Time Series Literature Research Articles

Modelling common bubbles in cryptocurrency prices

Bubbles and spikes in cryptocurrency prices increase considerably the risk on investments in these assets. In the traditional time series literature bubbles are viewed as nonstationary and non-estimable components of a process. In this paper, we adopt a different approach and consider the bubbles as inherent features of a strictly stationary causal-noncausal (mixed) Vector Autoregressive (VAR) process. This approach allows us to model and estimate the common bubbles and spikes in cryptocurrency prices. It also provides us linear combinations of cryptocurrencies that eliminate common bubbles analogously to the cointegrating vectors eliminating common trends in unit root processes. They are used to build cryptocurrency portfolios immune to the risk of common bubbles that ensure stable investment strategies. The mixed VAR model is estimated from the US Dollar prices of Bitcoin, Ethereum, Ripple, and Stellar over the period 2017–2019. We document the common bubbles and illustrate the behaviour of bubble-free portfolios.

A study on asset price bubble dynamics: explosive trend or quadratic variation?

This paper posits that when an asset exhibits a bubble, its price process can be unbounded from above in finite time with positive probability if a quadratic variation (QV) risk premium is large enough. Based on the local martingale theory of bubbles, we provide sufficient conditions under which price explosion occurs via the QV channel provided that bubbles are present. This QV channel of price explosions is new to the literature and distinct from the explosive autoregressive (AR) dynamics, which is often identified with the presence of bubbles as defined in the time series literature. Using the S&P 500 index and a sample of individual stocks over 1996–2021, we document the existence of price explosions during periods when bubbles occur. Almost all price explosion episodes discovered are associated with the QV and not AR drift channel.

A Literature Review on Some Trends in Artificial Neural Networks for Modeling and Simulation with Time Series

This paper reviews the application of artificial neural network (ANN) models to time series prediction tasks. We begin by briefly introducing some basic concepts and terms related to time series analysis, and by outlining some of the most popular ANN architectures considered in the literature for time series forecasting purposes: feedforward neural networks, radial basis function networks, recurrent neural networks, and self-organizing maps. We analyze the strengths and weaknesses of these architectures in the context of time series modeling. We then summarize some recent time series ANN modeling applications found in the literature, focusing mainly on the previously outlined architectures. In our opinion, these summarized techniques constitute a representative sample of the research and development efforts made in this field. We aim to provide the general reader with a good perspective on how ANNs have been employed for time series modeling and forecasting tasks. Finally, we comment on possible new research directions in this area.

Reviews and syntheses: Remotely sensed optical time series for monitoring vegetation productivity

Abstract. Vegetation productivity is a critical indicator of global ecosystem health and is impacted by human activities and climate change. A wide range of optical sensing platforms, from ground-based to airborne and satellite, provide spatially continuous information on terrestrial vegetation status and functioning. As optical Earth observation (EO) data are usually routinely acquired, vegetation can be monitored repeatedly over time, reflecting seasonal vegetation patterns and trends in vegetation productivity metrics. Such metrics include gross primary productivity, net primary productivity, biomass, or yield. To summarize current knowledge, in this paper we systematically reviewed time series (TS) literature for assessing state-of-the-art vegetation productivity monitoring approaches for different ecosystems based on optical remote sensing (RS) data. As the integration of solar-induced fluorescence (SIF) data in vegetation productivity processing chains has emerged as a promising source, we also include this relatively recent sensor modality. We define three methodological categories to derive productivity metrics from remotely sensed TS of vegetation indices or quantitative traits: (i) trend analysis and anomaly detection, (ii) land surface phenology, and (iii) integration and assimilation of TS-derived metrics into statistical and process-based dynamic vegetation models (DVMs). Although the majority of used TS data streams originate from data acquired from satellite platforms, TS data from aircraft and unoccupied aerial vehicles have found their way into productivity monitoring studies. To facilitate processing, we provide a list of common toolboxes for inferring productivity metrics and information from TS data. We further discuss validation strategies of the RS data derived productivity metrics: (1) using in situ measured data, such as yield; (2) sensor networks of distinct sensors, including spectroradiometers, flux towers, or phenological cameras; and (3) inter-comparison of different productivity metrics. Finally, we address current challenges and propose a conceptual framework for productivity metrics derivation, including fully integrated DVMs and radiative transfer models here labelled as “Digital Twin”. This novel framework meets the requirements of multiple ecosystems and enables both an improved understanding of vegetation temporal dynamics in response to climate and environmental drivers and enhances the accuracy of vegetation productivity monitoring.

