JPH05108652A - Estimating system for financial property price - Google Patents

Abstract

PURPOSE:To provide a system where a series of procedures are carried out many times to the property groups, the statistic value including the average estimated value, the standard deviation, etc., are calculated based on the estimated value calculated from the property groups, and the estimating accuracy is improved with use of a high performance computer like a supercomputer, etc., CONSTITUTION:A desired bond to be estimated is designated in a process 1. The inputted bond and N-1 pieces of bond names are selected with generation of the uniform random numbers in a process 2. In a process 3, the stock price data on a past T period of the name of e group N are read out of a stock price data base 5, an equation showing the price structure in the pest T period is decided by a prescribed method, and the price of the designated name is estimated. Then both processes 2 and 3 are carried out to a group consisting of N names including a relevant bond and the stock price is estimated in consideration of the mutual influences of bonds. Thus procedure is repeated by LL times for simulation with change of the component names of the group. Then the statistic value including the average estimated stock price, etc., obtained in the process 3 is outputted in a process 4 and the due procedure is complete.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a financial asset price forecasting system using a high-performance computer, and more particularly to improving the forecasting accuracy by a statistical method.

[0002]

2. Description of the Related Art An MTV model approach is known as a system for predicting price fluctuations of financial assets. This method is described in Takeaki Kariya, “Basics of Portfolio Econometric Analysis,” p49-p61, Toyo Keizai Shinposha. This is because q
There is a common state variable, and the state space model follows that asset prices fluctuate due to changes in the state variable. The state model consists of a system of two equations, an observation equation and a state equation. The observation equation expresses the relation between the asset price and the state variable, and the state equation expresses the temporal relation of the state variable. In the MTV model, the observation equation is determined from the principal component analysis, and the state equation is determined by the steady time series model based on the state variable obtained from it. Since the state equation expresses the time series relation of the state variables, the future state variable can be predicted, and the asset price can be predicted by the observation equation showing the state variable and the asset price.

[0003]

The above-mentioned prior art has the following problems in the accuracy of predicting asset prices.

First, when predicting the price of a certain individual asset, what kind of asset group should be prepared is not shown. Depending on the set of assets, the proportion explained by common variables may be small. At this time, the predictability should be low.

Secondly, when a certain asset price is analyzed by a certain asset group, the future stock price of the asset is given a deterministic numerical value. However, it is not possible to give the statistical confidence intervals necessary for using this predicted value.

Thirdly, when determining the structure of the state equation, the value of the state variable is obtained from the result of the principal component analysis of the observation equation and estimated by performing time series analysis, which is not a very accurate method.

[0007] Therefore, an object of the present invention is to provide a system for improving the accuracy of prediction of the price of financial assets by using a high performance computer such as a super computer in order to solve the above problems.

[0008]

In order to achieve the above object, the following means are provided.

For the first problem, means for selecting an asset group consisting of a large number of assets including the asset to be predicted is provided,
Prediction simulation was performed for each individual asset group, and a means for determining the predictability of the asset to be predicted in the asset group by the explanation rate by a common factor having a time series structure was provided.

For the second problem, a means for selecting using a uniform random number when selecting the asset group described in the means of the first problem is provided, and based on the price structure of each asset group. Calculate the predicted value of the stock you want to predict, and based on the result of the predicted value calculated by the individual simulation, the average value,
A means for calculating statistics such as standard deviation was provided.

For the third problem, a means for determining the structure of the state equation by the following repetition is provided. The initial value structure of the state equation is determined using the conventional method. Then, the Kalman filter means for obtaining the state variable at the time point t using only the time points 1 to t of the asset price, which is the observed value, as the data of the state variable is generated from the observation equation and the state equation, and the state equation structure is stabilized. Repeat until.

[0012]

The predicting method of the present invention operates as follows when an asset to be predicted is specified.

In the asset grouping unit, the input asset and a plurality of other assets are selected by generating a uniform random number. In the asset price prediction part, a state space model consisting of an observation equation and a state equation is estimated from past asset prices, and the predictability of the asset is calculated using the effective commonality calculated from the estimated coefficient of the observation equation. If it is determined that it is predictable, the state variable is predicted based on the state equation showing the time series structure of the estimated state variable, and the asset price is predicted from the observation equation based on the predicted state variable. This procedure is repeated for different asset groups that include the asset you want to predict, and based on the predicted values calculated for each asset group, you can obtain statistics such as the average value and standard deviation of the predicted values. , It is possible to know the reliability of the predicted value.

The model structure of the state space consisting of the observation equation and the state equation is determined as follows. The observation equation is estimated by factor analysis from past asset prices. For the state equation, first, the approximate value of the state variable is obtained from the structural equation, and the approximate structure is obtained by the steady time series analysis of the state equation. Then, the improved value of the state variable is obtained by the Kalman filter generated from the past asset price which is the observed data, the observation equation and the state equation, and the time series structure of the state variable is re-estimated based on the improved value. By repeating this procedure until the structure becomes stable, a more accurate asset price structure is required.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the financial asset forecasting system of the present invention will be described below with reference to the drawings. Here, a security will be described as an example of the target financial asset.

