Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

http://www.long-memory.com/volatility/Baillie1996.pdf

Long memory processes and fractional integration in econometrics

The paper proposes an additive cascade model of volatility components defined over different time periods. This volatility cascade leads to a simple AR-type model in the realized volatility with the feature of considering different volatility components realized over different time horizons and thus termed Heterogeneous Autoregressive model of Realized Volatility (HAR-RV). In spite of the simplicity of its structure and the absence of true long-memory properties, simulation results show that the HAR-RV model successfully achieves the purpose of reproducing the main empirical features of financial returns (long memory, fat tails, and self-similarity) in a very tractable and parsimonious way. Moreover, empirical results show remarkably good forecasting performance. (JEL: C13, C22, C51, C53)

A Simple Approximate Long-Memory Model of Realized Volatility

Probability and Measure

We test for the presence of long memory in daily stock returns and their squares using a robust semiparametric procedure. Spurious results can be produced by nonstationarity and aggregation.

Real and Spurious Long Memory Properties of Stock Market Data

We test for the presence of long memory in daily stock returns and their squares using a robust semiparametric procedure of Lobato and Robinson. Spurious results can be produced by nonstationarity and aggregation. We address these problems by analyzing subperiods of returns and using individual stocks. The test results show no evidence of long memory in the returns. By contrast, there is strong evidence in the squared returns.

Real and Spurious Long-Memory Properties of Stock-Market Data

An Automatic Portmanteau Test for Serial Correlation

This article examines consistent estimation of the long-memory parameters of stock-market trading volume and volatility. The analysis is carried out in the frequency domain by tapering the data instead of detrending them. The main theoretical contribution of the article is to prove a central limit theorem for a multivariate two-step estimator of the memory parameters of a nonstationary vector process. Using robust semiparametric procedures, the long-memory properties of trading volume for the 30 stocks in the Dow Jones Industrial Average index are analyzed. Two empirical results are found. First, there is strong evidence that stock-market trading volume exhibits long memory. Second, although it is found that volatility and volume exhibit the same degree of long memory for most of the stocks, there is no evidence that both processes share the same long-memory component.

/pdf/long-memory-in-stock-market-trading-volume-4f0p7k62va.pdf

Long Memory in Stock-Market Trading Volume

There is frequently interest in testing that a scalar or vector time series is I(0), possibly after first- differencing or other detrending, while the I(0) assumption is also taken for granted in autocorrelation-consistent variance estimation. We propose a test for I(0) against fractional alternatives. The test is non-parametric, and indeed makes no assumptions on spectral behaviour away from zero frequency. It seems likely to have good efficiency against fractional alternatives, relative to other nonparametric tests. The test is given large samle justification, subjected to a Monte Carlo analysis of finite sample behaviour, and applied to various empirical data series.

Ignacio N. Lobato

Papers

Real and Spurious Long Memory Properties of Stock Market Data

Real and Spurious Long-Memory Properties of Stock-Market Data

An Automatic Portmanteau Test for Serial Correlation

Long Memory in Stock-Market Trading Volume

A nonparametric test for i(0)