A time series is a sequence of observations taken sequentially in time. The autoregressive integrated moving average is a class of the model more used for times series data. However, this class of model has two critical limitations. It fits well onlyGaussian data with the linear structure of correlation. Here, I present a new model named as generalized autoregressive neural networks, GARNN. The GARNN is an extension of the generalized linear model where the mean marginal depends on the lagged values via the inclusion of the neural network in the link function. A practical application of the model is shown using a well-known poliomyelitis case number, originated analyzed by Zeger and Qaqish (1988),
Heteroskedasticity is a common feature of financial time series and is commonly addressed in the model building process through the use of ARCH and GARCH processes. More recently multivariate variants of these processes have been in the focus of research with attention given to methods seeking an efficient and economic estimation of a large number of model parameters. Due to the need for estimation of many parameters, however, these models may not be suitable for modeling now prevalent high-frequency volatility data. One potentially useful way to bypass these issues is to take a functional app…
Score-driven models, also known as generalized autoregressive score models, represent a class of observation-driven time series models. They possess powerful properties, such as the ability to model different conditional distributions and to consider time-varying parameters within a flexible framework. In this paper, we present ScoreDrivenModels.jl, an open-source Julia package for modeling, forecasting, and simulating time series using the framework of score-driven models. The package is flexible with respect to model definition, allowing the user to specify the lag structure and which parame…
One of the important and widely used classes of models for non-Gaussian time series is the generalized autoregressive model average models (GARMA), which specifies an ARMA structure for the conditional mean process of the underlying time series. However, in many applications one often encounters conditional heteroskedasticity. In this paper we propose a new class of models, referred to as GARMA-GARCH models, that jointly specify both the conditional mean and conditional variance processes of a general non-Gaussian time series. Under the general modeling framework, we propose three specific mod…
We consider a class of spatio-temporal models which extend popular econometric spatial autoregressive panel data models by allowing the scalar coefficients for each location (or panel) different from each other. To overcome the innate endogeneity, we propose a generalized Yule-Walker estimation method which applies the least squares estimation to a Yule-Walker equation. The asymptotic theory is developed under the setting that both the sample size and the number of locations (or panels) tend to infinity under a general setting for stationary and alpha-mixing processes, which includes spatial a…
In this paper, we introduce a new spatial model that incorporates heteroscedastic variance depending on neighboring locations. The proposed process is regarded as the spatial equivalent to the temporal autoregressive conditional heteroscedasticity (ARCH) model. We show additionally how the introduced spatial ARCH model can be used in spatiotemporal settings. In contrast to the temporal ARCH model, in which the distribution is known given the full information set of the prior periods, the distribution is not straightforward in the spatial and spatiotemporal setting. However, it is possible to e…
Autoregressive moving average and generalized autoregressive moving average are often used in statistical modeling. This study uses this method because the method uses data from the previous period to model the data for the current period. In addition, the technique is often used in data prediction. The familiar data used is count data. Count data is the data that most often cause data not to spread usually. Therefore, time series modeling, one of which is through arithmetic series, was developed. This study aims to obtain the best modeling results from positive confirmed cases of Covid 19 in …
This study was conducted to find an appropriate statistical model to forecast the volatilities of PSEi using the model Generalized Autoregressive Conditional Heteroskedasticity (GARCH). Using the R software, the log returns of PSEi is modeled using various ARIMA models and with the presence of heteroskedasticity, the log returns was modeled using GARCH. Based on the analysis, GARCH models are the most appropriate to use for the log returns of PSEi. Among the selected GARCH models, GARCH (1,2) has the lowest AIC value and also has the highest LL value implying that GARCH (1,2) is the best model…
The space time autoregressive model has been widely applied in science, in areas such as economics, public finance, political science, agricultural economics, environmental studies and transportation analyses. The classical space time autoregressive model is a linear model for describing spatial correlation. In this work, we expand the classical model to include related exogenous variables, possibly non-Gaussian, high volatility errors, and a nonlinear neural network component. The nonlinear neural network component allows for more model flexibility, the ability to learn and model nonlinear an…
