An autoregressive process with geometric α-laplace marginals

2004 ◽  
Vol 45 (3) ◽  
pp. 337-350 ◽  
Author(s):  
V. Seetha Lekshmi ◽  
K. K. Jose
Keyword(s):  
Autoregressive Process

On the generation and origin of I/f noise

1999 ◽  
Vol 4 ◽  
pp. 87-96 ◽  
Author(s):  
B. Kaulakys ◽  
T. Meškauskas
Keyword(s):  
Point Process ◽  
Solvable Model ◽  
Autoregressive Process ◽  
Wide Range ◽  
Occurrence Times

Simple analytically solvable model exhibiting 1/f spectrum in any desirably wide range of frequency is analysed. The model consists of pulses (point process) whose interevent times obey an autoregressive process with small damping. Analysis and generalizations of the model indicate to the possible origin of 1/f noise, i.e. random increments between the occurrence times of particles or pulses resulting in the clustering of the pulses.

News and Idiosyncratic Volatility: The Public Information Processing Hypothesis*

2020 ◽  
Author(s):  
Robert F Engle ◽  
Martin Klint Hansen ◽  
Ahmet K Karagozoglu ◽  
Asger Lunde
Keyword(s):  
Information Processing ◽  
Public Information ◽  
Selection Procedure ◽  
Autoregressive Process ◽  
Return Volatility ◽  
Market Outcomes ◽  
The Public ◽  
Additional Information ◽  
Financial News ◽  
The Impact

Abstract Motivated by the recent availability of extensive electronic news databases and advent of new empirical methods, there has been renewed interest in investigating the impact of financial news on market outcomes for individual stocks. We develop the information processing hypothesis of return volatility to investigate the relation between firm-specific news and volatility. We propose a novel dynamic econometric specification and test it using time series regressions employing a machine learning model selection procedure. Our empirical results are based on a comprehensive dataset comprised of more than 3 million news items for a sample of 28 large U.S. companies. Our proposed econometric specification for firm-specific return volatility is a simple mixture model with two components: public information and private processing of public information. The public information processing component is defined by the contemporaneous relation with public information and volatility, while the private processing of public information component is specified as a general autoregressive process corresponding to the sequential price discovery mechanism of investors as additional information, previously not publicly available, is generated and incorporated into prices. Our results show that changes in return volatility are related to public information arrival and that including indicators of public information arrival explains on average 26% (9–65%) of changes in firm-specific return volatility.

scholarly journals On the BIC for determining the number of control points in B-spline surface approximation in case of correlated observations

2020 ◽  
Vol 10 (1) ◽  
pp. 110-123
Author(s):  
Gaël Kermarrec ◽  
Hamza Alkhatib
Keyword(s):  
Shape Control ◽  
Simple Procedure ◽  
Spline Approximation ◽  
Autoregressive Process ◽  
Optimal Number ◽  
Information Criteria ◽  
General Effect ◽  
Control Points ◽  
B Spline ◽  
Correlated Observations

Abstract B-spline curves are a linear combination of control points (CP) and B-spline basis functions. They satisfy the strong convex hull property and have a fine and local shape control as changing one CP affects the curve locally, whereas the total number of CP has a more general effect on the control polygon of the spline. Information criteria (IC), such as Akaike IC (AIC) and Bayesian IC (BIC), provide a way to determine an optimal number of CP so that the B-spline approximation fits optimally in a least-squares (LS) sense with scattered and noisy observations. These criteria are based on the log-likelihood of the models and assume often that the error term is independent and identically distributed. This assumption is strong and accounts neither for heteroscedasticity nor for correlations. Thus, such effects have to be considered to avoid under-or overfitting of the observations in the LS adjustment, i.e. bad approximation or noise approximation, respectively. In this contribution, we introduce generalized versions of the BIC derived using the concept of quasi- likelihood estimator (QLE). Our own extensions of the generalized BIC criteria account (i) explicitly for model misspecifications and complexity (ii) and additionally for the correlations of the residuals. To that aim, the correlation model of the residuals is assumed to correspond to a first order autoregressive process AR(1). We apply our general derivations to the specific case of B-spline approximations of curves and surfaces, and couple the information given by the different IC together. Consecutively, a didactical yet simple procedure to interpret the results given by the IC is provided in order to identify an optimal number of parameters to estimate in case of correlated observations. A concrete case study using observations from a bridge scanned with a Terrestrial Laser Scanner (TLS) highlights the proposed procedure.

Some ARMA models for dependent sequences of poisson counts

1988 ◽  
Vol 20 (4) ◽  
pp. 822-835 ◽  
Author(s):  
Ed Mckenzie
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Joint Distribution ◽  
Autoregressive Process ◽  
Two Dimensional ◽  
Arma Models ◽  
Time Reversibility ◽  
Vector Autoregressive ◽  
Arma Processes ◽  
Vector Autoregressive Process

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

On Asymptotic Prediction Problems for Multivariate Autoregressive Models in the Unstable Nonexplosive Case

1987 ◽  
Vol 36 (1-2) ◽  
pp. 29-38 ◽  
Author(s):  
A. K. Basu ◽  
S. Sen Roy
Keyword(s):  
Autoregressive Process ◽  
Autoregressive Models ◽  
Multivariate Autoregressive Models ◽  
Prediction Problems ◽  
Dependent Error ◽  
Meansquare Error ◽  
Multivariate Autoregressive

This paper considers the prediction problems of a k-dimensional, pth order autoregressive process with unstable but non-explosive roots and dependent error variables. The estimated predictor has been shown to be asymptotically equivalent to the optimal predictor. An expression for the meansquare error of the estimated predictor has also been derived .

Temporal aggregation of random walk processes and implications for economic analysis

2019 ◽  
Vol 24 (2) ◽  
Author(s):  
Yamin S Ahmad ◽  
Ivan Paya
Keyword(s):  
Random Walk ◽  
Autoregressive Process ◽  
Potential Effect ◽  
Temporal Aggregation ◽  
Time Averaging ◽  
Fat Tails ◽  
Data Generating Process ◽  
Variance Ratios ◽  
Interval Sampling ◽  
The Impact

AbstractThis paper examines the impact of time averaging and interval sampling data assuming that the data generating process for a given series follows a random walk with iid errors. We provide exact expressions for the corresponding variances, and covariances, for both levels and higher order differences of the aggregated series, as well as that for the variance ratio, demonstrating exactly how the degree of temporal aggregation impacts these properties. We empirically investigate this issue on exchange rates and find that the values of the variance ratios and autocorrelation coefficients at different frequencies are consistent with our theoretical results. We also conduct a simulation exercise that illustrates the potential effect that conditional heteroskedasticity and fat tails may have on the temporal aggregation of a random walk and of a highly persistent autoregressive process.

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