Risk Modeling, Return Forecasting, and Optimal Portfolio Selection

A Study of Return, Liquidity of Sectoral Indices, Market Index Return of Indian Financial Market (BSE)

The purpose of this study is to identify the key macroeconomic variables that affected stock price fluctuations in Amman Stock Exchange during the period 1980-2018. Using Augmented Dickey-fuller (ADF) test, it was found that the variables did not have the same degree of integration. According to Breusch-Pagan-Godfrey test, the residuals violated the constant variance assumption under Ordinary Least Square (OLS) model. Therefore, the study employed Generalized Autoregressive Conditional Heteroskedasticity (GARCH) methodology to analyze the model after taking the first difference of natural logarithm for all variables to be stationary at the same level and to show the fluctuation in the variables. It was found that fluctuations in portfolio investment and in industrial production index are statically significant to lead fluctuations in the stock price index in Amman Stock Exchange and they follow the same direction, whereas fluctuations in real effective exchange rate, real interest rate, and Brent crude oil prices were statically significant to lead fluctuations in the stock price index but in the opposite direction.

This paper uses the prediction method of time series analysis to fit and predict the stock daily logarithmic return series of the four major banks. The ARMA model and the GARCH model are constructed and compared empirically. The results show that the GARCH model is better than that of the ARMA model in the fitting effect. In the prediction effect, The ARMA model is the best, followed by the GARCH model.

Based on the time series analysis method, this article develops a Bayesian method of detecting and repairing the cycle slips in the GNSS carrier-phase data. Firstly, this article analyses the characteristics of the cycle slips in the GNSS carrier-phase observations and establishes the relationships between the cycle slips and the additive outliers (AOs) in the stationary time series. When the ARMA (autoregressive moving-average) model is used to fit the stationary time series obtained by differencing the GNSS carrier-phase observations, the detection of cycle slips in the GNSS carrier-phase observations can be transformed to the detection of AOs in the ARMA model. Then, this article proposes a Bayesian method of detecting the AOs in the ARMA model, and the implementation of detecting the cycle slips in the GNSS carrier-phase observations is also developed. Finally, the new Bayesian method of detecting the cycle slips is used to the real GNSS carrier-phase data. From the comparison among the Bayesian method, the high-order differences method and ionospheric residual method, we can find that the Bayesian method has a better detection efficiency for several kinds of cycle slips in the GNSS carrier-phase observations than other methods.

The quarterly electricity consumption curve shows certain regularity due to factors such as temperature and holidays. The ARMA(Autoregressive Moving Average) model has a good fitting ability for such time series, but the quarterly electricity consumption is also affected by economic growth. It is an ascending time series, which is a nonstationary time series. It cannot be directly predicted by ARMA model. Therefore, it is necessary to make finite difference processing to the original time series to stationary time series. The original time series is suitable for ARIMA(Autoregressive Integrated Moving Average) model. Any prediction model can not avoid the generation of residuals. The K-means clustering algorithm is used to divide the residual sequence state. By exploring the relationship between states at different moments, the transition matrix is established to predict the probability distribution of the residual state at the next moment. The predicted state is restored to the residual prediction value, and the prediction of the residual is completed to implement the correction of the original prediction value. That is, by predicting the residual by establishing a Markov model, the predicted value of the ARIMA model is corrected, and the prediction accuracy is improved.

The background of this research is related to the boycott of companies that support Israel, which affects the composition of stock portfolios on the American Stock Exchange. The focus of this research is on key companies such as Apple (AAPL), Starbucks (SBUX), Amazon (AMZN), Google (GOOGL), and McDonald's (MCD). The problem to be solved is the identification of changes in optimal asset allocation in investment portfolios before and after the boycott. Using a mean-variance portfolio optimization model, historical stock price data is analyzed to model the transformation of portfolio composition as well as the associated risk level. The purpose of this study is to provide an in-depth understanding of the impact of the boycott on the investment portfolio structure of related companies on the American Stock Exchange. The result of this research is that there is a change in the allocation of assets held against stocks before the boycott and after the boycott. This research is expected to provide useful insights for investors, financial analysts, and other stakeholders in managing their investment portfolios, especially in anticipating and adjusting investment strategies amid dynamic changes in the stock market.

