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.

Removing observational noise from fisheries-independent time series data using ARIMA models

Abundance indices derived from fishery-independent surveys typically exhibit much higher interannual variability than is consistent with the within-survey variance or the life history of a species. This extra variability is essentially observation noise (i.e. measurement error); it probably reflects environmentally driven factors that affect catchability over time. Unfortunately, high observation noise reduces the ability to detect important changes in the underlying population abundance. In our study, a noise-reduction technique for uncorrelated observation noise that is based on autoregressive integrated moving average (ARIMA) time series modeling is investigated. The approach is applied to 18 time series of finfish abundance, which were derived from trawl survey data from the U.S. northeast continental shelf. Although the a priori assumption of a random-walk-plus-uncorrelated-noise model generally yielded a smoothed result that is pleasing to the eye, we recommend that the most appropriate ARIMA model be identified for the observed time series if the smoothed time series will be used for further analysis of the population dynamics of a species.

A general framework for integrating environmental time series into stock assessment models: model description, simulation testing, and example

We present a method to integrate environmental time series into stock assessment models and to test the significance of correlations between population processes and the environmental time series. Parameters that relate the environmental time series to population processes are included in the stock assessment model, and likelihood ratio tests are used to determine if the parameters improve the fit to the data significantly. Two approaches are considered to integrate the environmental relationship. In the environmental model, the population dynamics process (e.g. recruitment) is proportional to the environmental variable, whereas in the environmental model with process error it is proportional to the environmental variable, but the model allows an additional temporal variation (process error) constrained by a log-normal distribution. The methods are tested by using simulation analysis and compared to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. In the traditional method, the estimates of recruitment were provided by a model that allowed the recruitment only to have a temporal variation constrained by a log-normal distribution. We illustrate the methods by applying them to test the statistical significance of the correlation between sea-surface temperature (SST) and recruitment to the snapper (Pagrus auratus) stock in the Hauraki Gulf–Bay of Plenty, New Zealand. Simulation analyses indicated that the integrated approach with additional process error is superior to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. The results suggest that, for the snapper stock, recruitment is positively correlated with SST at the time of spawning.

Time series analyses of biological and environmental variables for Suisun Bay and the Sacramento and San Joaquin rivers

EXTRACT (SEE PDF FOR FULL ABSTRACT): Arima analysis was used to compute cross-correlations between principal component axes that described environmental variables, chlorophyll concentration and zooplankton density for the Sacramento and San Joaquin rivers and Suisun Bay. ... Cross-correlations among the time series may provide information about links between environmental and biological variables within the estuary and the possible influence of climate.

Accelerating Bayesian hierarchical clustering of time series data with a randomised algorithm.

We live in an era of abundant data. This has necessitated the development of new and innovative statistical algorithms to get the most from experimental data. For example, faster algorithms make practical the analysis of larger genomic data sets, allowing us to extend the utility of cutting-edge statistical methods. We present a randomised algorithm that accelerates the clustering of time series data using the Bayesian Hierarchical Clustering (BHC) statistical method. BHC is a general method for clustering any discretely sampled time series data. In this paper we focus on a particular application to microarray gene expression data. We define and analyse the randomised algorithm, before presenting results on both synthetic and real biological data sets. We show that the randomised algorithm leads to substantial gains in speed with minimal loss in clustering quality. The randomised time series BHC algorithm is available as part of the R package BHC, which is available for download from Bioconductor (version 2.10 and above) via http://bioconductor.org/packages/2.10/bioc/html/BHC.html. We have also made available a set of R scripts which can be used to reproduce the analyses carried out in this paper. These are available from the following URL. https://sites.google.com/site/randomisedbhc/.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

Comparing copepod time-series in the north of Spain: Spatial autocorrelation of community composition

