Statistical Properties Of Time Series Research Articles

Shifts in Borsa Istanbul return behaviour: an analysis with change-point detection

Purpose- In Turkey, there is an enormous increase in local investors’ stock market interest for the last several years (Altınbaş, 2021: 36). Increasing inflation, deteriorating welfare, lack of alternative investments seems to be the foremost reasons of this attention. As of November 2022, Borsa Istanbul 100 (BIST 100) index value level reached to historic highs (tripled in one year) and this trend is expected to continue. The index is exponentially increasing in overall and there are several retracement periods over the time. What drives, strengthens or changes this behaviour of market? Do political developments, economic news or any other events influence investors? To answer these questions, change points in statistical parameters of market return distributions are examined and detected dates are evaluated. Analysis period covers the dates between January 2009 and November 2022. Methodology- Change points/breakpoints in statistical properties of time series can be informative for specific events that influence the behaviour (Beltratti & Morana, 2006; Chatzikonstanti, 2017; Eizaguirre, Biscarri, & de Gracia Hidalgo, 2004; Khuong Nguyen & Bellalah, 2008; Malik, 2011). In this study, change points determination is done with pruned exact linear time (PELT) method (Killick, Fearnhead, & Eckley, 2012). This method is applied to daily return data of the index, and it estimates a single or multiple points at which the statistical properties change. Analysis is conducted in R statistical software (R Core Team, 2021) with package changepoint.np (Haynes, Killick, Fearnhead, Eckley, & Grose, 2022). This is a modified version of original change point detection technique which is used in cases where there is no assumption on the statistical properties of observations (Haynes, Fearnhead, & Eckley, 2017). Findings- Many changepoints detected. Some of these coincide with explicit/significant events, such as coup attempt in July 2016 or Covid-19 pandemic announcements. Interestingly, frequency of change points increased over the last one and a half year and most of them are very close to Monetary Policy Committee meetings. But some changes seem not to be directly related with important events, and some important events did not significantly change market behaviour. Conclusion- Findings indicate it is neither possible to generalize market behaviour shifts with specific event types nor certainly expect a change after an event. Deeper analysis and interpretation of individual events and their impact may further provide further insights. Keywords: Stock market, investor sentiment, pruned exact linear time, change-point detection. JEL Codes: C22, G12, G14, G4

Power law dependence in a random differential equation

This paper studies a random differential equation with random switch perturbations. We explore how the maximum displacement from the equilibrium state depends on the statistical properties of time series of the random switches. We show a power law dependence between the upper bound of displacement and the frequency of random perturbation switches, and the slope of power law dependence is dependent on the specific distribution of the intervals between switching times. This result suggests a quantitative connection between frequency modulation and amplitude modulation under random perturbations.

Stochastic Intermittency Fields in a von Kármán Experiment

We discuss the application of stochastic intermittency fields to describe and analyse the statistical properties of time series of the generalised turbulence intensity in an anisotropic and inhomogeneous turbulent flow and provide a parsimonious description of the one-, two-, and three-point statistics. In particular, we show that the three-point correlations can be predicted from observed two-point statistics. Our analysis is motivated by observed stylised features of the energy dissipation in homogeneous and isotropic situations where these statistical properties are well represented within the framework of stochastic intermittency fields. We find a close resemblance and conclude that stochastic intermittency fields may be relevant in more general situations.

Exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations of covariances or correlations

Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate amplitude distributions of such systems are of considerable interest. Extending previous work, we view a set of measured, non-stationary correlation matrices as an ensemble for which we set up a random matrix model. We use this ensemble to average the stationary multivariate amplitude distributions measured on short time scales and thus obtain for large time scales multivariate amplitude distributions which feature heavy tails. We explicitly work out four cases, combining Gaussian and algebraic distributions. The results are either of closed forms or single integrals. We thus provide, first, explicit multivariate distributions for such non-stationary systems and, second, a tool that quantitatively captures the degree of non-stationarity in the correlations.

Assessment of parameters and distribution of extremely heavy-rainfall events that occur several times per year

Applied analyses of a number of datasets containing several highwater-forming storm rainfall events (intense rain for short time periods) per year are examined. The use of data containing several events per year is demonstrated as justified for reliable determination of statistical properties of time series derived from short observation periods. The statistics of time series containing one to several events per year in the Ural Mountains are shown to be well correlated with the frequency of the observed events. Recommendations for recalculation of the time-series statistics containing several events per year versus statistics for one event per year were developed, and a brief comparative analysis of the methods used in Russia is provided.