Time series events are counted within time intervals usually for convenience and practical reasons. Time series data involving counts frequently follows Poison distribution. Integrated Autoregressive Moving Average (ARIMA) models were studied on simulated Poison data of different parameter and sample sizes. These models were used to capture Poison data with different phenomena. Data set were simulated from Poison process with ARIMA (p, d, q) were then fitted to the simulated data so as to examine the effect of the changes in parameter value of the Poison on the models’ performance across the sample size. Thereafter, the same models were used to fit and forecast the daily Covid-19 data, confirmed cases from inception to February 2023. It was concluded that ARIMA (2, 1, 2) and ARIMA (1, 1, 1) are obviously the best Models at different sample sizes respectively. Based on the Covid-19 analysis, the estimated coefficient values of all ARIMA (p,d,q) strictly conforms to the bounds of the parameter between -1 and 1 and this had made the model to be stationary comparing the ARIMA models in terms of the AIC, BIC and MSE. It is clearly preferred ARIMA (1, 0, 2) to other models since their estimated AIC, BIC and MSE are smaller as compared to other models. The forecast is quite accurate, and hereby confirms what was expected. It seems that ARIMA (1, 0, 2) does a very good job in capturing the dynamic nature of the data and forecasting. It was observed that the confirmed cases increase, and then keep stationary throughout the future times.

The study proposes to include the financial analysis (FA) in optimal portfolio selection. The role of FA in investment decisions is well recognized. While comparing two stocks on FA of their companies it is important to have both drawn from the same sector of economy. This reason motivated us to propose a sectoral portfolio optimization (SPO) which, instead of looking to optimize among all stocks together, focuses on optimizing stocks within each sector on the basis of FA. These stocks are then pooled together and an optimal portfolio is formed from them with their FA weights and mean returns. In context of FA, the four financial ratios included in present study are return on asset (profitable ratio), debt-assets ratio (solvency ratio), current ratio (liquidity ratio), and price-to-earning ratio (valuation ratio). The risk in a portfolio is quantified using the second order stochastic dominance and to this effect constraints are added in the selection process to generate optimal portfolios for rational risk averse investors. The performance of the optimal portfolios from the proposed model is tested against the portfolios from the traditional second order stochastic dominance model [named (SSDP) in this work], the benchmark index and four 5-star rated mutual funds of India from diversified equity. The out-of-sample analysis is carried on mean returns, Sharpe ratio, Sortino ratio, and also their ability to dominate the benchmark index in almost second order stochastic dominance sense over the tolerable violation regions. The stock price data for the period April 2004 to November 2014 of S&P BSE 500 index is used for testing the models. The optimal portfolios generated from the SPO perform better than the portfolios generated from the (SSDP), the benchmark index and the MFs, indicating effectiveness of FA in SPO framework.

Autoregressive moving average (ARMA) models are useful statistical tools to examine the dynamical characteristics of ecological time-series data. Here, we illustrate the utility and challenges of applying ARMA (p,q) models, where p is the dimension of the autoregressive component of the model, and q is the dimension of the moving average component. We focus on parameter estimation and model selection, comparing both maximum likelihood (ML) and restricted maximum likelihood (REML) parameter estimation. While REML estimation performs better (has less bias) than ML estimation for ARMA (p,q) models with p = 1 (as has been found previously), for models with p > 1 the performance of the estimators is complicated by multimodal likelihood functions. The resulting difficulties in estimation lead to our recommendation that likelihood functions be routinely investigated when applying ARMA (p,q) models. To aid this investigation, we provide MATLAB and R code for the ML and REML likelihood functions. We further explore the consequences of measurement error, showing how it can be explicitly and implicitly incorporated into estimation. In addition to parameter estimation, we also examine model selection for identifying the correct model dimensions (p and q). Finally, we estimate the characteristic return rate of the stochastic process to its stationary distribution, a quantity that describes a key property of population dynamics, and investigate bias that results from both estimation and model selection. While fitting ARMA models to ecological time series with complex dynamics has challenges, these challenges can be surmounted, making ARMA a useful and broadly applicable approach.

