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## Abstract

The Hurst exponent is the simplest numerical summary of self-similar long-range dependent stochastic processes. We consider the estimation of Hurst exponent in long-range dependent curve time series. Our estimation method begins by constructing an estimate of the long-run covariance function, which we use, via dynamic functional principal component analysis, in estimating the orthonormal functions spanning the dominant sub-space of functional time series. Within the context of functional autoregressive fractionally integrated moving average (ARFIMA) models, we compare finite-sample bias, variance and mean square error among some time- and frequency-domain Hurst exponent estimators and make our recommendations.

## Abstract

In this paper, new models are studied by proposing the family of generalized power series distributions with inflated parameter (IGPSD) for the innovation process of the INAR(1) model. The main properties of the process were established, such as mean, variance, autocorrelation and transition probability. The methods of estimation by Yule–Walker and the conditional maximum likelihood were used to estimate the parameters of the models. Two particular cases of the INAR$(1)$ model with IGPSD innovation were studied, named IPoINAR$(1)$ and IGeoINAR$(1)$. Finally, in the real data example, a good performance of the proposed new models was observed.

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## Abstract

In this work, our goal is to analyze the use of the Cross Recurrence Plot (CRP) and its quantification (CRQA) as tools to detect the possible existence of a relationship between two systems. To do that, we define three tests that are a bivariate extension of those proposed by Aparicio et al. (Aparicio, T., E. Pozo, and D. Saura. 2008. “Detecting Determinism Using Recurrence Quantification Analysis: Three Test Procedures.” Journal of Economic Behavior & Organization 65: 768–787, Aparicio, T., E. F. Pozo, and D. Saura. 2011. “Detecting Determinism Using Recurrence Quantification Analysis: A Solution to the Problem of Embedding.” Studies in Nonlinear Dynamics and Econometrics 15: 1–10) within the context of the Recurrence Quantification Analysis. These tests, based on the diagonal lines of the CRP, are applied to a large number of simulated pairs of series. The results obtained are not always satisfactory, with problems being detected specifically when the series have a high degree of laminarity. We study the identified problems and we implement a strategy that we consider adequate for the use of these tools. Finally, as an example, we apply this strategy to several economic series.

## Abstract

We consider multi-period cost-of-capital valuation of a liability cash flow subject to repeated capital requirements that are partly financed by capital injections from capital providers with limited liability. Limited liability means that, in any given period, the capital provider is not liable for further payment in the event that the capital provided at the beginning of the period turns out to be insufficient to cover both the current-period payments and the updated value of the remaining cash flow. The liability cash flow is modeled as a continuous-time stochastic process on $[0,T]$. The multi-period structure is given by a partition of $[0,T]$ into subintervals, and on the corresponding finite set of times, a discrete-time cost-of-capital-margin process is defined. Our main objective is the analysis of existence and properties of continuous-time limits of discrete-time cost-of-capital-margin processes corresponding to a sequence of partitions whose meshes tend to zero. Moreover, we provide explicit expressions for the limit processes when cash flows are given by Itô diffusions and processes with independent increments.

## Abstract

We develop and analyze an intertemporal cost of living index (ICOLI), also referred to as lifetime cost of living or cost of life index. The ICOLI is a geometric weighted average of effective prices, derived from constrained consumer utility maximization. Effective prices are both, money valued marginal utilities of the final unit consumed, and present values of prices for future consumption. Using the concept of duration, we derive analytical elasticities of the ICOLI with respect to consumer prices and interest rates and show their impact on lifetime welfare of consumers. We also provide empirical evidence for Germany, compute an ex post time series of the ICOLI, and gauge the welfare effects of low interest rate scenarios. We find that the financial repression policy of the ECB since 2010 contributed to substantial losses in the purchasing power of money and led to lasting welfare losses for consumers in Germany, in particular for the cohorts of young consumers. The ICOLI complements conventional price and inflation statistics and could serve as a valuable information tool for monetary policy.

## Abstract

This paper studies the identification of players’ preferences and beliefs in discrete choice games using experimental data. The experiment comprises a set of games that differ in their matrices of monetary payoffs. The researcher is interested in the identification of preferences (utility of money) and beliefs on the opponents’ expected behavior, without imposing equilibrium restrictions or parametric assumptions on utility and belief functions. We show that the hypothesis of unbiased/rational beliefs is testable as long as the set of games in the experiment imply variation in monetary payoffs of other players, keeping the own monetary payoff constant. We present conditions for the full identification of utility and belief functions at the individual level – without restrictions on players’ heterogeneity in preferences or beliefs. We apply our method to data from two experiments: a matching pennies game, and a public good game.

## Abstract

This paper takes a closer look at the consequences of using a market index as a proxy for the latent market return in the capital asset pricing model. In particular, the consequences of two major sources of misspecification are analyzed: (i) the use of inaccurate weights and (ii) the use of only a subset of the asset universe to construct the index. The consequences resulting from the use of a badly chosen market proxy reach from inconsistent parameter estimates to misinterpretation of test outcomes indicating the existence of abnormal returns.

A minimum distance approach of estimating the CAPM under measurement error is presented, which identifies the CAPM parameters by exploiting the cross-equation cross-sectional restrictions resulting from a common measurement error. The new approach allows for quantifying the impact of measurement error and for testing the presence of spurious abnormal returns. Practical guidelines are presented to mitigate potential biases in the estimated CAPM parameters.