Data processing: measuring – calibrating – or testing – Calibration or correction system – Sensor or transducer
Reexamination Certificate
2003-05-20
2004-08-17
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Calibration or correction system
Sensor or transducer
C705S035000
Reexamination Certificate
active
06778929
ABSTRACT:
PRIORITY INFORMATION
The present invention claims priority to Japanese Patent Application No. 2002-282167, filed Sep. 27, 2002, which is herein incorporated by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention generally relates to estimating meteorological quantities and, more particularly, to estimating meteorological quantities based on a meteorological time-series model.
2. Discussion of Background
As a derivative product for hedging reduction of sales amount and increase of cost resulting from variations of temperature, amount of rainfall and amount of snow coverage or the like, a weather derivative (transaction) is known. The weather derivative transaction is agreed between customers (enterprises, organizations, corporate organizations and associations, etc.) whose amount of sales is largely affected by weather conditions and, for example, product-liability insurance companies (banks, etc.). In the case of hedging the risk for reduction of sales amount because of a lower temperature in comparison with normal years, a customer and a product-liability insurance company agreed, for example, in the contract of following contents for the purpose of weather derivative transactions
(1) Observation period: from June 1st to August 31st
(2) Weather index: Average temperature (the number of days in which the average temperature of a day is less than 25° C.)
(3) Observation point: Tokyo
(4) Strike value: Four days (Compensatory payment may be received from a 5
th
day in the case where there are four or more days when the average temperature of a day is less than 25° C.)
(5) Compensatory payment: $10 per day (upper limit: $200)
(6) Premium: $50
When the weather derivative transaction of the contract content described above is executed, the amount of compensatory payment is different depending on estimation of weather index within the observation period. Therefore, estimation of weather index is very important for both the customer and the product-liability insurance company.
For estimation of meteorological quantities such as temperature and amount of rainfall, etc. as the weather index, a method has been introduced in which a meteorological time-series model has been formed first from historical data of meteorological quantities in the past at the observation point. Then fluctuation of meteorological quantities within the observation period has been estimated with the Monte-Carlo simulation based on this model.
As an example, we will explain the Dischel model which is famous as a weather time-series model for temperature of each day. The Dischel model is expressed by the Formula 1:
T
n
=
(
1
-
β
)
Θ
n
+
β
T
n
-
1
+
ϵ
n
ϵ
n
∼
Normal
[
μ
,
σ
2
]
[
Expression
1
]
Here, n represents the n-th day (for example, Feb. 1, 2000 when n=32) in the case where the desired day (for example, Jan. 1, 2000) is defined as the first day, &THgr;n represents the average temperature of the date corresponding to the n-th day (average temperature of several years in the past of the February 1 when n=32, for example), T
n
represents the temperature of the n-th day. Here, the parameters &bgr;, &mgr;, &sgr; are constants. Moreover, &egr;
n
is a stochastic variable which follows the normal distribution of average &mgr; and variation &sgr;
2
. In addition, &bgr; indicates a rate of dependence of temperature T
n
of the n-th day respectively on the average temperature &THgr;
n
of several years in the past of the object day and the temperature T
n−1
of the yesterday of the object day n. Values of three parameters are generally estimated using the least-squares method from the historical data of temperature of several years in the past at the observation point.
When the parameters are once determined, temperature time-series sequence T
1
, T
2
, T
3
, . . . can be sequentially estimated by giving the initial value T
0
and random number sequences &egr;
1
, &egr;
2
, &egr;
3
. . . . When the estimation period is ranged from n=1 to n=N, a set of estimated temperature time-series sequences is formed of T
1
, . . . , T
N
. Such estimated temperature time-series sequences are estimated from several thousands to several tens of thousands examples by changing the random number sequences.
An amount of compensatory payment to be paid to a customer from the product-liability insurance company is calculated in each estimated time-series sequence in order to calculate probability density distribution. The product-liability insurance company finally calculates a premium based on this probability density distribution. The premium calculation process has been summarized above.
Moreover, estimation of meteorological quantities such as temperature and amount of rainfall has very important significance for company strategy, completion of various events and activities. In addition, everyone is interested in the matters represented by meteorological quantities such as temperature and amount of rainfall.
SUMMARY OF THE INVENTION
A meteorological model used in the economic activities represented by weather derivative transaction is a simplified time-series model where attention is paid only to meteorological fluctuation at a spatial point, namely at the observation point. When parameters of the model are estimated only from the historical data of meteorological quantities, future forecast using a model only indicates an average tendency at the observation point. In other words, practical tendency of each year that it is likely to be cool this summer cannot be estimated.
Such detail estimation of meteorological phenomenon is always requested to introduce a large amount of processes and advanced skill to evaluate various data such as execution of simulation in the global scale based on the extremely detail meteorological mechanical model which has been done by the Meteorological Agency.
Actually, the Meteorological Agency announces long-range weather forecast data of the next one months and three months for temperature and amount of rainfall based on the references such as result of large scale simulation. The long-range forecasts are issued in three grades that the average temperature in the forecast period (amount of rainfall in the forecast period) is “below-normal”, “near-normal” and “above-normal”. The range of each grade is defined to provide equal appearance ratio (33%, respectively) during past 30 years. For example, in the one-month forecast (weather forecast for the period up to September 16 from August 17) of “Kanto and Koshinetsu Regions”, an average temperature of the coming month is that “probability for below-normal is 20%, probability for near-normal is 50% and probability for above-normal is 30%”. Accuracy of the long-range weather forecast is improved from year to year and this improvement is expected more and more in future with improvement in capability of computer system.
However, such long-range weather forecast provides only macroscopic information such as probability distribution of average temperature and amount of rainfall during the forecast period. Meanwhile, microscopic information such as probability distribution of temperature and amount of rainfall of each day is often requested for the economic activities represented by weather derivative transaction. In actuality, a meteorological time-series model such as Dischel model has a demerit that tendency of each year cannot be forecasted while it has a merit that microscopic information such as probability distribution of temperature and amount of rainfall of each day can be treated. Therefore, such a meteorological time-series model is considered to have been widely spread in the weather derivative transaction because of the merit described above.
It is important to note that an ideal meteorological times-series model having the merits of both macroscopic and microscopic information can be formed by reflecting the long-range weather forecast providing ma
Barlow John
Hitachi , Ltd.
Taylor Victor J.
LandOfFree
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