotic properties for the risk process will be studied when the number of risk units tends to infinity. The paper extends asymptotic properties for the classical risk process to more general processes. In the classical risk process the claim amounts are assumed independent and identically distributed, and the claim number process is a homogeneous Poisson process.

The key tool is point process theory with associated martingale theory. The results are illustrated by examples.     

There is a risk-return trade-off after all

This paper studies the intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns, the mixed data sampling (or MIDAS) approach. Using MIDAS, we find a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process and to controlling for variables associated with the business cycle. We compare the MIDAS results with tests of the intertemporal capital asset pricing model based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance.     

Smooth Transition ARCH Models: Estimation and Testing

In this paper, we suggest an extension of the ARCH model, the smooth-transition autoregressive conditional heteroskedasticity (STARCH) model. STARCH models endogenously allow for time-varying shifts in the parameters of the conditional variance equation. The most general form of the model that we consider is a double smooth-transition model, the STAR-STARCH model, which permits not only the conditional variance, but also the mean, to be a function of a smooth-transition term. The threshold ARCH model, the Markov-ARCH model and the standard ARCH model are special cases of our STARCH model. We also develop Lagrange multiplier tests of the hypothesis that the smooth-transition term in the conditional variance is zero. We apply our STARCH model to excess Treasury bill returns. We find some evidence of a smooth transition in excess returns, but in contrast to previous studies, we find almost no evidence of volatility persistence once we allow for smooth transitions in the conditional variance. Thus, the apparent persistence in the conditional variance reported by many researchers could be a mere statistical artifact. We conduct in-sample tests comparing STARCH models to nested competitors; these suggest that STARCH models hold promise for improved predictions. Finally, we describe further extensions of the STARCH model and suggest issues in finance to which they might profitably be applied.     

Trading Patterns and Prices in the Interbank Foreign Exchange Market

The behavior of quote arrivals and bid-ask spreads is examined for continuously recorded deutsche mark-dollar exchange rate data over time, across locations, and by market participants. A pattern in the intraday spread and intensity of market activity over time is uncovered and related to theories of trading patterns. Models for the conditional mean and variance of returns and bid-ask spreads indicate volatility clustering at high frequencies. The proposition that trading intensity has an independent effect on returns volatility is rejected, but holds for spread volatility. Conditional returns volatility is increasing in the size of the spread.