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The purpose of this paper is to propose an improved method which can shorten the calculation time and improve the calculation efficiency under the premise of ensuring the calculation accuracy for calculating the response of dynamic systems with periodic time-varying characteristics.

An improved method is proposed based on Runge–Kutta method according to the composition characteristics of the state space matrix and the external load vector formed by the reduction of the dynamic equation of the periodic time-varying system. The recursive scheme of the holistic matrix of the system using the Runge–Kutta method is improved to be the sub-block matrix that is divided into the upper and lower parts to reduce the calculation steps and the occupied computer memory.

The calculation time consumption is reduced to a certain extent about 10–35% by changing the synthesis method of the time-varying matrix of the dynamics system, and the method proposed of paper consumes 43–75% less calculation time in total than the original Runge–Kutta method without affecting the calculation accuracy. When the ode45 command that implements the Runge–Kutta method in the MATLAB software used to solve the system dynamics equation include the time variable which cannot provide its specific analytic function form, so the time variable value corresponding to the solution time needs to be determined by the interpolation method, which causes the calculation efficiency of the ode45 command to be substantially reduced.

The proposed method can be applied to solve dynamic systems with periodic time-varying characteristics, and can consume less calculation time than the original Runge–Kutta method without affecting the calculation accuracy, especially the superiority of the improved method of this paper can be better demonstrated when the degree of freedom of the periodic time-varying dynamics system is greater.

The purpose of this paper is to examine the nature and extent of instability of capital asset pricing model (CAPM) beta in a small emerging capital market.

Inter‐period as well as intra beta instability are examined. Inter‐period instability is examined by Mann‐Whitney z‐scores and Blume's regressions. Intra‐period beta instability is examined using Bruesch‐Pagan LM test and Chow break point test. Robustness tests are performed applying time‐varying parameter models.

Beta instability increases with increase in holding (sample) periods. There is evidence of inter‐period as well as intra‐period beta instability. Analysis of the full eight‐year interval reveals a very high incidence of beta instability, namely, about 26 per cent of the individual stocks tested and about 31 per cent of individual stocks have structural break. The extent of beta instability does not significantly decline when corrected for non‐synchronous trading and thin trading as represented by Dimson beta. However, the extent of beta instability is similar to that of developed market. Time‐varying parameter model under Kalman filter approach using AR(1) specification performs better than any other models in terms of in‐sample forecast errors. Dominance of AR(1) approach suggests that stock betas in DSE are time varying, and shocks to the conditional beta have some degree of persistence which ultimately reverts to a mean. This result is in contrast to the findings of Faff et al. revealing the dominance of Random Walk specification in Australian market, suggesting that shocks to stock beta in Australian market persist indefinitely into the future. These contrasting findings may indicate that beta instability in different markets and for different stocks in the same market are of different nature and different models may be suitable for different markets and different stocks in the same market in capturing the time‐varying nature of beta coefficients.

This study covers only 110 stocks of Dhaka Stock Exchange. It can be extended to include more stocks. The study can also be done in other developing markets.

While the issues of beta instability have been extensively explored for developed markets, evidence for emerging markets is less readily available. The present study contributes to the emerging market literature on beta instability by investigating the extent of beta instability and its time‐varying properties in Dhaka Stock Exchange (DSE), Bangladesh. Understanding the systematic risk behaviour of individual stocks in DSE is important for both local and international investors. With the saturation of investment opportunities in developed markets due to their high integration, and with the enhanced deregulation and liberalization of emerging economies, emerging financial markets like DSE provide suitable and a relatively safe investment environment for international investors and fund managers seeking global diversification for better risk‐return trade‐offs. When most of the world markets declined during the recent global financial crisis, stock prices in DSE experienced a continuous rise. This makes it more interesting as an emerging market to study beta instability.

This paper presents a new adaptive technique for forecasting the Yen/U.S. Dollar exchange rate. The proposed method assumes a time-varying model to describe the evolution of the exchange rate. Weekly predictions of the Yen/U.S. Dollar rate are dominated by weekly announcements of unexpected changes in the relative unemployment claims between the U.S. and Japan. Monthly predictions are more sensitive to monthly releases of the difference between the expected and announced value of the National Association of Purchasing Managers index. The predictive results of the proposed method are found more accurate than that of conventional ARMA techniques.

Existing empirical evidence suggests that episodes of financial stress (crises) can act as driver of growth of inequality. Consequently, in this study, the authors explore the time-varying predictive power of an index of financial stress for growth in income (and consumption) inequality in the UK. The authors focus on the UK since income (and consumption) inequality data are available at a high frequency, i.e. on a quarterly basis for over 40 years (June, 1975 to March, 2016).

The authors use Wang and Rossi's approach to analyze the time-varying impact of financial stress on inequality. Hence, the method provides a more appropriate inference of the effect rather than a constant parameter Granger causality method. Besides, understandably, the time-varying approach helps to depict the time-variation in the strength of predictability of financial stress on inequality.

This study’s findings point that financial distress correspond to subsequent increases in inequality, with the index of financial stress containing important information in predicting growth in income inequality for both in and out-of-sample periods. Interestingly, the strength of the in-sample predictive power is high post the period of the global financial crisis, as was observed in the early part of the sample. The authors believe these findings highlight an important role of financial stress for inequality – an area of investigation that has in general remained untouched.

Accurate prediction of inequality at a higher frequency should be more relevant to policymakers in designing appropriate policies to circumvent the wide-ranging negative impacts of inequality, compared to when predictions are only available at the lower annual frequency.

