Representative galaxy age-metallicity relationships

The ongoing surveys of galaxies and those for the next generation of telescopes will demand the execution of high-CPU consuming machine codes for recovering detailed star formation histories (SFHs) and hence age-metallicity relationships (AMRs). We present here an expeditive method which provides quick-look AMRs on the basis of representative ages and metallicities obtained from colour-magnitude diagram (CMD) analyses. We have tested its perfomance by generating synthetic CMDs for a wide variety of galaxy SFHs. The representative AMRs turn out to be reliable down to a magnitude limit with a photometric completeness factor higher than $\sim$ 85 per cent, and trace the chemical evolution history for any stellar population (represented by a mean age and an intrinsic age spread) with a total mass within ~ 40 per cent of the more massive stellar population in the galaxy.Comment: 12 pages, 11 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Societ

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.Publicad

Range Unit Root (RUR) Tests: Robust against Nonlinearities, Error Distributions, Structural Breaks and Outliers

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analysing time series with strong serial dependence in mean behaviour, the focus being placed on the detection of eventual unit roots in an autoregressive model fitted to the series. In this paper, we propose a completely different method to test for the type of long-wave patterns observed not only in unit-root time series but also in series following more complex data-generating mechanisms. To this end, our testing device analyses the unit-root persistence exhibited by the data while imposing very few constraints on the generating mechanism. We call our device the range unit-root (RUR) test since it is constructed from the running ranges of the series from which we derive its limit distribution. These nonparametric statistics endow the test with a number of desirable properties, the invariance to monotonic transformations of the series and the robustness to the presence of important parameter shifts. Moreover, the RUR test outperforms the power of standard unit-root tests on near-unit-root stationary time series; it is invariant with respect to the innovations distribution and asymptotically immune to noise. An extension of the RUR test, called the forward?backward range unit-root (FB-RUR) improves the check in the presence of additive outliers. Finally, we illustrate the performances of both range tests and their discrepancies with the Dickey?Fuller unit-root test on exchange rate series.Publicad

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.Cointegration; Counting statistics; Jumps; Nonlinearity; Ranges; Robustness; Small sample corrections; Structural breaks; Unit roots tests; 37M10; 62M10;

Taxes, Prisons, and CFOs: The Effects of Increased Punishment on Corporate Tax Compliance in Ecuador

This paper takes advantage of a rich firm level data set from Ecuador to analyze the effects of a reform in 2007 that introduced imprisonment for tax evasion and made a firm’s CFO liable for tax-crimes. Our dataset contains actual tax-return and financial-statement information for the universe of corporations in Ecuador from 2003 to 2007. We study the effects of higher punishment both at the intensive and extensive margins. We combine a difference-in-difference-in-difference approach with the DiNardo, Fortin and Lemieux decomposition method. This allows us to estimate the heterogeneous effects of the reform across the distribution of firms. We find that, at the intensive margin the reform led to an average 10% increase in real corporate tax payments. However, positive effects are only found at the right tail of the tax distribution (above the 75th percentile). At the extensive margin, the probability of entry into the tax-net increased, but most of the firms that entered the tax net claimed zero taxes.Tax evasion, corporate tax compliance, tax reform, developing country, punishment, Ecuador

Range Unit Root (RUR) Tests: Robust against Nonlinearities, Error Distributions, Structural Breaks and Outliers.

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analysing time series with strong serial dependence in mean behaviour, the focus being placed on the detection of eventual unit roots in an autoregressive model fitted to the series. In this paper, we propose a completely different method to test for the type of long-wave patterns observed not only in unit-root time series but also in series following more complex data-generating mechanisms. To this end, our testing device analyses the unit-root persistence exhibited by the data while imposing very few constraints on the generating mechanism. We call our device the range unit-root (RUR) test since it is constructed from the running ranges of the series from which we derive its limit distribution. These nonparametric statistics endow the test with a number of desirable properties, the invariance to monotonic transformations of the series and the robustness to the presence of important parameter shifts. Moreover, the RUR test outperforms the power of standard unit-root tests on near-unit-root stationary time series; it is invariant with respect to the innovations distribution and asymptotically immune to noise. An extension of the RUR test, called the forward?backward range unit-root (FB-RUR) improves the check in the presence of additive outliers. Finally, we illustrate the performances of both range tests and their discrepancies with the Dickey?Fuller unit-root test on exchange rate series.

The age-metallicity relationship in the Fornax spheroidal dwarf galaxy

We produce a comprehensive field star age-metallicity relationship (AMR) from the earliest epoch until ~ 1 Gyr ago for three fields in the Fornax dSph galaxy by using VI photometric data obtained with FORS1 at the VLT. We find that the innermost one does not contains dominant very old stars (age > 12 Gyr), whereas the relatively outer field does not account for representative star field populations younger than ~ 3 Gyr. When focusing on the most prominent stellar populations, we find that the derived AMRs are engraved by the evidence of a outside-in star formation process. The studied fields show bimodal metallicity distributions peaked at [Fe/H] = (-0.95 +- 0.15) dex and (-1.15 or -1.25 +- 0.05) dex, respectively, but only during the first half of the entire galaxy lifetime. Furthermore, the more metal-rich population appears to be more numerous in the outer fields, while in the innermost Fornax field the contribution of both metallicity populations seems to be similar. We also find that the metallicity spread ~ 6 Gyr ago is remarkable large, while the intrinsic metallicity dispersion at ~ 1-2 Gyr results smaller than that for the relatively older generations of stars. We interpret these outcomes as a result of a possible merger of two galaxies that would have triggered a star formation bursting process that peaked between ~ 6 and 9 Gyr ago, depending on the position of the field in the galaxy.Comment: 7 pages, 5 figures, MNRAS, in pres

The Star Formation History in a SMC field: IAC-star/IAC-pop at work

We present a progress report of a project to study the quantitative star formation history (SFH) in different parts of the Small Magellanic Cloud (SMC). We use the information in [(B-R), R] color-magnitude diagrams (CMDs), which reach down to the oldest main-sequence turnoffs and allow us to retrieve the SFH in detail. We show the first results of the SFH in a SMC field located in the Southern direction (at $\thicksim$1 kpc from the SMC center). This field is particularly interesting because in spite of being located in a place in which the HI column density is very low, it still presents a recent enhancement of star formation.Comment: Poster presented at: Stellar Populations as Building Blocks of Galaxies, Proceedings IAU Symposium No. 241, 200