Currently, cryptocurrency has become one of the most traded worldwide financial instruments. The nature of cryptocurrency is complex and is also deemed a perplexing finance problem. This study applied deep learning methods to predict and forecast the Bitcoin (BTC-USD) and Ethereum (ETH-USD) cryptocurrency market-adjusted close prices. Based on root mean square error (RMSE), the hybrid CNN-LSTM model with Attention Mechanism outperformed CNN and LSTM models in predicting the ETH-USD-adjusted close price. In addition, the traditional LSTM model predicted well the BTC-USD-adjusted close price. In forecasting, the hybrid CNN-LSTM model produced better results for both BTC-USD- and ETH-USD-adjusted close prices compared to individual models. Furthermore, the hybrid model performed well at shorter forecasting horizon and loses its forecasting ability when the horizon is long. The result plays a significant role in analyzing the future cryptocurrency market. The traders and financial analysts can easily understand the future market trend using the hybrid model. Thus, this may help traders to easily trade in the complex and challenging cryptocurrency markets.

In the presence of heteroscedastic errors, ordinary least square (OLS) estimators are not efficient and the usual test procedures lead to the improper conclusion. It may also lead to a wider confidence interval which increases the risk of Type-II error. In this situation, the generalised least squares estimator (GLSE) can be used which is not only unbiased but also efficient. In this paper, generalised least square ratio estimator (GLSRE) is proposed and showed that GLSRE is the same as least square ratio estimator (LSRE) under heteroscedasticity. Therefore, a simulation study is carried out to compare the performance of the generalised least square (GLS) estimator with the OLS estimator (OLSE) and the LSR estimator (LSRE) under heteroscedasticity by using total mean squared error (TMSE), mean absolute percentage error (MAPE) and false acceptance rate (FAR) as performance comparison measures. The simulation results show that LSRE outperforms the OLSE and GLSE in case of moderate to severe heteroscedasticity for all sample sizes and in case of weak to mild heteroscedasticity for relatively small samples. GLSE performs better than OLSE and LSRE irrespective of sample size as well as the level of heteroscedasticity in case of the small value of error variance and also in case of weak to mild heteroscedasticity for large samples. Performances of these methods are also compared based on a real-life application.

In recent years, financial market dynamics forecasting has been a focus of economic research. To predict the price indices of stock markets, we developed a hybrid non-stationary model with Elman's Recurrent Neural Networks (ERNN). The proposed model is non-stationary in trend component with lagged variable, average of all past observations and ERNN. This model can capture both linear and non-linear structures in time series. The non-linear structure is capture by ERNN. We derive the expression for the h-step ahead minimum mean square error (MMSE) forecast for the proposed model. Real data sets of stock prices were used to examine the forecasting accuracy of the proposed model and it is found that the proposed approach has the best forecasting accuracy.

Financial market data exhibits various forms of seasonal behaviour. In this work, the problem of seasonal effects on volatility models is discussed. We introduce moving average and autoregressive moving average representation with multiplicative seasonal GARCH errors. Derived an expression for the variance of the m-steps ahead forecast error of MA(q) model with seasonal GARCH errors and also for the squared series Yn+m. We also derived the expressions for the kurtosis of the error distribution. The evidence-based approach is carried out in R software. Real data set is used to illustrate the theoretical results.

The stock markets are among the most volatile market worldwide. The future of these markets is daily affected by political instability and different enacted economic and government policies. Thus, the prediction and forecast of these markets are very important. The Bombay Stock Exchange (BSE) is the oldest stock market in Asia and India. This paper applied deep learning methods to predict the five companies closing prices under BSE. The selected companies based on market capitalization were Reliance Industries Ltd (RELI), TATA Consultancy Services (TCS), HDFC Bank Ltd (HDBK), Infosys Ltd (INFY), and ICICI Bank Ltd (ICBK). Based on Root Mean Square Error (RMSE), the traditional Bidirectional Long Short-Term Model (Bi-LSTM) model predicted well the HDBK closing prices. The Convolution Neural Networks (CNN) outperformed other models in predicting the ICBK, RELI, and INFY. The proposed Hybrid CNN-LSTM model with Bayesian hyperparameter tuning outperformed the CNN and Bi-LSTM models in predicting the TCS close price. Moreover, the hybrid model ranked second in predicting closing prices in all the selected companies. The next 100 days forecast shows high price volatility in the selected companies. In the closing prices forecasts, the hybrid CNN-LSTM model with Bayesian hyperparameter tuning has captured well the trend of the historical data. Additionally, Traders and financial analysts may easily understand the future market trend using the methods. Therefore, the powerful computer and more complex hybrid model may be applied to bring the best performance in terms of accuracy.

