Jeffrey R. Russell

Autoregressive conditional duration : a new model for irregularly spaced transaction data

This paper proposes a new statistical model for the analysis of data which arrive at irregular intervals. The model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates. The conditional intensity is developed and compared with other self-exciting processes. Because the model focuses on the expected duration between events, it is called the autoregressive conditional duration (ACD) model. Asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to ARCH model results. Strong evidence is provided for duration clustering for the financial transaction data analyzed; both deterministic time-of-day effects and stochastic effects are important. The model is applied to the arrival times of trades and therefore is a model of transaction volume, and also to the arrival of other events such as price changes. Models for the volatility of prices are estimated with price-based durations, and examined from a market microstructure point of view.

A nonlinear autoregressive conditional duration model with applications to financial transaction data

Abstract This paper presents a new model that improves upon several inadequacies of the original autoregressive conditional duration (ACD) model considered in Engle and Russell (Econometrica 66(5) (1998) 1127–1162). We propose a threshold autoregressive conditional duration (TACD) model to allow the expected duration to depend nonlinearly on past information variables. Conditions for the TACD process to be ergodic and existence of moments are established. Strong evidence is provided to suggest that fast transacting periods and slow transacting periods of NYSE stocks have quite different dynamics. Based on the improved model, we identify multiple structural breaks in the transaction duration data considered, and those break points match nicely with real economic events.

Forecasting the Frequency of Changes in Quoted Foreign Exchange Prices with the Autoregressive Conditional Duration Model

This paper applies the Autoregressive Conditional Duration model to Foreign Exchange quotes arriving on Reuters screens. The Autoregressive Conditional Duration model, proposed in Engle and Russell (1995), is a new statistical model for the analysis of data that do not arrive in equal time intervals. When Dollar/Deutschmark data are examined, it is clear that many of the price quotes carry little information about the price process, as they are simply repeats of the previous quote. By selectively thinning the sample, we develop a measure and forecasts for the intensity of price changes. This measure is related to standard measures of volatility but is formulated in a way that better captures the irregular sampling intervals that are inherent to high frequency financial data. Continuous-stochastic-process theorems for crossing times are used to derive an exact relationship between the intensity of price changes and standard volatility measures. The model might be useful for traders and allows tests that other variables are useful in forecasting the intensity of price changes. Generally, little support is found for price leadership, but other variables influence the intensity of price changes.

True or Spurious Long Memory? A New Test

It is well known that long memory characteristics observed in data can be generated by nonstationary structural-break or slow regime switching models. We propose a statistical test to distinguish between true long memory and spurious long memory based on invariance of the long memory parameter for temporal aggregates of the process under the null of true long memory. Geweke Porter-Hudak estimates of the long memory parameter obtained from different temporal aggregates of the underlying time series are shown to be asymptotically jointly normal, leading to a test statistic that is constructed as the quadratic form of a demeaned vector of the estimates. The result is a test statistic that is very simple to implement. Simulations show the test to have good size and power properties for the classic alternatives to true long memory that have been suggested in the literature. The asymptotic distribution of the test statistic is also valid for a stochastic volatility with Gaussian long memory model. The test is applied to foreign exchange rate data. Based on all the models considered in this article, we conclude that the long memory property in exchange rate volatility is generated by a true long memory process.

Kurtosis of GARCH and stochastic volatility models with non-normal innovations

Both volatility clustering and conditional non-normality can induce the leptokurtosis typically observed in financial data. In this paper, the exact representation of kurtosis is derived for both GARCH and stochastic volatility models when innovations may be conditionally non-normal. We find that, for both models, the volatility clustering and non-normality contribute interactively and symmetrically to the overall kurtosis of the series.

