Small sample power of tests of normality when the alternative is an alpha-stable distribution

This paper is a Monte-Carlo study of the small sample power of six tests of a normality hypotheses when the alternative is an alpha-stable distribution with param- eter values similar to those estimated for monthly total returns on equity indices. In these circumstances a sample size of 2oo is required to detect departures from normality. In most cases only small samples of consistent monthly data on such to- tal returns are available and these are not sufficient to differentiate between normal and alpha-stable distributions.

Maximum Likelihood Estimates of Regression Coefficients with alpha-stable residuals and Day of Week effects in Total Returns on Equity Indices

This Paper summarizes the theory of Maximum Likelihood Estimation of regressions with alpha-stable residuals. Day of week effects in returns on equity indices, adjusted for dividends (total returns) are estimated and tested using this and traditional OLS methodology. I find that the alpha-stable methodology is feasible. There are some differences in the results from the two methodologies. The conclusion remains that if individual coefficients are of interest and the residuals have fat tails and a possible alpha-stable distribution, the results can be checked for robustness using methods such as those employed here.alpha stable distribution, regression, day of week effects

A RATS subroutine to implement the Chow-Lin distribution/interpolation procedure

This paper describes a RATS (www.estima.com) routine to implement the Chow Lin (1971) procedure for the best linear unbiased distribution and interpolation of time series by related series. Various versions of this procedure have been used in the Bank to distribute/interpolate annual to quarterly time series. One particular use of the routine described here has been to derive quarterly national accounts that have been used to estimate a quarterly macro model of the Irish economy and in various other research studies in the Bank. A zip archive containing a pdf version of the paper, the RATS routine, a sample program and data is available for download. The archive was created using Info-ZIP’s WIZ (http://www.info-zip.org/pub/infozip/WiZ.html) and may be expanded using this program or similar program.

Inflation and Money Growth - Evidence from a Multi-Country Data-Set

Using a multi-country data set strong correlation are found between average growth rates of monetary aggregates and average inflation. The correlation remains strong when countries with higher average inflation rates are removed from the sample. These results confirm the strong correlation found in the traditional literature but contradict those in De Grauwe and Polan (2001) who, in a recent analysis, find that the strong link vanishes when higher inflation countries are excluded. Further analysis confirms the unit response and bears out the value of monetary aggregates as an input to the making of monetary policy.

An Introduction to Matlab for Econometrics

This paper is an introduction to MATLAB for econometrics. It describes the MATLAB Desktop, contains a sample MATLAB session showing elementary MATLAB operations, gives details of data input/output, decision and loop structures, elementary plots, describes the LeSage econometrics toolbox and maximum likelihood using the LeSage toolbox. Various worked examples of the use of MATLAB in econometrics are also given. After reading this document the reader should be able to make better use of the MATLAB on-line help and manuals.Matlab, Econometric Software

Value at Risk (VaR) and the alpha-stable distribution

Volatility in financial markets is a matter of considerable concern to financial institutions and their supervisors. Already it is clear that this volatility has had an adverse effect on the real economy. Many measures of risk that are used today do not take full account of the kind of extreme changes in asset prices that have been observed. This paper finds that the Value at Risk measure of risk can be improved by the use of an alpha-stable distribution in place of more conventional measures. The paper describes the use of this measure and implements it for six total returns equity portfolios. We find that alpha-stable based measures are feasible and are better than conventional measures. They are a useful tool for the risk manager and the financial regulator.alpha stable distribution, Value at Risk, VaR

ECONOMETRICS AND TRUTH

I am grateful for comments received from colleagues in the Bank and would like to thank Tara Purcell and Mary Smith for the effort and skill put into the preparation of this paper. I remain responsible for any errors in the text. The views expressed in the Econometrics and Truth The second half of the sixties was, at first sight, the golden age of econometrics. At the time, it appeared that some minor advances in theory, data and computer facilities would allow us to construct an econometric model which would chart the course to universal prosperity. The seventies were to deal a cruel blow to these extravagant expectations. This rise and fall of econometrics is described in the first section of the paper. In the next two sections we look at some of the advances that have been made in the last twenty years as a response to these problems. Particular attention is paid to spurious regressions and cointegration, and to non-linear methods. A further section of the paper focuses on the use of statistical methods in the search for the truth in economics. These advances in theory would have been of no benefit without the availability of cheap but powerful computer facilities. A description of some of these systems, their limitations and some recommendations on their use are then set out. The paper closes with some comparisons of the meaning of truth in economics and the natural sciences. “The only way to a position in which our science might give positive advice on a large scale to politicians and business men, leads through quantitative work. For as long as we are unable to put our arguments into figures, the voice of our science, although it may occasionally be able to dispel gross errors, will never be heard by practical men. They are, by instinct, econometricians all of them, in their distrust of anything not amenable to exact proof”. From Joseph A Schumpeter: ‘The Common Sense of Econometrics’, Econometrica, 1 (1933), p. 12, as quoted in Hendry (1995)

Studies on the application of the alpha-stable distribution in economics

THESIS 8749Bubbles, booms and busts in asset prices give rise to a considerable misallocation of resources when they are growing and the subsequent adjustment can be very long and painful. Yet, there is no accepted diagnosis of a bubble. In effect, there is a sense in which a bubble and a bust cannot occur in the usual econometric models. These models, almost always, depend on the normal or Gaussian distribution. Yet when one looks at data for asset prices the number and size of extreme losses and gains are orders of magnitude greater than a normal distribution would predict. The very existence of these extreme values must lead one to question the validity of the normality assumption and to look for an alternative. From time to time several alternatives have been proposed. A common proposal is to use mixtures of normal distributions. The simplest such solution is to have a mixture of two normal distributions ? the first, with low volatility, represents the fundamental state with no bubble and the second, with high volatility, the bubble. The price of the asset in question is seen as switching from one state to the other with the switching being determined by some form of deterministic or stochastic process. Other solutions involve what are, in effect, infinite mixtures of normal distributions. Chief amongst these are the various GARCH proceses and the t-distribution. Various other ?fat-tailed? distributions have been proposed but these have not received universal acceptance and probably never will. While such distributions often fit the data well, We have not seen any convincing theoretical arguments why they should. The purpose of this thesis is to examine the use of the a-stable distribution in this context and to determine some of the consequences of its use. The a-stable distribution is a generalisation of the normal distribution. It was first proposed as a distribution for asset returns and commodity prices by Mandelbrot in the early 1960s. It attracted alot of attention up to the early 1970s and then interest faded. There were two reasons for the waning interest. First the advances made at the time in portfolio and option pricing theory were dependent on the normal distribution. At the time almost all of this work could not have been replicated without the normality assumption. Secondly for actual application the computer power available at the time was simply not sufficient to properly use the a-stable distribution. Thus a?stable analysis was primitive relative to the corresponding normal analysis

Inflation and money growth: evidence from a multi-country data-set

Using a multi-country data set strong correlation are found between average growth rates of monetary aggregates and average inflation. The correlation remains strong when countries with higher average inflation rates are removed from the sample. These results confirm the strong correlation found in the traditional literature but contradict those in De Grauwe and Polan (2001) who, in a recent analysis, find that the strong link vanishes when higher inflation countries are excluded. Further analysis confirms the unit response and bears out the value of monetary aggregates as an input to the making of monetary policy