Nonstationary analysis of tides using higher order stochastic cycles

Estuarine tides, currents and shelf phenomena are often non-stationary, with a frequency composition that evolves with time and forcing such as river flow and density structure. Such tides are difficult to characterize quantitatively, particularly against a background of significant, multi-scale sub-tidal and cusp energy. One challenge identified in past work is the separation of diurnal and subtidal components of the signal. The difficulty is exacerbated in basins such as the San Francisco Bay-Delta, where the diurnal species is subject to fortnightly fluctuation due to O1-K1 beating (the tropical spring-neap cycle) and the subsequent interaction with the semidiurnal species leads to the production of modulated terdiurnal energy. This paper extends the method of higher order stochastic cycles, a construct from the structural time series literature, for use in analyzing these nonstationary tides. Interpretable as a multi-species generalization of Butterworth low pass and bandpass filters, Stochastic Cycle Harmonic Analysis (SCHA) possesses an interpretable stationary frequency response and can accurately extract terdiurnal frequencies. Represented by a state space formulation and fit using a Markov Chain Monte Carlo (MCMC) method, the method can produce Bayesian confidence intervals for derived quantities such as amplitudes, is robust to patches of missing data, and is energy conserving. We evaluate the method on benchmark problems that test its time and frequency resolution. In a field application on the Sacramento River in the San Francisco Bay-Delta SCHA confirms that the declinational beating of O1 and K1, heavily modulated by river flow, dominates fortnightly variation in the tide and its terdiurnal response.

A computationally efficient algorithm to estimate the parameters of a two-dimensional chirp model with the product term

Chirp signal models and their generalizations have been used to model many natural and man-made phenomena in signal processing and time series literature. In recent times, several methods have been proposed for parameter estimation of these models. However, these methods are either statistically sub-optimal or computationally burdensome, especially for two dimensional chirp models. In this paper, we consider the problem of parameter estimation of two dimensional chirp models and propose a computationally efficient estimator and establish asymptotic theoretical properties of the proposed estimators. Moreover, the proposed estimators are observed to have the same rates of convergence as the least squares estimators. Further, the proposed estimators of chirp rate parameters are shown to be asymptotically optimal. Extensive and detailed numerical simulations are conducted, which support the theoretical results of the proposed estimators.

Impact of Petroleum Energy Price Volatility on Commodity Prices in Ghana

The purpose of this article is to demonstrate the relationship between petroleum energy volatility and commodity prices in Ghana, which are indexed (energy grains, meat, and cooking oil), as well as to provide an empirical specification of the impact's direction. With reference to time series literature, the paper examined energy and commodity price connection models such as augmented dickey fuller, granger causality, co-integration, vector autoregressive and the vector error correction models used in estimating the association among petroleum energy volatility and the three selected commodity variables. The paper found that, there is a long run relationship between petroleum energy volatility and commodity prices in Ghana from 2011 to 2022. A single equation error correction model suggested that, petroleum energy shocks increase prices of grains, meat and cooking oil in both the short and long run. Impulse response function and variance decomposition conducted on the variables also suggested that there is both short and long run association between the variables.

Optimal model averaging based on leave‐h‐out forward‐validation for threshold autoregressive models

The threshold autoregressive (TAR) model has received considerable attention in nonlinear time series literature. To weaken the impacts coming from model uncertainty and to improve the prediction accuracy, this paper develops a leave‐ ‐out forward‐validation model averaging (LhoFVMA) method to average predictions from the TAR model. We establish our method's asymptotic optimality in the sense of achieving the lowest possible squared prediction risk. Simulation experiments show that our method is generally more efficient than other methods. For illustration, we future apply the proposed method to the basis of CSI 300 stock index futures.

