On bayesian inference for almost periodic in mean autoregressive models

2016 ◽  
Vol 63 (3) ◽  
pp. 255-272
Author(s):  
Łukasz Lenart ◽  
Błażej Mazur
Keyword(s):  
Time Series ◽  
Bayesian Estimation ◽  
Real Data ◽  
Approximate Model ◽  
Model Parameters ◽  
Almost Periodic ◽  
Cyclical Fluctuations ◽  
Univariate Time Series ◽  
Mean Function ◽  
Mcmc Chain

The goal of the paper is to discuss Bayesian estimation of a class of univariate time-series models being able to represent complicated patterns of “cyclical” fluctuations in mean function. We highlight problems that arise in Bayesian estimation of parametric time-series model using the Flexible Fourier Form of Gallant (1981). We demonstrate that the resulting posterior is likely to be highly multimodal, therefore standard Markov Chain Monte Carlo (MCMC in short) methods might fail to explore the whole posterior, especially when the modes are separated. We show that the multimodality is actually an issue using the exact solution (i.e. an analytical marginal posterior) in an approximate model. We address that problem using two essential steps. Firstly, we integrate the posterior with respect to amplitude parameters, which can be carried out analytically. Secondly, we propose a non-parametrically motivated proposal for the frequency parameters. This allows for construction of an improved MCMC sampler that effectively explores the space of all the model parameters, with the amplitudes sampled by the direct approach outside the MCMC chain. We illustrate the problem using simulations and demonstrate our solution using two real-data examples.

Time Series Decomposition into Oscillation Components and Phase Estimation

2017 ◽  
Vol 29 (2) ◽  
pp. 332-367 ◽  
Author(s):  
Takeru Matsuda ◽  
Fumiyasu Komaki
Keyword(s):  
Time Series ◽  
State Space ◽  
Empirical Bayes ◽  
Real Data ◽  
Information Criterion ◽  
State Space Models ◽  
Model Parameters ◽  
Seasonal Adjustment ◽  
Phase Dynamics ◽  
Time Series Decomposition

Many time series are naturally considered as a superposition of several oscillation components. For example, electroencephalogram (EEG) time series include oscillation components such as alpha, beta, and gamma. We propose a method for decomposing time series into such oscillation components using state-space models. Based on the concept of random frequency modulation, gaussian linear state-space models for oscillation components are developed. In this model, the frequency of an oscillator fluctuates by noise. Time series decomposition is accomplished by this model like the Bayesian seasonal adjustment method. Since the model parameters are estimated from data by the empirical Bayes’ method, the amplitudes and the frequencies of oscillation components are determined in a data-driven manner. Also, the appropriate number of oscillation components is determined with the Akaike information criterion (AIC). In this way, the proposed method provides a natural decomposition of the given time series into oscillation components. In neuroscience, the phase of neural time series plays an important role in neural information processing. The proposed method can be used to estimate the phase of each oscillation component and has several advantages over a conventional method based on the Hilbert transform. Thus, the proposed method enables an investigation of the phase dynamics of time series. Numerical results show that the proposed method succeeds in extracting intermittent oscillations like ripples and detecting the phase reset phenomena. We apply the proposed method to real data from various fields such as astronomy, ecology, tidology, and neuroscience.

Random order autoregressive time series model with structural break

2020 ◽  
Vol 15 (3) ◽  
pp. 225-237
Author(s):  
Saurabh Kumar ◽  
Jitendra Kumar ◽  
Vikas Kumar Sharma ◽  
Varun Agiwal
Keyword(s):  
Time Series ◽  
Structural Breaks ◽  
Time Series Data ◽  
Structural Break ◽  
Random Order ◽  
Real Data ◽  
Series Data ◽  
Model Parameters ◽  
Multiple Time ◽  
Multiple Time Points

This paper deals with the problem of modelling time series data with structural breaks occur at multiple time points that may result in varying order of the model at every structural break. A flexible and generalized class of Autoregressive (AR) models with multiple structural breaks is proposed for modelling in such situations. Estimation of model parameters are discussed in both classical and Bayesian frameworks. Since the joint posterior of the parameters is not analytically tractable, we employ a Markov Chain Monte Carlo method, Gibbs sampling to simulate posterior sample. To verify the order change, a hypotheses test is constructed using posterior probability and compared with that of without breaks. The methodologies proposed here are illustrated by means of simulation study and a real data analysis.

