1,721,046 research outputs found
On bootstrapping panel factor series
No full textThis paper studies the asymptotic validity of sieve bootstrap for nonstationary panel factor series. Two main results are shown. Firstly, a bootstrap Invariance Principle is derived pointwise in i, obtaining an upper bound for the order of truncation of the AR polynomial that depends on n and T. Consistent estimation of the long run variances is also studied for (n,T)→∞. Secondly, joint bootstrap asymptotics is also studied, investigating the conditions under which the bootstrap is valid. In particular, the extent of cross sectional dependence which can be allowed for is investigated. Whilst we show that, for general forms of cross dependence, consistent estimation of the long run variance (and therefore validity of the bootstrap) is fraught with difficulties, however we show that "one-cross-sectional-unit-at-a-time" resampling schemes yield valid bootstrap based inference under weak forms of cross-sectional dependence
Testing for Exogeneity in Cointegrated Panels
Full text linkThis paper proposes a test for the null that, in a cointegrated panel, the long-run correlation between the regressors and the error term is different from zero. As is well known, in such case the OLS estimator is T-consistent, whereas it is NT-consistent when there is no endogeneity. Other estimators can be employed, such as the FM-OLS, that are NT-consistent irrespective of whether exogeneity is present or not. Using the difference between the former and the latter estimator, we construct a test statistic which diverges at a rate N under the null of endogeneity, whilst it is bounded under the alternative of exogeneity, and employ a randomization approach to carry out the test. Monte Carlo evidence shows that the test has the correct size and good power
On the asymptotic t-test for large nonstationary panel models
No full textThe asymptotic t -test for the long-run average in a heterogeneous nonstationary panel model is derived. The asymptotics of the Least Squares Dummy Variable (LSDV) and of the Pooled-OLS (POLS) estimators for the slope parameter are studied under various circumstances (serial correlation, strong cross-sectional dependence in the errors and in the regressors and mixed stationary/nonstationary errors) and a modified estimator of the asymptotic variance is derived. The asymptotic variance is computed up to a simple transformation of the residual and no nuisance parameters need to be estimated. The resulting t-statistics are shown to have a standard normal limiting distribution. Asymptotic tests based on the standardized version of the t-statistic are shown to have good power properties, and the correct size, even for n as small as 25
Testing for (in)finite moments
Full text linkThis paper proposes a test to verify whether the k-th moment of a random variable is Önite. We use the fact that, under general assumptions, sample moments either converge to a Önite number or diverge to inÖnity according as the corresponding population moment is Önite or not. Building on this, we propose a test for the null that the k-th moment does not exist. Since, by construction, our test statistic diverges under the null and converges under the alternative, we propose a randomised testing procedure to discern between the two cases. We study the application of the test to raw data, and to regression residuals. Monte Carlo evidence shows that the test has the correct size and good power; the results are further illustrated through an application to Önancial data
Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences
Full text linkThis note contains a Chover-type Law of the k-Iterated Logarithm for weighted sums of strong mixing sequences of random variables with a distribution in the domain of a stable law. We show that the upper part of the LIL is similar to other studies in the literature; conversely, the lower half is substantially different. In particular, we show that, due to the failure of the classical version of the second Borel–Cantelli lemma, the upper and the lower bounds are separated, with the lower bound being further and further away as the memory of the sequence increases
Testing for Common Trends in Nonstationary Large Datasets
Full text linkWe propose a testing-based procedure to determine the number of common trends in a large nonstationary dataset. Our procedure is based on a factor representation, where we determine whether there are (and how many) common factors (i) with linear trends, and (ii) with stochastic trends. Cointegration among the factors is also permitted. Our analysis is based on the fact that those largest eigenvalues of a suitably scaled covariance matrix of the data corresponding to the common factor part diverge, as the dimension N of the dataset diverges, whilst the others stay bounded. Therefore, we propose a class of randomized test statistics for the null that the pth largest eigenvalue diverges, based directly on the estimated eigenvalue. The tests only requires minimal assumptions on the data-generating process. Monte Carlo evidence shows that our procedure has very good finite sample properties, clearly dominating competing approaches when no common trends are present. We illustrate our methodology through an application to the U.S. bond yields with different maturities observed over the last 30 years
A randomised sequential procedure to determine the number of factors
Full text linkThis paper proposes a procedure to estimate the number of common factors k in a static approximate factor model. The building block of the analysis is the fact that the first k eigenvalues of the covariance matrix of the data diverge, whilst the others stay bounded. On the grounds of this, we propose a test for the null that the i-th eigenvalue diverges, using a randomised test statistic based directly on the estimated eigenvalue. The test only requires minimal assumptions on the data, and no assumptions are required on factors, loadings or idiosyncratic errors. The randomised tests are then employed in a sequential procedure to determine k
A test for strict stationarity in a random coefficient autoregressive model of order 1
Full text linkWe propose a test for the null of strict stationarity in a Random Coefficient AutoRe-gression (RCAR) of order 1. The test can also be used in the case of a standard AR(1) model, and it can be applied under minimal requirements on the existence of moments-in both cases without requiring any modifications or prior knowledge
Testing for strict stationarity in a random coefficient autoregressive model
Full text linkWe propose a procedure to decide between the null hypothesis of (strict) stationarity and the alternative of non-stationarity, in the context of a Random Coefficient AutoRegression (RCAR). The procedure is based on randomising a diagnostic which diverges to positive infinity under the null, and drifts to zero under the alternative. Thence, we propose a randomised test which can be used directly and-building on it-a decision rule to discern between the null and the alternative. The procedure can be applied under very general circumstances: albeit developed for an RCAR model, it can be used in the case of a standard AR(1) model, without requiring any modifications or prior knowledge. Also, the test works (again with no modification or prior knowledge being required) in the presence of infinite variance, and in general requires minimal assumptions on the existence of moments
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