Information quantity evaluation of nonlinear time series processes and applications

Among several models proposed in the time series literature, the Self-Exciting Threshold Autoregressive (SETAR) model is non-linear and considers threshold values to model time series affected by regimes. Beyond the linear models, the computation of information and dependence metrics in non-linear time series is of great interest to compare processes and test non-linearity. This paper considers the stationary marginal density of a SETAR(2;1,1) process to compute explicit differential entropy and Kullback–Leibler and Jeffrey’s divergences. In addition, an asymptotic homogeneity test for statistical significance of the disparity between two SETAR(2;1,1) processes was built. Numerical illustrations and applications to fish condition factor and Chilean economic perception time series are presented to illustrate the proposed methodology. Besides, a numerical algorithm based on Riemann–Stieltjes integral definition is implemented to calculate information measures based on stationary cumulative density functions of other types of nonlinear stationary stochastic processes, such as the first-order double autoregressive bilinear threshold moving average and threshold autoregressive moving average processes.

Estimation of multivariate asymmetric power GARCH models

We suggest a new class of multivariate power transformed asymmetric models. It includes several functional forms of multivariate GARCH models which are of great interest in financial modeling and time series literature. We provide an explicit necessary and sufficient condition to establish the strict stationarity of the model. The asymptotic properties of the quasi-maximum likelihood estimator of the parameters are established. The asymptotic results are illustrated by Monte Carlo experiments and an application to real financial data is studied.

A notable Gamma‐Lindley first‐order autoregressive process: An application to hydrological data

AbstractA new Gamma‐Lindley (GaL) first‐order autoregressive process (AR) is introduced, called GaL‐AR(1). The distribution for the GaL‐AR(1) innovation process and some of its structural properties are derived, such as the Laplace transform for its bivariate distribution, the conditional variance and expected value, and the spectral and autocorrelation functions. We propose two different estimation procedures whose asymptotic properties are studied by Monte Carlo experiments. An application to actual data from hydrology is performed. Results point out that our process outperforms other six non‐Gaussian AR(1) models that are well defined in the time series literature.

MLTF: Model less time-series forecasting

Multi-step ahead long term forecasting remains a pertinent challenge in time series literature due to non-stationary behaviour of real-world data. Predominantly most traditional time series models are parametric in nature and they use the predicted values to generate forecast for future time steps. This leads to error accumulation in each step of the forecasting horizon which causes increasingly poorer forecast in long-term. Other than the problem of error accumulation, most parametric algorithms also require significant pre-processing, hyper-parameter tuning, training and post-processing which can often put high computational burden on the system. Therefore, this paper proposes, Model Less Time-series Forecasting (MLTF), a non-parametric approach for forecasting which does not require any pre-processing or traditional training (i.e. Backpropagation). MLTF is a non-parametric method which uses statistical representations such as trend, linearity, entropy etc. to cluster series from a pre-defined repository and the series from same cluster are tagged as similar series. The trajectory of the target series is extracted from these similar series after applying an adaptive re-sampling technique. There is minimal training involved in MLTF, therefore this framework is computationally very efficient. The model-less nature also enables it to not suffer from error accumulation in long-horizon forecast. MLTF is validated empirically with a rich set of experiments involving M1, M3 competition dataset, Electricity, Volatility and COVID-19 data (over 4500 independent uni-variate series of different frequencies i.e. Hourly, Daily, Monthly, Quarterly and Yearly). The experiments demonstrate that, MLTF is significantly faster while being similar (or better) in terms of forecasting accuracy than the state-of-the-art DL methods and other non-parametric time series model.

Clustering high‐frequency financial time series based on information theory

AbstractClustering large financial time series data enables pattern extraction that facilitates risk management. The knowledge gathered from unsupervised learning is useful for improving portfolio optimization and making stock trading recommendations. Most methods available in the literature for clustering financial time series are based on exploiting linear relationships between time series. However, prices of different assets (stocks) may have non‐linear relationships which may be quantified using information based measures such as mutual information (MI). To estimate the empirical mutual information between time series of stock returns, we employ a novel kernel density estimator (KDE) based jackknife mutual information estimation (JMI), and compare it with the widely‐used binning method. We then propose an average distance gradient change algorithm and an algorithm based on the average silhouette criterion that use pairwise and groupwise MI of high‐frequency financial stock returns. Through numerical studies, we provide insights into the impact of the clustering on asset allocation and risk management based on the nonlinear information structure of the US stock market.

