Single step estimation of ARMA roots for non-fundamental nonstationary fractional models

We propose a single step estimator for the autoregressive and moving-average roots (without imposing causality or invertibility restrictions) of a nonstationary Fractional ARMA process. These estimators employ an efficient tapering procedure, which allows for a long memory component in the process, but avoid estimating the nonstationarity component, which can be stochastic and/or deterministic. After selecting automatically the order of the model, we robustly estimate the AR and MA roots for trading volume for the thirty stocks in the Dow Jones Industrial Average Index in the last decade. Two empirical results are found. First, there is strong evidence that stock market trading volume exhibits non-fundamentalness. Second, non-causality is more common than non-invertibility.

New estimation method for periodic autoregressive time series of order 1 with additive noise

The periodic behavior of real data can be manifested in the time series or in its characteristics. One of the characteristics that often manifests the periodic behavior is the sample autocovariance function. In this case, the periodically correlated (PC) behavior is considered. One of the main models that exhibits PC property is the periodic autoregressive (PARMA) model that is considered as the generalization of the classical autoregressive moving average (ARMA) process. However, when one considers the real data, practically the observed trajectory corresponds to the “pure” model with the additional noise which is a result of the noise of the measurement device or other external forces. Thus, in this paper we consider the model that is a sum of the periodic autoregressive (PAR) time series and the additive noise with finite-variance distribution. We present the main properties of the considered model indicating its PC property. One of the main goals of this paper is to introduce the new estimation method for the considered model’s parameters. The novel algorithm takes under consideration the additive noise in the model and can be considered as the modification of the classical Yule–Walker algorithm that utilizes the autocovariance function. Here, we propose two versions of the new method, namely the classical and the robust ones. The effectiveness of the proposed methodology is verified by Monte Carlo simulations. The comparison with the classical Yule–Walker method is presented. The approach proposed in this paper is universal and can be applied to any finite-variance models with the additive noise.

Value-at-Risk and Expected Shortfall approaches for option premiums and the probability of default estimation based on ARMA models

The need to address the issue of risk management has given rise to a number of models for estimation the probability of default, as well as a special tool that allows to sell credit risk – a credit default swap (CDS). From the moment it appeared in 1994 until the crisis of 2008, that the CDS market was actively growing, and then sharply contracted. Currently, there is practically no CDS market in emerging economies (including Russia). This article is to improve the existing CDS valuation models by using discrete-time models that allow for more accurate assessment and forecasting of the selected asset dynamics, as well as new option pricing models that take into account the degree of risk acceptance by the option seller. This article is devoted to parametric discrete-time option pricing models that provide more accurate results than the traditional Black-Scholes continuous-time model. Improvement in the quality of assessment is achieved due to three factors: a more detailed consideration of the properties of the time series of the underlying asset (in particular, autocorrelation and heavy tails), the choice of the optimal number of parameters and the use of Value-at-Risk approach. As a result of the study, expressions were obtained for the premiums of European put and call options for a given level of risk under the assumption that the return on the underlying asset follows a stationary ARMA process with normal or Student's errors, as well as an expression for the credit spread under similar assumptions. The simplicity of the ARMA process underlying the model is a compromise between the complexity of model calibration and the quality of describing the dynamics of assets in the stock market. This approach allows to take into account both discreteness in asset pricing and take into account the current structure and the presence of interconnections for the time series of the asset under consideration (as opposed to the Black–Scholes model), which potentially allows better portfolio management in the stock market.

Significance and Causality in Continuous Wavelet and Wavelet Coherence Spectra Applied to Hydrological Time Series

Wavelet transform, wavelet spectra, and coherence are popular tools for studying fluctuations in time series in the form of a bidimensional time and scale representation. We discuss two aspects of wavelet analysis—namely the significance and stochastic/deterministic character of the wavelet spectra. Real-time series of discharge, sodium, and sulfate concentrations in the alpine Rhône River, Switzerland, are used to illustrate these issues. First, the consequences of using an arbitrary stochastic process (usually, AR (1)) instead of the best-fitted general ARMA process in the evaluation of the significance of wavelet spectra are analyzed. Using a general ARMA instead of AR (1) decreases the significance level of the differences in wavelet power spectra (WPS) of ARMA and AR (1) compared to the WPS of the time series in all cases studied and points to a possible systematic overestimation of significance in many published studies. Besides, the significance of particular patches in the spectra is affected by multiple testing. A (conservative) way to circumvent this problem, using global wavelet spectra and global coherence spectra, is evaluated. Finally, we discuss the issue of causality and investigated it in the three measured time series mentioned above. Even if the use of the best fitted ARMA pointed to no deterministic features being present in the corrected series studied (i.e., stochastic processes are dominant in the three data series), coherence spectra between variables allowed to reveal cause-effect relationships between two “coherent” variables and/or the existence of a common effect on both variables. Therefore, such type of analysis provides a useful tool to better understand data causal relationships.

ARMA model for short-term forecasting of solar potential: application to a horizontal surface of Dakar site

This paper presents a model for short-term forecasting of solar potential on a horizontal surface. This study is carried out in to the context of valuing of energy production from photovoltaic solar sources in the Sahelian zone. In this study, Autoregressive Moving Average (ARMA) process is applied to predict global solar potential upon 24 hours ahead. The ARMA (p, q) is based on finding optimum parameters p and q to better fit considered variable (sunshine). Data used for the model calibrating are measured at the station of Ecole Supérieure Polytechnique of Dakar. Records are hourly and range from October 2016 to September 2017. The choice of this model is justified by its robustness and its applicability on several scales through the world. Simulation is done using the RStudio software. The Akaike information criterion shows that ARMA (29, 0) gives the best representation of the data. We then applied a white noise test to validate the process. It confirms that the noise is of white type with zero mean, variance of 1.252 and P-value of about 26% for a significant level of 5%.Verification of the model is doneby analyzing some statistical performance criteria such the RMSE =0.629 (root mean squared error), the R² = 0.963 (Coefficient of determination), the MAE=0.528 (Mean Absolut Error) and the MBE=0.012 (Mean BiasError). Statistics criteria show that the ARMA (29,0) is reliable; then, can help to improve planning of photovoltaic solar power plants production in the Sahelian zone.

Semiparametric estimation of the canonical permanent‐transitory model of earnings dynamics

This paper presents identification and estimation results for a flexible state space model. Our modification of the canonical model allows the permanent component to follow a unit root process and the transitory component to follow a semiparametric model of a higher‐order autoregressive‐moving‐average (ARMA) process. Using panel data of observed earnings, we establish identification of the nonparametric joint distributions for each of the permanent and transitory components over time. We apply the identification and estimation method to the earnings dynamics of U.S. men using the Panel Survey of Income Dynamics (PSID). The results show that the marginal distributions of permanent and transitory earnings components are more dispersed, more skewed, and have fatter tails than the normal and that earnings mobility is much lower than for the normal. We also find strong evidence for the existence of higher‐order ARMA processes in the transitory component, which lead to much different estimates of the distributions of and earnings mobility in the permanent component, implying that misspecification of the process for transitory earnings can affect estimated distributions of the permanent component and estimated earnings dynamics of that component. Thus our flexible model implies earnings dynamics for U.S. men different from much of the prior literature.