Seasonal Unit Roots Research Articles

Measuring persistence in Croatian tourism: evidence from the Adriatic region

This study examines the degree of persistence in foreign tourist arrivals and overnight stays for seven Croatian coastal counties over the period January 1998 to December 2013 using fractional integration techniques. Our findings reveal that the respective regional tourism indicators exhibit seasonal unit roots which require seasonal first differences to render the respective time series stationary. With respect to the long-run evolution of the respective time series, both the parametric and semi-parametric fractional integration approaches show the degree of persistence is greater than zero, but significantly less than one for the majority of the coastal counties. Impulse response analysis reveals indeed shocks to the deseasonalized time series, either foreign tourist arrivals or foreign tourist overnight stays, appear short-lived with the exception of Istria and Primorje-Gorski kotar counties. Policy implications of the results are also discussed.

Prediction and simulation using simple models characterized by nonstationarity and seasonality

In this paper, we provide new evidence on the empirical usefulness of various simple seasonal models, and underscore the importance of carefully designing criteria by which one judges alternative models. In particular, we underscore the importance of both choice of forecast or simulation horizon and choice between minimizing point or distribution based loss measures. Our empirical analysis centers around the implementation of a series of simulation and prediction experiments, as well as a discussion of the stochastic properties of seasonal unit root models. Our prediction experiments are based on an analysis of a group of 14 variables which have been chosen to closely mimic the set of indicators used by the Federal Reserve to help in setting U.S. monetary policy, and our simulation experiments are based on a comparison of simulated and historical distributions of said variables using the testing approach of Corradi and Swanson (2007a). A key impetus for this paper stems from the fact that various financial service companies routinely create “economic scenarios”, whereby seasonal and nonstationary financial and economic variables such as those examined here are simulated (and predicted) using relatively simple time series models. These “economic scenarios” are subsequently used in risk management and asset allocation, as is often mandated by various world financial regulatory authorities. Our findings suggest that a simple version of the seasonal unit root (SUROOT) model performs very well in predicting 8 of 14 variables, when the forecast horizon is 1-step ahead. However, for horizons greater than one-step ahead, our SUROOT model performs poorly when used for prediction, suggesting that parameter estimation error is crucial to understanding the empirical performance of such models. This “parameter estimation error” result is confirmed via a series of Monte Carlo experiments. Simulation experiments yield similar conclusions, although SUROOT models in this case are useful for constructing “forward” conditional distributions at 1- and 3-step ahead horizons. Interestingly, simple periodic autoregressions do not have this property, and are found to perform very well in both prediction and simulation experiments, at all horizons up to 60months ahead.

Modeling the degree of persistence in Croatian tourism

The Croatian tourism sector has been affected by a number of negative and positive shocks since the beginning of the 1990s. To examine the impact of shocks on tourism, the authors employ fractional integration techniques as a means to gauge the degree of persistence of such shocks. Based on monthly data from January 1995 to December 2013, they find that the respective tourism indicators contain seasonal unit roots. An examination of the seasonally differenced tourism time series reveals that the fractional differencing parameter, d, with allowance for an autocorrelated error process, is strictly below 1, implying that shocks are transitory and disappear relatively quickly.

The Performance of Lag Selection and Detrending Methods for HEGY Seasonal Unit Root Tests

This paper analyzes two key issues for the empirical implementation of parametric seasonal unit root tests, namely generalized least squares (GLS) versus ordinary least squares (OLS) detrending and the selection of the lag augmentation polynomial. Through an extensive Monte Carlo analysis, the performance of a battery of lag selection techniques is analyzed, including a new extension of modified information criteria for the seasonal unit root context. All procedures are applied for both OLS and GLS detrending for a range of data generating processes, also including an examination of hybrid OLS-GLS detrending in conjunction with (seasonal) modified AIC lag selection. An application to quarterly U.S. industrial production indices illustrates the practical implications of choices made.

Numerical distribution functions for seasonal unit root tests

It is often necessary to test for the presence of seasonal unit roots when working with time series data observed at intervals of less than a year. One of the most widely used methods for doing thi...

Explaining money demand in China during the transition from a centrally planned to a market-based monetary system

Fundamental changes in institutions during the transition from a centrally planned to a market economy present a formidable challenge to monetary policy decision makers. For the case of China, we examine the institutional changes in the monetary system during the process of transition and develop money demand functions that reflect these institutional changes. We consider seasonal unit roots and estimate long-run, equilibrium money demand functions, explicitly taking into consideration the changes in the institutional characteristics of China's financial system. Using a newly compiled dataset that covers an unprecedentedly long period, 1984—2010, with quarterly frequency, we are able to draw conclusions on the transitions in households', firms' and aggregate money demand, on the role of the credit plan and interest rates, on the mechanisms of macroeconomic control during economic transition, and on theoretical questions in the development and money literature.

