Ana Elizabeth García Sipols

Nonlinear Cointegration and Nonlinear Error Correction: Record Counting Cointegration Tests

In this article we propose a record counting cointegration (RCC) test that is robust to nonlinearities and certain types of structural breaks. The RCC test is based on the synchronicity property of the jumps (new records) of cointegrated series, counting the number of jumps that simultaneously occur in both series. We obtain the rate of convergence of the RCC statistics under the null and alternative hypothesis. Since the asymptotic distribution of RCC under the null hypothesis of a unit root depends on the short-run dependence of the cointegrated series, we propose a small sample correction and show by Monte Carlo simulation techniques their excellent small sample behaviour. Finally, we apply our new cointegration test statistic to several financial and macroeconomic time series that have certain structural breaks and nonlinearities.

A time series bootstrap procedure for interpolation intervals

A sieve bootstrap procedure for constructing interpolation intervals for a general class of linear processes is proposed. This sieve bootstrap provides consistent estimators of the conditional distribution of the missing values, given the observed data. A Monte Carlo experiment is used to show the finite sample properties of the sieve bootstrap and finally, the performance of the proposed method is illustrated with a real data example.

Forecasting financial short time series

We study the application of time series forecasting methods to massive datasets of short financial time series. In our example, the time series arise from analyzing monthly expenses and incomes in personal financial records. Differently from traditional time series forecasting applications, we work with series of very short depth (as short as 24 data points), which prevents from using classical exponential smoothing methods. However, this shortcoming is compensated by the the size of our dataset: millions of time series. The latter allows tackling the problem of time series prediction from a pattern recognition perspective. Specifically, we propose a method for short time series prediction based on time series clustering and distance-based regression. We experimentally show that this strategy leads to improved accuracy compared to exponential smoothing methods. We additionally describe the underlying big data platform developed to carry out the forecasts in an efficient manner (comparisons to millions of elements in near real-time).

A new Cramer-Von Misses cointegration test with application to environmental Kuznets curve

ABSTRACT This article introduces a new Cramer-Von Misses (CVM) cointegration test robust to nonlinearities. We characterize nonlinear cointegration in terms of a nonlinear moving-average filter (high pass filter) of a matrix based on permutation matrices on the discrepancy of empirical distributions. A Cramer-Von Misses (CVM) test statistic is proposed for testing the null hypothesis of two independent random walks against a broad range of cointegrating alternatives with monotonic nonlinearities and level shifts in the cointegration relationship. We derive the asymptotic distribution of this induced-order Cramer-Von Misses (CVM) cointegration test. This new non-parametric test statistic has two important properties: the invariance to monotonic transformations of the series and the robustness for the presence of several parameter shifts or structural changes. We analyse the small sample properties of this test by Monte Carlo simulations and evaluate the power of the test. Finally, this CVM test is applied to the analysis of long run environmental Kuznets curve which relates economic growth and pollution. In particular, we consider a nonlinear cointegration between gross domestic product (GDP) and CO2 emissions. Our new CVM test is able to find evidence of cointegration while classical single equation cointegration tests are not.

A Detrended Range Unit Root (DRUR) Test

We extend the Range Unit Root test in two directions. First, we consider the process with time trend and prove that the modified standardized number of new records converges to a sum of two Rayleigh distributions. Second, more general structures of autocorrelated disturbances are also taken into account. Monte Carlo experiments show the good sample properties of this nonparametric unit root test.

Behavior of the Size in the Unit Root Testing Under Contamination

This article investigates the relative small sample performance of some robust unit root tests by means of a simulation study. We propose to investigate the stability of unit root test under various kinds of contamination models, and then the article proposes two new statistics that perform better than the celebrated Dickey-Fuller statistic. We illustrate the performances of the tests and their discrepancies with the Dickey-Fuller unit root test through an empirical example based on the US/Finland real exchange rate series.

Records Properties of Non Stationary Time Series

This article compares the statistical properties of the records from independent and identically distributed time series with those of time series containing a single unit root. It is shown that there are important differences in both the limiting distributions and the convergence rates of the associated record counting processes. Since the record properties of independent and identically distributed time series are shared by a large class of stationary time series, the reported differences underline the possibility of using record-based statistics for robust testing procedures of the unit root hypothesis. We make an extension of the nonparametric test for the Range Unit Root test (RUR) proposed in Aparicio et al. (2006). We prove some properties for the test statistic in the context of the renewal theory and we suggest two new candidates to test the hypothesis of random walk with positive and negative drift.