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We develop a multivariate functional autoregressive model (MFAR), which captures the cross-correlation among multiple functional time series and thus improves forecast accuracy. We estimate the parameters under the Bayesian dynamic linear models (DLM) framework. In order to capture Granger causality from one FAR series to another we employ Bayes Factor. Motivated by the broad application of functional data in finance, we investigate the causality between the yield curves of two countries. Furthermore, we illustrate a climatology example, examining whether the weather conditions Granger cause pollutant daily levels in a city.

Historical daily data for eleven years of the fifty constituent stocks of the NIFTY index traded on the National Stock Exchange have been analyzed to check for the stylized facts in the Indian market. It is observed that while some stylized facts of other markets are also observed in Indian market, there are significant deviations in three main aspects, namely leverage, asymmetry and autocorrelation. Leverage and asymmetry are both reversed making this a more promising market to invest in. While significant autocorrelation observed in the returns points towards market inefficiency, the increased predictive power is better for investors.

For a long investment time horizon, it is preferable to rebalance the portfolio weights at intermediate times. This necessitates a multi-period market model. Usually, dynamic programming techniques are applied to optimize the portfolio for the multi-period model. However, this assumes a known distribution for the parameters of the financial time series. We consider the situation where the distribution of parameters is unknown and is estimated directly from the dynamically arriving data. We implement the Bayesian filtering method through dynamic linear models to sequentially update the parameters. We also acknowledge the uncertain investment lifetime to make the model more adaptive to the market conditions. These updated parameters are put into the dynamic mean–variance problem to arrive at optimal efficient portfolios. Implementing this model to the S&P500 illustrates that the data strongly favor the Bayesian updating and is practically implementable.

Orthopedic problems are on ever increasing trend. The crisis could be offset largely so far due to the development of newer surgical procedures, bone prostheses, and rehabilitation methods. In last 80 years or so, a large number of materials have evolved for bone replacement, repair, or regeneration. In search of ideal biomaterial for orthopedic applications, people have explored anatomical grafts, metals, natural and synthetic polymeric materials, and ceramics over different timelines. Bone tissue engineering has emerged as an exciting field for improved osteoinduction, osteoconduction, osteintegration, and a potential tool for improvement in prosthesis life and function. Recently it has been understood that nano-sized materials exhibit extraordinary properties as compared to micro and nano-sized materials due to large surface area to volume ratio. A new direction has started emerging in the form of fiber-reinforced nanobiocomposites for developing longer life prostheses. This review explores present status of orthopedic implant materials for different applications with particular reference to biomaterials and trend in development of fiber nanobiocomposites.

For high dimensional data some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper we explore these modifications. We start with important problem of estimating high dimensional covariance matrix. Then we explore some of the important statistical techniques such as high dimensional regression, principal component analysis, multiple testing problems and classification. We describe some of the fast algorithms that can be readily applied in practice.

Recent advancements in technology have led to wide availability of high-frequency financial data. The aim of this paper is to study the behavior of the Indian stock market. In particular, we analyze the returns at 5 min interval from NSE using the index NIFTY and the stocks State Bank of India and Infosys. A non-parametric approach is taken to detect jumps in the return process. The analysis shows that index jumps relate very closely with the general market news and announcements while individual stock jumps are associated with company specific news. We find that volatility of the market is best captured by asymmetric power ARCH models.

Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.

We develop time series analysis of functional data observed discretely, treating the whole curve as a random realization from a distribution on functions that evolve over time. The method consists of principal components analysis of functional data and subsequently modeling the principal component scores as vector autoregressive moving averag (VARMA) process. We justify the method by showing that an underlying ARMAH structure of the curves leads to a VARMA structure on the principal component scores. We derive asymptotic properties of the estimators, fits, and forecast. For term structures of interest rates, these provide a unified framework for studying the time and maturity components of interest rates under one setup with few parametric assumptions. We apply the method to the yield curves of USA and India. We compare our forecasts to the parametric model that is based on Nelson-Siegel curves. In another application, we study the dependence of long-term interest rate on the short-term interest rate using functional regression.

Financial interdependence indicates a process through which transmission of shock originating in the financial market of one economy spreads to others. This paper provides a new idea of Residual and Recurrence Times of high or low values for bivariate time series to detect extreme dependence or contagion. In presence of financial extreme dependence, the distributions of residual and recurrence times are not the same. We examine the equality of two distributions using the permutation test. In comparison to other methods in multivariate extreme value theory, our proposed method does not need the i.i.d. assumption. Our method can handle the situation where the extremes for different components do not occur at the same time. We justify our methods in two ways: first using thorough simulation studies and then applying the proposed method to real data on weekly stock indices from sixteen markets.

With increasing availability of data, in many situations it is now possible to reasonably estimate the probability density function (pdf) of a random variable. This is far more informative than using a few summary statistics like mean or variance. In this paper, we propose a method of forecasting the density function based on a time series of estimated density functions. The proposed method uses kernel estimation to pre-process the raw data followed by dimension reduction using functional principal components analysis (FPCA). Then we fit Vector ARMA models to the reduced data to make a prediction of the principal component scores, which can then be used to obtain the forecast for density function. We need to transform and scale the forecasts to ensure non-negativeness and integration to one. We compared our method to [1] for histogram forecasts, on simulated data as well as real data from S&P 500 and the Bombay Stock Exchange. The results showed that our method performed better on both the datasets and the simulation using uniform and Hilbert distance. The time dependence and complexity of density function are different for the two markets, which is captured by our analysis.

