Asymmetric Time Series Research Articles

Robust clustering of COVID-19 cases across U.S. counties using mixtures of asymmetric time series models with time varying and freely indexed covariates

In this paper, we develop a mixture of autoregressive (MoAR) process model with time varying and freely indexed covariates under the flexible class of two–piece distributions using the scale mixtures of normal (TP-SMN) family. This novel family of time series (TP-SMN-MoAR) models was used to examine flexible and robust clustering of reported cases of Covid-19 across 313 counties in the U.S. The TP-SMN distributions allow for symmetrical/ asymmetrical distributions as well as heavy-tailed distributions providing for flexibility to handle outliers and complex data. Developing a suitable hierarchical representation of the TP-SMN family enabled the construction of a pseudo-likelihood function to derive the maximum pseudo-likelihood estimates via an EM-type algorithm.

LM Tests for Shock Induced Asymmetries in Time Series

This paper develops a Lagrange multiplier test statistic and its variants to test for the null hypothesis of no asymmetric effects of shocks on time series. In asymmetric time series models that allow for different responses to positive and negative past shocks the likelihood functions are, in general, non-differentiable. By making use of the theory of generalized functions Lagrange multiplier type tests and the resulting asymptotics are derived. The test statistics possess standard asymptotic limiting behavior under the null hypothesis. Monte Carlo experiments illustrate the accuracy of the asymptotic approximation and show that conventional model selection criteria can be used to estimate the required lag length. We provide an empirical application to the U.S. unemployment rate.

Price relationships between qualitatively differentiated agricultural products: organic and conventional wheat in Germany

AbstractOrganic agriculture, which produces commodities that can be qualitatively differentiated from conventional food products, has grown into an important market in many countries. The dynamics of commodity prices in both sectors are partly interdependent, but are also shaped by independent determinants and have rarely been studied. We analyze organic food markets and their interdependencies with conventional markets in the context of wheat markets in Germany, which have been subject to a number of fundamental changes during the last two decades. Based on institutional market characteristics, we suggest a flexible Markov‐switching asymmetric time series model. We find a pronounced temporal sequence of market phases that differ in their asymmetric dynamics and the extent to which the organic price is influenced by the conventional price. Organic wheat prices tend to be increasingly connected to prices of conventional wheat.

Recent results in the theory and applications of CARMA processes

Just as ARMA processes play a central role in the representation of stationary time series with discrete time parameter, \((Y_n)_{n\in \mathbb {Z}}\), CARMA processes play an analogous role in the representation of stationary time series with continuous time parameter, \((Y(t))_{t\in \mathbb {R}}\). Levy-driven CARMA processes permit the modelling of heavy-tailed and asymmetric time series and incorporate both distributional and sample-path information. In this article we provide a review of the basic theory and applications, emphasizing developments which have occurred since the earlier review in Brockwell (2001a, In D. N. Shanbhag and C. R. Rao (Eds.), Handbook of Statistics 19; Stochastic Processes: Theory and Methods (pp. 249–276), Amsterdam: Elsevier).

The Performance Of Nonlinearity Tests On Asymmetric Nonlinear Time Series

This paper examines nonlinearity tests of asymmetric time series in a controlled Monte Carlo setting with the goal of exploring how well existing nonlinear test statistics performed in a variety of typical time series settings. The data generation processes and sample sizes were allowed to vary in a controlled fashion. The study confirmed that none of the test statistics were dominant relative to the others. Also, dependent upon the data generating process, the test statistics exhibited very different powers. Finally, our research showed that the test performance was heavily dependent upon sample size and the degree of asymmetric mechanism.

How Asymmetric is U.S. Stock Market Volatility?

