Maxwell L. King

Forecasting international quarterly tourist flows using error-correction and time-series models

Abstract This paper compares a range of forecasting models in the context of predicting quarterly tourist flows into Australia from the major tourist markets of USA, Japan, UK and New Zealand. Models considered include the error-correction model, the autoregressive model, the autoregressive integrated moving average model, the basic structural model and a regression based time series model. Seasonality is an important feature of these series that requires careful handling. The relative performance of each model varies from country to country. The main conclusion is that relative to the time-series models, the error correction models perform poorly. This may be caused by the way in which decisions on how best to model nonstationarity and seasonality are made.

Comments on testing economic theories and the use of model selection criteria

Abstract This paper outlines difficulties with testing economic theories, particularly that the theories may be vague, may relate to a decision interval different from the observation period, and may need a metric to convert a complicated testing situation to an easier one. We argue that it is better to use model selection procedures rather than formal hypothesis testing when deciding on model specification. This is because testing favors the null hypothesis, typically uses an arbitrary choice of significance level, and researchers using the same data can end up with different final models.

Towards a Theory of Point Optimal Testing

This paper puts the case for the inclusion of point optimal tests in the econometricians repertoire. They do not suit every testing situation but the current evidence, which is reviewed here, indicates that they can have extremely useful Small-sample power properties. As well as being most powerful at a nominated point in the alternative hypothesis parameter space, they may also have optimum power at a number of other points and indeed be uniformly most powerful when such a test exists. Point optimal tests can also be used to trace out the maxemum attainable power envelope for a given testing problem, thus providing a benchmark against which test procedures can be evaluated. In some cases, point optimal tests can be constructed from tests of simple null hypothesis against a simple alternative. For a wide range of models of interst to econometricians, this paper shows how one can check whether a point optimal test can be constructed in this way. When it cannot, one may wish to consider approximately point...

A Bayesian approach to bandwidth selection for multivariate kernel density estimation

Kernel density estimation for multivariate data is an important technique that has a wide range of applications. However, it has received significantly less attention than its univariate counterpart. The lower level of interest in multivariate kernel density estimation is mainly due to the increased difficulty in deriving an optimal data-driven bandwidth as the dimension of the data increases. We provide Markov chain Monte Carlo (MCMC) algorithms for estimating optimal bandwidth matrices for multivariate kernel density estimation. Our approach is based on treating the elements of the bandwidth matrix as parameters whose posterior density can be obtained through the likelihood cross-validation criterion. Numerical studies for bivariate data show that the MCMC algorithm generally performs better than the plug-in algorithm under the Kullback-Leibler information criterion, and is as good as the plug-in algorithm under the mean integrated squared error (MISE) criterion. Numerical studies for five-dimensional data show that our algorithm is superior to the normal reference rule. Our MCMC algorithm is the first data-driven bandwidth selector for multivariate kernel density estimation that is applicable to data of any dimension.

Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors

Abstract Inference on the autocorrelation coefficient ϱ of a linear regression model with first-order autoregressive normal disturbances is studied. Both stationary and nonstationary processes are considered. Locally best and point-optimal invariant tests for any given value of ϱ are derived. Special cases of these tests include tests for independence and tests for unit-root hypotheses. The powers of alternative tests are compared numerically for a number of selected testing problems and for a range of design matrices. The results suggest that point-optimal tests are usually preferable to locally best tests, especially for testing values of ϱ greater than or equal to one.

A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances

This article considers the twin problems of testing for autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH disturbances in the linear regression model. A feature of these testing problems, ignored by the standard Lagrange multiplier test, is that they are onesided in nature. A test that exploits this one-sided aspect is constructed based on the sum of the scores. The small-sample-size and power properties of two versions of this test under both normal and leptokurtic disturbances are investigated via a Monte Carlo experiment. The results indicate that both versions of the new test typically have superior power to two versions of the Lagrange multiplier test and possibly also more accurate asymptotic critical values.

A point optimal test for autoregressive disturbances

Abstract This paper is concerned with testing for first-order autoregressive disturbances in the linear regression model and recommends an alternative test to the Durbin-Watson test. The new test is most powerful invariant in a given neighbourhood of the alternative hypothesis parameter space. An empirical power comparison indicates that the test is generally more powerful than the Durbin-Watson test. The comparison also suggests that for many economic applications, the difference in power will be small, although circumstances do exist in which the power advantage of the new test is very real. Selected bounds for the tests significance points are tabulated.

NONPARAMETRIC SPECIFICATION TESTING FOR NONLINEAR TIME SERIES WITH NONSTATIONARITY

This paper considers a nonparametric time series regression model with a nonstationary regressor. We construct a nonparametric test for whether the regression is of a known parametric form indexed by a vector of unknown parameters. We establish the asymptotic distribution of the proposed test statistic. Both the setting and the results differ from earlier work on nonparametric time series regression with stationarity. In addition, we develop a bootstrap simulation scheme for the selection of suitable bandwidth parameters involved in the kernel test as well as the choice of simulated critical values. An example of implementation is given to show that the proposed test works in practice.

Specification testing in nonlinear and nonstationary time series autoregression

This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution of the proposed test. Both the setting and the results differ from earlier work on nonparametric autoregression with stationarity. In addition, we develop a new bootstrap simulation scheme for the selection of a suitable bandwidth parameter involved in the kernel test as well as the choice of a simulated critical value. The finitesample performance of the proposed test is assessed using one simulated example and one real data example.

Autocorrelation pre-testing in the linear model: Estimation, testing and prediction

Abstract This paper explores by means of a Monte Carlo experiment the consequences of autocorrelation pre-testing on estimation, hypothesis testing and prediction in the linear regression model with first-order autoregressive disturbances. We find that overall, pre-testing is preferable to pure OLS regression techniques and generally compares favourably with the strategy of always correcting for possible autocorrelation. More surprising findings include the degree to which the regression matrix affects the relative performance of the various strategies and the degree to which the familiar OLS based t -test can lose power in the presence of autocorrelation.