This paper derives a Minimum Message Length (MML) criterion for the model selection of the Autoregressive Moving Average (ARMA) time series model. The MML87 performances on the ARMA model compared with other well known model selection criteria, Akaike Information Criterion (AIC), Corrected AIC (AICc), Bayesian Information Criterion (BIC), and Hannan Quinn (HQ). The experimental results show that the MML87 is outperformed the other model selection criteria as it select most of the models with lower prediction errors and the models selected by MML87 to have a lower mean squared error in different in-sample and out-sample sizes.
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…
In this paper, we consider a continuous-time autoregressive fractionally integrated moving average (CARFIMA) model, which is defined as the stationary solution of a stochastic differential equation driven by a standard fractional Brownian motion. Like the discrete-time ARFIMA model, the CARFIMA model is useful for studying time series with short memory, long memory and antipersistence. We investigate the stationarity of the model and derive its covariance structure. In addition, we derive the spectral density function of a stationary CARFIMA process.
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 …
In practice, several time series exhibit long-range dependence or persistence in their observations, leading to the development of a number of estimation and prediction methodologies to account for the slowly decaying autocorrelations. The autoregressive fractionally integrated moving average (ARFIMA) process is one of the best-known classes of long-memory models. In the package afmtools for R, we have implemented some of these statistical tools for analyzing ARFIMA models. In particular, this package contains functions for parameter estimation, exact autocovariance calculation, predictive abi…
A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the general case, it is shown that the model is weakly stationary. The lowest dimension of the state-space representation is given along with the one-step linear predictors and their mean squared errors. The maximum likelihood estimation procedure is discussed, and their finite-sample behavior is assessed through Monte Carlo experiments. These experiments show tha…
Fractionally integrated autoregressive moving average (FIARMA) processes have been widely and successfully used to model and predict univariate time series exhibiting long range dependence. Vector and functional extensions of these processes have also been considered more recently. Here we study these processes by relying on a spectral domain approach in the case where the processes are valued in a separable Hilbert space H0. In this framework, the usual univariate long memory parameter d is replaced by a long memory operator D acting on H0, leading to a class of H0-valued FIARMA(D, p, q) proc…
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…
The Vector AutoRegressive Moving Average (VARMA) model is fundamental to the theory of multivariate time series; however, identifiability issues have led practitioners to abandon it in favor of the simpler but more restrictive Vector AutoRegressive (VAR) model. We narrow this gap with a new optimization-based approach to VARMA identification built upon the principle of parsimony. Among all equivalent data-generating models, we use convex optimization to seek the parameterization that is "simplest" in a certain sense. A user-specified strongly convex penalty is used to measure model simplicity,…
The study was conducted to develop an appropriate model that could predict the weekly reported Malaria incidence in the Philippines using the Box-Jenkins method.The data were retrieved from the Department of Health(DOH) website in the Philippines. It contains 70 data points of which 60 data points were used in model building and the remaining 10 data points were used for forecast evaluation. The R Statistical Software was used to do all the necessary computations in the study. Box-Cox Transformation and Differencing was done to make the series stationary. Based on the results of the analysis, …
An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for identifying and modeling noncausal and noninvertible autoregressive-moving average processes. We establish asymptotic normality and consistency for rank-based estimators of all-pass model parameters. The estimators are obtained by minimizing the rank-based residual dispersion function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These estimators …
The object of this paper is to study the asymptotic dependence structure of the linear time series models with infinitely divisible innovations by the use of their characteristic functions. Autoregressive moving-average (ARMA) models and fractional autoregressive integrated moving-average (FARIMA) models are analyzed. As examples of infinitely divisible innovations, the class of radially absolute continuous distributions and general non-symmetric stable distributions are considered. The finite dimensional distributionsn of these models are also obtained.
