Extreme Yield Movements and Dynamic Density Forecasts for the Term Structure of Interest Rates

Analyzing Oil Futures with a Dynamic Nelson‐Siegel Model

“…This indicates that prices in general have increased over time. This is in contrast to the evidence from the interest rate market presented in Diebold and Li () and Noureldin (). The slope factor is predominantly positive for the first part of the sample until 2008–2009 and then it turns negative.…”

“…The curvature factor changes time several times throughout the sample. This pattern is also observed for interest rates by Diebold and Li () and Noureldin (). We analyze the time series properties of the factors to determine how the model should be specified.…”

“…This indicates a downward sloping term structure in the first part of the sample and an upward sloping term structure in the last part of the sample. In the interest rate market Diebold and Li () and Noureldin () find that the slope factor is negative almost all the time. The curvature factor changes time several times throughout the sample.…”

“…Futures contracts are characterized by their time to maturity, so a good way of forecasting is to consider a time series of prices of contracts with the same time to maturity. Such a time series is not observed, but it could be constructed by interpolation, see Diebold and Li () or Noureldin () for examples from the interest rate literature. Another possibility is to consider the time series of prices for this particular contract, 2012M (delivery in June 2012) and fit an autoregressive model.…”

“…Therefore models from the fixed income literature are often applied to analyze commodity futures contracts. In this paper, we apply the dynamic Nelson–Siegel model, Nelson and Siegel () and Diebold and Li () using a modeling approach inspired by Noureldin (). The dynamic Nelson–Siegel model is based on three factors and thus allows for a substantial dimension reduction which facilitates the analysis.…”