Small-Sample Improved Seasonal Unit Root Tests for Trending and Breaking Series

In this article three unit root tests that allow for a break in both the seasonal mean and linear trend of the data are proposed. The tests, which can be seen as small-sample corrected versions of already known asymptotic tests, are shown to perform very well in simulations, and much better than their asymptotic counterparts.

: HEGY (Testing of Seasonal Unit Roots: A Simple Test and Test HEGY)

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.

International Tourists Arrival to Thailand: Forecasting by Non-linear Model

The aim of this study is to provide non-linear forecasting models for prediction of the international tourist arrival to Thailand by using data from period 1998-2014(Feb.). The seasonal unit root test (HEGY-test extent version) was carried out to test this data. Based on this testing is found that the number of international tourist arrivals to Thailand was affected by seasonal unit root process for during period of this study. Therefore, both the MS-VAR model and AR model are employed to predict this data for future of Thailand. The empirical results from this research was concluded that in high seasonal period can be use AR (2)-MLE, AR (2)-MLE-bootstrapping, and AR(1)-ME-bootstrapping to predict the number of international tourist arrivals to Thailand for future years. However, in low seasonal period only AR(1)-ME-bootstrapping can be used to predict the number of international tourist arrival to Thailand for future years.

Numerical distribution functions for seasonal stability tests

The seasonal stability tests of Canova and Hansen (1995) (CH) provide a method complementary to that of Hylleberg et al. (1990) for testing for seasonal unit roots. But the distributions of the CH tests are unknown for small samples. We present a method for numerically computing critical values and P -values for the CH tests for any sample size and any seasonal periodicity. In fact, this method is applicable to the types of seasonality which are commonly in use, but also to any other.

Empleo del comportamiento estacional para mejorar el pronóstico de un commodity: El caso del mercado internacional del azúcar

This paper studies the behavior of seasonal patterns in the international sugar price. Using seasonal unit root test and a monthly sample from 1989 to 2010, a non‐stationary stochastic seasonal pattern was observed. This pattern implies that a “summer” could become a “winter”, a result that had not been previously documented for this market. On the other hand, using these findings, our results show that is possible to create an AutoRegressive Moving Average (ARMA) model that out‐performs other approaches that do not take in account this kind of seasonality when forecasting the sugar price.

Spatial integration of the Caspian Sea bony fish market: An application of the seasonal co-integration approach to monthly data

Analysis of spatial integration (co-integration) will make an important contribution to the literature of market structure. The analysis presents an index of spatial markets' efficiency and tests law of one price in the fish markets of Guilan and Mazandaran. The seasonal and monthly nature of price series creates fluctuating market conditions. So this study was done to investigate spatial integration of markets for different types of marine bony fish in Guilan and Mazandaran over a period of 120 months from 2001:1 to 2010:12. Given that the fishing season is from October to late April, all prices of illegal fishing registered in the Iran Fisheries Organization were used for the remaining five months (May to September). The modern approach of analyzing seasonal unit roots and estimating Seasonal Error Correction Model (SECM) was used in the study. Results showed that there has been seasonal co-integration in markets for different types of bony fish and spatial markets obeyed law of one price in both Mazandaran and Guilan. Therefore, this long run seasonal dynamics approach needs to be considered in error correction computations and finally forecasting and policymaking for future situation in the various fish markets. Otherwise, price policy and market planning will fail to achieve appropriate efficiency in terms of spatial markets in the long-term.

Testing for seasonal unit roots by frequency domain regression

This paper develops univariate seasonal unit root tests based on spectral regression estimators. An advantage of the frequency domain approach is that it enables serial correlation to be treated non-parametrically. We demonstrate that our proposed statistics have pivotal limiting distributions under both the null and near seasonally integrated alternatives when we allow for weak dependence in the driving shocks. This is in contrast to the popular seasonal unit root tests of, among others, Hylleberg et al. (1990) which treat serial correlation parametrically via lag augmentation of the test regression. Our analysis allows for (possibly infinite order) moving average behaviour in the shocks. The size and power properties of our proposed frequency domain regression-based tests are explored and compared for the case of quarterly data with those of the tests of Hylleberg et al. (1990) in simulation experiments.