Lehigh University（理海大学）；Xiamen University of Technology（厦门理工学院）
Extreme multi-label text classification (XMTC) is a task for tagging a given text with the most relevant labels from an extremely large label set. We propose a novel deep learning method called APLC-XLNet. Our approach fine-tunes the recently released generalized autoregressive pretrained model (XLNet) to learn a dense representation for the input text. We propose Adaptive Probabilistic Label Clusters (APLC) to approximate the cross entropy loss by exploiting the unbalanced label distribution to form clusters that explicitly reduce the computational time. Our experiments, carried out on five b…
The autoregressive Hilbertian model (ARH) was introduced in the early 90's by Denis Bosq. It was the subject of a vast literature and gave birth to numerous extensions. The model generalizes the classical multidimensional autoregressive model, widely used in Time Series Analysis. It was successfully applied in numerous fields such as finance, industry, biology. We propose here to compare the classical prediction methodology based on the estimation of the autocorrelation operator with a neural network learning approach. The latter is based on a popular version of Recurrent Neural Networks : the…
We show Vector Autoregressive Moving Average models with scalar Moving Average components could be estimated by generalized least square (GLS) for each fixed moving average polynomial. The conditional variance of the GLS model is the concentrated covariant matrix of the moving average process. Under GLS the likelihood function of these models has similar format to their VAR counterparts. Maximum likelihood estimate can be done by optimizing with gradient over the moving average parameters. These models are inexpensive generalizations of Vector Autoregressive models. We discuss a relationship b…
Neural autoregressive models are explicit density estimators that achieve state-of-the-art likelihoods for generative modeling. The D-dimensional data distribution is factorized into an autoregressive product of one-dimensional conditional distributions according to the chain rule. Data completion is a more involved task than data generation: the model must infer missing variables for any partially observed input vector. Previous work introduced an order-agnostic training procedure for data completion with autoregressive models. Missing variables in any partially observed input vector can be i…
We propose Neural GARCH, a class of methods to model conditional heteroskedasticity in financial time series. Neural GARCH is a neural network adaptation of the GARCH 1,1 model in the univariate case, and the diagonal BEKK 1,1 model in the multivariate case. We allow the coefficients of a GARCH model to be time varying in order to reflect the constantly changing dynamics of financial markets. The time varying coefficients are parameterised by a recurrent neural network that is trained with stochastic gradient variational Bayes. We propose two variants of our model, one with normal innovations …
Fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) arises in modeling of financial time series. FIGARCH is essentially governed by a system of nonlinear stochastic difference equations ${u_t}$ = ${z_t}$ $(1-\sum\limits_{j=1}^q β_j L^j)σ_{t}^2 = ω+(1-\sum\limits_{j=1}^q β_j L^j - (\sum\limits_{k=1}^p φ_k L^k) (1-L)^d) u_t^2$, where $ω\in$ R, and $β_j\in$ R are constant parameters, $\{u_t\}_{{t\in}^+}$ and $\{σ_t\}_{{t\in}^+}$ are the discrete time real valued stochastic processes which represent FIGARCH (p,d,q) and stochastic volatility, respectively. Mo…
Time Series forecasting (univariate and multivariate) is a problem of high complexity due the different patterns that have to be detected in the input, ranging from high to low frequencies ones. In this paper we propose a new model for timeseries prediction that utilizes convolutional layers for feature extraction, a recurrent encoder and a linear autoregressive component. We motivate the model and we test and compare it against a baseline of widely used existing architectures for univariate and multivariate timeseries. The proposed model appears to outperform the baselines in almost every cas…
Spatial autoregressive model, introduced by Clif and Ord in 1970s has been widely applied in many areas of science and econometrics such as regional economics, public finance, political sciences, agricultural economics, environmental studies and transportation analyses. As information technology grows rapidly, observations are seldom independent from others so a space autoregressive models can take this dependence into account and draw more reliable conclusions between covariates and the target variable itself. Based on the classical spatial model, Su and Jin proposed a semi-parametric model n…
ETH Zurich（苏黎世联邦理工学院）；EPFL Lausanne（洛桑联邦理工学院）；TalkingData Co., Ltd.（北京腾云天下科技有限公司）