A new explainable robust high-order intuitionistic fuzzy time-series method

Fuzzy time series, based on type-1 fuzzy sets, continue to have a wide range of use in the literature. These methods use only membership values to determine the fuzzy relations. However, intuitionistic fuzzy time series models use both membership values and non-membership values. So it can be considered that the use of intuitionistic fuzzy time forecasting models will be able to increase the forecasting performance because the intuitionistic fuzzy sets have more information than fuzzy sets. Therefore, intuitionistic fuzzy time series models have started to employ for forecasting the real-life series in the fuzzy time series literature. A novel, explainable, robust high-order intuitionistic fuzzy time series forecasting method is proposed based on a newly defined model. In the proposed method, the intuitionistic fuzzy c-means algorithm is used for the fuzzification of observations, and a robust regression method employed for determining fuzzy relations. With the use of robust regression in determining the fuzzy relationships, all inputs of the proposed method can be explainable and they can be tested and commented on statistically. Applications of this study are made by using energy data of Primary Energy Consumption between the years 1965 and 2016 for 23 countries in the region of Europe-Eurasia. The forecasting performance of the proposed method is compared with the performance of some selected benchmarks, and the obtained results are discussed.

CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data

This paper investigates the central limit theorem for linear spectral statistics of high dimensional sample covariance matrices of the form \({\mathbf {B}}_n=n^{-1}\sum _{j=1}^{n}{\mathbf {Q}}{\mathbf {x}}_j{\mathbf {x}}_j^{*}{\mathbf {Q}}^{*}\) under the assumption that \(p/n\rightarrow y>0\), where \({\mathbf {Q}}\) is a \(p\times k\) nonrandom matrix and \(\{{\mathbf {x}}_j\}_{j=1}^n\) is a sequence of independent k-dimensional random vector with independent entries. A key novelty here is that the dimension \(k\ge p\) can be arbitrary, possibly infinity. This new model of sample covariance matrix \({\mathbf {B}}_n\) covers most of the known models as its special cases. For example, standard sample covariance matrices are obtained with \(k=p\) and \({\mathbf {Q}}={\mathbf {T}}_n^{1/2}\) for some positive definite Hermitian matrix \({\mathbf {T}}_n\). Also with \(k=\infty \) our model covers the case of repeated linear processes considered in recent high-dimensional time series literature. The CLT found in this paper substantially generalizes the seminal CLT in Bai and Silverstein (Ann Probab 32(1):553–605, 2004). Applications of this new CLT are proposed for testing the AR(1) or AR(2) structure for a causal process. Our proposed tests are then used to analyze a large fMRI data set.

Panel data measures of price discovery

This paper considers disaggregated price data that are observed not only for multiple markets over extended periods of time, but also for a large number of assets. The previous literature has argued that in such data rich environments, which arise frequently in applied work, the analysis of price discovery can be made more precise by accounting for the panel structure of the data. Moreover, since the individual assets are not that interesting anyways, little is lost by taking the overall panel perspective. These arguments are, however, mainly based on empirical observations, and there is little in terms of econometric support. The purpose of the present study is to fill this gap in the literature. This is done by offering a full-blown econometric analysis of panel analogs of the information share and permanent–transitory measures of price discovery, which are the workhorses of the time series literature. Both measures are shown to be consistent and they support standard normal inference, which is in contrast to the time series case, where such inference is only possible for the permanent–transitory measure.

