QUANTILE DOUBLE AUTOREGRESSION

Many financial time series have varying structures at different quantile levels, and also exhibit the phenomenon of conditional heteroskedasticity at the same time. However, there is presently no time series model that accommodates both of these features. This paper fills the gap by proposing a novel conditional heteroskedastic model called “quantile double autoregression”. The strict stationarity of the new model is derived, and self-weighted conditional quantile estimation is suggested. Two promising properties of the original double autoregressive model are shown to be preserved. Based on the quantile autocorrelation function and self-weighting concept, three portmanteau tests are constructed to check the adequacy of the fitted conditional quantiles. The finite sample performance of the proposed inferential tools is examined by simulation studies, and the need for use of the new model is further demonstrated by analyzing the S&P500 Index.

ROBUST TESTS FOR WHITE NOISE AND CROSS-CORRELATION

Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung–Box tests can be significantly distorted. This paper adapts standard correlogram and portmanteau tests to accommodate hidden dependence and nonstationarities involving heteroskedasticity, thereby uncoupling these tests from limiting assumptions that reduce their applicability in empirical work. To enhance the Ljung–Box test for non-i.i.d. data, a new cumulative test is introduced. Asymptotic size of these tests is unaffected by hidden dependence and heteroskedasticity in the series. Related extensions are provided for testing cross-correlation at various lags in bivariate time series. Tests for the i.i.d. property of a time series are also developed. An extensive Monte Carlo study confirms good performance in both size and power for the new tests. Applications to real data reveal that standard tests frequently produce spurious evidence of serial correlation.

A Monte Carlo Simulation Study on the Power of Autocorrelation Tests for ARMA Models

It is often the case when assessing the goodness of fit for an ARMA time series model that a portmanteau test of the residuals is conducted to assess residual serial correlation of the fitted ARMA model. Of the many portmanteau tests available for this purpose, one of the most famous and widely used is a variant of the original Box-Pierce test, the Ljung-Box test. Despite the popularity of this test, however, there are several other more modern portmanteau tests available to assess residual serial autocorrelation of the fitted ARMA model. These include two portmanteau tests proposed by Monti and Peña and Rodríguez. This paper focuses on the results of a power analysis comparing these three different portmanteau tests against different fits of ARMA - derived time series, as well as the behavior of the three different test statistics examined when applied to a real-world data set. We confirm that for situations in which the moving average component of a fitted ARMA model is underestimated or when the sample size is small, the portmanteau test proposed by Monti is a viable alternative to the Ljung-Box test. We show new evidence that the Peña and Rodríguez may also be a viable option for testing for residual autocorrelation for data with small sample sizes. KEYWORDS: Time Series; Monte Carlo; ARMA Models; Power; Simulation; Autocorrelation Tests; Portmanteau Tests; Monti; Ljung-Box; Peña and Rodríguez