Estimating conditional volatility with neural networks

It is well known that one of the obstacles to effective forecasting of exchange rates is heteroscedasticity (non-stationary conditional variance). The autoregressive conditional heteroscedastic (ARCH) model and its variants have been used to estimate a time dependent variance for many financial time series. However, such models are essentially linear in form and we can ask whether a non-linear model for variance can improve results just as non-linear models (such as neural networks) for the mean have done. In this paper we consider two neural network models for variance estimation. Mixture Density Networks (Bishop 1994, Nix and Weigend 1994) combine a Multi-Layer Perceptron (MLP) and a mixture model to estimate the conditional data density. They are trained using a maximum likelihood approach. However, it is known that maximum likelihood estimates are biased and lead to a systematic under-estimate of variance. More recently, a Bayesian approach to parameter estimation has been developed (Bishop and Qazaz 1996) that shows promise in removing the maximum likelihood bias. However, up to now, this model has not been used for time series prediction. Here we compare these algorithms with two other models to provide benchmark results: a linear model (from the ARIMA family), and a conventional neural network trained with a sum-of-squares error function (which estimates the conditional mean of the time series with a constant variance noise model). This comparison is carried out on daily exchange rate data for five currencies.

Exchange rate exposure : do size and foreign operations matter?

Purpose – The purpose of this paper is to examine the effect of firm size and foreign operations on the exchange rate exposure of UK non-financial companies from January 1981 to December 2001. Design/methodology/approach – The impact of the unexpected changes in exchange rates on firms’ stock returns is examined. In addition, the movements in bilateral, equally weighted (EQW) and trade-weighted and exchange rate indices are considered. The sample is classified according to firm size and the extent of firms’ foreign operations. In addition, structural changes on the relationship between exchange rate changes and individual firms’ stock returns are examined over three sub-periods: before joining the exchange rate mechanism (pre-ERM), during joining the ERM (in-ERM), and after departure from the ERM (post-ERM). Findings – The findings indicate that a higher percentage of UK firms are exposed to contemporaneous exchange rate changes than those reported in previous studies. UK firms’ stock returns are more affected by changes in the EQW, and US$ European currency unit exchange rate, and respond less significantly to the basket of 20 countries’ currencies relative to the UK pound exchange rate. It is found that exchange rate exposure has a more significant impact on stock returns of the large firms compared with the small and medium-sized companies. The evidence is consistent across all specifications using different exchange rate. The results provide evidence that the proportion of significant foreign exchange rate exposure is higher for firms which generate a higher percentage of revenues from abroad. The sensitivities of firms’ stock returns to exchange rate fluctuations are most evident in the pre-ERM and post-ERM periods. Practical implications – This study provides important implications for public policymakers, financial managers and investors on how common stock returns of various sectors react to exchange rate fluctuations. Originality/value – The empirical evidence supports the view that UK firms’ stock returns are affected by foreign exchange rate exposure.

The microstructure of the foreign exchange market:the determinants of bid-ask spreads in the foreign exchange market

The purpose of this thesis is to shed more light in the FX market microstructure by examining the determinants of bid-ask spread for three currencies pairs, the US dollar/Japanese yen, the British pound/US dollar and the Euro/US dollar in different time zones. I examine the commonality in liquidity with the elaboration of FX market microstructure variables in financial centres across the world (New York, London, Tokyo) based on the quotes of three exchange rate currency pairs over a ten-year period. I use GARCH (1,1) specifications, ICSS algorithm, and vector autoregression analysis to examine the effect of trading activity, exchange rate volatility and inventory holding costs on both quoted and relative spreads. ICSS algorithm results show that intraday spread series are much less volatile compared to the intraday exchange rate series as the number of change points obtained from ICSS algorithm is considerably lower. GARCH (1,1) estimation results of daily and intraday bid-ask spreads, show that the explanatory variables work better when I use higher frequency data (intraday results) however, their explanatory power is significantly lower compared to the results based on the daily sample. This suggests that although daily spreads and intraday spreads have some common determinants there are other factors that determine the behaviour of spreads at high frequencies. VAR results show that there are some differences in the behaviour of the variables at high frequencies compared to the results from the daily sample. A shock in the number of quote revisions has more effect on the spread when short term trading intervals are considered (intra-day) compared to its own shocks. When longer trading intervals are considered (daily) then the shocks in the spread have more effect on the future spread. In other words, trading activity is more informative about the future spread when intra-day trading is considered while past spread is more informative about the future spread when daily trading is considered

Long memory and multifractality:a joint test

The properties of statistical tests for hypotheses concerning the parameters of the multifractal model of asset returns (MMAR) are investigated, using Monte Carlo techniques. We show that, in the presence of multifractality, conventional tests of long memory tend to over-reject the null hypothesis of no long memory. Our test addresses this issue by jointly estimating long memory and multifractality. The estimation and test procedures are applied to exchange rate data for 12 currencies. Among the nested model specifications that are investigated, in 11 out of 12 cases, daily returns are most appropriately characterized by a variant of the MMAR that applies a multifractal time-deformation process to NIID returns. There is no evidence of long memory.

Exchange rate exposure:do size and foreign operations matter?

Purpose – The purpose of this paper is to examine the effect of firm size and foreign operations on the exchange rate exposure of UK non-financial companies from January 1981 to December 2001. Design/methodology/approach – The impact of the unexpected changes in exchange rates on firms’ stock returns is examined. In addition, the movements in bilateral, equally weighted (EQW) and trade-weighted and exchange rate indices are considered. The sample is classified according to firm size and the extent of firms’ foreign operations. In addition, structural changes on the relationship between exchange rate changes and individual firms’ stock returns are examined over three sub-periods: before joining the exchange rate mechanism (pre-ERM), during joining the ERM (in-ERM), and after departure from the ERM (post-ERM). Findings – The findings indicate that a higher percentage of UK firms are exposed to contemporaneous exchange rate changes than those reported in previous studies. UK firms’ stock returns are more affected by changes in the EQW, and US$ European currency unit exchange rate, and respond less significantly to the basket of 20 countries’ currencies relative to the UK pound exchange rate. It is found that exchange rate exposure has a more significant impact on stock returns of the large firms compared with the small and medium-sized companies. The evidence is consistent across all specifications using different exchange rate. The results provide evidence that the proportion of significant foreign exchange rate exposure is higher for firms which generate a higher percentage of revenues from abroad. The sensitivities of firms’ stock returns to exchange rate fluctuations are most evident in the pre-ERM and post-ERM periods. Practical implications – This study provides important implications for public policymakers, financial managers and investors on how common stock returns of various sectors react to exchange rate fluctuations. Originality/value – The empirical evidence supports the view that UK firms’ stock returns are affected by foreign exchange rate exposure.

Long memory and multifractality:a joint test

The properties of statistical tests for hypotheses concerning the parameters of the multifractal model of asset returns (MMAR) are investigated, using Monte Carlo techniques. We show that, in the presence of multifractality, conventional tests of long memory tend to over-reject the null hypothesis of no long memory. Our test addresses this issue by jointly estimating long memory and multifractality. The estimation and test procedures are applied to exchange rate data for 12 currencies. In 11 cases, the exchange rate returns are accurately described by compounding a NIID series with a multifractal time-deformation process. There is no evidence of long memory.