The stock markets all over the world have been experiencing fluctuations. These fluctuations are due to some political and administrative decisions. For example, in Tanzania, structural transformations in the economic sectors have been happening time after time, which resulted in fluctuations in the stock market. In this paper, the stock market's volatility was modelled using Markov-Switching GARCH (MS GARCH) and the mixture of GARCH type models. The Bayesian Information Criterion (BIC) was employed to get the best GARCH type models with respective conditional distributions. The GARCH (1, 1) with skewed normal distribution, EGARCH (1, 1) with student's t-distribution and Glosten, Jagannathan and Runkle-GARCH (GJR GARCH) (1, 1) with generalized error distribution selected for further analysis. The study found that the three-state heterogeneous regime MS GARCH and Mixture of the selected GARCH type models provide the best fit and the dynamic feedback between components for the DSEI All-share stock data. The Bayesian Markov Chain Monte Carlo (MCMC) method resulted in an acceptance rate of 28.7%, which lies between 20% and 50% as the requirement of the rule of thumb. The different sample sizes employed on the Bayesian MCMC technique have also proven the fitted model's powerfulness since all acceptance sampler rate falls within the range. Furthermore, the forecasting results for the next 30, 60, 90, and 120 days have shown a continuous fluctuation in the DSEI All-share Stock Index.

The image de-noising is the process to remove the noise from the image naturally corrupted by the noise. The wavelet method is one among the various methods for recovering infinite dimensional objects like curves, densities, images etc. The wavelet techniques are very effective to remove the noise because of its ability to capture the energy of a signal in few energy transform values. The wavelet methods are based on shrinking the wavelet coefficients in the wavelet domain. This paper concentrates on selecting a threshold for wavelet function estimation. A new threshold value is pro-posed to shrink the wavelet coefficients obtained by wavelet decomposition of a noisy image by considering that the sub band coefficients have a generalized Gaussian distribution. The proposed threshold value is based on the power of 2 in the size 2^J x 2^J of the data that can be computed efficiently. The experiment has been conducted on various test images to compare with the established threshold parameters. The result shows that the proposed threshold value removes the noise significantly.

Recent decades have witnessed a series of damages in the financial sector due to the unpleasant movements of prices beyond certain limits. These movements are commonly termed as Financial Bubbles. The formation and burst of a bubble creates huge damage in the field of finance. Hence in order to prevent the market from facing damages, the detection and modeling of financial bubble is very essential. We proposed improved test procedures for detecting financial bubbles by combining the existing Max test and Supremum Augmented Dickey Fuller (SADF) test generally used for detecting bubbles. The performance of proposed test is compared with existing tests via Monte Carlo simulation. It is observed that the proposed test have higher power compared to the existing tests, for detecting collapsible bubble irrespective of window length and collapsible probability. Further the power of proposed test increases as window size decreases. The empirical study of S&P 500 monthly data from January 2006 to December 2010 is carried out to demonstrate the advantages of proposed test procedures over existing tests.

In this paper, the best GARCH type model was selected and compared with the machine learning models, such as Extreme Learning Machine (ELM) and Multilayer Perceptron Neural Network (MLP-NN) models in modeling and forecasting monthly return of the financial market data. The objective of the study was to compare the best model in forecasting New York and Shanghai Stock Composite indices, for the period 01.01.1996 to 01.09.2019. The GJR-GARCH model outperformed other GARCH type models based on the Schwarz Bayesian Information Criterion (SSBIC). The Monte Carlo simulation carried at 1000, 2000, 3000, 4000 and 5000 finite sample (window) sizes to test the consistency of the GJR-GARCH model parameters has shown perfect results between true and the simulated coefficients. Finally, the GJR-GARCH model was compared with the MLPNN and ELM machine learning models. The monthly return forecasting of two years (24 months) was done starting from period 01.09.2019 to 01.09.2021. The study found the MLP-NN model as the best in the modeling and forecasting monthly returns of the two composite stock indices for the two years by considering the Root Mean Square Error (RMSE).The study recommends that further research should focus on the formulation of the hybrid model that combines machine learning and the GJR-GARCH models in forecasting stock market volatility.

Outlier detection and robust estimation are the integral part of data mining and has attracted much attention recently. Generally, the data contain abnormal or extreme values either due to the characteristics of the individual or due to the errors in tabulation, data entry etc. The presence of outliers may badly affect the data modeling and analysis. Analysis of semi-parametric regression with design matrix as the parameter component and covariate as the nonparametric component is considered in this paper. The regression estimate and the cross validation technique can behave very badly in the presence of outliers in the data or when the errors are heavy-tailed. The cross-validation technique to estimate the optimum smoothing parameter will also be affected badly by the presence of outliers. A robust method, which is not influenced by the presence of outliers in the data, is proposed to fit the semi-parametric regression with design matrix as the parameter component and covariate as the nonparametric component. Robust M-kernel weighted local linear regression smoother is used to fit the regression function. The cross-validation technique to estimate the optimum smoothing parameter will also be affected badly by the presence of outliers. A robust cross-validation technique is proposed to estimate the smoothing parameter. The proposed method is useful to compare the treatments after eliminating the covariate effect. The method is illustrated through simulated and field data.

