## An Applied Example

In the previous sections of this chapter we have highlighted that it is possible to determine ex-ante the transaction cost, the volatility, the estimated returns as well as the correlation between linear individual forecasters such as moving averages. This provides us with the necessary statistical tools to establish a framework for a mean-variance allocation model of trend-following rules. Though we could use a larger sample of linear trading rules such as simple, weighted, exponential moving...

## Appendix B

The tile WD_PCA.xls on the accompanying CD-Rom is an illustration of the PCA method. In the Data sheet of the workbook, and for the sake of simplicity, we retain 122 temperature records in degrees Celsius from 01 09 93 to 31 12 93 for five weather stations. A 10-day period of missing data is artificially created between 01 11 93 and 10 11 93. The common dataset for step 1 of the PCA goes until 31 10 93. In the Step 1 sheet of the workbook, to obtain principal components and factor weights, we...

## Univariate Models

The Excel spreadsheets Bourgoin001.xls and Bourgoin002.xls both have a common set-up Column A and B should have the dates and the security used for analysis, here, the S& P 500 index. Column C calculates the log returns for the index. Column D specifies the volatility equation. Column E calculates the log-likelihood function for each date (when we do an optimisation, which is not the case for the RiskMetrics Volatility model). Column F calculates the annualised volatility using the...

## Multivariate Models

In this section, we will show how to perform multivariate models to calculate conditional correlation estimation and forecast the term structure using Excel. Several models will be considered, the J.P. Morgan RiskMetrics, the optimal decay model and three GARCH models the full diagonal GARCH, and its simpler derivative with variance targeting, and the superfast GARCH model (Bourgoin, 2002). For convenience purposes and simplicity, we will consider only a two-variable system, more can be added...

## Application To International Equities

In this section we describe an application of the cointegration tools and techniques described above to data from those international equities which comprised the STOXX 50 index as of 4 July 2002. We describe this analysis with reference to the accompanying Excel workbook named equity coint.xls on the CD-Rom. The set of equities which constitute our universe are listed in the first sheet of the workbook (named Constituents). The full set of equities included in the analysis are listed in Table...

## The Volatility program

There do not exist statistical packages to easily and directly estimate28 SV models and thus the necessary routines have been developed with Ox (version 3.20), a programming 28 Linear state space models can be estimated with the Kalman filter in EViews, with the Gauss package FANPAC or the Ox package SSFPack (see also STAMP). Thus the linearised version (8.6) could be estimated with a quasi-maximum likelihood approach. For the switching regime models, see also MSVAR, an Ox package developed by...

## About the Contributors

Albanis is currently working at Hypovereinsbank - HVB Group. He obtained his PhD from City University Business School, London and holds a BSc in Economics from the University of Piraeus, Greece and Master's degrees in Business Finance and in Decision Modelling and Information Systems from Brunei University, London. An experienced programmer, his interests are applications of advanced nonlinear techniques for financial prediction in fixed income and credit derivatives markets, and...

## Weather Data And Weather Derivatives

13.2.1 The importance of weather data for weather derivatives pricing The history of the weather derivatives market dates back to 1996, when electricity deregulation in the USA caused the power market to begin changing from series of local monopolies to competitive regional wholesale markets. Energy companies realising the impact of weather on their operations took control of their weather risk and created a new market around it. While a number of pioneering trades were made as early as 1996,...

## The Exchange Rate And Volatility Data

The motivation for this research implies that the success or failure to develop profitable volatility trading strategies clearly depends on the possibility to generate accurate volatility forecasts and thus to implement adequate volatility modelling procedures. Numerous studies have documented the fact that logarithmic returns of exchange rate time series exhibit volatility clustering properties, that is periods of large volatility tend to cluster together followed by periods of relatively...

## References

Batchelor 2001 , 21 Nonlinear Ways to Beat the Market. In Developments in Forecast Combination and Portfolio Choice, Dunis C, Moody J, Timmermann A eds John Wiley Chichester. Baillie, R. T. and T. Bollerslev 1989 , The Message in Daily Exchange Rates A Conditional Variance Tale. Journal of Business and Economic Statistics 7 297-305. Baillie, R. T. and T. Bollerslev 1990 , Intra-day and Inter-market Volatility in Foreign Exchange Rates. Review of Economic Studies 58...

## The Exchange Rate And Related Financial Data

The FX market is perhaps the only market that is open 24 hours a day, seven days a week. The market opens in Australasia, followed by the Far East, the Middle East and Europe, and finally America. Upon the close of America, Australasia returns to the market and begins the next 24-hour cycle. The implication for forecasting applications is that in certain circumstances, because of time-zone differences, researchers should be mindful when considering which data and which subsequent time lags to...

## Bivariate Models For Price Change And Duration

In this section, we introduce a model that considers jointly the process of price change and the associated duration. As mentioned before, many intraday transactions of a stock result in no price change. Those transactions are highly relevant to trading intensity, but they do not contain direct information on price movement. Therefore, to simplify the complexity involved in modeling price change, we focus on transactions that result in a price change and consider a price change and duration PCD...

## The Stochastic Parameter Regression Model And The Kalman Filter The Best Way To Estimate Factor Sensitivities

The procedures that have been described so far involve a single regression equation with constant betas. These procedures use ordinary or weighted least squares in order to repeatedly estimate new model coefficients from adjacent windows of observations. The stochastic parameter model, however, is based on a conceptually different approach see Gourieroux et al. 1997 , or Harvey 1989 . The beta coefficients are not assumed 11 Although this rate is usually set a priori, one could also estimate...

## The Neural Network Volatility Forecasts 441 NNR modelling

Over the past few years, it has been argued that new technologies and quantitative systems based on the fact that most financial time series contain nonlinearities have made traditional forecasting methods only second best. NNR models, in particular, have been applied with increasing success to economic and financial forecasting and would constitute the state of the art in forecasting methods see, for instance, Zhang et al. 1998 . It is clearly beyond the scope of this chapter to give a...

## Accuracy

As noted by Dunis et al. 2001a , today most researchers would agree that individual forecasting models are misspecified in some dimensions and that the identity of the best model changes over time. In this situation, it is likely that a combination of forecasts will perform better over time than forecasts generated by any individual model that is kept constant. Accordingly, we build two rather simple model combinations to add to our three existing volatility forecasts, the GARCH 1,1 , NNR and...

## Info

An example of this transformation can be reviewed in Sheet 1 column C of the oos_Naive.xls Excel spreadsheet, and is also presented in Figure 1.5. See also the comment in cell C4 for an explanation of the calculations within this column. An advantage of using a returns series is that it helps in making the time series stationary, a useful statistical property. Formal confirmation that the EUR USD returns series is stationary is confirmed at the 1 significance level by both the Augmented...

## Naive strategy

The naive strategy simply assumes that the most recent period change is the best predictor of the future. The simplest model is defined by where Yt is the actual rate of return at period t and Yt 1 is the forecast rate of return for the next period. The naive forecast can be reviewed in Sheet 1 column E of the oos_Naive.xls Excel spreadsheet, and is also presented in Figure 1.5. Also, please note the comments within the spreadsheet that document the calculations used within the naive, ARMA,...