The approximation of a stationary time-series by finite order autoregressive (AR) and moving averages (MA) is a problem that occurs in many applications. In this paper we study asymptotic behavior of the spectral density of finite order approximations of wide sense stationary time series. It is shown that when the on the spectral density is non-vanishing in $[-π,π]$ and the covariance is summable, the spectral density of the approximating autoregressive sequence converges at the origin. Under additional mild conditions on the coefficients of the Wold decomposition it is also shown that the spe…
A statistical indicator for dynamic stability known as the $Υ$ indicator is used to gauge the stability and hence detect approaching tipping points of simulation data from a reduced 5-box model of the North-Atlantic Meridional Overturning Circulation (AMOC) exposed to a time dependent hosing function. The hosing function simulates the influx of fresh water due to the melting of the Greenland ice sheet and increased precipitation in the North Atlantic. The $Υ$ indicator is designed to detect changes in the memory properties of the dynamics, and is based on fitting ARMA (auto-regressive moving-a…
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 mo…
This study aimed to find temporal clusters for several commodity prices using the threshold non-linear autoregressive model. It is expected that the process of determining the commodity groups that are time-dependent will advance the current knowledge about the dynamics of co-moving and coherent prices, and can serve as a basis for multivariate time series analyses. The clustering of commodity prices was examined using the proposed clustering approach based on time series models to incorporate the time varying properties of price series into the clustering scheme. Accordingly, the primary aim …
We demonstrate the use of conditional autoregressive generative models (van den Oord et al., 2016a) over a discrete latent space (van den Oord et al., 2017b) for forward planning with MCTS. In order to test this method, we introduce a new environment featuring varying difficulty levels, along with moving goals and obstacles. The combination of high-quality frame generation and classical planning approaches nearly matches true environment performance for our task, demonstrating the usefulness of this method for model-based planning in dynamic environments.
Hainan University（海南大学）；University of Chinese Academy of Science（中国科学院大学）
Traffic flow forecasting is hot spot research of intelligent traffic system construction. The existing traffic flow prediction methods have problems such as poor stability, high data requirements, or poor adaptability. In this paper, we define the traffic data time singularity ratio in the dropout module and propose a combination prediction method based on the improved long short-term memory neural network and time series autoregressive integrated moving average model (SDLSTM-ARIMA), which is derived from the Recurrent Neural Networks (RNN) model. It compares the traffic data time singularity …
A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed data and the specification of second-order moments. The second definition provided is more flexible in the sense that it allows for considering other distributional assumptions. The statistical properties are investigated along with the one-step linear predictors and their mean squared errors. It is established that the process is strictly stationary under no…
We present an outline of the theory of certain Lévy-driven, multivariate stochastic processes, where the processes are represented by rational transfer functions (Continuous-time AutoRegressive Moving Average or CARMA models) and their applications in non-Gaussian time series modelling. We discuss in detail their definition, their spectral representation, the equivalence to linear state space models and further properties like the second order structure and the tail behaviour under a heavy-tailed input. Furthermore, we study the estimation of the parameters using quasi-maximum likelihood estim…
Bounded time series consisting of rates or proportions are often encountered in applications. This manuscript proposes a practical approach to analyze bounded time series, through a beta regression model. The method allows the direct interpretation of the regression parameters on the original response scale, while properly accounting for the heteroskedasticity typical of bounded variables. The serial dependence is modeled by a Gaussian copula, with a correlation matrix corresponding to a stationary autoregressive and moving average process. It is shown that inference, prediction, and control c…
We introduce the concept of autoregressive moving average (ARMA) filters on a graph and show how they can be implemented in a distributed fashion. Our graph filter design philosophy is independent of the particular graph, meaning that the filter coefficients are derived irrespective of the graph. In contrast to finite-impulse response (FIR) graph filters, ARMA graph filters are robust against changes in the signal and/or graph. In addition, when time-varying signals are considered, we prove that the proposed graph filters behave as ARMA filters in the graph domain and, depending on the impleme…
Most time-series models assume that the data come from observations that are equally spaced in time. However, this assumption does not hold in many diverse scientific fields, such as astronomy, finance, and climatology, among others. There are some techniques that fit unequally spaced time series, such as the continuous-time autoregressive moving average (CARMA) processes. These models are defined as the solution of a stochastic differential equation. It is not uncommon in astronomical time series, that the time gaps between observations are large. Therefore, an alternative suitable approach t…
Tel Aviv University（特拉维夫大学）；Facebook AI Research（Facebook AI研究院）
We revisit recent methods that employ graph neural networks for decoding error correcting codes and employ messages that are computed in an autoregressive manner. The outgoing messages of the variable nodes are conditioned not only on the incoming messages, but also on an estimation of the SNR and on the inferred codeword and on two downstream computations: (i) an extended vector of parity check outcomes, (ii) the mismatch between the inferred codeword and the re-encoding of the information bits of this codeword. Unlike most learned methods in the field, our method violates the symmetry condit…
In this paper we discuss dynamic ARMA-type regression models for time series taking values in $(0,\infty)$. In the proposed model, the conditional mean is modeled by a dynamic structure containing autoregressive and moving average terms, time-varying regressors, unknown parameters and link functions. We introduce the new class of models and discuss partial maximum likelihood estimation, hypothesis testing inference, diagnostic analysis and forecasting.