Mortality models incorporating long memory for life table estimation: a comprehensive analysis

AbstractMortality projection and forecasting of life expectancy are two important aspects of the study of demography and life insurance modelling. We demonstrate in this work the existence of long memory in mortality data. Furthermore, models incorporating long memory structure provide a new approach to enhance mortality forecasts in terms of accuracy and reliability, which can improve the understanding of mortality. Novel mortality models are developed by extending the Lee–Carter (LC) model for death counts to incorporate a long memory time series structure. To link our extensions to existing actuarial work, we detail the relationship between the classical models of death counts developed under a Generalised Linear Model (GLM) formulation and the extensions we propose that are developed under an extension to the GLM framework known in time series literature as the Generalised Linear Autoregressive Moving Average (GLARMA) regression models. Bayesian inference is applied to estimate the model parameters. The Deviance Information Criterion (DIC) is evaluated to select between different LC model extensions of our proposed models in terms of both in-sample fits and out-of-sample forecasts performance. Furthermore, we compare our new models against existing models structures proposed in the literature when applied to the analysis of death count data sets from 16 countries divided according to genders and age groups. Estimates of mortality rates are applied to calculate life expectancies when constructing life tables. By comparing different life expectancy estimates, results show the LC model without the long memory component may provide underestimates of life expectancy, while the long memory model structure extensions reduce this effect. In summary, it is valuable to investigate how the long memory feature in mortality influences life expectancies in the construction of life tables.

A Comparative Study of Gamma Markov Chains for Temporal Non-Negative Matrix Factorization

Non-negative matrix factorization (NMF) has become a well-established class of methods for the analysis of non-negative data. In particular, a lot of effort has been devoted to probabilistic NMF, namely estimation or inference tasks in probabilistic models describing the data, based for example on Poisson or exponential likelihoods. When dealing with time series data, several works have proposed to model the evolution of the activation coefficients as a non-negative Markov chain, most of the time in relation with the Gamma distribution, giving rise to so-called temporal NMF models. In this paper, we review four Gamma Markov chains of the NMF literature, and show that they all share the same drawback: the absence of a well-defined stationary distribution. We then introduce a fifth process, an overlooked model of the time series literature named BGAR(1), which overcomes this limitation. These temporal NMF models are then compared in a MAP framework on a prediction task, in the context of the Poisson likelihood.

On explaining the surprising success of reservoir computing forecaster of chaos? The universal machine learning dynamical system with contrast to VAR and DMD.

Machine learning has become a widely popular and successful paradigm, especially in data-driven science and engineering. A major application problem is data-driven forecasting of future states from a complex dynamical system. Artificial neural networks have evolved as a clear leader among many machine learning approaches, and recurrent neural networks are considered to be particularly well suited for forecasting dynamical systems. In this setting, the echo-state networks or reservoir computers (RCs) have emerged for their simplicity and computational complexity advantages. Instead of a fully trained network, an RC trains only readout weights by a simple, efficient least squares method. What is perhaps quite surprising is that nonetheless, an RC succeeds in making high quality forecasts, competitively with more intensively trained methods, even if not the leader. There remains an unanswered question as to why and how an RC works at all despite randomly selected weights. To this end, this work analyzes a further simplified RC, where the internal activation function is an identity function. Our simplification is not presented for the sake of tuning or improving an RC, but rather for the sake of analysis of what we take to be the surprise being not that it does not work better, but that such random methods work at all. We explicitly connect the RC with linear activation and linear readout to well developed time-series literature on vector autoregressive (VAR) averages that includes theorems on representability through the Wold theorem, which already performs reasonably for short-term forecasts. In the case of a linear activation and now popular quadratic readout RC, we explicitly connect to a nonlinear VAR, which performs quite well. Furthermore, we associate this paradigm to the now widely popular dynamic mode decomposition; thus, these three are in a sense different faces of the same thing. We illustrate our observations in terms of popular benchmark examples including Mackey-Glass differential delay equations and the Lorenz63 system.

The Linkages between Crude Oil and Food Prices

This paper aims to indicate the linkages between crude oil prices and selected food price indexes (dairy, meat, oils, cereals, and sugar) and provide an empirical specification of the direction of the impact. This paper reviews the fuel–food price linkage models with consideration to the time series literature. This study adopts several methods, namely the Augmented Dickey–Fuller test, Granger causality test, the cointegration test, the vector autoregression model, and the vector error correction model, for studying the price transmission among the crude oil and five selected food groups. The data series covers the period between January 1990 and September 2020. The empirical results from the paper indicate that there are long-term relationships between crude oil and meat prices. The linkage of crude oil prices occurred with food, cereal, and oil prices in the short term. Furthermore, the linkages between the analyzed variables increased in 2006–2020.