This chapter proposes a vector autoregressive VAR model with structural shocks (SVAR) that are identified using sign restrictions, and whose distribution is subject to time varying skewness. The authors also present an efficient Bayesian algorithm to estimate the model. The model allows tracking joint asymmetric risks to macroeconomic variables included in the SVAR, and provides a structural narrative to the evolution of those risks. When faced with euro area data, our estimation suggests that there has been a significant variation in the skewness of demand, supply and monetary policy shocks. Such variation can explain a significant proportion of the joint dynamics of real GDP growth and inflation, and also generates important asymmetric tail risks in those macroeconomic variables. Finally, compared to the literature on growth- and inflation-at-risk, the authors find that financial stress indicators are not enough to explain all the macroeconomic tail risks.

Discusses recursive estimation techniques which can be used to update or revise estimates of the parameters of an economic model to account for new data. Such methods admit the possibility of proceeding with the gathering of observed data until a specified accuracy of the parameters is achieved or if the economic processes are time‐varying the parameters can be tracked. Recursive methods can also be used for adaptive learning, forecasting and control. Examines both single equation ‐ static as well as dynamic ‐ economic models.

Farmer exchange rate (FER) is the ratio between a farmer's income and expenditure and is also an indicator of farmers’ welfare. There is little research regarding its use in risk modeling in crop insurance. This study seeks to propose a design for a household margin insurance scheme of the agricultural sector based on FER.

This research employs various risk modeling concepts, i.e. value at risk, loss models and premium calculation, to construct the proposed model. The standard linear, static and time-varying copula models are used to identify the dependency between variables involved in calculating FER.

First, FER can be considered as the primary variable for risk modeling in agricultural household margin insurance because it demonstrates farmers’ financial ability. Second, temporal dependence estimated using the time-varying copula can minimize errors, reduce the premium rate and result in a tighter guarantee's level of security.

This research extends the previous similar studies related to the use of index ratio in margin insurance loss modeling. Its authenticity is in the use of FER, which represents the farmers' trading capability. FER determines farmers’ losses by considering two aspects: the farmers’ income rate and their ability to fulfill their life and farming needs. Also, originality exists in the use of the time-varying copulas in identifying the dependence of the indices involved in calculating FER.

The purpose of this paper is to introduce a generalization of the time-varying correlation elliptical copula models and to analyse its impact on the tail risk of a portfolio of foreign currencies during the Covid-19 pandemic.

The authors consider a multivariate time series model where marginal dynamics are driven by an autoregressive moving average (ARMA)–Glosten-Jagannathan-Runkle–generalized autoregressive conditional heteroscedastic (GARCH) model, and the dependence structure among the residuals is given by an elliptical copula function. The correlation coefficient follows an autoregressive equation where the autoregressive coefficient is a function of the past values of the correlation. The model is applied to a portfolio of a couple of exchange rates, specifically US dollar–Japanese Yen and US dollar–Euro and compared with two alternative specifications of the correlation coefficient: constant and with autoregressive dynamics.

The use of the new model results in a more conservative evaluation of the tail risk of the portfolio measured by the value-at-risk and the expected shortfall suggesting a more prudential capital allocation policy.

The main contribution of the paper consists in the introduction of a time-varying correlation model where the past values of the correlation coefficient impact on the autoregressive structure.

Due to the non‐stationarity of vibration signals resulting from either varying operating conditions or natural deterioration of machinery, both the frequency components and their magnitudes vary with time. However, little research has been done on the parameter estimation of time‐varying multivariate time series models based on adaptive filtering theory for condition‐based maintenance purposes. This paper proposes a state‐space model of non‐stationary multivariate vibration signals for the online estimation of the state of rotating machinery using a modified extended Kalman filtering algorithm and spectral analysis in the time‐frequency domain. Adaptability and spectral resolution capability of the model have been tested by using simulated vibration signal with abrupt changes and time‐varying spectral content. The implementation of this model to detect machinery deterioration under varying operating conditions for condition‐based maintenance purposes has been conducted by using real gearbox vibration monitoring signals. Experimental results demonstrate that the proposed model is able to quickly detect the actual state of the rotating machinery even under highly non‐stationary conditions with abrupt changes and yield accurate spectral information for an early warning of incipient fault in rotating machinery diagnosis. This is achieved through combination with a change detection statistic in bi‐spectral domain.

We examine the behavior of the Russian stock market as one of the leading indices of economic health, reflecting investors’ expectations about future returns. The sample period includes the global financial crisis, a recovering period, and the recent crisis in the Russian economy 2014–2015.

We assume that the Russian stock market strongly depends on the global market, but the market is not fully integrated. This chapter investigates whether specific risk factors such as high dependence of the Russian economy on oil prices and currency volatility are priced in the Russian stock market, using International CAPM with time-variant parameters and conditional heteroskedasticity. The results show that the global financial crisis has had a profound negative impact on the Russian market, and that the expected return and liquidity has declined. The risk of investing in the Russian market is estimated as higher than in the developed market and even in other emerging markets after the global recession. We find that oil price exposure and currency risk to be priced in the Russian stock market and indicate that international investors require higher compensation for bearing these risks. The price of the currency risk has decreased since the implementation of the floating exchange rate regime by the Central Bank of Russia in 2014, but still significant.

Some opportunities to overcome the present stagnation and drive for a sustainable development are discussed.