Study of financial bubbles is the extremely important topic in the modern society. Their formation and dramatic bursts are frequently considered to have a massive impact on most of the fields all over the world. Although the literature presents plenty of reviews on bubbles, crashes, and financial c rises, the debate is still open even on whether or not bubbles can persist in modern asset markets. The idea of usage of econometric tests to detect these bubbles are not new and can be classified into 6 groups namely, tests based on the variance, tests based on unit root, tests based on regimes, tests based on Johansen-Ledoit-Sornette model, tests based on durations and tests based on neural networks. This paper presents a review of research in these areas of detection and analysis of the financial bubbles.

The main objective in developing a statistical model is to improve accuracy in forecasting. In this paper, we propose a hybrid non-stationary model for forecasting financial time series. The proposed model is non-stationary in trend with a regressor and a GARCH (1, 1) error. We derive the expression for h-step ahead forecast along with forecast variance. A simulation study is carried out to examine the performance of the proposed model with other existing model. Estimation based on the proposed model performs better than existing models in terms of mean squared error criterion. Real data sets of stock prices were used to examine the forecasting accuracy of the proposed model and it is found that the proposed approach has the best forecasting accuracy.

S tochastic volatility models are considerable interest in empirical finance. We investigate the use of a semiparametric model for estimating volatility.  ARCH models are commonly used to estimate volatility. But there are situations where influence of some exogenous factors on volatility is seen in practice in addition to the ARCH component. In this paper a new model for volatility is presented which includes a regressors (exogenous variable) in addition to ARCH component. The regression part is estimated using nonparametric Kernel smoothing technique and ARCH component is estimated by parametric approach. Further two methods are connected to build a combination forecasting model by combining nonparametric estimator of the regression function and parametric estimator of the ARCH effect. The practical application of the proposed model for forecasting volatility is examined for a sample of gold price returns. The proposed model shows minimum mean square error compared with existing models.

BACKGROUND:With modernization, rapid urbanization and industrialization, the price that the society is paying is tremendous load of "Non-Communicable" diseases, referred to as "Lifestyle Diseases". Coronary artery disease (CAD), one of the lifestyle diseases that manifests at a younger age can have divesting consequences for an individual, the family and society. Prevention of these diseases can be done by studying the risk factors, analyzing and interpreting them using various statistical methods. OBJECTIVE:To determine, using logistic regression the relative contribution of independent variables according to the intensity of their influence (proven by statistical significance) upon the occurrence of values of the dependent cardio vascular risk scores. Additionally, we wanted to assess whether non parametric smoothing of the cardio vascular risk scores can be used as a better statistical method as compared to the existing methods. MATERIALS AND METHODS:The study includes 498 students in the age group of 18-29 years. FINDINGS:Prevalence of over weight (BMI 23-25 kg/m(2)) and obesity (BMI > 25 Kg/m(2)) was found among individuals of 22 years and above. Non smokers had decreased odds (OR = 0.041, CI = 0.015-0.107) and also increase in LDL Cholesterol (OR = 1.05, CI = 1.021-1.055) and BMI (OR = 1.42, CI = 1.244-1.631) were significantly contributing towards the risk of CVD. Localite students had decreased odds of developing CVD in the next 10 years (OR = 0.27, CI = 0.092-0.799) as compared to students residing in hostel or paying guests.

This study is about the development of a robust ridge regression estimator. It is based on weighted ridge MM-estimator (WRMM) and is believed to have potentials in remedying the problems of multicollinearity. The proposed method has been compared with several existing estimators, namely ordinary least squares (OLS), robust regression based on MM estimator, ridge regression (RIDGE), weighted ridge (WRID) and ridge MM-estimator (RMM) using two criteria; biasness and root mean square error (RMSE). The efficiency of the proposed method relative to the alternatives has been examined using MSE ratios. In general, it has been found that the proposed estimator scores well against the five existing estimators when the error term is non-normal. Key-Words: multicollinearity; ridge regression; MM-estimator; robust; weighted ridge MM

A data-driven technique is proposed to estimate the trend and relative growth rate of time series data. The method is based on the local linear regression smoother and the only assumption about the form of the trend and growth rate function is that they are smooth functions of time. We also extended the method for handling sudden shifts or changes in the trend or growth rate functions by adding dummy variables for the jumps. Simulation studies are carried out to see the performance of the proposed procedure. The method is applied to study the trend and growth rate of wheat production in India from 1951–2005.

Estimators for jump location curve and jump size function of a two dimensional jump regression function (jump regression surface) are proposed. The estimators are obtained by fitting kernel weighted least squares regression based on the observations in the four quadrants of a neighborhood of a given point. The proposed procedure can be used in the case of jump in the regression surface and/or in its slope (jump in the partial derivatives). The limiting distributions and the asymptotic properties of the estimators are investigated. The procedure is illustrated through a simulation study.

This paper deals with the estimation of location and size of jump in the equally spaced fixed design nonparametric regression function itself and/or in its first derivative. The estimators are based on the analysis of residuals from the nonparametric kernel regression estimate. The proposed estimators are used to accommodate discontinuities in the nonparametric regression function estimate. The method is illustrated through simulation study.