Mean Reversion Expectations and the 1987 Stock Market Crash: An Empirical Investigation

After the stock market crash of 1987, Fischer Black proposed a model in which he explained the crash by inconsistencies in the formation of expectations of mean reversion in stock returns. Following this explanation, a model that allows for mean reversion in stock returns is estimated on daily stock index data around the crash of 1987. The results strongly support Black’s hypothesis. Simulations show that on Friday Oct 16, 1987, a crash of 20 percent or more had a probability of more than seven percent.stock-market crash, mean reversion, stock return predictability, change-points

Overlaying Time Scales and Persistence Estimation in GARCH(1,1) Models

A common finding in the empirical literature is that financial volatility exhibits high persistence, or slow mean reversion of the order of months. We present evidence that financial volatility data contains more than a single time scale. After showing that the expectation of the sum of the estimates of the autoregressive coefficients of a GARCH(1,1) model is one when there are unknown parameter changes, we explore the phenomenon in simulations. For parameter changes within realistic ranges for stock-price volatility we obtain global estimates close to integration while the average data- generating mean reversion is of the order of a few days. Spectral analysis of the Dow Jones Industrial Average and the S&P500 index between 1985 and 2001 reveals a short time scale of the magnitude of 5- 10 days present in the data. Thus, two different time scales exist in the data, one of the order of months corresponding to different volatility regimes, and one of the order of days corresponding to the average mean reversion within regimes.GARCH, volatility persistence, regime switching, long memory, short memory, structural change

A structural break in the effects of Japanese foreign exchange intervention on yen/dollar exchange rate volatility

While up to the late 1990s Japanese foreign exchange intervention was fully sterilized, Japanese monetary authorities left foreign exchange intervention unsterilized when Japan entered the liquidity trap in 1999. According to previous research on foreign exchange intervention, unsterilized intervention has a higher probability of success than sterilized intervention. Based on a GARCH framework and change point detection, we test for a structural break in the effectiveness of Japanese foreign exchange intervention. We find a changing impact of Japanese foreign exchange intervention on exchange rate volatility at the turn of the millennium when Japanese foreign exchange intervention started to remain unsterilized. JEL Classification: E58, F31, F33, G15Change Point Detection, Exchange rate volatility, foreign exchange intervention, GARCH, Japan, Structural Breaks

The Effects of Japanese Foreign Exchange Intervention: GARCH Estimation and Change Point Detection

We study the impact of Japanese foreign exchange intervention on the volatility of the yen/dollar exchange rate since the early 1990s based on a GARCH framework. Using daily intervention data provided by the Japanese Ministry of Finance, we show that the success of interventions varies over time. Measured on the total sample between 1991 and 2003 the estimation results for the impact of foreign exchange intervention on the yen/dollar exchange rate volatility are inconclusive. Sub-dividing the sample into yearly sub-periods and into intervention clusters suggests a structural break. From 1991 up to the late 1990s Japanese foreign exchange intervention seems to have increased the volatility of the yen/dollar exchange rate. In contrast in the new millennium, Japa- nese foreign exchange intervention is associated with less exchange rate volatility. Non-arbitrary segmentation by change point detection leads to similar results. The evidence in favour of recent successful Japanese foreign exchange intervention is line with theoretical evidence which implies successful intervention is the case of un-sterilized intervention.Japan, Foreign Exchange Intervention, Exchange Rate Volatility, GARCH, Change Point Detection, Liquidity Trap

Forecasting realized volatility models:the benefits of bagging and nonlinear specifications

We forecast daily realized volatilities with linear and nonlinear models and evaluate the benefits of bootstrap aggregation (bagging) in producing more precise forecasts. We consider the linear autoregressive (AR) model, the Heterogeneous Autoregressive model (HAR), and a non-linear HAR model based on a neural network specification that allows for logistic transition effects (NNHAR). The models and the bagging schemes are applied to the realized volatility time series of the S&P500 index from 3-Jan-2000 through 30-Dec-2005. Our main findings are: (1) For the HAR model, bagging successfully averages over the randomness of variable selection; however, when the NN model is considered, there is no clear benefit from using bagging; (2) including past returns in the models improves the forecast precision; and (3) the NNHAR model outperforms the linear alternatives.

Asymmetries, breaks, and long-range dependence: An estimation framework for daily realized volatility

We study the simultaneous occurrence of long memory and nonlinear effects, such as structural breaks and thresholds, in autoregressive moving average (ARMA) time series models and apply our modeling framework to series of daily realized volatility. Asymptotic theory for the quasi-maximum likelihood estimator is developed and a sequence of model specification tests is described. Our framework allows for general nonlinear functions, including smoothly changing intercepts. The theoretical results in the paper can be applied to any series with long memory and nonlinearity. We apply the methodology to realized volatility of individual stocks of the Dow Jones Industrial Average during the period 1995 to 2005. We find strong evidence of nonlinear effects and explore different specifications of the model framework. A forecasting exercise demonstrates that allowing for nonlinearities in long memory models yields significant performance gains.Realized volatility, structural breaks, smooth transitions, nonlinear models, long memory, persistence.

Japanese Foreign Exchange Intervention and the Yen/Dollar Exchange Rate: A Simultaneous Equations Approach Using Realized Volatility

We use realized volatility to study the influence of central bank interventions on the yen/dollar exchange rate. Realized volatility is a technical innovation that allows specifying a system of equations for returns, realized volatility, and interventions without endogeneity bias. We find that during the period 1995 through 1999, interventions of the Japanese monetary authorities did not have the desired effect with respect to the exchange rate level and we measure an increase in volatility associated with interventions. During the period 1999 through 2004, the estimations are consistent with successful interventions, both in depreciating the yen and in reducing exchange rate volatility.