In this paper, we propose an interpretable LSTM recurrent neural network, i.e., multi-variable LSTM for time series with exogenous variables. Currently, widely used attention mechanism in recurrent neural networks mostly focuses on the temporal aspect of data and falls short of characterizing variable importance. To this end, our multi-variable LSTM equipped with tensorized hidden states is developed to learn variable specific representations, which give rise to both temporal and variable level attention. Preliminary experiments demonstrate comparable prediction performance of multi-variable L…
University College London（伦敦大学学院）；Biomediq A/S（Biomediq公司）；University of Copenhagen（哥本哈根大学）；Cerebriu A/S（Cerebriu公司）
Learning temporal patterns from multivariate longitudinal data is challenging especially in cases when data is sporadic, as often seen in, e.g., healthcare applications where the data can suffer from irregularity and asynchronicity as the time between consecutive data points can vary across features and samples, hindering the application of existing deep learning models that are constructed for complete, evenly spaced data with fixed sequence lengths. In this paper, a novel deep learning-based model is developed for modeling multiple temporal features in sporadic data using an integrated deep …
In this paper, we propose multi-variable LSTM capable of accurate forecasting and variable importance interpretation for time series with exogenous variables. Current attention mechanism in recurrent neural networks mostly focuses on the temporal aspect of data and falls short of characterizing variable importance. To this end, the multi-variable LSTM equipped with tensorized hidden states is developed to learn hidden states for individual variables, which give rise to our mixture temporal and variable attention. Based on such attention mechanism, we infer and quantify variable importance. Ext…
Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaos
Courant Institute of Mathematical Sciences, New York University, USA（Courant数学科学研究所，纽约大学，美国）；Center for Data Science, New York University, USA（数据科学中心，纽约大学，美国）
Multivariate binary distributions can be decomposed into products of univariate conditional distributions. Recently popular approaches have modeled these conditionals through neural networks with sophisticated weight-sharing structures. It is shown that state-of-the-art performance on several standard benchmark datasets can actually be achieved by training separate probability estimators for each dimension. In that case, model training can be trivially parallelized over data dimensions. On the other hand, complexity control has to be performed for each learned conditional distribution. Three p…
Autoregressive neural network models have been used successfully for sequence generation, feature extraction, and hypothesis scoring. This paper presents yet another use for these models: allocating more computation to more difficult inputs. In our model, an autoregressive model is used both to extract features and to predict observations in a stream of input observations. The surprisal of the input, measured as the negative log-likelihood of the current observation according to the autoregressive model, is used as a measure of input difficulty. This in turn determines whether a small, fast ne…
This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and exploit the thinning representation to derive stationarity conditions and the stationary distribution of the process. We provide a Bayesian inference method and an efficient posterior approximation procedure based on Monte Carlo. Numerical illustrations on both simulated and real data show the effectiveness of the proposed inference.
This paper considers a semiparametric generalized autoregressive conditional heteroskedasticity (S-GARCH) model. For this model, we first estimate the time-varying long run component for unconditional variance by the kernel estimator, and then estimate the non-time-varying parameters in GARCH-type short run component by the quasi maximum likelihood estimator (QMLE). We show that the QMLE is asymptotically normal with the parametric convergence rate. Next, we construct a Lagrange multiplier test for linear parameter constraint and a portmanteau test for model checking, and obtain their asymptot…
Bayesian Generalized Network Autoregressive Model with Structured Shrinkage and Persistence Priors
Human-Centered Artificial Intelligence Research Institute, Ewha Womans University（梨花女子大学人类中心人工智能研究所）；Department of Statistics and Actuarial Science, Soongsil University（崇实大学统计与精算科学系）
Estimation of causal effects is fundamental in situations were the underlying system will be subject to active interventions. Part of building a causal inference engine is defining how variables relate to each other, that is, defining the functional relationship between variables given conditional dependencies. In this paper, we deviate from the common assumption of linear relationships in causal models by making use of neural autoregressive density estimators and use them to estimate causal effects within the Pearl's do-calculus framework. Using synthetic data, we show that the approach can r…
Institute for Computer Science and Control (SZTAKI)（计算机科学与控制研究所（SZTAKI））；Hungarian Academy of Sciences (MTA)（匈牙利科学院（MTA））
A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here, we suggest a finite sample approach, called ScoPe, to construct distribution-free confidence regions around the QML estimate, which have exact coverage probabilities, despite no additional assumptions …