Statistical properties of fluctuations of time series representing appearances of words in nationwide blog data and their applications: An example of modeling fluctuation scalings of nonstationary time series.

To elucidate the nontrivial empirical statistical properties of fluctuations of a typical nonsteady time series representing the appearance of words in blogs, we investigated approximately 3×10^{9} Japanese blog articles over a period of six years and analyze some corresponding mathematical models. First, we introduce a solvable nonsteady extension of the random diffusion model, which can be deduced by modeling the behavior of heterogeneous random bloggers. Next, we deduce theoretical expressions for both the temporal and ensemble fluctuation scalings of this model, and demonstrate that these expressions can reproduce all empirical scalings over eight orders of magnitude. Furthermore, we show that the model can reproduce other statistical properties of time series representing the appearance of words in blogs, such as functional forms of the probability density and correlations in the total number of blogs. As an application, we quantify the abnormality of special nationwide events by measuring the fluctuation scalings of 1771 basic adjectives.

Empirical evidence for latitude dependence and asymmetry of geomagnetic spatial variation in mainland China

AbstractSpatiotemporal geomagnetic variation is a significant research topic of geomagnetism and space physics. Generated by convection and flows within the fluid outer core, latitude dependence and asymmetry, as the inherent spatiotemporal properties of geomagnetic field, have been extensively studied. We apply and modify an extension of existing method, Hidden Markov Model (HMM), which is an efficient tool for modeling the statistical properties of time series. Based on ground magnetic measurement data set in mainland China, first, we find the parameters of HMM can be used as the geomagnetic statistical signature to represent the spatiotemporal geomagnetic variations for each site. The results also support the existence of the geomagnetic latitude dependence more apparently. Furthermore, we provide solid empirical evidence for geomagnetic asymmetry relying on such ground magnetic measurement data set.

Forecasting Death Rates Using Exogenous Determinants

ABSTRACTMortality models used for forecasting are predominantly based on the statistical properties of time series and do not generally incorporate an understanding of the forces driving secular trends. This paper addresses three research questions: Can the factors found in stochastic mortality‐forecasting models be associated with real‐world trends in health‐related variables? Does inclusion of health‐related factors in models improve forecasts? Do resulting models give better forecasts than existing stochastic mortality models? We consider whether the space spanned by the latent factor structure in mortality data can be adequately described by developments in gross domestic product, health expenditure and lifestyle‐related risk factors using statistical techniques developed in macroeconomics and finance. These covariates are then shown to improve forecasts when incorporated into a Bayesian hierarchical model. Results are comparable or better than benchmark stochastic mortality models. Copyright © 2014 John Wiley & Sons, Ltd.

The Reaction Function of Three Central Banks of Visegrad Group

The aim of our paper is to formulate and empirically verify the simple backward looking econometric model of the monetary policy rule, which would be able to describe the development of monetary policy rate, namely only on the basis of statistically measured and at the given time available information. We focus on the Czech National Bank, the National Bank of Poland and the Magyar Nemzeti Bank in the period of January 1999 to April 2012. In the present paper we discuss some methodological problems associated with the ex-post empirical verifi cation of the central bank’s monetary policy rule. We construct an empirical model of the monetary policy rule, justify the choice and the inclusion of explanatory variables, analyse the statistical properties of time series, and verify the alternative forms of econometric models. Our analysis showed that the development of monetary policy rate in the reporting period can be explained by the past and present development of four explanatory variables: yearly infl ation rate, exchange rate, ECB main refi nancing rate and growth rate of M2. The annualized infl ation rate proved to be statistically insignifi cant in the model. We fi nd interesting that the statistical quality of the estimated model was further increased after a six-month lag of the annual infl ation rate added to the model.

