Modeling foreign exchange rate pass-through using the exponential GARCH

In this chapter, the authors use an EGARCH-ECM to estimate the pass-through effects of Foreign Exchange (FX) rate changes and changes in producers' prices for 20 U.K. export sectors. The long-run adjustments of export prices to FX rate changes and changes in producers' prices are within the range of -1.02% (for the Textiles sector) and -17.22% (for the Meat sector). The contemporaneous Pricing-To-Market (PTM) coefficients are within the range of -72.84% (for the Fuels sector) and -8.05% (for the Textiles sector). Short-run FX rate pass-through is not complete even after several months. Rolling EGARCH-ECMs show that the short and long-run effects of changes in FX rate and producers' prices vary substantially, as do asymmetry and volatility estimates before equilibrium is achieved.

Modelling stock volatilities during financial crises:a time varying coefficient approach

We examine how the most prevalent stochastic properties of key financial time series have been affected during the recent financial crises. In particular we focus on changes associated with the remarkable economic events of the last two decades in the volatility dynamics, including the underlying volatility persistence and volatility spillover structure. Using daily data from several key stock market indices, the results of our bivariate GARCH models show the existence of time varying correlations as well as time varying shock and volatility spillovers between the returns of FTSE and DAX, and those of NIKKEI and Hang Seng, which became more prominent during the recent financial crisis. Our theoretical considerations on the time varying model which provides the platform upon which we integrate our multifaceted empirical approaches are also of independent interest. In particular, we provide the general solution for time varying asymmetric GARCH specifications, which is a long standing research topic. This enables us to characterize these models by deriving, first, their multistep ahead predictors, second, the first two time varying unconditional moments, and third, their covariance structure.

Combining the wavelet transform and forecasting models to predict gas forward prices

This paper presents a forecasting technique for forward energy prices, one day ahead. This technique combines a wavelet transform and forecasting models such as multi- layer perceptron, linear regression or GARCH. These techniques are applied to real data from the UK gas markets to evaluate their performance. The results show that the forecasting accuracy is improved significantly by using the wavelet transform. The methodology can be also applied to forecasting market clearing prices and electricity/gas loads.

Energy forward price prediction with a hybrid adaptive model

This paper presents a forecasting technique for forward electricity/gas prices, one day ahead. This technique combines a Kalman filter (KF) and a generalised autoregressive conditional heteroschedasticity (GARCH) model (often used in financial forecasting). The GARCH model is used to compute next value of a time series. The KF updates parameters of the GARCH model when the new observation is available. This technique is applied to real data from the UK energy markets to evaluate its performance. The results show that the forecasting accuracy is improved significantly by using this hybrid model. The methodology can be also applied to forecasting market clearing prices and electricity/gas loads.

Modeling equity market integration using smooth transition analysis:a study of Eastern European stock markets

This paper assesses the extent to which the equity markets of Hungary, Poland the Czech Republic and Russia have become less segmented. Using a variety of tests it is shown there has been a consistent increase in the co-movement of some Eastern European markets and developed markets. Using the variance decompositions from a vector autoregressive representation of returns it is shown that for Poland and Hungary global factors are having an increasing influence on equity returns, suggestive of increased equity market integration. In this paper we model a system of bivariate equity market correlations as a smooth transition logistic trend model in order to establish how rapidly the countries of Eastern Europe are moving away from market segmentation. We find that Hungary is the country which is becoming integrated the most quickly. © 2005 ELsevier Ltd. All rights reserved.

Using monthly returns to model conditional heteroscedasticity

This empirical study examines the extent of non-linearity in a multivariate model of monthly financial series. To capture the conditional heteroscedasticity in the series, both the GARCH(1,1) and GARCH(1,1)-in-mean models are employed. The conditional errors are assumed to follow the normal and Student-t distributions. The non-linearity in the residuals of a standard OLS regression are also assessed. It is found that the OLS residuals as well as conditional errors of the GARCH models exhibit strong non-linearity. Under the Student density, the extent of non-linearity in the GARCH conditional errors was generally similar to those of the standard OLS. The GARCH-in-mean regression generated the worse out-of-sample forecasts.