This paper explores differences in the impact of equally large positive and negative surprise return shocks in the aggregate U.S. stock market on: 1) the volatility predictions of asymmetric time series models, 2) implied volatility, and 3) realized volatility. Both asymmetric time series models and implied volatility predict an increase in volatility following large negative surprise returns and ex post realized volatility normally rises as predicted. However, while asymmetric time series models, such as the EGARCH and GJR models, predict an increase in volatility following a large positive return shocks (albeit a much smaller increase than following a negative shock of the same magnitude), both implied and realized volatility generally fall sharply. While asymmetric time-series models predict a decline in volatility following near-zero returns, both implied and realized volatility are normally little changed from levels observed prior to the stable market. Reasons for the differences are explored.

How asymmetric is U.S. stock market volatility?

This paper explores differences in the impact of equally large positive and negative surprise return shocks in the aggregate U.S. stock market on: (1) the volatility predictions of asymmetric time-series models, (2) implied volatility, and (3) realized volatility. Following large negative surprise return shocks, both asymmetric time-series models (such as the EGARCH and GJR models) and implied volatility predict an increase in volatility and, consistent with this, ex post realized volatility normally rises as predicted. Following large positive return shocks, asymmetric time-series models predict an increase in volatility (albeit a much smaller increase than following a negative shock of the same magnitude), but both implied and realized volatilities generally fall sharply. While asymmetric time-series models predict a decline in volatility following near-zero returns, both implied and realized volatility are normally little changed from levels observed prior to the stable market. The reasons for the differences are explored.

An instrumental variable approach for tests of unit roots and seasonal unit roots in asymmetric time series models

The unit root tests of Caner and Hansen (Econometrica 69 (2001) 1555) for asymmetric time series models based on the ordinary least squares estimator (OLSE) have asymptotic null distributions that depend on parameters of asymmetry. We resolve this parameter dependency by adopting the instrumental variable estimation of Shin and Lee (J. Business & Economic Statist. 19 (2001) 233) and the recursive mean adjustment of Shin and So (J. Time Series Anal. 22 (2001b) 595). If the threshold parameter is known, the limiting null distribution of the proposed Wald test does not depend on any nuisance parameter and is chi-squared. If the threshold parameter is unknown and is estimated from data, then under threshold effect, the limiting null distributions of the proposed Wald tests are chi-squared as those for model with known threshold parameter whereas, under no threshold effect, they are chi-squared only conditionally on the weak limit of the estimated threshold parameter. Our Wald tests extend to seasonal models retaining the chi-square asymptotics regardless of the parameter of seasonality, which is not the case of the OLSE-based tests. Moreover, the proposed tests can be modified into one-sided Wald tests which are significantly more powerful than the tests of Caner and Hansen (2001). We apply our method to the monthly US unemployment rate and find some evidences of seasonal unit roots, suggesting nonstationarity rather than the strong stationarity of Caner and Hansen (2001).

Bayesian model selection and parameter estimation for possibly asymmetric and non-stationary time series using a reversible jump Markov chain Monte Carlo approach

A Markov chain Monte Carlo (MCMC) approach, called a reversible jump MCMC, is employed in model selection and parameter estimation for possibly non-stationary and non-linear time series data. The non-linear structure is modelled by the asymmetric momentum threshold autoregressive process (MTAR) of Enders & Granger (1998) or by the asymmetric self-exciting threshold autoregressive process (SETAR) of Tong (1990). The non-stationary and non-linear feature is represented by the MTAR (or SETAR) model in which one ( 𝜌 1 ) of the AR coefficients is greater than one, and the other ( 𝜌 2 ) is smaller than one. The other non-stationary and linear, stationary and nonlinear, and stationary and linear features, represented respectively by ( 𝜌 1 = 𝜌 2 = 1 ), ( 𝜌 1 p 𝜌 2 < 1 ) and ( 𝜌 1 = 𝜌 2 < 1 ), are also considered as possible models. The reversible jump MCMC provides estimates of posterior probabilities for these four different models as well as estimates of the AR coefficients 𝜌 1 and 𝜌 2 . The proposed method is illustrated by analysing six series of US interest rates in terms of model selection, parameter estimation, and forecasting.