Attributes characterizing spontaneous ultra-weak photon signals of human subjects

Sixty visible range photon signals spontaneously emitted from the dorsal side of both hands of fifteen human subjects are analyzed with the aim of finding their attributes. The signals are of 30min duration and detected in bins of 50ms by two synchronized photo multipliers sensitive in the range (290–630nm). Each signal is a time series of 36,000 elements. The attributes of its signal are determined from the statistical properties of time series. The mean and variance of time series determine the attributes signal strength and intercept (p0) and slope (p1) of the Fano Factor curve. The photon count distribution of the time series determines squeezed state parameters |α|, r, θ and ϕ, squeezed state index (SSI), and sum of the squares of residue (SSR). The correlation between simultaneously detected signals determines intercept (c0) and slope (c1) of their correlation curve. The variability of attributes is studied by calculating them in smaller intervals covering the entire signal. The profile of attribute at 12 sites in a subject is more informative and biologically relevant.

Forecasting Death Rates Using Exogenous Determinants

Mortality models used for forecasting are predominantly based on the statistical properties of time series and do not generally incorporate an understanding of the forces driving secular trends. This paper addresses three research questions: Can the factors found in stochastic mortality-forecasting models be associated with real-world trends in health-related variables? Does inclusion of health-related factors in models improve forecasts? Do resulting models give better forecasts than existing stochastic mortality models? We consider whether the space spanned by the latent factor structure in mortality data can be adequately described by developments in gross domestic product, health expenditure and lifestyle-related risk factors using statistical techniques developed in macroeconomics and finance. These covariates are then shown to improve forecasts when incorporated into a Bayesian hierarchical model. Results are comparable or better than benchmark stochastic mortality models. Copyright © 2014 John Wiley & Sons, Ltd.

Je možné předpovídat repo sazbu ČNB na základě zpět hledícího měnového pravidla?

The aim of our paper is to formulate and empirically verify the simple backward looking econometric model of the monetary rule, which would be able to describe the development of CNB repo rate, namely only on the basis of statistically measured and in the given time available information. We focus on the period after 1998, when the CNB's inflation targeting policy is implemented and the repo rate (14 days) plays the role of the monetary policy rate. In the paper we discuss some methodological problems associated with the ex post empirical verification of the central bank monetary rule. We construct an empirical model of the monetary rule, justify the choice and the inclusion of explanatory variables, we analyze the statistical properties of time series and verify the alternative forms of econometric models. Our analysis showed that the development of CNB repo rate in the reporting period can be explained by the past and present evolution of three explanatory variables: the yearly inflation rate, the exchange rate and the ECB repo rate. The annualized inflation rate proved to be statistically insignificant in the model. We find interesting that the statistical quality of the estimated model was further increased after a six-month delay of the yearly inflation rate. The obtained results indicate that in determining the CNB repo rate the expected future level of the yearly inflation rate does not play important role and the last yearly inflation rate is more important than its present level.

RECURRENCE-BASED TIME SERIES ANALYSIS BY MEANS OF COMPLEX NETWORK METHODS

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related to the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.

Time Series Properties of ARCH Processes with Persistent Covariates

We consider ARCH processes with persistent covariates and provide asymptotic theories that explain how such covariates affect various characteristics of volatility. Specifically, we propose and study a volatility model, named ARCH-NNH model, that is an ARCH(1) process with a nonlinear function of a persistent, integrated or nearly integrated, explanatory variable. Statistical properties of time series given by this model are investigated for various volatility functions. It is shown that our model generates time series that have two prominent characteristics: high degree of volatility persistence and leptokurtosis. Due to persistent covariates, the time series generated by our model has the long memory property in volatility that is commonly observed in high frequency speculative returns. On the other hand, the sample kurtosis of the time series generated by our model either diverges or has a well-defined limiting distribution with support truncated on the left by the kurtosis of the innovation, which successfully explains the empirical finding of leptokurtosis in financial time series. We present two empirical applications of our model. It is shown that the default premium (the yield spread between Baa and Aaa corporate bonds) predicts stock return volatility, and the interest rate differential between two countries accounts for exchange rate return volatility. The forecast evaluation shows that our model generally performs better than GARCH(1,1) and FIGARCH at relatively lower frequencies.

