The serial correlation structure for a random process with steps

Summary We derive the detailed correlation structure for the simple “staircase model”: a process where white noise is superimposed on a deterministic step function that has equal rises and equal treads. It turns out that this structure is an immediate generalisation of that for a linear trend (which, for discrete data, can be alternatively considered as a step function with equal rises and unit treads). We compare the structure obtained with that for a random walk, and those for a subset of other ARIMA(p, 1,q) models, and those of general ARIMA(p, d, q) processes withd>1.     

Accounting for the impact of higher order moments in foreign equity option pricing model

This paper investigates the pricing of foreign equity option whose value depends on foreign equity prices and exchange rate. We assume that the underlying asset returns of foreign equity option is not a Brownian motion, and use the Gram-Charlier series expansion to augment a normal density with two additional terms to capture the effects of skewness and kurtosis. The empirical study shows that the higher order moments (skewness and kurtosis) clearly affect the estimated prices of foreign equity options. This approach enables us to capture more accurately the foreign equity option prices.     

Government spending and economic growth in the OECD countries

Using panel data from 1995 to 2011 for 34 OECD countries, we examine the effects of government consumption spending, public social spending, and public investment on economic growth. We use a generalized method of moments estimation technique to solve inconsistency problems with fixed effects and random effects panel estimation. We find that an increase in public social spending has a significant negative effect on subsequent economic growth. Government consumption spending and public investment have no significant effect on subsequent economic growth.     

Moments of cross-sectional stock market returns and the German business cycle

Based on monthly data covering the period from 1987 to 2021, we analyse whether cross-sectional moments of stock market returns may provide information about the future position of the German business cycle. We apply in-sample forecasting regressions with and without leading indicators as control variables, pseudo-out-of-sample exercises, autoregressive distributed lag models, and impulse-response functions estimated by local projections. We find in-sample predictive power of the first and third cross-section moments for the future growth of industrial production, even if one controls for well-established leading indicators for the German business cycle. Out-of-sample tests show that these variables reduce the relative mean squared error compared with benchmark models. We do not find a long-run relation between the moment series and industrial production. The dynamic response of industrial production to a shock on the cross-section moments is in line with the other results.     

Superkurtosis

Very little is known on how traditional risk metrics behave under intraday trading. We fill this void by examining the finiteness of the returns' moments and assessing the impact of their infinity in a risk management framework. We show that when intraday trading is considered, assuming finite higher order moments, potential losses are materially larger than what the theory predicts, and they increase exponentially as the trading frequency increases—a phenomenon we call $superkurtosis$. Hence, the use of the current risk management techniques under intraday trading imposes threats to the stability of financial markets, as capital ratios are severely underestimated.