Modelling financial time series with switching state space models

The deficiencies of stationary models applied to financial time series are well documented. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We use a dynamic switching (modelled by a hidden Markov model) combined with a linear dynamical system in a hybrid switching state space model (SSSM) and discuss the practical details of training such models with a variational EM algorithm due to [Ghahramani and Hilton,1998]. The performance of the SSSM is evaluated on several financial data sets and it is shown to improve on a number of existing benchmark methods.

Dynamical local models for segmentation and prediction of financial time series

In the analysis and prediction of many real-world time series, the assumption of stationarity is not valid. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We introduce a new model which combines a dynamic switching (controlled by a hidden Markov model) and a non-linear dynamical system. We show how to train this hybrid model in a maximum likelihood approach and evaluate its performance on both synthetic and financial data.

Modelling nonlinear stochastic dynamics in financial time series

For analysing financial time series two main opposing viewpoints exist, either capital markets are completely stochastic and therefore prices follow a random walk, or they are deterministic and consequently predictable. For each of these views a great variety of tools exist with which it can be tried to confirm the hypotheses. Unfortunately, these methods are not well suited for dealing with data characterised in part by both paradigms. This thesis investigates these two approaches in order to model the behaviour of financial time series. In the deterministic framework methods are used to characterise the dimensionality of embedded financial data. The stochastic approach includes here an estimation of the unconditioned and conditional return distributions using parametric, non- and semi-parametric density estimation techniques. Finally, it will be shown how elements from these two approaches could be combined to achieve a more realistic model for financial time series.

Independent component analysis and feature extraction of financial time series

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Diagnostic Tests Based on Quantile Residuals for Nonlinear Time Series Models

This thesis studies quantile residuals and uses different methodologies to develop test statistics that are applicable in evaluating linear and nonlinear time series models based on continuous distributions. Models based on mixtures of distributions are of special interest because it turns out that for those models traditional residuals, often referred to as Pearson's residuals, are not appropriate. As such models have become more and more popular in practice, especially with financial time series data there is a need for reliable diagnostic tools that can be used to evaluate them. The aim of the thesis is to show how such diagnostic tools can be obtained and used in model evaluation. The quantile residuals considered here are defined in such a way that, when the model is correctly specified and its parameters are consistently estimated, they are approximately independent with standard normal distribution. All the tests derived in the thesis are pure significance type tests and are theoretically sound in that they properly take the uncertainty caused by parameter estimation into account. -- In Chapter 2 a general framework based on the likelihood function and smooth functions of univariate quantile residuals is derived that can be used to obtain misspecification tests for various purposes. Three easy-to-use tests aimed at detecting non-normality, autocorrelation, and conditional heteroscedasticity in quantile residuals are formulated. It also turns out that these tests can be interpreted as Lagrange Multiplier or score tests so that they are asymptotically optimal against local alternatives. Chapter 3 extends the concept of quantile residuals to multivariate models. The framework of Chapter 2 is generalized and tests aimed at detecting non-normality, serial correlation, and conditional heteroscedasticity in multivariate quantile residuals are derived based on it. Score test interpretations are obtained for the serial correlation and conditional heteroscedasticity tests and in a rather restricted special case for the normality test. In Chapter 4 the tests are constructed using the empirical distribution function of quantile residuals. So-called Khmaladze s martingale transformation is applied in order to eliminate the uncertainty caused by parameter estimation. Various test statistics are considered so that critical bounds for histogram type plots as well as Quantile-Quantile and Probability-Probability type plots of quantile residuals are obtained. Chapters 2, 3, and 4 contain simulations and empirical examples which illustrate the finite sample size and power properties of the derived tests and also how the tests and related graphical tools based on residuals are applied in practice.

Integer-valued APARCH processes in the analysis of time series of counts

The Asymmetric Power Arch representation for the volatility was introduced by Ding et al.(1993) in order to account for asymmetric responses in the volatility in the analysis of continuous-valued financial time series like, for instance, the log-return series of foreign exchange rates, stock indices or share prices. As reported by Brannas and Quoreshi (2010), asymmetric responses in volatility are also observed in time series of counts such as the number of intra-day transactions in stocks. In this work, an asymmetric power autoregressive conditional Poisson model is introduced for the analysis of time series of counts exhibiting asymmetric overdispersion. Basic probabilistic and statistical properties are summarized and parameter estimation is discussed. A simulation study is presented to illustrate the proposed model. Finally, an empirical application to a set of data concerning the daily number of stock transactions is also presented to attest for its practical applicability in data analysis.