scholarly journals The KM-Algorithm Identifies Regulated Genes in Time Series Expression Data

2009 ◽  
Vol 2009 ◽  
pp. 1-10
Author(s):  
Martina Bremer ◽  
R. W. Doerge
Keyword(s):  
Gene Expression ◽  
Time Series ◽  
Statistical Power ◽  
Regulatory Networks ◽  
Real Data ◽  
Model Parameters ◽  
Expression Data ◽  
Data Set ◽  
Gene Expression Time Series ◽  
Expression Time

We present a statistical method to rank observed genes in gene expression time series experiments according to their degree of regulation in a biological process. The ranking may be used to focus on specific genes or to select meaningful subsets of genes from which gene regulatory networks can be built. Our approach is based on a state space model that incorporates hidden regulators of gene expression. Kalman (K) smoothing and maximum (M) likelihood estimation techniques are used to derive optimal estimates of the model parameters upon which a proposed regulation criterion is based. The statistical power of the proposed algorithm is investigated, and a real data set is analyzed for the purpose of identifying regulated genes in time dependent gene expression data. This statistical approach supports the concept that meaningful biological conclusions can be drawn from gene expression time series experiments by focusing on strong regulation rather than large expression values.

BAYESIAN ESTIMATION IN RANDOM CENSORSHIP MODEL FOR WEIBULL DISTRIBUTION UNDER DIFFERENT LOSS FUNCTIONS

2012 ◽  
Vol 04 (03) ◽  
pp. 1250021 ◽  
Author(s):  
MUHAMMAD YAMEEN DANISH ◽  
MUHAMMAD ASLAM
Keyword(s):  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Real Data ◽  
Loss Functions ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Estimation Of Parameters ◽  
Random Censorship

This paper deals with Bayesian estimation of parameters in the proportional hazards model of random censorship for the Weibull distribution under different loss functions. We consider both the informative and noninformative priors on the model parameters to obtain the Bayes estimates using Gibbs sampling scheme. Maximum likelihood estimates are also obtained for comparison purposes. A simulation study is carried out to observe the behavior of the proposed estimators for different sample sizes and for different censoring parameters. One real data analysis is performed for illustration.

Multivariate Time Series Decomposition into Oscillation Components

2017 ◽  
Vol 29 (8) ◽  
pp. 2055-2075 ◽  
Author(s):  
Takeru Matsuda ◽  
Fumiyasu Komaki
Keyword(s):  
Time Series ◽  
Empirical Bayes ◽  
Multivariate Time Series ◽  
Phase Relationship ◽  
Information Criterion ◽  
Model Parameters ◽  
Phase Dynamics ◽  
Univariate Time Series ◽  
Linear State ◽  
The Given

Many time series are considered to be a superposition of several oscillation components. We have proposed a method for decomposing univariate time series into oscillation components and estimating their phases (Matsuda & Komaki, 2017 ). In this study, we extend that method to multivariate time series. We assume that several oscillators underlie the given multivariate time series and that each variable corresponds to a superposition of the projections of the oscillators. Thus, the oscillators superpose on each variable with amplitude and phase modulation. Based on this idea, we develop gaussian linear state-space models and use them to decompose the given multivariate time series. The model parameters are estimated from data using the empirical Bayes method, and the number of oscillators is determined using the Akaike information criterion. Therefore, the proposed method extracts underlying oscillators in a data-driven manner and enables investigation of phase dynamics in a given multivariate time series. Numerical results show the effectiveness of the proposed method. From monthly mean north-south sunspot number data, the proposed method reveals an interesting phase relationship.

scholarly journals ROBUST TESTS FOR WHITE NOISE AND CROSS-CORRELATION

2020 ◽  
pp. 1-29
Author(s):  
Violetta Dalla ◽  
Liudas Giraitis ◽  
Peter C. B. Phillips
Keyword(s):  
Time Series ◽  
Serial Correlation ◽  
Cross Correlation ◽  
Empirical Work ◽  
Monte Carlo Study ◽  
Real Data ◽  
Asymptotic Size ◽  
Univariate Time Series ◽  
Portmanteau Tests ◽  
Robust Tests

Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung–Box tests can be significantly distorted. This paper adapts standard correlogram and portmanteau tests to accommodate hidden dependence and nonstationarities involving heteroskedasticity, thereby uncoupling these tests from limiting assumptions that reduce their applicability in empirical work. To enhance the Ljung–Box test for non-i.i.d. data, a new cumulative test is introduced. Asymptotic size of these tests is unaffected by hidden dependence and heteroskedasticity in the series. Related extensions are provided for testing cross-correlation at various lags in bivariate time series. Tests for the i.i.d. property of a time series are also developed. An extensive Monte Carlo study confirms good performance in both size and power for the new tests. Applications to real data reveal that standard tests frequently produce spurious evidence of serial correlation.

scholarly journals Modeling and forecasting seasonal and cyclical events using retrospective data

2020 ◽  
Vol 217 ◽  
pp. 06007
Author(s):  
Anatoly Darmanyan ◽  
Aleksey Rogachev
Keyword(s):  
Time Series ◽  
Confidence Interval ◽  
Russian Federation ◽  
Electricity Generation ◽  
Moving Average ◽  
Real Data ◽  
Stationary Time Series ◽  
Model Parameters ◽  
The Russian Federation

Based on the data of the Ministry of energy of Russian Federation for the period of 2012-2019 years the mathematical modeling of statistics of power production were performed using time series analysis in Statistica. To describe the statistical data, the exponential smoothing model was used, its parameter was found and short-term forecasting of electricity generation in Russia for 2019 was performed. For long-term forecasting the seasonal model of autoregression and integrated moving average ARIMA - (0,1,1)(0,1,1) is chosen, its parameters are defined and its adequacy to real data is proved. With the help of the found model, the forecasting of electricity generation in the Russian Federation within 90% of the confidence interval for twelve months 2019-2020 is performed. The non-stationary time series of the studied statistics, the presence of a trend and a seasonal component in it are proved. The model parameters are defined as ARIMA(0,1,1)(0,1,1) by means of the Statistica software, and the adequacy of this model to real data is proved. Using the found mathematical model, a long – term forecast (period-12 months) of electricity generation in the Russian Federation with a 90% confidence interval was performed.

A COMPARATIVE STUDY BETWEEN UNIVARIATE AND BIVARIATE TIME SERIES MODELS FOR CRUDE PALM OIL INDUSTRY IN PENINSULAR MALAYSIA

2020 ◽  
Vol 5 (1) ◽  
pp. 374
Author(s):  
Pauline Jin Wee Mah ◽  
Nur Nadhirah Nanyan
Keyword(s):  
Time Series ◽  
Palm Oil ◽  
Moving Average ◽  
Forecast Accuracy ◽  
Peninsular Malaysia ◽  
Time Series Models ◽  
Crude Palm Oil ◽  
Univariate Time Series ◽  
Import And Export ◽  
Bivariate Time Series

The main purpose of this study is to compare the performances of univariate and bivariate models on four time series variables of the crude palm oil industry in Peninsular Malaysia. The monthly data for the four variables, which are the crude palm oil production, price, import and export, were obtained from Malaysian Palm Oil Board (MPOB) and Malaysian Palm Oil Council (MPOC). In the first part of this study, univariate time series models, namely, the autoregressive integrated moving average (ARIMA), fractionally integrated autoregressive moving average (ARFIMA) and autoregressive autoregressive (ARAR) algorithm were used for modelling and forecasting purposes. Subsequently, the dependence between any two of the four variables were checked using the residuals’ sample cross correlation functions before modelling the bivariate time series. In order to model the bivariate time series and make prediction, the transfer function models were used. The forecast accuracy criteria used to evaluate the performances of the models were the mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE). The results of the univariate time series showed that the best model for predicting the production was ARIMA  while the ARAR algorithm were the best forecast models for predicting both the import and export of crude palm oil. However, ARIMA  appeared to be the best forecast model for price based on the MAE and MAPE values while ARFIMA  emerged the best model based on the RMSE value.  When considering bivariate time series models, the production was dependent on import while the export was dependent on either price or import. The results showed that the bivariate models had better performance compared to the univariate models for production and export of crude palm oil based on the forecast accuracy criteria used.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

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