Simulation and Prediction Evidence on the Usefulness of Seasonal Models

In this paper, we provide new evidence on the empirical usefulness of various simple seasonal models, and underscore the importance of carefully designing criteria by which one judges alternative models. In particular, we underscore the importance of both choice of forecast or simulation horizon and choice between minimizing point or distribution based loss measures. Our empirical analysis centers around the implementation of a series of simulation and prediction experiments, as well as a discussion of the stochastic properties of seasonal unit root models. Our prediction experiments are based on analysis of a group of 14 variables have been chosen to closely mimic the set of indicators used by the Federal Reserve to help in setting U.S. monetary policy, and our simulation experiments are based on a comparison of simulated and historical distributions of said variables using the testing approach of Corradi and Swanson (2007a). A key impetus for this paper stems from the fact that various financial service companies routinely create scenarios, whereby seasonal and nonstationary financial and economic variables such as those examined here are simulated (and predicted) using relatively simple time series models. These scenarios are subsequently used in risk management and asset allocation, as is often mandated by various world financial regulatory authorities. Our findings suggest that a simple version of the seasonal unit root (SUR) model performs very well for predicting 8 of 14 variables, when the forecast horizon is 1-step ahead. However, for horizons of greater than one-step ahead, our SUR model perform poorly when used for prediction, suggesting that estimation is crucial to understanding the empirical performance of such models. This parameter estimation error result is confirmed via a series of Monte Carlo experiments. Simulation experiments yield similar conclusions, although SUR models in this case are useful for constructing forward conditional distributions at 1- and 3-step ahead horizons. Interestingly, simple periodic autoregressions do not have this property, and are found to perform very well in both prediction and simulation experiments, at all horizons up to 60 months ahead.

Government revenue and expenditure nexus in South Africa

This paper investigates the nexus between government expenditure and government revenue in South Africa within the framework of a vector autoregressive (VAR) approach. It uses the Hylleberg et al. (1990) method to test for seasonal unit roots and finds that government revenue and government expenditure have unit roots at all frequencies. The Johansen procedure test results reveal that these variables are cointegrated. It is further established that revenue and expenditure are linked bidirectionally by Granger causality in the long-run, while there is no evidence of Granger causalityin the short-run in South Africa.

Numerical distribution functions for seasonal unit root tests

It is often necessary to test for the presence of seasonal unit roots when working with time series data observed at intervals of less than a year. One of the most widely used methods for doing this is based on regressing the seasonal difference of the series over the transformations of the series by applying specific filters for each seasonal frequency. This provides test statistics with non-standard distributions. A generalisation of this method for any periodicity is presented and a response surface regressions approach is used to calculate the P-values of the statistics whatever the periodicity and sample size of the data. The algorithms are prepared with the Gretl open source econometrics package and two empirical examples are presented.

Business cycle modelling - The case of mergers and acquisitions

Business cycle models involve exploiting movements of the economy to gain competitive advantage over rivals. Business cycles are applicable to mergers and acquisitions (M&A) which occur in waves. Econometricians have attempted to model these waves. The paper demonstrates that, with respect to each of several major stylized facts about business cycles, the seasonal cycle displays the same characteristics as the business cycle. Therefore the patterns in merger and acquisitions measured as merger waves could be investigated using seasonality models. Using a modified seasonal unit root procedure we model the cyclical behaviour in the quarterly M&A data from 2000 to 2010 for Turkey. Our analysis is based on the methodology developed by Hylleberg, Engle, Granger and Yoo (HEGY procedure). Based upon an empirical analysis of the merger and acquisition variables, our results indicate that seasonal unit roots appear to deal value, number of deals with known value variables when possible structural changes in one or more seasons during the 2001 and 2008 crisis years have been taken into account. Key words: Merger and acquisitions, Turkish economy, Hylleberg, Engle, Granger and Yoo (HEGY) seasonal unit root test, deterministic seasonality, structural breaks.

An Extension of the Seasonal KPSS Test

The limit theory of the seasonal KPSS test is established under the null hypothesis using seasonal dummy variables. Taking these variables into account can result in improved finite sample performance of the test. The seasonal KPSS test can be interpreted as a test of deterministic seasonality and it may be used in addition to seasonal unit root tests to analyze the dynamic properties of time series. The seasonal indicator variables provide the test with an explicit model-based regression that in itself constitutes a support for its limit theory.

ON AUGMENTED HEGY TESTS FOR SEASONAL UNIT ROOTS

In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (1984, Biometrika 71, 599–607) and Chang and Park (2002, Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t-statistics for unit roots at the zero and Nyquist frequencies and joint F-type statistics are pivotal, whereas those of the t-statistics at the harmonic seasonal frequencies depend on nuisance parameters that derive from the lag parameters characterizing the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park (2002); in particular, an o(T1/2) rate is shown to be sufficient.

Summit Ties Sustainability to Improved Public Health

Summit Ties Sustainability to Improved Public Health