Estimating mode coupling effects on shallow-water propagation uncertainty

The introduction of unknown aberrations to the background sound speed of the ocean waveguide and sediments, as well as unknown free-surface excursions and bottom bathymetry, causes uncertainty in the characteristics of acoustic time series. Not all of this uncertainty can be adequately explained by simply assuming that energy in various paths is perturbed only in phase and travel time. Data and simulations both clearly show that significant mode coupling is introduced by even small aberrations introduced over significant ranges. This talk estimates the effects of mode coupling introduced by statistically characterized sound-speed defects on the statistical properties of time series in shallow water. In this approach EOF decompositions of the sound-speed field are used, along with the differential form of the coupled -modeequations and perturbation expressions for mode-coupling coefficients. Results are compared to previously derived expressions for the statistical properties of time series obtained under the adiabatic approximation [Work supported by ONR.]

Single-molecule kinetics with time-dependent rates: a generating function approach.

A theoretical strategy for calculating the statistical properties of time series generated by single molecule measurements is presented. Emphasis is placed on the case where observable states interconvert via rate "constants" exhibiting stochastic time dependence. Such is the case for measurements of single fluorophores coupled to biomolecules undergoing conformational fluctuations [H. P. Lu, L. Xun, and X. S. Xie, Science 282, 1877 (1998)]]. In contrast to previous studies, we focus on the number of fluorophore blinking events occurring within a given amount of time as our stochastic variable. This formulation allows for an elementary analysis within the generating function framework.

Nonstationary nonlinear heteroskedasticity

In this paper, we consider time series with the conditional heteroskedasticities that are given by nonlinear functions of integrated processes. Such time series are said to have nonlinear nonstationary heteroskedasticity (NNH), and the functions generating conditional heterogeneity are called heterogeneity generating functions (HGF's). Various statistical properties of time series with NNH are investigated for a wide class of HGF's. For NNH models with a variety of HGF's, volatility clustering and leptokurtosis, which are common features of ARCH type models, are manifest. In particular, it is shown that the sample autocorrelations of their squared processes vanish only very slowly, or do not even vanish at all, in the limit. Volatility clustering is therefore well expected. The NNH models with certain types of HGF's indeed have sample characteristics that are very similar to those of ARCH type models. Moreover, the sample kurtosis of the NNH model either diverges or has a stable limiting distribution with support truncated on the left by the kurtosis of the innovations. This would well explain the presence of leptokurtosis in many observed time series data. To illustrate the empirical relevancy of our model, we analyze the spreads between the forward and spot rates of USD/DM exchange rates. It is found that the conditional variances of the spreads can be well modelled as a nonlinear function of the levels of the spot rates.

Markov chain test for time dependence and homogeneity: An analytical and empirical evaluation

This paper evaluates the small and large sample properties of Markov chain time-dependence and time-homogeneity tests. First, we present the Markov chain methodology to investigate various statistical properties of time series. Considering an auto-regressive time series and its associated Markov chain representation, we derive analytical measures of the statistical power of the Markov chain time-dependence and time-homogeneity tests. We later use Monte Carlo simulations to examine the small-sample properties of these tests. It is found that although Markov chain time-dependence test has desirable size and power properties, time-homogeneity test does not perform well in statistical size and power calculations.

On Rational Bubbles and Fat Tails

This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982). Using insights on the behavior of multiplicative stochastic processes, we demonstrate that the tails of the unconditional distribution emerging from such bubble processes follow power-laws (exhibit hyperbolic decline). More precisely, we find that rational bubbles predict a fat power tail for both the bubble component and price differences with an exponent µ smaller than 1. The distribution of returns is dominated by the same power-law over an extended range of large returns. Although power-law tails are a pervasive feature of empirical data, these numerical predictions are in disagreement with the usual empirical estimates. It therefore appears that exogenous rational bubbles are hardly reconcilable with some of the stylized facts of financial data at a very elementary level.

On Rational Bubbles and Fat Tails

This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982). Using insights on the behavior of multiplicative stochastic processes, we demonstrate that the tails of the unconditional distribution emerging from such bubble processes follow power-laws (exhibit hyperbolic decline). More precisely, we find that rational bubbles predict a fat power tail for both the bubble component and price differences with an exponent m smaller than 1. The distribution of returns is dominated by the same power-law over an extended range of large returns. Although power-law tails are a pervasive feature of empirical data, these numerical predictions are in disagreement with the usual empirical estimates. It, therefore, appears that exogenous rational bubbles are hardly reconcilable with some of the stylized facts of financial data at a very elementary level.