Trend stationarity versus long-range dependence in time series analysis

Empirically, it is difficult to offer unequivocal judgment as to whether many real economic variables are fractionally integrated or trend stationary. The objective of this paper is to study the effects of spurious detrending of a nonstationary fractionally integrated NFI(d), dE (1/2, 3/2). With respect to the performance of the traditional least squares estimators and tests we prove that the estimated time trend coefficient is consistent but that the corresponding t-Student test diverges. We also analyze a local version in the frequency domain of least squares. We are able to show the consistency of this estimator and that, after conveniently adjusting variance estimates, its t-ratio has a well-defined but nonstandard limiting distribution. Nonetheless, in this latter case it is possible to obtain a set of critical values giving rise to the correct size for any given dE (1/2, 3/2).Publicad

Residual log-periodogram inference for long-run relationships

We assume that some consistent estimator of an equilibrium relation between non-stationary series integrated of order d(0.5,1.5) is used to compute residuals (or differences thereof). We propose to apply the semiparametric log-periodogram regression to the (differenced) residuals in order to estimate or test the degree of persistence δ of the equilibrium deviation ut. Provided converges fast enough, we describe simple semiparametric conditions around zero frequency that guarantee consistent estimation of δ. At the same time limiting normality is derived, which allows to construct approximate confidence intervals to test hypotheses on δ. This requires that d-δ>0.5 for superconsistent , so the residuals can be good proxies of true cointegrating errors. Our assumptions allow for stationary deviations with long memory, 0δ<0.5, as well as for non-stationary but transitory equilibrium errors, 0.5<δ<1. In particular, if xt contains several series we consider the joint estimation of d and δ. Wald statistics to test for parameter restrictions of the system have a limiting χ2 distribution. We also analyse the benefits of a pooled version of the estimate. The empirical applicability of our general cointegration test is investigated by means of Monte Carlo experiments and illustrated with a study of exchange rate dynamics.Publicad

Residual Log-Periodogram Inference for Long-Run-Relationships

We assume that some consistent estimator of an equilibrium relation between non-stationary series integrated of order d E (0:5; 1:5) is used to compute residuals ˆut = yt - xt (or differences there of). We propose to apply the semiparametric log-periodogram regression to the (differenced) residuals in order to estimate or test the degree of persistence ± of the equilibrium deviation ut. Provided converges fast enough, we describe simple semiparametric conditions around zero frequency that guarantee consistent estimation of ±. At the same time limiting normality is derived, which allows to construct approximate confidence intervals to test hypotheses on ±. This requires that d ¡ ± > 0:5 for superconsistent b¯, so the residuals can be good proxies of true cointegrating errors. Our assumptions allow for stationary deviations with long memory, 0 · ± < 0:5, as well as for non-stationary but transitory equilibrium errors, 0:5 < ± < 1. In particular, if xt contains several series we consider the joint estimation of d and ±. Wald statistics to test for parameter restrictions of the system have a limiting Â2 distribution. We also analyze the benefits of a pooled version of the estimate. The empirical applicability of our general cointegration test is investigated by means of Monte Carlo experiments and illustrated with a study of exchange rate dynamics

Residual Log-Periodogram Inference for Long-Run-Relationships.

We assume that some consistent estimator of an equilibrium relation between non-stationary series integrated of order d E (0:5; 1:5) is used to compute residuals ˆut = yt - xt (or differences there of). We propose to apply the semiparametric log-periodogram regression to the (differenced) residuals in order to estimate or test the degree of persistence ± of the equilibrium deviation ut. Provided converges fast enough, we describe simple semiparametric conditions around zero frequency that guarantee consistent estimation of ±. At the same time limiting normality is derived, which allows to construct approximate confidence intervals to test hypotheses on ±. This requires that d ¡ ± > 0:5 for superconsistent b¯, so the residuals can be good proxies of true cointegrating errors. Our assumptions allow for stationary deviations with long memory, 0 · ±

Spurius regression theory with nonstationary fractionally integrated processes

This paper develops an analytical study of the asymptotic distributions obtained when we run linear regressions in the levels of nonstationary fractionally integrated FI(d) processes, that are spuriously related in a multivariate single-equation setting which aIIows for the existence of co integrating relationships and quite general deterministic components. In doing this, the analytical studies of PhiIIips (1986), haldrup (1994) and Marmol (1995, 1996) are embedded in our results

Residual log-periodogram inference for long-run relationships.