In this paper we derive closed-form formulas of feedback capacity and nonfeedback achievable rates, for Additive Gaussian Noise (AGN) channels driven by nonstationary autoregressive moving average (ARMA) noise (with unstable one poles and zeros), based on time-invariant feedback codes and channel input distributions. From the analysis and simulations follows the surprising observations, (i) the use of time-invariant channel input distributions gives rise to multiple regimes of capacity that depend on the parameters of the ARMA noise, which may or may not use feedback, (ii) the more unstable th…
Two simple Markov processes are examined, one in discrete and one in continuous time, arising from idealized versions of a transmission protocol for mobile, delay-tolerant networks. We consider two independent walkers moving with constant speed on either the discrete or continuous circle, and changing directions at independent geometric (respectively, exponential) times. One of the walkers carries a message that wishes to travel as far and as fast as possible in the clockwise direction. The message stays with its current carrier unless the two walkers meet, the carrier is moving counter-clockw…
In this paper, we use convolutional neural networks to address the problem of model identification for autoregressive moving average time series models. We compare the performance of several neural network architectures, trained on simulated time series, with likelihood based methods, in particular the Akaike and Bayesian information criteria. We find that our neural networks can significantly outperform these likelihood based methods in terms of accuracy and, by orders of magnitude, in terms of speed.
The feedback capacity of additive stationary Gaussian noise channels is characterized as the solution to a variational problem. Toward this end, it is proved that the optimal feedback coding scheme is stationary. When specialized to the first-order autoregressive moving average noise spectrum, this variational characterization yields a closed-form expression for the feedback capacity. In particular, this result shows that the celebrated Schalkwijk-Kailath coding scheme achieves the feedback capacity for the first-order autoregressive moving average Gaussian channel, positively answering a long…
The feedback capacity of the stationary Gaussian additive noise channel has been open, except for the case where the noise is white. Here we find the feedback capacity of the stationary first-order moving average additive Gaussian noise channel in closed form. Specifically, the channel is given by $Y_i = X_i + Z_i,$ $i = 1, 2, ...,$ where the input $\{X_i\}$ satisfies a power constraint and the noise $\{Z_i\}$ is a first-order moving average Gaussian process defined by $Z_i = αU_{i-1} + U_i,$ $|α| \le 1,$ with white Gaussian innovations $U_i,$ $i = 0,1,....$ We show that the feedback capacity …
We consider the two-receiver memoryless broadcast channel with states where each receiver requests both common and private messages, and may know part of the private message requested by the other receiver as receiver message side information (RMSI). We address two categories of the channel (i) channel with states known causally to the transmitter, and (ii) channel with states known non-causally to the transmitter. Starting with the channel without RMSI, we first propose a transmission scheme and derive an inner bound for the causal category. We then unify our inner bound for the causal catego…
Just as there are frictional losses associated with moving masses on a surface, what if there were frictional losses associated with moving information on a substrate? Indeed, many modes of communication suffer from such frictional losses. We propose to model these losses as proportional to "bit-meters," i.e., the product of mass of information (i.e., the number of bits) and the distance of information transport. We use this "information- friction" model to understand fundamental energy requirements on encoding and decoding in communication circuitry. First, for communication across a binary i…
Delay and Disruption Tolerant Networks (DTNs) may lack continuous network connectivity. Routing in DTNs is thus a challenge since it must handle network partitioning, long delays, and dynamic topology. Meanwhile, routing protocols of the traditional Mobile Ad hoc NETworks (MANETs) cannot work well due to the failure of its assumption that most network connections are available. In this article, a geographic routing protocol is proposed for MANETs in delay tolerant situations, by using no more than one-hop information. A utility function is designed for implementing the under-controlled replica…