Time series analysis for minority game simulations of financial markets

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolution. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Financial Development and Economic Growth: Time Series Evidence from Albania

The main objective of this thesis is to explore the short and long run causality patterns in the finance – growth nexus and finance-growth-trade nexus before and after the global financial crisis, in the case of Albania. To this end we use quarterly data on real GDP, 13 proxy measures for financial development and the trade openness indicator for the period 1998Q1 – 2013Q2 and 1998Q1-2008Q3. Causality patterns will be explored in a VAR-VECM framework. For this purpose we will proceed as follows: (i) testing for the integration order of the variables; (ii) cointegration analysis and (iii) performing Granger causality tests in a VAR-VECM framework. In the finance-growth nexus, empirical evidence suggests for a positive long run relationship between finance and economic growth, with causality running from financial development to economic growth. The global financial crisis seems to have not affected the causality direction in the finance and growth nexus, thus supporting the finance led growth hypothesis in the long run in the case of Albania. In the finance-growth-trade openness nexus, we found evidence for a positive long run relationship the variables, with causality direction depending on the proxy used for financial development. When the pre-crisis sample is considered, we find evidence for causality running from financial development and trade openness to economic growth. The global financial crisis seems to have affected somewhat the causality direction in the finance-growth-trade nexus, which has become sensible to the proxy used for financial development. On the short run, empirical evidence suggests for a clear unidirectional relationship between finance and growth, with causality mostly running from economic growth to financial development. When we consider the per-crisis sub sample results are mixed, depending on the proxy used for financial development. The same results are confirmed when trade openness is taken into account.

Simulation-based density estimation for time series using covariate data

This paper proposes a simulation-based density estimation technique for time series that exploits information found in covariate data. The method can be paired with a large range of parametric models used in time series estimation. We derive asymptotic properties of the estimator and illustrate attractive finite sample properties for a range of well-known econometric and financial applications.

Studies on Binary Time Series Models with Applications to Empirical Macroeconomics and Finance

This thesis studies binary time series models and their applications in empirical macroeconomics and finance. In addition to previously suggested models, new dynamic extensions are proposed to the static probit model commonly used in the previous literature. In particular, we are interested in probit models with an autoregressive model structure. In Chapter 2, the main objective is to compare the predictive performance of the static and dynamic probit models in forecasting the U.S. and German business cycle recession periods. Financial variables, such as interest rates and stock market returns, are used as predictive variables. The empirical results suggest that the recession periods are predictable and dynamic probit models, especially models with the autoregressive structure, outperform the static model. Chapter 3 proposes a Lagrange Multiplier (LM) test for the usefulness of the autoregressive structure of the probit model. The finite sample properties of the LM test are considered with simulation experiments. Results indicate that the two alternative LM test statistics have reasonable size and power in large samples. In small samples, a parametric bootstrap method is suggested to obtain approximately correct size. In Chapter 4, the predictive power of dynamic probit models in predicting the direction of stock market returns are examined. The novel idea is to use recession forecast (see Chapter 2) as a predictor of the stock return sign. The evidence suggests that the signs of the U.S. excess stock returns over the risk-free return are predictable both in and out of sample. The new "error correction" probit model yields the best forecasts and it also outperforms other predictive models, such as ARMAX models, in terms of statistical and economic goodness-of-fit measures. Chapter 5 generalizes the analysis of univariate models considered in Chapters 2 4 to the case of a bivariate model. A new bivariate autoregressive probit model is applied to predict the current state of the U.S. business cycle and growth rate cycle periods. Evidence of predictability of both cycle indicators is obtained and the bivariate model is found to outperform the univariate models in terms of predictive power.

Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data

Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called `early warning signals', and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.

Genetic Algorithm Search for Predictive Patterns in Multidimensional Time Series

Based on an algorithm for pattern matching in character strings, we implement a pattern matching machine that searches for occurrences of patterns in multidimensional time series. Before the search process takes place, time series are encoded in user-designed alphabets. The patterns, on the other hand, are formulated as regular expressions that are composed of letters from these alphabets and operators. Furthermore, we develop a genetic algorithm to breed patterns that maximize a user-defined fitness function. In an application to financial data, we show that patterns bred to predict high exchange rates volatility in training samples retain statistically significant predictive power in validation samples.

Income ineqaulity from 1960-2012: a brief time-series history of capital and labour

This commentary examines two principal forms of inequality and their evolution since the 1960s: the division of national income between capital and labour, and the share of total income held by the top 1 per cent of earners. Trends are linked to current discussions of inequality drivers such as financialisation, and a brief time-series analysis of the effects of trade and financial sector growth on top incomes is presented.

Relativistic time effects in financial dynamics

Financial time series have a complex dynamic nature. Many techniques were adopted having in mind standard paradigms of time flow. This paper explores an alternative route involving relativistic effects. It is observed that the measuring perspective influences the results and that we can have different time textures.