scholarly journals “Plug-in” Statistical Forecasting of Vector Autoregressive Time Series with Missing Values

2016 ◽  
Vol 34 (2) ◽  
Author(s):  
Yuriy Kharin ◽  
Aliaksandr Huryn
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Numerical Experiments ◽  
Missing Values ◽  
Asymptotic Properties ◽  
Mean Square ◽  
Unknown Parameters ◽  
Autoregressive Time Series ◽  
Statistical Forecasting ◽  
Vector Autoregressive

The problems of statistical forecasting of vector autoregressive time series with missing values are considered. The maximum likelihood forecast is constructed and its mean square risk is evaluated for the case of known parameters. The “plug-in” forecast and statistical estimators are constructed for unknown parameters. Asymptotic properties of constructed estimators are analyzed. Results of numerical experiments are presented.

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

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.

scholarly journals QML Estimators in Linear Regression Models with Functional Coefficient Autoregressive Processes

2010 ◽  
Vol 2010 ◽  
pp. 1-30 ◽  
Author(s):  
Hongchang Hu
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Models ◽  
Asymptotic Properties ◽  
Asymptotic Distributions ◽  
Autoregressive Processes ◽  
Linear Regression Models ◽  
Unknown Parameters ◽  
Quasi Maximum Likelihood ◽  
Functional Coefficient

This paper studies a linear regression model, whose errors are functional coefficient autoregressive processes. Firstly, the quasi-maximum likelihood (QML) estimators of some unknown parameters are given. Secondly, under general conditions, the asymptotic properties (existence, consistency, and asymptotic distributions) of the QML estimators are investigated. These results extend those of Maller (2003), White (1959), Brockwell and Davis (1987), and so on. Lastly, the validity and feasibility of the method are illuminated by a simulation example and a real example.

scholarly journals Multitemporal Soil Moisture Retrieval over Bare Agricultural Areas by Means of Alpha Model with Multisensor SAR Data

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Xiang Zhang ◽  
Xinming Tang ◽  
Xiaoming Gao ◽  
Hui Zhao
Keyword(s):  
Time Series ◽  
Soil Moisture ◽  
Root Mean Square Error ◽  
Field Measurements ◽  
Mean Square ◽  
Approximation Model ◽  
Unknown Parameters ◽  
Sar Data ◽  
Agricultural Areas ◽  
Moisture Estimation

The objective of this research is to optimize the Alpha approximation model for soil moisture retrieval using multitemporal SAR data. The Alpha model requires prior knowledge of soil moisture range to constrain soil moisture estimation. The solution of the Alpha model is an undetermined problem due to the fact that the number of observation equations is less than the number of unknown parameters. This research primarily focused on the optimization of Alpha model by employing multisensor and multitemporal SAR data. The disadvantage of the Alpha model can be eliminated by the combination of multisensor SAR data. The optimized Alpha model was evaluated on the basis of a comprehensive campaign for soil moisture retrieval, which acquired multisensor time series SAR data and coincident field measurements. The agreement between the estimated and measured soil moisture was within a root mean square error of 0.08 cm3/cm3 for both methods. The optimized Alpha model shows an obvious improvement for soil moisture retrieval. The results demonstrated that multisensor and multitemporal SAR data are favorable for time series soil moisture retrieval over bare agricultural areas.

scholarly journals Nowcasting Austrian Short Term Statistics

2018 ◽  
Vol 34 (2) ◽  
pp. 503-522
Author(s):  
Markus Fröhlich
Keyword(s):  
Time Series ◽  
Missing Values ◽  
Multivariate Time Series ◽  
Seasonal Adjustment ◽  
Short Term ◽  
Vector Autoregressive ◽  
Adjustment Program ◽  
Time Series Approach ◽  
Total Turnover ◽  
Vector Error Correction Models

Abstract Early estimates for Austrian short term indices were produced using multivariate time-series models. The article presents a simulation study with different models (vector error correction models, vector autoregressive models in levels – both with unadjusted and seasonally adjusted time-series) used for estimating total turnover, production, etc. In a preliminary step, before time-series were provided for nowcasting, the data had to undergo an editing process. In this case a time-series approach was selected for data-editing as well, because of the very specific structure of Austrian enterprises. For this task basically the seasonal adjustment program X13Arima-Seats was used for identifying and replacing outlying observations, imputation of missing values and generating univariate forecasts for every single time series.

scholarly journals Implemetasi Model Autoregressive (AR) Dan Autoregressive Conditional Heteroskedasticity (ARCH) Untuk Memprediksi Harga Emas

2018 ◽  
Vol 3 (2) ◽  
pp. 29
Author(s):  
Ni Luh Ketut Dwi Murniati ◽  
Indwiarti Indwiarti ◽  
Aniq Atiqi Rohmawati
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Mean Absolute Error ◽  
Likelihood Estimation ◽  
Absolute Error ◽  
Gold Price ◽  
Conditional Heteroskedasticity ◽  
Mean Square ◽  
Basic Information ◽  
Estimation Of Parameters

Gold is a one of  high selling value items in the market, and it  can be used as an investment item. The price of gold in the market tends to be stable and not undergoing too significant changes which makes gold be a very valuable item. The aim of this research is to predict gold price using AR (1) and ARCH (1) model which are the part of time series methods. The data of gold price is obtained from ANTAM's daily historical website from 2007 - 2017. Here, the basic information about data is given by using descriptive statistic and the estimation of parameters in each model is condacted by using <em>Maximum Likelihood Estimation</em> (MLE). To evaluate the model, <em>Mean Absolute Error</em> (MAE) and <em>Root Mean Square Error</em> (RMSE) are used. In this research, the estimated model of AR (1) and ARCH (1) given as X_t = -0.012X_{t-1}+epsion_t and X_t = epsilon_t sqrt{0.000053+0.011958X^2_{t-1}} respectively. Moreover, the result of MAE and RMSE using AR (1) model are 0.0261 and 0.0342 respectively, meanwhile for ARCH (1) model  are 0.0170 and 0.0251 respectively.

Sign in / Sign up

Export Citation Format

Share Document