FIG. 1 is a block diagram of a financial asset forecasting system according to the present invention, and FIGS. 2, 3 and 4 are detailed diagrams showing the modeling and forecasting method of securities prices.

In the process 1, a security desired to be predicted is designated. In process 2, the input securities and N-1 securities issues other than that are generated by generating uniform random numbers and selected. For example, when the selected population is the constituents (about 1000) listed on the First Section of the Tokyo Stock Exchange, N is preferably about 50. In the process 3, the stock price data of the N issues in the past T period is read from the stock price database 5, the equation showing the price structure in the past T period is determined by the method described later, and the price of the designated issue is predicted. To do. As T, the condition of T> N is required. It is desirable to set the period about twice N. Stock price forecasting is performed for the group consisting of N issues including the securities in consideration of the mutual influence of securities, but this is repeated LL times by changing the constituents of the group to perform the simulation. To do. It is desirable that the number of repetitions is large. In this case, 1000 times or more is suitable. Then, after LL times of simulation, in process 4, the statistical value such as the average value of the predicted stock price obtained in process 3 is output, and the process ends. Such processing is practical only when a high-performance computer such as a super computer is used.

Next, the processing of the method for determining the price structure of the N issue of securities will be described. Takeaki Kariya "Basics of Portfolio Econometric Analysis" There is a state space model described in Toyo Keizai, Inc. p50-p51. Price-earnings ratio of the time t of N stocks (revenue per 1 _{yen) X t = (x 1t,} x 2t, ..,
Behind (x _Nt ), there are q common factor variables f _t = (f _1t , f _2t , ..., F _qt ) as common fluctuation factors. This is a model in which X # varies depending on the variation of the common factor. Hereafter, the variables that have been called state variables until now will be called common factor variables. At this time, it consists of the following two equations.

1. Observation equation: A model expressing the relationship between X _t and f _t

[0020]

[Equation 1]

Here, ε _it is white noise.

2. State equation: A model that expresses the time-varying structure of the common factor f _t

[0023]

[Equation 2]

Here, η _it is white noise.

Process 3 is a process of determining the structure of the observation equation and the state equation, checking the predictability of the designated brand, and obtaining the predicted value. 2, 3 and 4 show the details of each.

A method of determining the observation equation will be described with reference to FIG.

In process 11, the stock prices of N stocks of the target group from period 1 to T are read from the stock price database 5. That is, if the stock price of the stock i at time t is P _it , then P _it
(I = 1, ..., N, t = 1, ..., T) are set.

In process 12, the continuous rate of return xx _it , which is the continuous yield of stock prices, is determined by the following formula.

[0029]

[Equation 3]

In the process 13, the average value μ and the standard deviation σ are obtained from the continuous rate of return data obtained in the process 12 of the period 1 to T-1 for each issue, and the standardized continuous rate of return x _it
Is calculated by the following formula.

[0031]

[Equation 4]

In the following, for simplicity, the standardized continuous rate of return will be simply referred to as the rate of return.

In process 14, a known factor analysis model (for example, Multivariate Analysis Handbook 7
Chapter p183-p223 Hyundai Mathematics Co., Ltd.) is applied. The input is T-1 pieces of profit rate data for each issue obtained in the process 13. As a result of the factor analysis, the number q of common factors and the factor load matrix a _ij (i = 1, ..., N, j =
1 ,. ． , Q), factor score (value of common factor) f _it (i =
1 ,. ． , Q, t = 1 ,. ． , T-1), and the magnitude of variance Var (ε _i ) of the unique term ε _it for each issue.

Next, a method of determining the state equation <Equation 2> will be described with reference to FIG.

In process 21, the common factor values obtained in process 14 are used to estimate each common factor by an AR model (autoregressive model) known as a time series model. This method is described in, for example, Taku Yamamoto, "Economy Time Series Analysis," p56-p76, Sobunsha. As a result, the j-th time-series structure in <Equation 2> is shown.
The order kj of the time series structure of factors and the coefficient b _jk (k =
1 ,. ． , Kj), the magnitude of the variance of the disturbance term η _jt Var
(Η _j ) is obtained. This is an approximate value of the state equation structure.

In the process 22, the state equation previously obtained and
Using the Kalman filter algorithm generated from the observation equation obtained in process 14, the common factor f _jt (j =
1 ,. ． , Q, t = 1 ,. ． , T-1) is re-estimated.
The Kalman filter algorithm is the observed value x _it (i =
1 ,. ． , N, t = 1 ,. ． , T-1), the best estimator of the common factor, which is a state variable, is derived. This arithmetic method is described, for example, in Taku Arimoto, “Kalman Filter,” Chapter 3, Industrial Books.

In the process 23, the re-estimated common factor f
_{For jt} (j = 1, .., q, t = 1, .., T-1), similar to the process 21, for each common factor, A
R model

The state equation structure is estimated by (autoregressive model). This allows

In Equation 2, the order kj of the time series structure of the j-th factor indicating the time series structure, the coefficient b _jk (k = 1, ..., kj), and the magnitude of the variance Var (η _j ) of the disturbance term η _jt. Is required. This is the improved value of the state equation structure.

