Anton Skrobotov

On Trend Breaks and Initial Condition in Unit Root Testing

Recent approaches in unit root testing have taken into account the influences of initial condition, trend, and breaks in data using pre-testing and union of rejection testing strategies based on obtained information. This paper proposes an extension of the Harvey et al. (2012b) approach to address the case of uncertainty over the initial condition. It has been shown that this approach has low power under a large initial condition because it includes GLS-based tests. Therefore, the efficiency of some ADF-type unit root tests with breaks under various magnitudes of initial condition will be investigated, and new decision rules will be proposed. Additionally, the modifications of the proposed algorithm, using pre-testing for the trend co- efficient and the possible presence of multiple structural trend breaks, are also discussed. The asymptotic behaviors of all tests are analyzed under both a local-to-unity representation of the autoregressive root and a local-to-zero representation of trend and breaks magnitudes. The proposed tests show good asymptotic and finite sample properties under various magnitudes of nuisance parameters.

Confidence Sets for the Break Date in Cointegrating Regressions

In this paper, we propose constructing confidence sets for a break date in cointegrating regressions by inverting a test for the break location, which is obtained by maximizing the weighted average of power. It is found that the limiting distribution of the test depends on the number of I(1) regressors whose coefficients sustain structural change and the number of I(1) regressors whose coefficients are fixed throughout the sample. By Monte Carlo simulations, we then show that compared with a confidence interval developed by using the existing method based on the limiting distribution of the break point estimator under the assumption of the shrinking shift, the confidence set proposed in the present paper has a more accurate coverage rate, while the length of the confidence set is comparable. By using the method developed in this paper, we then investigate the cointegrating regressions of Russian macroeconomic variables with oil prices with a break.

Тестирование Гипотезы О Наличии Единичного Корня Для Независимых Панелей (Testing the Hypothesis of a Unit Root for Independent Panels)

Russian Abstract: Тестирование наличия единичных корней в данных имеет большое значение для эмпирического анализа. Практически ни одно макроэкономическое исследование не обходится без тестирования того, является ли конкретный временный ряд стационарным относительно тренда (trend stationary, TS) или является стационарным в первых разностях (difference stationary, DS). В первом случае, если ряд является стационарным относительно тренда, то моделировать ряд необходимо в уровнях. В противном случае нужно перейти к первым разностям временного ряда, если моделируется именно этот конкретный ряд по отдельности, или переходить к анализу коинтеграции нескольких временных рядов, каждый из которых является нестационарным. Наличие коинтеграции позволяет дать экономическое обоснование долгосрочных зависимостей и краткосрочной корректировки к долгосрочным состояниям равновесия. English Abstract: Testing of a unit root in the data is of great importance for the empirical analysis. Almost one or macroeconomic study is not without testing whether a particular stationary time series against the trend (trend stationary, TS) or It is stationary in first differences (difference stationary, DS). In the first If the number is stationary relative to the trend, the number of simulated necessary levels. Otherwise, you need to go to the first difference time series if it is modeled by this specific number separately,or proceed to the cointegration analysis of multiple time series, each which is non-stationary. The presence of cointegration allows us to give feasibility study of long-term and short-term dependency adjustments to long-term equilibrium.

Wild Bootstrap Seasonal Unit Root Tests for Time Series with Periodic Non-Stationary Volatility

ABSTRACT We investigate the behavior of the well-known Hylleberg, Engle, Granger and Yoo (HEGY) regression-based seasonal unit root tests in cases where the driving shocks can display periodic nonstationary volatility and conditional heteroskedasticity. Our set up allows for periodic heteroskedasticity, nonstationary volatility and (seasonal) generalized autoregressive-conditional heteroskedasticity as special cases. We show that the limiting null distributions of the HEGY tests depend, in general, on nuisance parameters which derive from the underlying volatility process. Monte Carlo simulations show that the standard HEGY tests can be substantially oversized in the presence of such effects. As a consequence, we propose wild bootstrap implementations of the HEGY tests. Two possible wild bootstrap resampling schemes are discussed, both of which are shown to deliver asymptotically pivotal inference under our general conditions on the shocks. Simulation evidence is presented which suggests that our proposed bootstrap tests perform well in practice, largely correcting the size problems seen with the standard HEGY tests even under extreme patterns of heteroskedasticity, yet not losing finite sample relative to the standard HEGY tests.