We assume that some consistent estimator of an equilibrium relation between non-stationary series integrated of order d(0.5,1.5) is used to compute residuals (or differences thereof). We propose to apply the semiparametric log-periodogram regression to the (differenced) residuals in order to estimate or test the degree of persistence δ of the equilibrium deviation ut. Provided converges fast enough, we describe simple semiparametric conditions around zero frequency that guarantee consistent estimation of δ. At the same time limiting normality is derived, which allows to construct approximate confidence intervals to test hypotheses on δ. This requires that d-δ>0.5 for superconsistent , so the residuals can be good proxies of true cointegrating errors. Our assumptions allow for stationary deviations with long memory, 0δFractional cointegration; Semiparametric inference; Limiting normality; Long memory; Non-stationarity; Exchange rates;

Fractional integration versus trend stationary in time series analysis

The objective of this paper is to study the effects of spurious detrending of a nonstationary fractionally integrated process (NFI(d), d ~5) on the performance of the traditional least squares estimators and tests. We extend previous work on the subject undertaken by Durlauf and Phillips (1988) which considered only the leading difference stationary (d = 1) case. Moreover, we also consider the possibility of a double misspecification both in the stochastic and in the nonstochastic trends. Standard t-Student tests are shown to diverge in distribution invalidating any inference concerning the presence of time trends. On the other hand, we prove that, even under this double misspecification, the Durbin-Watson statistic remains to be a useful misspecification test

The Effect of a Threshold Proportional Reinsurance Strategy on Ruin Probabilities

In the context of a compound Poisson risk model, we define a threshold proportional reinsurance strategy: A retention level k1 is applied whenever the reserves are less than a determinate threshold b, and a retention level k2 is applied in the other case. We obtain the integro-differential equation for the Gerber-Shiu function (defined in Gerber and Shiu (1998)) in this model, which allows us to obtain the expressions for ruin probability and Laplace transforms of time of ruin for several distributions of the claim sizes. Finally, we present some numerical results.time of ruin, threshold proportional reinsurance strategy, ruin probability, gerber-shiu function

Customized Interfaces for Modern Storage Devices

In the past decade, we have seen two major evolutions on storage technologies: flash storage and non-volatile memory. These storage technologies are both vastly different in their properties and implementations than the disk-based storage devices that current soft- ware stacks and applications have been built for and optimized over several decades. The second major trend that the industry has been witnessing is new classes of applications that are moving away from the conventional ACID (SQL) database access to storage. The resulting new class of NoSQL and in-memory storage applications consume storage using entirely new application programmer interfaces than their predecessors. The most significant outcome given these trends is that there is a great mismatch in terms of both application access interfaces and implementations of storage stacks when consuming these new technologies. In this work, we study the unique, intrinsic properties of current and next-generation storage technologies and propose new interfaces that allow application developers to get the most out of these storage technologies without having to become storage experts them- selves. We first build a new type of NoSQL key-value (KV) store that is FTL-aware rather than flash optimized. Our novel FTL cooperative design for KV store proofed to simplify development and outperformed state of the art KV stores, while reducing write amplification. Next, to address the growing relevance of byte-addressable persistent memory, we build a new type of KV store that is customized and optimized for persistent memory. The resulting KV store illustrates how to program persistent effectively while exposing a simpler interface and performing better than more general solutions. As the final component of the thesis, we build a generic, native storage solution for byte-addressable persistent memory. This new solution provides the most generic interface to applications, allow- ing applications to store and manipulate arbitrarily structured data with strong durability and consistency properties. With this new solution, existing applications as well as new “green field” applications will get to experience native performance and interfaces that are customized for the next storage technology evolution