A Discrete-State Continuous-Time Model of Financial Transactions Prices and Times: The Autoregressive Conditional Multinomial-Autoregressive Conditional Duration Model

Financial transaction prices typically lie on a discrete grid of values and arrive at random times. This paper proposes an econometric model with this structure. The distribution of each price change is a multinomial, conditional on past information and the time interval between the transactions. The proposed autoregressive conditional multinomial (ACM) model is not restricted to be Markov or symmetric in response to shocks; however, such restrictions can be imposed. The duration between trades is modeled as an autoregressive conditional duration (ACD) model following Engle and Russell (1998). Maximum likelihood estimation and testing procedures are developed. The model is estimated with 12 months of tick data on a moderately frequently traded NYSE stock, Airgas. The preferred model is estimated, with three lags for the ACM model and two lags for the ACD model. Both price returns and squared returns influence future durations and present and past durations affect price movements. The model exhibits reversals in transaction prices in the short run due to bid–ask bounce and clustering of large moves of either sign in the longer run. Evidence of symmetry in the dynamics of prices is seen, but the response to durations is clearly nonsymmetric. It is found that the volatility per second of trades is highest for short-duration trades and that expected returns are lower for longer-duration trades.

Measuring and Modeling Execution Cost and Risk

We introduce a new analysis of transaction costs that explicitly recognizes the importance of the timing of execution in assessing transaction costs. Time induces a risk/cost tradeoff. The price of immediacy results in higher costs for quickly executed orders while more gradual trading results in higher risk since the value of the asset can vary more over longer periods of time. We use a novel data set that allows a sequence of transactions to be associated with individual orders and measure and model the expected cost and risk associated with different order execution approaches. The model yields a risk/cost tradeoff that depends upon the state of the market and characteristics of the order. We show how to assess liquidation risk using the notion of liquidation value at risk (LVAR).

Using High-Frequency Data in Dynamic Portfolio Choice

This article evaluates the economic benefit of methods that have been suggested to optimally sample (in an MSE sense) high-frequency return data for the purpose of realized variance/covariance estimation in the presence of market microstructure noise (Bandi and Russell, 2005a, 2008). We compare certainty equivalents derived from volatility-timing trading strategies relying on optimally-sampled realized variances and covariances, on realized variances and covariances obtained by sampling every 5 minutes, and on realized variances and covariances obtained by sampling every 15 minutes. In our sample, we show that a risk-averse investor who is given the option of choosing variance/covariance forecasts derived from MSE-based optimal sampling methods versus forecasts obtained from 5- and 15-minute intervals (as generally proposed in the literature) would be willing to pay up to about 80 basis points per year to achieve the level of utility that is guaranteed by optimal sampling. We find that the gains yielded by optimal sampling are economically large, statistically significant, and robust to realistic transaction costs.

Econometric Analysis of Discrete-Valued Irregularly-Spaced Financial Transactions Data Using a New Autoregressive Conditional Multinomial Model

This paper proposes a new approach to modeling financial transactions data. A new model for discrete valued time series is proposed in the context of generalized linear models. Since the model is specified conditional on both the previous state, as well as the historic distribution, we call the model the Autoregressive Conditional Multinomial (ACM) model. When the data are viewed as a marked point process, the ACD model proposed in Engle and Russell (1998) allows for joint modeling of the price transition probabilities and the arrival times of the transactions. In this marked point process context, the transition probabilities vary continuously through time and are therefore duration dependent. Finally, variations of the model allow for volume and spreads to impact the conditional distribution of price changes. Impulse response studies show the long run price impact of a transaction can be very sensitive to volume but is less sensitive to the spread and transaction rate.

Analysis of High-Frequency Data

Publisher Summary The introduction of widely available ultra high-frequency data sets over the past decade has spurred interest in empirical market microstructure. Intraday transaction-by-transaction dynamics of asset prices, volume, and spreads are available for analysis. Classic asset pricing research assumes only that prices eventually reach their equilibrium value; the route taken and speed of achieving equilibrium are not specified. The introduction of widely available ultra-high-frequency data sets over the past decade has spurred interest in empirical market microstructure. The black box determining equilibrium prices in financial markets has been opened up. Intraday transaction-by-transaction dynamics of asset prices, volume, and spreads are available for analysis. These vast data sets present new and interesting challenges to econometricians. While artificially discretizing the time intervals at which prices (or other marks) is a common practice in the literature, it does not come without cost. Different discretizing schemes trade of bias associated with temporally aggregating with variance. Averaging reduces the variability but blurs the timing of events.