Stock price reaction following large one-day price changes: UK evidence

We examine the short-term price reaction of 424 UK stocks to large one-day price changes. Using the GJR-GARCH(1,1), we find no statistical difference amongst the cumulative abnormal returns (CARs) of the Single Index, the Fama–French and the Carhart–Fama–French models. Shocks bigger or equal to 5% are followed by a significant one-day CAR of 1% for all the models. Whilst shocks smaller or equal to -5% are followed by a significant one-day CAR of -0.43% for the Single Index, the CARs are around -0.34% for the other two models. Positive shocks of all sizes and negative shocks maller or equal to -5% are followed by return continuations, whilst the market is efficient following larger negative shocks. The price reaction to shocks is unaffected when we estimate the CARs using the conditional covariances of the pricing variables.

The sensitivity of US banks' stock returns to interest and exchange rate changes

Purpose – The purpose of this paper is to investigate the impact of foreign exchange and interest rate changes on US banks’ stock returns. Design/methodology/approach – The approach employs an EGARCH model to account for the ARCH effects in daily returns. Most prior studies have used standard OLS estimation methods with the result that the presence of ARCH effects would have affected estimation efficiency. For comparative purposes, the standard OLS estimation method is also used to measure sensitivity. Findings – The findings are as follows: under the conditional t-distributional assumption, the EGARCH model generated a much better fit to the data although the goodness-of-fit of the model is not entirely satisfactory; the market index return accounts for most of the variation in stock returns at both the individual bank and portfolio levels; and the degree of sensitivity of the stock returns to interest rate and FX rate changes is not very pronounced despite the use of high frequency data. Earlier results had indicated that daily data provided greater evidence of exposure sensitivity. Practical implications – Assuming that banks do not hedge perfectly, these findings have important financial implications as they suggest that the hedging policies of the banks are not reflected in their stock prices. Alternatively, it is possible that different GARCH-type models might be more appropriate when modelling high frequency returns. Originality/value – The paper contributes to existing knowledge in the area by showing that ARCH effects do impact on measures of sensitivity.

Stock index reaction to large price changes:evidence frommajor Asian stock indexes

We examine the short-term price behavior of ten Asian stock market indexes following large price changes or “shocks”. Under the standard OLS regression, there is stronger support for return continuations particularly following positive and negative price shocks of less than 10% in absolute size. The results under the GJR-GARCH method provide stronger support for market efficiency, especially for large price shocks. For example, for the Hong Kong stock index, negative shocks of less than -5% but more than -10% generate a significant one day cumulative abnormal return (CAR) of-0.754% under the OLS method, but an insignificant CAR of 0.022% under the GJR-GARCH. We find no support for the uncertainty information hypothesis. Furthermore, the CARs following the period after the Asian financial crisis adjust more quickly to price shocks.

Techniques to improve forecasting models: applications to energy demand and price

This thesis is a study of three techniques to improve performance of some standard fore-casting models, application to the energy demand and prices. We focus on forecasting demand and price one-day ahead. First, the wavelet transform was used as a pre-processing procedure with two approaches: multicomponent-forecasts and direct-forecasts. We have empirically compared these approaches and found that the former consistently outperformed the latter. Second, adaptive models were introduced to continuously update model parameters in the testing period by combining ?lters with standard forecasting methods. Among these adaptive models, the adaptive LR-GARCH model was proposed for the fi?rst time in the thesis. Third, with regard to noise distributions of the dependent variables in the forecasting models, we used either Gaussian or Student-t distributions. This thesis proposed a novel algorithm to infer parameters of Student-t noise models. The method is an extension of earlier work for models that are linear in parameters to the non-linear multilayer perceptron. Therefore, the proposed method broadens the range of models that can use a Student-t noise distribution. Because these techniques cannot stand alone, they must be combined with prediction models to improve their performance. We combined these techniques with some standard forecasting models: multilayer perceptron, radial basis functions, linear regression, and linear regression with GARCH. These techniques and forecasting models were applied to two datasets from the UK energy markets: daily electricity demand (which is stationary) and gas forward prices (non-stationary). The results showed that these techniques provided good improvement to prediction performance.