Four time-series of copepod species biomass in the north of Spain were contrasted to demonstrate spatial autocorrelation of local communities and their responses to short-term local and regional variability in oceanographic conditions. The series represented coastal and oceanic environments along a marked gradient of influence of seasonal upwelling from Galicia to the Mar Cantábrico (S Bay of Biscay), and each one included at least 10 years of continuous data collected at monthly frequency. Community composition (i.e. species number and diversity) was very consistent through the region, but local variations in the presence of new species and the relative proportions of common species allowed for the characterisation of the response to the environment at each site. Small-sized species were more frequent near the coast. A few species, however, captured the main patterns of variability in all series. Calanus helgolandicus and Acartia (mainly Acartia clausi) were generally the main contributors to total biomass, while other species as Paracalanus parvus and Clausocalanus spp. were important only at some locations. Most copepod indices were positively correlated with upwelling, either considering the whole community (biomass, species richness and diversity) or individual species, but only in the coastal series analysed since 1991. Copepods in the nearby ocean, however, showed negative correlations with upwelling in the period 1960–1986. The effects of upwelling may have been modulated by local factors, as showed by the increases in biomass, number of species and diversity in associations with increases in sea surface temperature in Galicia, while in the Mar Cantábrico only the warming-tolerant species increased and those typical of upwelling decreased. Density stratification of the water column was associated with decreases in total copepod biomass in Galicia, while it favoured the increase in species richness in the Mar Cantábrico. Nearly all significant responses of copepods to environmental variability were delayed by up to 5 months, showing the importance of considering time-lags in the analysis of temporal responses of zooplankton.

A comparison of two zooplankton time series data collected in the Gulf of Maine

Interannual and seasonal trends of zooplankton abundance and species composition were compared between the Bongo net and Continuous Plankton Recorder (CPR) time series in the Gulf of Maine. Data from 5799 Bongo and 3118 CPR samples were compared from the years 1978–2006. The two programs use different sampling methods, with the Bongo time series composed of bimonthly vertically integrated samples from locations throughout the region, while the CPR was towed monthly at 10 m depth on a transect that bisects the region. It was found that there was a significant correlation between the interannual (r = 0.67, P < 0.01) and seasonal (r = 0.95, P < 0.01) variability of total zooplankton counts. Abundance rankings of individual taxa were highly correlated and temporal trends of dominant copepods were similar between samplers. Multivariate analysis also showed that both time series equally detected major shifts in community structure through time. However, absolute abundance levels were higher in the Bongo and temporal patterns for many of the less abundant taxa groups were not similar between the two devices. The different mesh sizes of the samplers probably caused some of the discrepancies; but diel migration patterns, damage to soft bodied animals and avoidance of the small CPR aperture by some taxa likely contributed to the catch differences between the two devices. Nonetheless, Bongo data presented here confirm the previously published patterns found in the CPR data set, and both show that the abundance increase of the 1990s has been followed by average to below average levels from 2002 to 06.

Comparisons of zooplankton time series

Evidence for climate-correlated low frequency variability of various components of marine ecosystems has accumulated rapidly over the past 2 decades. There has also been a growing recognition that society needs to learn how the fluctuations of these various components are linked, and to predict the likely amplitude and steepness of future changes. Demographic characteristics of marine zooplankton make them especially suitable for examining variability of marine ecosystems at interannual to decadal time scales. Their life cycle duration is short enough that there is little carryover of population membership from year to year, but long enough that variability can be tracked with monthly-to-seasonal sampling. Because zooplankton are rarely fished, comparative analysis of changes in their abundance can greatly enhance our ability to evaluate the importance of and interaction between physical environment, food web, and fishery harvest as causal mechanisms driving ecosystem level changes. A number of valuable within-region analyses of zooplankton time series have been published in the past decade, covering a variety of modes of variability including changes in total biomass, changes in size structure and species composition, changes in spatial distribution, and changes in seasonal timing. But because most zooplankton time series are relatively short compared to the time scales of interest, the statistical power of local analyses is often low, and between-region and between-variable comparisons are also needed. In this paper, we review the results of recent within- and between-region analyses, and suggest some priorities for future work.

