Vector linear time series models

This paper presents proofs of the strong law of large numbers and the central limit theorem for estimators of the parameters in quite general finite-parameter linear models for vector time series. The estimators are derived from a Gaussian likelihood (although Gaussianity is not assumed) and certain spectral approximations to this. An important example of finite-parameter models for multiple time series is the class of autoregressive moving-average (ARMA) models and a general treatment is given for this case. This includes a discussion of the problems associated with identification in such models.

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Limiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroscedastic errors

10.1214/aos/1030563979 ◽

1998 ◽

Vol 26 (1) ◽

pp. 84-125 ◽

Cited By ~ 69

Author(s):

Shiqing Ling ◽

W. K. Li

Keyword(s):

Time Series ◽

Maximum Likelihood ◽

Moving Average ◽

Maximum Likelihood Estimators ◽

Autoregressive Moving Average ◽

Limiting Distributions ◽

Heteroscedastic Errors

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FORECASTING OF OIL AND AGRICULTURAL COMMODITY PRICES: VARMA VERSUS ARMA

Annals of Financial Economics ◽

10.1142/s2010495217500129 ◽

2017 ◽

Vol 12 (03) ◽

pp. 1750012 ◽

Cited By ~ 2

Author(s):

MUSTAFA GÜLERCE ◽

GAZANFER ÜNAL

Keyword(s):

Moving Average ◽

Commodity Prices ◽

Wavelet Coherence ◽

Autoregressive Moving Average ◽

Multiple Time ◽

Energy Prices ◽

Agricultural Commodity ◽

Vector Autoregressive ◽

Dynamic Correlations ◽

Model Free

The aim of this paper is to show that the estimates made with vector autoregressive–moving-average (ARMA) models based on the coherent time intervals of the multiple time series give more precise results than the univariate case. The previous literature on dynamic correlations (co-movement) in between food and energy prices has mixed results and mainly based on parametric approaches. Therefore, partial wavelet coherence (PWC) and multiple wavelet coherence (MWC) methods are used, respectively, to uncover the coherency simultaneously for time and frequency domains. In our study; world oil, corn, soybeans, wheat and sugar prices are examined instead of the return and volatility relationship between oil and agricultural commodities due to model-free approach of wavelet analysis.

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The time series regression analysis in evaluating the economic impact of COVID-19 cases in Indonesia

Model Assisted Statistics and Applications ◽

10.3233/mas-210533 ◽

2021 ◽

Vol 16 (3) ◽

pp. 197-210

Author(s):

Utriweni Mukhaiyar ◽

Devina Widyanti ◽

Sandy Vantika

Keyword(s):

Time Series ◽

Exchange Rate ◽

Moving Average ◽

Autoregressive Moving Average ◽

Transfer Function Model ◽

Function Model ◽

Time Series Regression ◽

Vector Autoregressive ◽

Daily Data ◽

The Impact

This study aims to determine the impact of COVID-19 cases in Indonesia on the USD/IDR exchange rate using the Transfer Function Model and Vector Autoregressive Moving-Average with Exogenous Regressors (VARMAX) Model. This paper uses daily data on the COVID-19 case in Indonesia, the USD/IDR exchange rate, and the IDX Composite period from 1 March to 29 June 2020. The analysis shows: (1) the higher the increase of the number of COVID-19 cases in Indonesia will significantly weaken the USD/IDR exchange rate, (2) an increase of 1% in the number of COVID-19 cases in Indonesia six days ago will weaken the USD/IDR exchange rate by 0.003%, (3) an increase of 1% in the number of COVID-19 cases in Indonesia seven days ago will weaken the USD/IDR exchange rate by 0.17%, and (4) an increase of 1% in the number of COVID-19 cases in Indonesia eight days ago will weaken the USD/IDR exchange rate by 0.24%.

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Least absolute deviation estimation for general fractionally integrated autoregressive moving average time series models

Statistics & Probability Letters ◽

10.1016/j.spl.2014.07.008 ◽

2014 ◽

Vol 94 ◽

pp. 69-76 ◽

Cited By ~ 4

Author(s):

Rongning Wu

Keyword(s):

Time Series ◽

Moving Average ◽

Autoregressive Moving Average ◽

Time Series Models ◽

Least Absolute Deviation ◽

Absolute Deviation ◽

Least Absolute Deviation Estimation

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Load Forecasting using Time Series Techniques

Design Engineering ◽

10.17762/de.vi.4248 ◽

2021 ◽

pp. 11343-11357

Author(s):

Shahida Khatoon, Ibraheem, Priti, Mohammad Shahid

Keyword(s):

Time Series ◽

Linear Models ◽

Linear Trend ◽

Moving Average ◽

Load Forecasting ◽

Electric Load ◽

Time Data ◽

Efficient Operation ◽

Use Of Time ◽

Distribution Company

Load Forecasting is of great significance for effective and efficient operation of power system. Use of time series is of much importance in load forecasting. In this study, effectiveness of different time series techniques is identified to gathered valuable information. The objective is to predict electric load efficiently and effectively. This paper analyses the prediction accuracy of variety of time series method in modeling Electric load forecasts. The study examines the time series forecasting methods applied to estimate future electric load, specifically, Moving Average (MA), Linear Trend, the Exponential and Parabolic Trend. A comparison of different forecasting techniques of Time Series is demonstrated on real time data. The data utilized for forecast is made available through a distribution company of India. The traditional linear models and hybrid models along with ANN are developed. These models are appraised for the forecasting capability.

