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.

Alternate Entropy Computations by Applying Recurrence Matrix Masking

In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined within these confining borders can be influenced more or less by truncation effects depending upon the system under evaluation. In this study, the question being asked is what if the boundary borders were tilted, what would be the effect on all recurrence variables? This question was prompted by the observation that line entropy values are maximized for highly periodic systems in which the infinitely long line elements are truncated to different unique lengths. However, by redefining the recurrence plot area to a 45-degree tilted box within the triangular area, the diagonal lines would consequently be truncated to identical lengths. Such masking would minimize the line entropy to 0.000 bits/bin. However, what new truncation influences would be imposed on the other recurrence variables? This question is examined by comparing recurrence variables computed with the triangular recurrence area versus boxed recurrence area. Examples include the logistic equation (mathematical series), the Dow Jones Industrial Average over a decade (real-word data), and a square wave pulse (toy series). Good agreement among the variables in terms of timing and amplitude was found for most, but not all variables. These important results are discussed.

Sunspots, GDP, and the Stock Market

A correlation has been observed between the US GDP and the number of sunspots as well as between the Dow Jones Industrial Average and the number of sunspots. The data cover 80 years of history. The observed correlations permit forecasts for the GDP and for the stock market in America with a future horizon of 10 years. Both being above their long-term trend they are forecasted to go over a peak around Jun-2008.

The Effect of Dow Jones Industrial Average, Nikkei 225 Index and Shanghai Composite Index on IDX Composite Index

The purpose of this study is to determine the effect of the Dow Jones Industrial Average, the Nikkei 225 index and the Shanghai Composite Index on IDX Composite Index. The population and samples used in this study are the Dow Jones Industrial Average, the Nikkei 225 Index, the Shanghai Composite Index, and the IDX Composite Index for the period January 2 to April 30, 2020. The type of data is secondary data. The analysis method used are classical assumption test which consists of normality test, multicollinearity test and autocorrelation test and multiple regression analysis. Hypothesis test using F-test and t-test. The results of the study found that the Dow Jones Industrial Average and the Nikkie 225 index partially affected the IDX Composite Index positively and significantly. The Shanghai Composite Index has no significant effect on IDX Composite Index.

Stock Markets in Changing Times

The impact of COVID-19 on the stock markets of US, UK, and India has been analyzed. Daily market returns of the stock indices (Dow Jones Industrial Average, FTSE-100, Nifty 50 Index, and Nifty Bank Index) have been examined using paired t-test for 40 days before and after the reporting of the first case. Index performance has also been investigated for the quarter ending June 2020 along with comparative performance analysis of the indices with Nifty Bank Index. The results showed that markets have borne substantially negative returns, but they are not statistically significant. This indicates the resilience of these markets to restore to previous index levels after taking a short-term hit. This paper adds value to the literature by acting as a resource for academia as well as industry by spelling out changes in markets during this pandemic and supporting evidence from Indian banks that are catalysts of growth for businesses in uncertain times.

Modelling and forecasting stock volatility and return: a new approach based on quantile Rogers–Satchell volatility measure with asymmetric bilinear CARR model

This paper proposes quantile Rogers–Satchell (QRS) measure to ensure robustness to intraday extreme prices. We add an efficient term to correct the downward bias of Rogers–Satchell (RS) measure and provide scaling factors for different interquantile range levels to ensure unbiasedness of QRS. Simulation studies confirm the efficiency of QRS measure relative to the intraday squared returns and RS measures in the presence of extreme prices. To smooth out noises, QRS measures are fitted to the CARR model with different asymmetric mean functions and error distributions. By comparing to two realised volatility measures as proxies for the unobserved true volatility, results from Standard and Poor 500 and Dow Jones Industrial Average indices show that QRS estimates using asymmetric bilinear mean function provide the best in-sample model fit based on two robust loss functions with heavier penalty for under-prediction. These fitted volatilities are then incorporated into return models to capture the heteroskedasticity of returns. Model with a constant mean, Student-t errors and QRS estimates gives the best in-sample fit. Different value-at-risk (VaR) and conditional VaR forecasts are provided based on this best return model. Performance measures including Kupiec test for VaRs are evaluated to confirm the accuracy of the VaR forecasts.