Investigating the JPY/DEM-rate: arbitrage opportunities and a case for asymmetry

Deviations from the triangular equality are observed on foreign exchange (FX) markets when the respective rates are sampled at very high frequencies. Within the framework of nonstationary but cointegrated time series the triangular equation may be regarded as a long-run equilibrium. A time invariant and symmetric vector error correction model seems appropriate to explain the evolution of FX-returns depending on recent returns and on lagged deviations from the triangular equality. High frequency FX-rates are typically unequally spaced. Kalman recursions cope with the issue of missing values making (Quasi-) Maximum-Likelihood estimation feasible. The in-sample and out-of-sample forecasting performance of the common vector error correction model is compared to that of alternative specifications including a moving average process, periodic autoregressions, and asymmetric generalizations of the symmetric vector autoregression. For the actual JPY/DEM-rate the employed asymmetric time series models yield superior forecasting results compared to the remaining empirical models. Time dependent processes allowing for intra-day seasonality provide only minor improvements compared to time invariant models of corresponding autoregressive order.

On time-irreversibility and other non-linear features in time series

Time-irreversibility, asymmetry of the distribution, and the occurrence of sudden bursts are considered, amongst others, as non-linear features in time series modeling. The implication is often made that time series showing these features must be analyzed using non-linear models. In contrast, this paper shows that time-irreversible asymmetric time series showing certain types of sudden bursts may be generated by linear models with adequate input sequences. Thus some non-linear time series features may be caused by the pattern in the input sequence rather than by non-linearity in the model. Examples are considered to illustrate the situation.

Asymmetric Time Series and Temporal Aggregation

The detection of nonlinearities could depend on the sampling frequency. Asymmetric monthly series may become symmetric when aggregated to quarterly or annual frequencies. We test against nonlinearity using the nonlinear autoregressive asymmetric moving average (ARasMA) model, which nests the linear ARMA model as a special case. Using monthly, quarterly, and annual Swedish unemployment series, we find support for symmetry/linearity in the annual series but not in the monthly and quarterly series.

Learning and Asymmetric Business Cycles

It is known that a variety of economic time series exhibit asymmetry in the sense that the arrival of a recession is prompt, while the recovery from a recession appears protracted. This paper provides an explanation for the asymmetric movement of economic time series over business cycles by considering learning and information aggregation, given risk aversion on the part of economic agents. A model is constructed in which the underlying state of nature changes according to a symmetric first-order Markov process. Risk-averse agents make capital utilization choices which partially reveal their private information on the underlying state of nature. Risk aversion prevents them from acting promptly on receiving good news, while it encourages them to act quickly on receiving bad news. When this cautious response at the individual level is combined with aggregate noise, an economy-wide asymmetric time series is generated. A numerical simulation is carried out to derive the empirical distribution of movements of such a time series.Journal of Economic LiteratureClassification Numbers: D83, E32, E37.

Are Business Cycles Asymmetric? A Correction

Neftci (1984) proposed a nonparametric test procedure for determining whether business cycles are asymmetric in the sense that contractions are steeper than expansions. He found evidence of this type of asymmetry in postwar quarterly U.S. unemployment variables.' This comment identifies a probable error in Neftci's empirical work that reverses the significance of his results for the unemployment rate, and it suggests that this test may have low power and be sensitive to measurement error.

Asymmetric Time Series

Abstract Asymmetric time series respond to innovations with one of two different rules according to whether the innovation is positive or negative. Quoted industrial prices are apparently such a series. It has been observed that when market conditions change, quoted prices are not revised immediately. This delay operates more strongly against reductions in price quotations than against increases. A statistical model for such asymmetric times series is developed and analyzed. An estimation procedure is given as well as a statistical test of the hypothesis of symmetry versus the alternative of asymmetry. Asymmetric time series models are fit to several economic time series.

Asymmetric Time Series

Asymmetric Time Series