Forecasting Exchange Rates: The Multi-State Markov-Switching Model with Smoothing

This paper presents an exchange rate forecasting model which combines the multi-state Markov-switching model with smoothing techniques. The model outperforms a random walk at short horizons and its superior forecastability appears to be robust over different sample spans. Our finding hinges on the fact that exchange rates tend to follow highly persistent trends and accordingly, the key to beating the random walk is to identify these trends. An attempt to link the trends in exchange rates to the underlying macroeconomic determinants further reveals that fundamentals-based linear models generally fail to capture the persistence in exchange rates and thus are incapable of outforecasting the random walk.Exchange Rate, Forecasting, Markov-Switching, Smoothing, HP-Filter

Single-index modulated multiple testing

In the context of large-scale multiple testing, hypotheses are often accompanied with certain prior information. In this paper, we present a single-index modulated (SIM) multiple testing procedure, which maintains control of the false discovery rate while incorporating prior information, by assuming the availability of a bivariate $p$-value, $(p_1,p_2)$, for each hypothesis, where $p_1$ is a preliminary $p$-value from prior information and $p_2$ is the primary $p$-value for the ultimate analysis. To find the optimal rejection region for the bivariate $p$-value, we propose a criteria based on the ratio of probability density functions of $(p_1,p_2)$ under the true null and nonnull. This criteria in the bivariate normal setting further motivates us to project the bivariate $p$-value to a single-index, $p(\theta)$, for a wide range of directions $\theta$. The true null distribution of $p(\theta)$ is estimated via parametric and nonparametric approaches, leading to two procedures for estimating and controlling the false discovery rate. To derive the optimal projection direction $\theta$, we propose a new approach based on power comparison, which is further shown to be consistent under some mild conditions. Simulation evaluations indicate that the SIM multiple testing procedure improves the detection power significantly while controlling the false discovery rate. Analysis of a real dataset will be illustrated.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1222 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Effective Construction of a Class of Bent Quadratic Boolean Functions

In this paper, we consider the characterization of the bentness of quadratic Boolean functions of the form $f(x)=\sum_{i=1}^{\frac{m}{2}-1} Tr^n_1(c_ix^{1+2^{ei}})+ Tr_1^{n/2}(c_{m/2}x^{1+2^{n/2}}) ,$ where $n=me$, $m$ is even and $c_i\in GF(2^e)$. For a general $m$, it is difficult to determine the bentness of these functions. We present the bentness of quadratic Boolean function for two cases: $m=2^vp^r$ and $m=2^vpq$, where $p$ and $q$ are two distinct primes. Further, we give the enumeration of quadratic bent functions for the case $m=2^vpq$

A power comparison between nonparametric regression tests

In this paper, we consider three major types of nonparametric regression tests that are based on kernel and local polynomial smoothing techniques. Their asymptotic power comparisons are established systematically under the fixed and contiguous alternatives, and are also illustrated through non-asymptotic investigations and finite-sample simulation studies. --Goodness-of-fit,Local alternative,Local polynomial regression,Power,Smoothing parameter

Application of Multiple imputation in Analysis of missing data in a study of Health-related quality of life

When a new treatment has similar efficacy compared to standard therapy in medical or social studies, the health-related quality of life (HRQL) becomes the main concern of health care professionals and can be the basis for making a decision in patient management. National Surgical Adjuvant Breast and Bowel Protocol (NSABP) C-06 clinical trial compared two therapies: intravenous (IV) fluorouracil (FU) plus Leucovorin (LV) and oral uracil/ftorafur (UFT) plus LV, in treatment of colon cancer. However, there was a high proportion of missing values among the HRQL measurements that only 481 (59.8%) UFT patients and 421 (52.4%) FU patients submitted the forms at all time points. Ignoring the missing data issue often leads to inefficient and sometime biased estimates. The primary objective of this thesis is to evaluate the impact of missing data on the estimated the treatment effect. In this thesis, we analyzed the HRQL data with missing values by multiple imputation. Both model-based and nearest neighborhood hot-deck imputation methods were applied. Confidence intervals for the estimated treatment effect were generated based on the pooled imputation analysis. The results based on multiple imputation indicated that missing data did not introduce major bias in the earlier analyses. However, multiple imputation was worthwhile since the most estimation from the imputation datasets are more efficient than that from incomplete data. These findings have public health importance: they have implications for development of health policies and planning interventions to improve the health related quality of life for those patients with colon cancer

A Note on Cyclic Codes from APN Functions

Cyclic codes, as linear block error-correcting codes in coding theory, play a vital role and have wide applications. Ding in \cite{D} constructed a number of classes of cyclic codes from almost perfect nonlinear (APN) functions and planar functions over finite fields and presented ten open problems on cyclic codes from highly nonlinear functions. In this paper, we consider two open problems involving the inverse APN functions $f(x)=x^{q^m-2}$ and the Dobbertin APN function $f(x)=x^{2^{4i}+2^{3i}+2^{2i}+2^{i}-1}$. From the calculation of linear spans and the minimal polynomials of two sequences generated by these two classes of APN functions, the dimensions of the corresponding cyclic codes are determined and lower bounds on the minimum weight of these cyclic codes are presented. Actually, we present a framework for the minimal polynomial and linear span of the sequence $s^{\infty}$ defined by $s_t=Tr((1+\alpha^t)^e)$, where $\alpha$ is a primitive element in $GF(q)$. These techniques can also be applied into other open problems in \cite{D}