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ORBITS

Proceedings of the VLDB Endowment ◽

10.14778/3430915.3430920 ◽

2020 ◽

Vol 14 (3) ◽

pp. 294-306

Author(s):

Mourad Khayati ◽

Ines Arous ◽

Zakhar Tymchenko ◽

Philippe Cudré-Mauroux

Keyword(s):

Time Series ◽

Linear Time ◽

Multiple Time ◽

Multiple Time Series ◽

Online Data ◽

Incremental Computation ◽

Online Recovery ◽

Recovery Technique ◽

Centroid Decomposition

With the emergence of the Internet of Things (IoT), time series streams have become ubiquitous in our daily life. Recording such data is rarely a perfect process, as sensor failures frequently occur, yielding occasional blocks of data that go missing in multiple time series. These missing blocks do not only affect real-time monitoring but also compromise the quality of online data analyses. Effective streaming recovery (imputation) techniques either have a quadratic runtime complexity, which is infeasible for any moderately sized data, or cannot recover more than one time series at a time. In this paper, we introduce a new online recovery technique to recover multiple time series streams in linear time. Our recovery technique implements a novel incremental version of the Centroid Decomposition technique and reduces its complexity from quadratic to linear. Using this incremental technique, missing blocks are efficiently recovered in a continuous manner based on previous recoveries. We formally prove the correctness of our new incremental computation, which yields an accurate recovery. Our experimental results on real-world time series show that our recovery technique is, on average, 30% more accurate than the state of the art while being vastly more efficient.

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ARMA processes have maximal entropy among time series with prescribed autocovariances and impulse responses

Advances in Applied Probability ◽

10.1017/s0001867800015421 ◽

1985 ◽

Vol 17 (04) ◽

pp. 810-840 ◽

Cited By ~ 1

Author(s):

Jürgen Franke

Keyword(s):

Time Series ◽

Impulse Response ◽

Moving Average ◽

Autoregressive Process ◽

Natural Generalization ◽

Maximal Entropy ◽

Autoregressive Moving Average ◽

Moving Average Process ◽

Arma Process ◽

Arma Processes

The maximum-entropy approach to the estimation of the spectral density of a time series has become quite popular during the last decade. It is closely related to the fact that an autoregressive process of order p has maximal entropy among all time series sharing the same autocovariances up to lag p. We give a natural generalization of this result by proving that a mixed autoregressive-moving-average process (ARMA process) of order (p, q) has maximal entropy among all time series sharing the same autocovariances up to lag p and the same impulse response coefficients up to lag q. The latter may be estimated from a finite record of the time series, for example by using a method proposed by Bhansali (1976). By the way, we give a result on the existence of ARMA processes with prescribed autocovariances up to lag p and impulse response coefficients up to lag q.

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Justification of Wold’s Theorem and the Unbiasedness of a Stable Vector Autoregressive Time Series Model Forecasts

International Journal of Statistics and Probability ◽

10.5539/ijsp.v6n2p1 ◽

2017 ◽

Vol 6 (2) ◽

pp. 1

Author(s):

Iberedem A. Iwok

Keyword(s):

Time Series ◽

Moving Average ◽

Autoregressive Process ◽

Time Series Model ◽

Average Process ◽

Moving Average Process ◽

Autoregressive Time Series ◽

Vector Autoregressive ◽

Vector Autoregressive Process ◽

Vector Time Series

In this work, the multivariate analogue to the univariate Wold’s theorem for a purely non-deterministic stable vector time series process was presented and justified using the method of undetermined coefficients. By this method, a finite vector autoregressive process of order [] was represented as an infinite vector moving average () process which was found to be the same as the Wold’s representation. Thus, obtaining the properties of a process is equivalent to obtaining the properties of an infinite process. The proof of the unbiasedness of forecasts followed immediately based on the fact that a stable VAR process can be represented as an infinite VEMA process.

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Continuous Autoregressive Moving Average Models

Methodologies and Applications of Computational Statistics for Machine Intelligence - Advances in Systems Analysis, Software Engineering, and High Performance Computing ◽

10.4018/978-1-7998-7701-1.ch007 ◽

2021 ◽

pp. 118-141

Author(s):

Yakup Ari

Keyword(s):

Time Series ◽

Parameter Estimation ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Discrete Time ◽

Moving Average ◽

Likelihood Estimation ◽

Real Data ◽

Autoregressive Moving Average ◽

The Difference

The financial time series have a high frequency and the difference between their observations is not regular. Therefore, continuous models can be used instead of discrete-time series models. The purpose of this chapter is to define Lévy-driven continuous autoregressive moving average (CARMA) models and their applications. The CARMA model is an explicit solution to stochastic differential equations, and also, it is analogue to the discrete ARMA models. In order to form a basis for CARMA processes, the structures of discrete-time processes models are examined. Then stochastic differential equations, Lévy processes, compound Poisson processes, and variance gamma processes are defined. Finally, the parameter estimation of CARMA(2,1) is discussed as an example. The most common method for the parameter estimation of the CARMA process is the pseudo maximum likelihood estimation (PMLE) method by mapping the ARMA coefficients to the corresponding estimates of the CARMA coefficients. Furthermore, a simulation study and a real data application are given as examples.

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