Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

Compliance with international financial reporting standards (IFRS) and the value relevance of accounting information in emerging stock markets : evidence from Kuwait

Since the 1960s, the value relevance of accounting information has been an important topic in accounting research. The value relevance research provides evidence as to whether accounting numbers relate to corporate value in a predicted manner (Beaver, 2002). Such research is not only important for investors but also provides useful insights into accounting reporting effectiveness for standard setters and other users. Both the quality of accounting standards used and the effectiveness associated with implementing these standards are fundamental prerequisites for high value relevance (Hellstrom, 2006). However, while the literature comprehensively documents the value relevance of accounting information in developed markets, little attention has been given to emerging markets where the quality of accounting standards and their enforcement are questionable. Moreover, there is currently no known research that explores the association between level of compliance with International Financial Reporting Standards (IFRS) and the value relevance of accounting information. Motivated by the lack of research on the value relevance of accounting information in emerging markets and the unique institutional setting in Kuwait, this study has three objectives. First, it investigates the extent of compliance with IFRS with respect to firms listed on the Kuwait Stock Exchange (KSE). Second, it examines the value relevance of accounting information produced by KSE-listed firms over the 1995 to 2006 period. The third objective links the first two and explores the association between the level of compliance with IFRS and the value relevance of accounting information to market participants. Since it is among the first countries to adopt IFRS, Kuwait provides an ideal setting in which to explore these objectives. In addition, the Kuwaiti accounting environment provides an interesting regulatory context in which each KSE-listed firm is required to appoint at least two external auditors from separate auditing firms. Based on the research objectives, five research questions (RQs) are addressed. RQ1 and RQ2 aim to determine the extent to which KSE-listed firms comply with IFRS and factors contributing to variations in compliance levels. These factors include firm attributes (firm age, leverage, size, profitability, liquidity), the number of brand name (Big-4) auditing firms auditing a firm’s financial statements, and industry categorization. RQ3 and RQ4 address the value relevance of IFRS-based financial statements to investors. RQ5 addresses whether the level of compliance with IFRS contributes to the value relevance of accounting information provided to investors. Based on the potential improvement in value relevance from adopting and complying with IFRS, it is predicted that the higher the level of compliance with IFRS, the greater the value relevance of book values and earnings. The research design of the study consists of two parts. First, in accordance with prior disclosure research, the level of compliance with mandatory IFRS is examined using a disclosure index. Second, the value relevance of financial statement information, specifically, earnings and book value, is examined empirically using two valuation models: price and returns models. The combined empirical evidence that results from the application of both models provides comprehensive insights into value relevance of accounting information in an emerging market setting. Consistent with expectations, the results show the average level of compliance with IFRS mandatory disclosures for all KSE-listed firms in 2006 was 72.6 percent; thus, indicating KSE-listed firms generally did not fully comply with all requirements. Significant variations in the extent of compliance are observed among firms and across accounting standards. As predicted, older, highly leveraged, larger, and profitable KSE-listed firms are more likely to comply with IFRS required disclosures. Interestingly, significant differences in the level of compliance are observed across the three possible auditor combinations of two Big-4, two non-Big 4, and mixed audit firm types. The results for the price and returns models provide evidence that earnings and book values are significant factors in the valuation of KSE-listed firms during the 1995 to 2006 period. However, the results show that the value relevance of earnings and book values decreased significantly during that period, suggesting that investors rely less on financial statements, possibly due to the increase in the available non-financial statement sources. Notwithstanding this decline, a significant association is observed between the level of compliance with IFRS and the value relevance of earnings and book value to KSE investors. The findings make several important contributions. First, they raise concerns about the effectiveness of the regulatory body that oversees compliance with IFRS in Kuwait. Second, they challenge the effectiveness of the two-auditor requirement in promoting compliance with regulations as well as the associated cost-benefit of this requirement for firms. Third, they provide the first known empirical evidence linking the level of IFRS compliance with the value relevance of financial statement information. Finally, the findings are relevant for standard setters and for their current review of KSE regulations. In particular, they highlight the importance of establishing and maintaining adequate monitoring and enforcement mechanisms to ensure compliance with accounting standards. In addition, the finding that stricter compliance with IFRS improves the value relevance of accounting information highlights the importance of full compliance with IFRS and not just mere adoption.