scholarly journals GPS time series modeling by autoregressive moving average method: Application to the crustal deformation in central Japan

2000 ◽  
Vol 52 (3) ◽  
pp. 155-162 ◽  
Author(s):  
Jianxin Li ◽  
Kaoru Miyashita ◽  
Teruyuki Kato ◽  
Shinichi Miyazaki
Keyword(s):  
Time Series ◽  
Crustal Deformation ◽  
Average Method ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Time Series Modeling ◽  
Central Japan ◽  
Gps Time Series

Modeling and Forecasting Sales Data by Time Series Analysis

1981 ◽  
Vol 18 (1) ◽  
pp. 94-100 ◽  
Author(s):  
S. G. Kapoor ◽  
P. Madhok ◽  
S. M. Wu
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Time Series Modeling ◽  
Average Model ◽  
Sales Data ◽  
Autoregressive Moving Average Model ◽  
Deterministic Function ◽  
Modeling And Forecasting ◽  
Moving Average Model

Time series modeling technique is used to model a series of sales data in which seasonality causes distinct spike peaks. The analysis of actual sales data shows that the seasonality in the data can be approximated by a deterministic function and the stochastic component is a sixth-order autoregressive moving average model. Use of the combined deterministic and stochastic models to derive the minimum mean squared forecast yields reliable results.

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

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%.

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

1985 ◽  
Vol 17 (04) ◽  
pp. 810-840 ◽  
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.

Continuous Autoregressive Moving Average Models

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.

scholarly journals Common Mode Component and Its Potential Effect on GPS-Inferred Three-Dimensional Crustal Deformations in the Eastern Tibetan Plateau

2019 ◽  
Vol 11 (17) ◽  
pp. 1975 ◽  
Author(s):  
Yuanjin Pan ◽  
Ruizhi Chen ◽  
Hao Ding ◽  
Xinyu Xu ◽  
Gang Zheng ◽  
...  
Keyword(s):  
Time Series ◽  
Tibetan Plateau ◽  
Crustal Deformation ◽  
Three Dimensional ◽  
Vertical Component ◽  
Eastern Tibetan Plateau ◽  
Frequency Spectra ◽  
Common Mode ◽  
Time Frequency ◽  
Gps Time Series

Surface and deep potential geophysical signals respond to the spatial redistribution of global mass variations, which may be monitored by geodetic observations. In this study, we analyze dense Global Positioning System (GPS) time series in the Eastern Tibetan Plateau using principal component analysis (PCA) and wavelet time-frequency spectra. The oscillations of interannual and residual signals are clearly identified in the common mode component (CMC) decomposed from the dense GPS time series from 2000 to 2018. The newly developed spherical harmonic coefficients of the Gravity Recovery and Climate Experiment Release-06 (GRACE RL06) are adopted to estimate the seasonal and interannual patterns in this region, revealing hydrologic and atmospheric/nontidal ocean loads. We stack the averaged elastic GRACE-derived loading displacements to identify the potential physical significance of the CMC in the GPS time series. Interannual nonlinear signals with a period of ~3 to ~4 years in the CMC (the scaled principal components from PC1 to PC3) are found to be predominantly related to hydrologic loading displacements, which respond to signals (El Niño/La Niña) of global climate change. We find an obvious signal with a period of ~6 yr on the vertical component that could be caused by mantle-inner core gravity coupling. Moreover, we evaluate the CMC’s effect on the GPS-derived velocities and confirm that removing the CMC can improve the recognition of nontectonic crustal deformation, especially on the vertical component. Furthermore, the effects of the CMC on the three-dimensional velocity and uncertainty are presented to reveal the significant crustal deformation and dynamic processes of the Eastern Tibetan Plateau.

A Bayesian Approach to Kalman Filter for Elliptically Contoured Distribution and its Application in Time Series Models

1994 ◽  
Vol 44 (1-2) ◽  
pp. 11-28 ◽  
Author(s):  
A. K. Basu ◽  
J. K. Das
Keyword(s):  
Time Series ◽  
Kalman Filter ◽  
Moving Average ◽  
State Equation ◽  
Autoregressive Moving Average ◽  
Missing Observations ◽  
Estimation Of Parameters ◽  
Bayesian Formulation ◽  
Set Up ◽  
Elliptically Contoured

This paper develops a Bayesian formulation of Kalman filter under the errors having elliptically contoured distributions in both observation equation and system (or state) equation, using some recent results in multivariate analysis. Estimation of parameters in case of missing observations and prediction of missing observations as well are dealt with under the above set up of autoregressive-moving average process in time series. Two illustrative examples are presented with the help of AR(1) model and ARMA (1, 1) model.

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