A time-domain approach to the analysis and modeling of on-body propagation characteristics using synchronized measurements at 2.45 GHz

Modeling of on-body propagation channels is of paramount importance to those wishing to evaluate radio channel performance for wearable devices in body area networks (BANs). Difficulties in modeling arise due to the highly variable channel conditions related to changes in the user's state and local environment. This study characterizes these influences by using time-series analysis to examine and model signal characteristics for on-body radio channels in user stationary and mobile scenarios in four different locations: anechoic chamber, open office area, hallway, and outdoor environment. Autocorrelation and cross-correlation functions are reported and shown to be dependent on body state and surroundings. Autoregressive (AR) transfer functions are used to perform time-series analysis and develop models for fading in various on-body links. Due to the non-Gaussian nature of the logarithmically transformed observed signal envelope in the majority of mobile user states, a simple method for reproducing the failing based on lognormal and Nakagami statistics is proposed. The validity of the AR models is evaluated using hypothesis testing, which is based on the Ljung-Box statistic, and the estimated distributional parameters of the simulator output compared with those from experimental results.

NON-GAUSSIAN STATISTICS OF OIL PRICING TIME-SERIES: A CASE STUDY

The stochastic nature of oil price fluctuations is investigated over a twelve-year period, borrowing feedback from an existing database (USA Energy Information Administration database, available online). We evaluate the scaling exponents of the fluctuations by employing different statistical analysis methods, namely rescaled range analysis (R/S), scale windowed variance analysis (SWV) and the generalized Hurst exponent (GH) method. Relying on the scaling exponents obtained, we apply a rescaling procedure to investigate the complex characteristics of the probability density functions (PDFs) dominating oil price fluctuations. It is found that PDFs exhibit scale invariance, and in fact collapse onto a single curve when increments are measured over microscales (typically less than 30 days). The time evolution of the distributions is well fitted by a Levy-type stable distribution. The relevance of a Levy distribution is made plausible by a simple model of nonlinear transfer. Our results also exhibit a degree of multifractality as the PDFs change and converge toward to a Gaussian distribution at the macroscales.

Limitations of instantaneous water quality sampling in surface-water catchments: Comparison with near-continuous phosphorus time-series data.

The validity of load estimates from intermittent, instantaneous grab sampling is dependent on adequate spatial coverage by monitoring networks and a sampling frequency that re?ects the variability in the system under study. Catchments with a ?ashy hydrology due to surface runoff pose a particular challenge as intense short duration rainfall events may account for a signi?cant portion of the total diffuse transfer of pollution from soil to water in any hydrological year. This can also be exacerbated by the presence of strong background pollution signals from point sources during low flows. In this paper, a range of sampling methodologies and load estimation techniques are applied to phosphorus data from such a surface water dominated river system, instrumented at three sub-catchments (ranging from 3 to 5 km2 in area) with near-continuous monitoring stations. Systematic and Monte Carlo approaches were applied to simulate grab sampling using multiple strategies and to calculate an estimated load, Le based on established load estimation methods. Comparison with the actual load, Lt, revealed signi?cant average underestimation, of up to 60%, and high variability for all feasible sampling approaches. Further analysis of the time series provides an insight into these observations; revealing peak frequencies and power-law scaling in the distributions of P concentration, discharge and load associated with surface runoff and background transfers. Results indicate that only near-continuous monitoring that re?ects the rapid temporal changes in these river systems is adequate for comparative monitoring and evaluation purposes. While the implications of this analysis may be more tenable to small scale ?ashy systems, this represents an appropriate scale in terms of evaluating catchment mitigation strategies such as agri-environmental policies for managing diffuse P transfers in complex landscapes.

Detecting sequence dependent transcriptional pauses from RNA and protein number time series

Background: Evidence suggests that in prokaryotes sequence-dependent transcriptional pauses a?ect the dynamics of transcription and translation, as well as of small genetic circuits. So far, a few pause-prone sequences have been identi?ed from in vitro measurements of transcription elongation kinetics.

Results: Using a stochastic model of gene expression at the nucleotide and codon levels with realistic parameter values, we investigate three di?erent but related questions and present statistical methods for their analysis. First, we show that information from in vivo RNA and protein temporal numbers is su?cient to discriminate between models with and without a pause site in their coding sequence. Second, we demonstrate that it is possible to separate a large variety of models from each other with pauses of various durations and locations in the template by means of a hierarchical clustering and a random forest classi?er. Third, we introduce an approximate likelihood function that allows to estimate the location of a pause site.

Conclusions: This method can aid in detecting unknown pause-prone sequences from temporal measurements of RNA and protein numbers at a genome-wide scale and thus elucidate possible roles that these sequences play in the dynamics of genetic networks and phenotype.