In the decision 24, it is decided whether or not the time series structure of the state equation has converged. The judgment conditions are that the order of the time series structure of each common factor is invariant and that the coefficient b _jk (j =
1 ,. ． ． q, k = 1 ,. ． , Kj) is below a certain value, it is determined that a converged equation of state is obtained.
If not converged, the processings 22 and 23 are repeated again,
Seeking improved structure.

In FIG. 4, the predictability is checked by grouping the stocks including the stock to be predicted. The conditions for predictability are that the ratio that can be explained by the common factors related to the issue is large, and that the common factors have a time series structure.

In the judgment 31, it is judged whether or not the effective commonality showing the above condition is a fixed value (1 or less) or more. If it is over a certain value, it is judged that the predictability of this grouping is low and it is rejected. When the value is equal to or larger than the certain value, the process proceeds to the prediction process of process 32. Effective predictability is calculated as follows.

[0042]

[Equation 5]

That is, it is the sum of squares of the elements of the factor loading matrix for the relevant stock i except for the degree of the time series of the state equation of the common factor f _jt other than 0 (at this time, white noise has no predictability). .. The value of the constant value is, for example, about 0.4. Generally, if this value is made large, the predictability is high, but if the condition is satisfied, it will be rejected less often.

In process 32, the stock price in the m-th future is predicted.
First, the common factor variable is predicted in order from the period T to the period T + m-1. At this time, when future data comes to the right side,
Replace with the predicted value obtained previously. In addition, 0 is set for a factor having no time-series structure, as is clear from the equation. Next, a prediction is made for the rate of return of the designated brand from the period T to the period T + m-1. And the brand i of m-term ahead
The stock price P _{iT + m} is the current stock price P _iT and the period T to T + m−
It is calculated based on the forecast rate of return until the first quarter. Where μ,
σ is, as shown in <Numerical expression> 4, the analysis period (1, ...,
It is an average value and standard deviation of stock data in T).

Returning to FIG. 1, the processing 4 will be described. As described above, the prediction by the multivariate analysis was performed on the group including the stock i in the processing 2 and the processing 3, and the stock price of the stock i was predicted when the prediction was possible. In process 4, statistics such as the average value, standard deviation, and t value of the stock price forecast values for issue i are calculated and output from the forecast results of a plurality of trials, and the stock price forecast ends. The user can know the average of the predicted values of the stock price from the average value, can know the degree of dispersion of the predicted values from the standard deviation, and can know the confidence interval.

[0046]

The financial asset prediction system of the present invention has the following effects.

First, the prediction of an individual asset is associated with a plurality of assets using multivariate analysis to improve the predictability, and the prediction of the asset desired to be predicted is made based on the price structure based on the estimated state space model. Giving a way to determine if there is a possibility. Then, by using a super computer, it is possible to execute a large number of simulations for a group of assets including assets to be predicted, and since statistical processing is performed based on the predicted price obtained by each simulation, the predicted value There is a feature that you can know statistics such as reliability.

Secondly, since the structure of the state equation can be accurately estimated by the Kalman filter based on the observation equation and the state equation, the predictability is increased.

When the present invention was applied to the stocks constituting the Nikkei 225, the variance of the prediction error could be improved by 5% compared with the conventional method.

[Brief description of drawings]

FIG. 1 is a block diagram of a financial asset prediction system according to an embodiment of the present invention.

FIG. 2 is a method of estimating an observation equation.

FIG. 3 is a method of estimating a state equation.

FIG. 4 is a predictability check and prediction method.

[Explanation of symbols]

Claims (3)

[Claims] 1. A means for designating a financial asset whose price is to be predicted, a means for generating a uniform random number together with the asset to create an asset group composed of a plurality of other selected assets, and an asset for the asset group. Based on a state space model consisting of observation equations and state equations described by prices and state variables, a means for estimating the structure of the assets that make up the asset group from the past prices, and estimating the predictability of the assets. When it is judged that the effective commonality calculated from the coefficient of the observed equation is determined and it is predictable, a means for predicting a state variable based on the state equation, and the observation equation based on the predicted state variable A means for more predicting the asset price, and a means for carrying out the series of procedures for the asset group a number of times to obtain a statistic such as an average value or standard deviation of the forecast values based on the forecast values calculated by the asset group Equipped with Financial asset price prediction system according to claim Rukoto. 2. The asset price prediction, wherein the structure estimation of the observation equation in the state space model according to claim 1 is determined from a past price of assets constituting the asset group using a factor analysis model. system. 3. The structure estimation of the state equation in the state space model according to claim 1, the approximate value of the state variable is obtained from the structural equation for which structure estimation has been completed, and the state is determined by a steady time series analysis on the approximate state variable data. The approximate structure of the equation is obtained, the past asset price as the observation data, the improved value of the state variable is obtained by the Kalman filter generated from the observed equation and the state equation, and the state is obtained by the steady time series analysis for the improved value. An asset price forecasting system characterized by re-estimating the structure of an equation and repeating the procedure until the state equation structure converges.