Testing for unit roots in bounded time series

Many key economic and financial series are bounded either by construction or through policy controls. Conventional unit root tests are potentially unreliable in the presence of bounds, since they tend to over-reject the null hypothesis of a unit root, even asymptotically. So far, very little work has been undertaken to develop unit root tests which can be applied to bounded time series. In this paper we address this gap in the literature by proposing unit root tests which are valid in the presence of bounds. We present new augmented Dickey–Fuller type tests as well as new versions of the modified ‘M’ tests developed by Ng and Perron [Ng, S., Perron, P., 2001. LAG length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554] and demonstrate how these tests, combined with a simulation-based method to retrieve the relevant critical values, make it possible to control size asymptotically. A Monte Carlo study suggests that the proposed tests perform well in finite samples. Moreover, the tests outperform the Phillips–Perron type tests originally proposed in Cavaliere [Cavaliere, G., 2005. Limited time series with a unit root. Econometric Theory 21, 907–945]. An illustrative application to U.S. interest rate data is provided

Testing Seasonal Unit Roots in Data at Any Frequency, an HEGY approach

This paper generalizes the HEGY-type test to detect seasonal unit roots in data at any frequency, based on the seasonal unit root tests in univariate time series by Hylleberg, Engle, Granger and Yoo (1990). We introduce the seasonal unit roots at first, and then derive the mechanism of the HEGY-type test for data with any frequency. Thereafter we provide the asymptotic distributions of our test statistics when different test regressions are employed. We find that the F-statistics for testing conjugation unit roots have the same asymptotic distributions. Then we compute the finite-sample and asymptotic critical values for daily and hourly data by a Monte Carlo method. The power and size properties of our test for hourly data is investigated, and we find that including lag augmentations in auxiliary regression without lag elimination have the smallest size distortion and tests with seasonal dummies included in auxiliary regression have more power than the tests without seasonal dummies. At last we apply the our test to hourly wind power production data in Sweden and shows there are no seasonal unit roots in the series.

Testing for Seasonal Unit Roots when Residuals Contain Serial Correlations under HEGY Test Framework

This paper introduces a corrected test statistic for testing seasonal unit roots when residuals contain serial correlations, based on the HEGY test proposed by Hylleberg,Engle, Granger and Yoo (1990). The serial correlations in the residuals of test regressionare accommodated by making corrections to the commonly used HEGY t statistics. Theasymptotic distributions of the corrected t statistics are free from nuisance parameters.The size and power properties of the corrected statistics for quarterly and montly data are investigated. Based on our simulations, the corrected statistics for monthly data havemore power compared with the commonly used HEGY test statistics, but they also have size distortions when there are strong negative seasonal correlations in the residuals.

Why do Australians, New Zealanders and Americans travel to Fiji? Evidence from cointegration, unit roots and parameter stability tests

The aim of this study was to estimate the demand for Fiji’s tourism from its three main source markets—Australia, New Zealand, and the US—using the bounds testing approach to cointegration. Our main finding was that visitor arrivals to Fiji and its key determinants are cointegrated over the 1970–2000 period. We then used the autoregressive distributed lag model to estimate short-run and long-run elasticities and found that income in origin countries, transport costs, and prices were significant determinants of Fiji’s tourism demand. We also found that coups negatively impact visitor arrivals from all markets. In testing for parameter stability, we established that the series were integrated of order one in the presence of a structural break. We then used the Hansen test for parameter stability and found that the parameters of our long-run model are stable over time.

Structural breaks and unit roots in Australian macroeconomic time series

We examine the unit root properties of 16 Australian macroeconomic time series using monthly data spanning the period 1960–2004. In addition to the standard Augmented Dickey Fuller (ADF) test, we implement one- and two-break endogenous structural break ADF-type unit root tests as well as one- and two-break Lagrange multiplier (LM) unit root tests. While the ADF test provides relatively little evidence against the unit root null hypothesis, once we allow for structural breaks we are able to reject the unit root null for just under half of the variables at the 10% level or better.

Testing for unit roots in panel time-series models with multiple level breaks

This paper proposes two new unit root tests that are appropriate in the presence of an unknown number of structural breaks in the level of the data. One is based on a single time series and the other is based on a panel of multiple series. For the estimation of the number of breaks and their locations, a simple procedure based on outlier detection is proposed. The limiting distributions of the tests are derived and evaluated in small samples using simulation experiments. The implementation of the tests is illustrated using as an example purchasing power parity.

Unit roots and the welfare gains of cycle smoothing

li consumption is log-Normal and is decomposed into a linear deterministic trend and a stationary cycle, a surprising result in business-cycle research is that the welfare gains of eliminating uncertainty are relatively small. A possible problem with such calculations is the dichotomy between the trend and the cyclical components of consumption. In this paper, we abandon this dichotomy in two ways. First, we decompose consumption into a deterministic trend, a stochastic trend, and a stationary cyclical component, calculating the welfare gains of cycle smoothing. Calculations are carried forward only after a careful discussion of the limitations of macroeconomic policy. Second, still under the stochastic-trend model, we incorporate a variable slope for consumption depending negatively on the overall volatility in the economy. Results are obtained for a variety of preference parameterizations, parameter values, and different macroeconomic-policy goals. They show that, once the dichotomy in the decomposition in consumption is abandoned, the welfare gains of cycle smoothing may be substantial, especially due to the volatility effect.

Testing for a Unit Root in Panels with Dynamic Factors

This paper studies testing for a unit root for large n and T panels in which the cross-sectional units are correlated. To model this cross-sectional correlation, we assume that the data is generated by an unknown number of unobservable common factors. We propose unit root tests in this environment and derive their (Gaussian) asymptotic distribution under the null hypothesis of a unit root and local alternatives. We show that these tests have significant asymptotic power when the model has no incidental trends. However, when there are incidental trends in the model and it is necessary to remove heterogeneous deterministic components, we show that these tests have no power against the same local alternatives. Through Monte Carlo simulations, we provide evidence on the finite sample properties of these new tests.

Do shocks to G7 stock prices have a permanent effect? : evidence from panel unit root tests with structural change

There is a plethora of studies that investigate evidence for the behaviour of stock prices using univariate techniques for unit roots. Whether or not stock prices are characterised by a unit root have implications for the efficient market hypothesis, which asserts that returns of a stock market are unpredictable from previous price changes. The extant literature has found mixed evidence on the integrational properties of stock prices. In this paper, for the first time, we provide evidence on the unit root hypothesis for G7 stock price indices using the Lagrangian multiplier panel unit root test that allows for structural breaks. Our main finding is that stock prices are stationary processes, inconsistent with the efficient market hypothesis.

A new unit root test with two structural breaks in level and slope at unknown time

In this paper, we propose a new augmented Dickey–Fuller-type test for unit roots which accounts for
two structural breaks. We consider two different specifications: (a) two breaks in the level of a trending data series and (b) two breaks in the level and slope of a trending data series. The breaks whose time of occurrence is assumed to be unknown are modeled as innovational outliers and thus take effect gradually. Using Monte Carlo simulations, we showthat our proposed test has correct size, stable power, and identifies the structural breaks accurately.