No abstract

Models based on factors such as size or value are ubiquitous in asset pricing.Therefore, portfolio allocation and risk management require estimates of the volatility of these factors. While realized volatility has become a standard tool for liquid assets, this measure is difficult to obtain for asset pricing factors such as size and value that include smaller illiquid stocks that are not traded at a high frequency. Here, we provide a simple approach to estimate the volatility of these factors. The efficacy of this approach is demonstrated using Monte Carlo simulations and forecasts of the market volatility.

No abstract

No abstract

For modeling and forecasting time series it is essential to know whether the series are stationary or non-stationary since many commonly applied statistical methods (such as OLS) are invalid under non-stationarity. Two features that cause a time series to be non-stationary are considered here. On the one hand a time series can be subject to a change in mean, i.e. the expected value of the series changes over time. On the other hand a time series can be subject to a break in the autocovariance often referred to as a change in persistence, i.e. the dependence structure of the series changes over time. Potential examples for both a change in mean and a change in persistence can be found in Figure 1. Figure 1: Left: log squared returns of the NASDAQ index between 2006 and 2009, right: crude oil price over time.The left plot presents the daily log squared returns of the NASDAQ index between 2006 and 2009. It can be seen that in the second part of the series the mean of the log squared return seems to be larger than in the first part of the series. This is evidence for a change in mean, which is likely to be caused by the financial crisis started in August 2007. The right plot shows the monthly price of crude oil between 1986 and 2019. It can be seen that the series is more variable in the second part from year 2000 onwards. This might be caused by a change in the autocovariance structure (i.e. a change in persistence) of the series.The memochange package is an R (R Core Team, 2019) package that identifies such changes in mean and persistence. This helps to avoid model misspecification and improves forecasts of the time series.