Тестирование Изменения Инерционности и Влияние На Качество Прогнозов (Testing of Changes in Persistence and Their Effect on the Forecasting Quality)

Russian Abstract: В данной работе приводится обзор исследований, связанных с тестированием изменения инерционности временных рядов. Мы обсуждаем как тесты на проверку гипотез о постоянной/изменяющейся инерционности, включая методы анализа нескольких сдвигов в инерционности, так и процедуры оценивания дат сдвигов в инерционности и построение доверительных интервалов.English Abstract: This paper provides a review of contributions to the field of change in persistence testing. We discuss both the constant/changed persistence testing (including multiple changes in persistence testing) and methods of estimation and inference for the dates of persistence changes.

Тестирование Сезонных Единичных Корней: Простейшие Тесты и Тест HEGY (Testing for Seasonal Unit Roots: A Simple Test and HEGY Tests)

Russian Abstract: В работе рассматриваются тесты на сезонные единичные корни, разработанные в последние 25 лет. Основное внимание уделено тесту HEGY и его различным модификациям. Помимо тестов из класса HEGY-тестов, мы рассматриваем некоторые простейшие тесты на сезонные единичные корни, в частности, тест Дики-Хасза-Фуллера. English Abstract: This paper covers seasonal unit roots tests developed in the last 25 years. The main attention is given to HEGY test and its different modifications. Also we study some simple tests for seasonal unit roots, in particular, Dickey-Hasza-Fuller test.

Моделирование Сезонности: Сезонная Интегрированность, Детерминированная Сезонность и Сезонные Структурные Сдвиги (Modeling Seasonality: Seasonal Integration, Deterministic Seasonality and Seasonal Structural Breaks)

Russian Abstract: В работе рассматриваются методы тестирования сезонных единичных корней, детерминированной сезонности и сезонных структурных сдвигов во временных рядах. Отметим, что среди тестов на сезонные единичные корни мы рассматриваем LМ-тесты, тесты отношения правдоподобий и отношения дисперсий, а также принципы построения эффективных тестов, и не рассматриваем простейшие методы тестирования наличия единичных корней и тесты типа HEGY. В работе мы также представляем результаты тестирования российских макроэкономических рядов на наличие сезонных единичных корней.English Abstract: The paper deals with methods of testing for seasonal unit root, deterministic seasonality and seasonal structural breaks in the time series. Note that among the tests for seasonal unit roots, we consider the LM-tests, likelihood ratio tests and the variance ratio tests, as well as principles of construction of effective tests, and do not consider the simplest methods for seasonal unit roots testing and class of HEGY of tests. In this paper we present the results of seasonal unit roots testing for Russian macroeconomic time series.

A Simple Modification of the Busetti-Harvey Stationarity Tests with Structural Breaks at Unknown Time

In this paper a modification of the Busetti and Harvey (2001) test with structural break at unknown time is proposed. As the stationarity test with a super-consistent break date estimator is effective under large breaks and the infimum-test is effective under small breaks, although it has serious size distortions under large breaks, we propose a simple decision rule based on pre-testing for the presence of a break. The proposed modification shows good size properties. Also, an extension for the case of multiple structural breaks is proposed

Некоторые Подходы К Тестированию Значимости Детерминированных Трендов в Данных (Some Approaches to Testing Significance of Deterministic Trends in Panel Data)

Russian Abstract: Тесты на единичный корень как для аддиктивных, так и для инновационных выбросов, основываются на предположении, что структурные сдвиги существуют и их количество выбрано правильно. Если же при этом сдвиги не происходят - то никакие асимптотические результаты больше не выполняются, так как при нулевой гипотезе оценка доли сдвига имеет невыраженное предельное распределение на интервале (0,1) вместо того, чтобы сходиться к 0, либо к 1.English Abstract: Tests on a singular root for addictive and innovative emissions are based on the assumption that there are structural changes and their number is selected correctly. If, however, this shift does not happen, then asymptotic results are no longer fulfilled, since given the null hypothesis the evaluation of the share shift has unexpressed limit distribution on the interval (0,1) instead of converging to 0 or a 1.

On GLS-detrending for deterministic seasonality testing

In this paper we propose tests based on GLS-detrending for testing the null hypothesis of deterministic seasonality. Unlike existing tests for deterministic seasonality, our tests do not suffer from asymptotic size distortions under near integration. We also investigate the behavior of the proposed tests when the initial condition is not asymptotically negligible.