Modeling and forecast of the monthly, quarterly and half-yearly usd Libor Rates

1. Summary
2. Introduction
3. Contents
4. Processing
6. Conclusion and recommendation
7. Bibliography
8. Annexes

SUMMARY

In this work is analyzed the performance of the LIBOR (London Interbanking Offered Rate) usd interest rate for the monthly, quarterly and half-yearly periods, forecasting their expecting values from April the 30th, 2006 to March the 31st, 2009, applying the Box & Jenkins Computerized Methodology and the Juncture Analysis, which permit to evaluate the actual financial impact of bank loans and their future offers that use this type of variable interest rates.

1. The future has been, a constant human endeavor all along its existence, and the cause of multiple quests focused in its prediction. None the less, it is important to point out that this obsession, almost compulsive, responds to the rational interest to exert preventive actions before events that may bring adverse influences in the future.

   In correspondence with this assertion, the theme has been present in the development of science, since the nineties, motivated by the accelerated growth of the Management Information Systems which have permitted to process huge amounts of data at very high speed, a very important aspect to achieve well based forecasts in a short time notice.

   The executive must be first a good forecaster and then comes the rest.

   These facts show their influence in the modern enterprise which must count with standard analysis, forecasting and control, applying computer tools to process the over all data generated to predict it, like cash flows, sales, interest schemes, accounts payable and receivables, prepare over all strategies, etc.

   Taking into account these aspects, this work was prepared to analyze the LIBOR (London Interbanking Offered Rate) usd rate for the monthly, quarterly and half-yearly periods, forecasting their expected values since April the 30th, 2006 to March the 31st, 2009, applying the Box & Jenkins Computerized Methodology and the Juncture Analysis, which permit evaluate the financial impact of the current bank credits and future offers that use this variable interest rate.

2. INTRODUCTION

   II.1 Introduction

   The object of any research is to obtain the necessary, sufficient and trustworthy data about the subject under study, because without them, is impossible to achieve practical results.

   This explanation leads us to two objectives: the search for sufficient data which permit to apply the statistical theory and validate it. These aspects are analyzed as follow:

   II. 2 Source

   One way to gather this type of data is through the search in the Finance web sites, like: www.megabolsa.com, www.finanzas.com, www.economagic.com, choosing the last one, offering besides the required LIBOR periodical usd interest rates since January the 2nd, 1987 to the download on March the 24th, 2006, and had the advantage of offering the whole data in one workfile.

   II. 3 Time series analysis

   Once selected the LIBOR periods and their time series, we had more than 4800 interest rate items for each period, more than enough.

   Having in mind the methodology characteristics of this work, then choose to analyze the monthly, quarterly and half-yearly time series to forecast their future performance. In order to diminish the great number of items for each period, we took the last month LIBOR interest rate, amounting to more than 200 items for each time series.

3. CONTENTS
4. PROCESSING

Once determined the data source, the periods to analyze and the time series to process, applied the Box & Jenkins Computerized Methodology to analyze, forecast and control univariate short-run (3 to 5 years) time series, also known as ARIMA models (Annex B), composed by autoregressive integrated with moving average polynomial terms, which from 50 items on, offer the smallest error possible in the forecast, compared with any other methodology, to the present time, after 30 years of practical experience. It was also applied the Juncture Analysis to the LIBOR monthly time series to know their trend cycles.

The Box & Jenkins Methodology can not be applied if the time series do not have a Normal distribution (0, δ2).

This Methodology is composed of the following steps:

1. Mathematical model identification. Applying the autocorrelation function and its differences could determine the possible time series seasonality periods and the significant polynomial terms that will integrate the model.
2. Model estimation, fitting and checking. The computer program calculates the polynomial values of the model and their standard deviations, besides calculates the percentage Chi squared statistics of at least 20 residual autocorrelation function lags, to know if the identified model satisfactorily fits, otherwise go to the first point.
3. Model forecasting. The model forecasts, in each computer run, as many expected future values, fix by the number of the seasonality period with the confidence interval needed and also backforecasting a few years in order to know the average month percentage error, to recognize its reliance. This average month percentage error should not exceed the 10% level, otherwise, re-start in the first point, modifying the model to obtain satisfactory results.

Applying the above mention Methodology, the time series statistical results, were analyse.