The seemingly complex nature of river flow and the significant variability it exhibits in both time and space, have largely led to the development and application of the stochastic process concept for its modelling, forecasting, and other ancillary purposes. Towards this end, in this study, attempt was made at stochastic modelling of the daily streamflow process of the Benue River. In this regard, Autoregressive Moving Average (ARMA) models and its derivative, the Periodic Autoregressive (PAR) model were developed and used for forecasting. Comparative forecast performances of the different models indicate that despite the shortcomings associated with univariate time series, reliable forecasts can be obtained for lead times, 1 to 5 day-ahead. The forecast results also showed that the traditional ARMA model could not robustly simulate high flow regimes unlike the periodic AR (PAR). Thus, for proper understanding of the dynamics of the river flow and its management, especially, flood defense, in the light of this study, the traditional ARMA models may not be suitable since they do not allow for real-time appraisal. To account for seasonal variations, PAR models should be used in forecasting the streamflow processes of the Benue River. However, since almost all mechanisms involved in the river flow processes present some degree of nonlinearity thus, how appropriate the stochastic process might be for every flow series may be called to question.

An autoregressive moving average (ARMA) is a time series model that is applied in everyday life for pattern recognition and forecasting. The ARMA model contains a noise which is assumed to have a specific distribution. The noise is often considered to have a Gaussian distribution. However in applications, the noise is sometimes found that does not have a Gaussian distribution. The first objective is to develop the ARMA model in which noise has a Laplacian distribution. The second objective is to estimate the parameters of the ARMA model. The ARMA model parameters include ARMA model orders, ARMA model coefficients, and noise variance. The parameter estimation of the ARMA model is carried out in the Bayesian framework. In the Bayesian framework, the ARMA model parameters are treated as a variable that has a prior distribution. The prior distribution for the ARMA model parameters is combined with the likelihood function for the data to get the posterior distribution for the parameter. The posterior distribution for parameters has a complex form so that the Bayes estimator cannot be determined analytically. The reversible jump Markov chain Monte Carlo (MCMC) algorithm was adopted to determine the Bayes estimator. The first result, the ARMA model can be developed by assuming Laplacian distribution noise. The second result, the performance of the algorithm was tested using simulation studies. The simulation shows that the reversible jump MCMC algorithm can estimate the parameters of the ARMA model correctly.

Objective To establish an autoregression moving average (ARMA) model for predicting general traffic accidents and analyzing distributional difference on time series and frequency of common traffic accident so as to provide certain basis for a prediction model with better stability and accuracy. Methods The data of road traffic accidents in one newly developed zone of Chongqing in 2000-2005 were collected. The monthly distribution regularity of road traffic accidents was analyzed with descriptive epidemiologic method. ARMA model was set up for retrospective and prospective prediction. The predicted data were compared. Results Based on the characteristics of monthly distribution, the frequency of general traffic accidents in this area showed a cyclic fashion. The frequency of general traffic accidents predicted by ARMA model had over 80% of coincidence with the actual value. Conclusion The ARMA model can be used to predict the frequency of general traffic accidents, with better accuracy of short-term prediction than the long-term prediction. Key words: Accidents, traffic; ARMA; Time series; Prediction model

The merits of the modelling philosophy of Box \& Jenkins (1970) are illustrated with a summary of our recent work on seasonal river flow forecasting. Specifically, this work demonstrates that the principle of parsimony, which has been questioned by several authors recently, is helpful in selecting the best model for forecasting seasonal river flow. Our work also demonstrates the importance of model adequacy. An adequate model for seasonal river flow must incorporate seasonal periodic correlation. The usual autoregressive-moving average (ARMA) and seasonal ARMA models are not adequate in this respect for seasonal river flow time series. A new diagnostic check, for detecting periodic correlation in fitted ARMA models is developed in this paper. This diagnostic check is recommended for routine use when fitting seasonal ARMA models. It is shown that this diagnostic check indicates that many seasonal economic time series also exhibit periodic correlation. Since the standard forecasting methods are inadequate on this account, it can be concluded that in many cases, the forecasts produced are sub-optimal. Finally, a limitation of the arbitrary combination of forecasts is also illustrated. Combining forecasts from an adequate parsimonious model with an inadequate model did not improve the forecasts whereas combining the two forecasts of two inadequate models did yield an improvement in forecasting performance. These findings also support the model building philosophy of Box \& Jenkins. The non-intuitive findings of Newbold \& Granger (1974) and Winkler \& Makridakis (1983) that the apparent arbitrary combination of forecasts from similar models will lead to forecasting performance is not supported by our case study with river flow forecasting.

Long memory time series and short term forecasts

Optimal Portfolio Selection in Ex Ante Stock Price Bubble and Furthermore Bubble Burst Scenario from Dhaka Stock Exchange with Relevance to Sharpe’s Single Index Model