Interdependence of international equity market volatility

This paper investigates whether equity market volatility in one major market is related to volatility elsewhere. This paper models the daily conditional volatility of equity market wide returns as a GARCH-(1,1) process. Such a model will capture the changing nature of the conditional variance through time. It is found that the correlation between the conditional variances of major equity markets has increased substantially over the last two decades. This supports work which has been undertaken on conditional mean returns which indicates there has been an increase in equity market integration.

Conditional volatility and firm size:an empirical analysis of UK equity portfolios

The techniques and insights from two distinct areas of financial economic modelling are combined to provide evidence of the influence of firm size on the volatility of stock portfolio returns. Portfolio returns are characterized by positive serial correlation induced by the varying levels of non-synchronous trading among the component stocks. This serial correlation is greatest for portfolios of small firms. The conditional volatility of stock returns has been shown to be well represented by the GARCH family of statistical processes. Using a GARCH model of the variance of capitalization-based portfolio returns, conditioned on the autocorrelation structure in the conditional mean, striking differences related to firm size are uncovered.

Exchange controls and the transmission of equity market volatility:the case of the UK

The paper investigates the impact that the relaxation of UK exchange controls in October 1979, had on the transmission of equity market volatility from the UK to other major equity markets. It is suggested that the existence of exchange controls in the UK was an important source of market segmentation which disturbed the transmission of shocks from one country to another, even when shocks contained global information. It is found that when a spillover GARCH(1,1) model is estimated for the five years before and after the removal of exchange controls, volatility shocks spill over from the UK to other markets much more strongly after the removal of exchange controls. This appears to suggest that volatility as well as returns have become more closely related since the UK removed exchange controls.

Statnote 14: the correlation of two variables (Pearson's 'r')

Pearson's correlation coefficient (‘r’) is one of the most widely used of all statistics. Nevertheless, care needs to be used in interpreting the results because with large numbers of observations, quite small values of ‘r’ become significant and the X variable may only account for a small proportion of the variance in Y. Hence, ‘r squared’ should always be calculated and included in a discussion of the significance of ‘r’. The use of ‘r’ also assumes that the data follow a bivariate normal distribution (see Statnote 17) and this assumption should be examined prior to the study. If the data do not conform to such a distribution, the use of a non-parametric correlation coefficient should be considered. A significant correlation should not be interpreted as indicating ‘causation’ especially in observational studies, in which the two variables may be correlated because of their mutual correlations with other confounding variables.

Data analysis methods in optometry. Part 5: correlation

1. Pearson's correlation coefficient only tests whether the data fit a linear model. With large numbers of observations, quite small values of r become significant and the X variable may only account for a minute proportion of the variance in Y. Hence, the value of r squared should always be calculated and included in a discussion of the significance of r. 2. The use of r assumes that a bivariate normal distribution is present and this assumption should be examined prior to the study. If Pearson's r is not appropriate, then a non-parametric correlation coefficient such as Spearman's rs may be used. 3. A significant correlation should not be interpreted as indicating causation especially in observational studies in which there is a high probability that the two variables are correlated because of their mutual correlations with other variables. 4. In studies of measurement error, there are problems in using r as a test of reliability and the ‘intra-class correlation coefficient’ should be used as an alternative. A correlation test provides only limited information as to the relationship between two variables. Fitting a regression line to the data using the method known as ‘least square’ provides much more information and the methods of regression and their application in optometry will be discussed in the next article.