https://www.nber.org/system/files/working_papers/t0264/t0264.pdf

Long memory and regime switching

The theoretical and empirical econometric literatures on long memory and regime switching have evolved largely independently, as the phenomena appear distinct. We argue, in contrast, that they are intimately related, and we substantiate our claim in several environments, including a simple mixture model, Engle and Lee's (1999) stochastic permanent break model, and Hamilton's (1989) Markov switching model. In particular, we show analytically that stochastic regime switching is easily confused with long memory, even asymptotically, so long as only a small' amount of regime switching occurs, in a sense that we make precise. A Monte Carlo analysis supports the relevance of the theory and produces additional insights.

Long Memory and Regime Switching

This paper estimates an equilibrium model of stock price behaviour in which changes in exponentially de-trended dividends and prices are normally distributed and exogenous "noise traders" interact with "smart-money" investors who have constant absolute risk aversion. The model can explain the volatility and predictability of U.S. stock returns in the period 1871-1986 using either a low discount rate (4% or below) and a large constant risk discount on the stock price, or a higher discount rate (5% or above) and noise trading correlated with fundamentals. The data are not well able to distinguish between these explanations.

https://dash.harvard.edu/bitstream/handle/1/3208217/campbell_smartnoise.pdf

Smart Money, Noise Trading and Stock Price Behaviour

We give the theoretical basis of a possible explanation for two stylized facts observed in long log-return series: the long-range dependence (LRD) in volatility and the integrated GARCH (IGARCH). Both these effects can be explained theoretically if one assumes that the data are nonstationary.

https://rmgsc.cr.usgs.gov/outgoing/threshold_articles/Mikosch_Starica2004.pdf

Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects

Traditional asset-pricing theories assume complete market participation, despite considerable empirical evidence that most investors participate in a limited number of markets. The authors show that once the participation decision is endogenized, market properties change dramatically. First, limited market participation can amplify the effect of liquidity trading relative to full participation; under certain circumstances, an arbitrarily small aggregate liquidity shock can cause significant price volatility. Second, there exist multiple equilibria with very different participation regimes and levels of asset-price volatility. Third, under plausible conditions the equilibria can be Pareto-ranked; the Pareto-preferred equilibrium is characterized by greater participation and lower volatility. Copyright 1994 by American Economic Association.

Limited market participation and volatility of asset prices

A simple construction that will be referred to as an error-duration model is shown to generate fractional integration and long memory. An error-duration representation also exists for many familiar ARMA models, making error duration an alternative to autoregression for explaining dynamic persistence in economic variables. The results lead to a straightforward procedure for simulating fractional integration and establish a connection between fractional integration and common notions of structural change. Two examples show how the error-duration model could account for fractional integration in aggregate employment and in asset price volatility.

/pdf/what-is-fractional-integration-4ijs7zf78t.pdf

What is fractional integration

Gong and Samaniego (1981) define pseudo maximum likelihood estimation and derive the asymptotic distribution of the resulting estimates. This note gives a simpler and more elegant expression for the asymptotic variance of a pseudo maximum likelihood estimate.

/pdf/pseudo-maximum-likelihood-estimation-the-asymptotic-464a3xr95s.pdf

Pseudo Maximum Likelihood Estimation: The Asymptotic Distribution

The simplest variance-bounds inequality says that the price of stock should be less volatile than the present value of actual future dividends, assuming that the former can be taken to equal the conditional expectation of the latter. This is so because under the assumption just stated the price of stock equals the present value of dividends less a forecast error which, under rational expectations, is orthogonal to price. Therefore the variance of the present value of future dividends-the ex post rational stock price -should exceed the variance of the actual price by an amount equal to the variance of the forecast error. Despite the intuitive appeal of the variance inequality just stated, empirical implementation is far from straightforward. An important econometric problem is that if the unconditional population variances change over time then sample variances, not being consistent estimates of the population variances that are subject to the inequality, are uninterpretable from the viewpoint of the variance-bounds theorems. Sample variances are of interest only if some data transformation can be found which ensures that the relevant variables are stationary and which at the same time preserves the variance-bounds theorems. The original papers that formulated the variance-bounds relation, Robert J. Shiller (1979, 1981) and LeRoy and Richard D. Porter (1981), employed different corrections to attain stationarity. Shiller (1981) fitted a log-linear trend to stock prices and took the residuals from this trend to be the series restricted by the variance-bounds inequalities. LeRoy and Porter, on the other hand, assumed that the trend in prices was attributable to inflation and retained earnings and implemented a procedure to reverse the effects of these factors on stock prices. Subsequent criticism indicated that both procedures were flawed. Allan W. Kleidon (1986a) showed that if the underlying price series has a unit root, as does a random walk, then the supposedly trend-adjusted series as calculated by Shiller (1979, 1981) will still be nonstationary. Further, if the variance-bounds tests are implemented despite the nonstationarity of the underlying series, they will be strongly biased toward rejection. Kleidon's analysis obviously raised questions about the finding of excess volatility that Shiller reported. Kleidon (1983) also pointed out an error in LeRoy and Porter's implementation of the correction for earnings retention.1 Here we correct for trend in stock prices in an entirely different way: by dividing dividends into price. In other words, we conduct variance-bounds tests on the ratio of

Stock Price Volatility: Tests Based on the Geometric Random Walk

http://economics.illinoisstate.edu/gawater/files/docs/EGTARCH.pdf

An evolutionary game theory explanation of ARCH effects

THIS PAPER PRESENTS a numerical algorithm for computing full information maximum likelihood (FIML) and nonlinear three-stage least squares (3SLS) coefficient estimates for large nonlinear models. (The proposed algorithm will be denoted algorithm A.) Although the theory of FIML estimation has been available for thirty years [20], FIML estimation has long been regarded as impossible on large nonlinear models.2 The more recently proposed nonlinear 3SLS estimator [191 also poses difficulties for large models.3 Using the algorithm presented in this paper, FIML and 3SLS are now feasible alternatives for estimation of large nonlinear models. The principles behind algorithm A's efficiency can be summarized as follows. First, most of the algorithm's steps explicitly control the mean of each equation's residuals. Large changes in those means are avoided because the FIML and 3SLS estimation problems are extremely sensitive to the residuals' means. Second, the coefficients are grouped by equations and the groups are treated separately during most of each iteration. This focus on individual equations is effective because coefficients within the same equation are generally more

/pdf/an-algorithm-for-fiml-and-3sls-estimation-of-large-nonlinear-givx9nr16k.pdf

William R. Parke

Papers

What is fractional integration

Pseudo Maximum Likelihood Estimation: The Asymptotic Distribution

Stock Price Volatility: Tests Based on the Geometric Random Walk

An evolutionary game theory explanation of ARCH effects

An algorithm for fiml and 3sls estimation of large nonlinear models1