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.