We presented Bayesian portfolio selection strategy, via the $k$ factor asset pricing model. If the market is information efficient, the proposed strategy will mimic the market; otherwise, the strategy will outperform the market. The strategy depends on the selection of a portfolio via Bayesian multiple testing methodologies. We present the "discrete-mixture prior" model and the "hierarchical Bayes model with horseshoe prior." We define the Oracle set and prove that asymptotically the Bayes rule attains the risk of Bayes Oracle up to $O(1)$. Our proposed Bayes Oracle test guarantees statistical power by providing the upper bound of the type-II error. Simulation study indicates that the proposed Bayes oracle test is suitable for the efficient market with few stocks inefficiently priced. However, as the model becomes dense, i.e., the market is highly inefficient, one should not use the Bayes oracle test. The statistical power of the Bayes Oracle portfolio is uniformly better for the $k$-factor model ($k>1$) than the one factor CAPM. We present the empirical study, where we considered the 500 constituent stocks of S\&P 500 from the New York Stock Exchange (NYSE), and S\&P 500 index as the benchmark for thirteen years from the year 2006 to 2018. We showed the out-sample risk and return performance of the four different portfolio selection strategies and compared with the S\&P 500 index as the benchmark market index. Empirical results indicate that it is possible to propose a strategy which can outperform the market., 23 pages, 8 figures, 9 tables

We introduce a functional volatility process for modeling volatility trajectories for high frequency observations in financial markets and describe functional representations and data-based recovery of the process from repeated observations. A study of its asymptotic properties, as the frequency of observed trades increases, is complemented by simulations and an application to the analysis of intra-day volatility patterns of the S&P 500 index. The proposed volatility model is found to be useful to identify recurring patterns of volatility and for successful prediction of future volatility, through the application of functional regression and prediction techniques.

By perceiving a regime switching model as an example of a nonlinear dynamical system, we employ recurrence time distribution of a chosen event to derive a test statistic for testing the null hypothesis of one regime versus the alternative of having two or more regimes involved in a time series. This simple chi-square type of statistic is compared with existing likelihood ratio based ones that are all, in general, very complex in construction. The power of our proposed test is rather satisfactory and the computing load required is significantly more economical.

We show that it is possible to avoid the discrepancies of continuous path models for stock prices and still be able to hedge options if one models the stock price process as a birth and death process. One needs the stock and another market traded derivative to hedge an option in this setting. However, unlike in continuous models, the number of extra traded derivatives required for hedging does not increase when the intensity process is stochastic. We obtain parameter estimates using Generalized Method of Moments and describe the Monte Carlo algorithm to obtain option prices. We show that one needs to use filtering equations for inference in the stochastic intensity setting. We present real data applications to study the performance of our modeling and estimation techniques.

It is well known that unequal income distribution, yielding poverty, can be a serious social and economic problem. Therefore, reliable inequality analysis of total population and the sub-populations is required in order to make efficient policy decisions. Among many inequality measures, Gini coefficient is the most popular and widely used. Other interesting measures used in this study are Zenga index and K-index. Non-parametric estimators of the indices are presented and analyzed in terms of the bias, efficiency and normality in order to study the small sample bias of the indices. Confidence intervals for these indices are studied for simple random samples using normal approximation, bootstrap percentile and bootstrap-t intervals. The methods are applied to real data on socioeconomic indicators for different states of India

This article considers models that describe how people browse the Web. We restrict our attention to navigation patterns within a single site, and base our study on standard Web server access logs. Given a visitor's previous activities on the site, we propose models that predict their next page request. If the prediction is reasonably accurate, we might consider “prefetching” the page before the visitor requests it. A more conservative use for such predictions would be to simply update the freshness records in a proxy or network cache, eliminating unnecessary If-Modified-Since requests. Using data from the Web site for the Computing and Mathematical Sciences Research Division of Lucent Technologies (cm.bell-labs.com) we first evaluate the predictive performance of low-order Markov models. We next consider mixtures of first-order Markov models, achieving a kind of clustering of Web pages in the site. This approach is shown to perform well, while significantly reducing the space required to store the model. ...

This chapter discusses information transmission across stock and bond markets. It is part of a collection which approaches the material from the practitioner's viewpoint and familiarizes readers with how volatility is linked to speculation, trading volume, and information arrival.

Use of high-frequency return data has led to dramatic improvements in both theoretical and applied finance research. Estimators of covariance among multiple processes have been proposed, such as realized variance and Hayashi-Yoshida estimator. We are introducing a new estimator, random lead-lag estimator (RLLE), which coincides with the Hayashi-Yoshida estimator at very high frequency and with the realized covariance at low frequency. We studied the performance of RLLE both with and without microstructure noise for non-synchronous data and obtained the optimal estimation with good bias-variance trade-off. Our result is conformed by simulation and real data applications in stock and online auction markets.