Purpose This paper aims to examine the weak form of efficiency for price series of four precious metals, i.e. gold, silver, platinum and palladium, using a generalized spectral method. Design/methodology/approach The method has the advantage of detecting both linear and non-linear serial dependence in the conditional mean, and it is robust to various forms of conditional heteroscedasticity. The authors use three different rolling windows for the purpose of robustness. Findings The authors report weak form of efficiency across metals series for almost all rolling windows. The optimum efficiency for Gold and Palladium is achieved through 250 days rolling window estimates whereas it is 500 days rolling window for silver. Platinum has similar efficiency levels across rolling windows. The degree of efficiency for metal prices is observed to be varying over time with silver market possessing highest levels of efficiency. The efficiency synchronization also varies across rolling windows and metals. Research limitations/implications The results reveal that metal markets are efficient for most times implying the low predictability and the low likelihood of earning abnormal returns by speculating in these markets. Originality/value The study uses a relatively new statistical technique, the generalized spectral test, to capture linear and non-linear serial dependence. Therefore, the results possess adequate power against departure from market efficiency.

Herein, we propose a novel non-parametric frequency Granger causality test. We apply a filtering process in the time domain to remove possible spurious causality, thereby eliminating potential interference. Thereafter, in the frequency domain, we perform a local kernel regression for each frequency and test the non-causality hypothesis from the distance between each estimate to zero. We provide asymptotic results for strict stationary series concerning 𝛼-mixing conditions. Our method can also perform group causality tests, a feature that is absent in most alternative methods. Monte Carlo experiments illustrate that our method is comparable, and in some cases, performs better than alternative methods in the literature. Finally, we test the causality between monetary policy variables and stock prices.

Here, we present an unexplored issue regarding temporal aggregation. When a model contains frequency‐dependent coefficients, such as a distinct long‐ and short‐term coefficient, temporal aggregation leads to inconsistent least squares estimates. Because the sub‐sampled variable's spectrum is equal to its folded original spectrum, the low‐frequency variable may exhibit a mixture of distinct linear relations for a given frequency. We propose a new method to disentangle the frequencies superposition based on band spectrum regression, thus avoiding the inconsistency problem. As a result, we can test for the presence of frequency‐dependent coefficients. We use stationary and non‐stationary linear semi‐parametric models to demonstrate our findings. Our Monte Carlo simulations show good finite sample size and power properties. Finally, our empirical study rejects the presence of a single coefficient for all frequencies between quarterly GDP and monthly US indicators.

In this paper, we propose a robust test of monotonicity in asset returns that is valid under a general setting. We develop a test that allows for dependent data and is robust to conditional heteroskedasticity or heavy-tailed distributions of return differentials. Many postulated theories in economics and finance assume monotonic relationships between expected asset returns and certain underlying characteristics of an asset. Existing tests in literature fail to control the probability of a type 1 error or have low power under heavy-tailed distributions of return differentials. Monte Carlo simulations illustrate that our test statistic has a correct empirical size under all data-generating processes together with a similar power to other tests. Conversely, alternative tests are nonconservative under conditional heteroskedasticity or heavy-tailed distributions of return differentials. We also present an empirical application on the monotonicity of returns on various portfolios sorts that highlights the usefulness of our approach.