Testing for random coefficient autoregressive and stochastic unit root models

The random coefficient autoregressive model has been utilized for modeling financial time series because it possesses features that are often observed in financial time series. When the mean of the random coefficient is one, it is called the stochastic unit root model. This paper proposes two Lagrange multiplier tests for the null hypotheses of random coefficient autoregressive and stochastic unit root models against a more general model. We apply our Lagrange multiplier tests to several stock index data, and find that the stochastic unit root model is rejected, whereas the random coefficient autoregressive model is not. This result indicates that it is important to check the validity of the stochastic unit root model prior to applying it to financial time series data, which may be better modeled by the random coefficient autoregressive model with the mean being not equal to one.

Probabilistic forecasting of bubbles and flash crashes

Summary We propose a near-explosive random coefficient autoregressive model (NERC) to obtain predictive probabilities of the apparition and devolution of bubbles. The distribution of the autoregressive coefficient of this model is allowed to be centred at an O(T−α) distance of unity, with α ∈ (0, 1). When the expectation of the autoregressive coefficient lies on the explosive side of unity, the NERC helps to model the temporary explosiveness of time series and obtain related predictive probabilities. We study the asymptotic properties of the NERC and provide a procedure for inference on the parameters. In empirical illustrations, we estimate predictive probabilities of bubbles or flash crashes in financial asset prices.

Locally Most Powerful Test for the Random Coefficient Autoregressive Model

In this article, we study the problem of testing the constancy of the coefficient in a class of stationary first-order random coefficient autoregressive (RCAR(1)) model. We construct a new test statistic based on the locally most powerful-type (LMP) test. Under the null hypothesis, we derive the limiting distribution of the proposed test statistic. In the simulation, we compare the power between LMP test and empirical likelihood (EL) test and find that the accuracy of using LMP is 6.7%, 28.8%, and 26.1% higher than that of EL test under normal, student’s t, and symmetric contamination errors, respectively. A real life data is given to illustrate the practical effectiveness of our test.