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Utilization of statistics and statistical method is frequently seen in everyday life. The terms, which show economic trends such as unemployment rate, consumer price index, and wholesale price index, are frequently used on television and in newspapers. Likewise, new developments have been made in the way data is collected and analyzed with close relevance to the way people live.

## §1 Japanese economy examined through AR model

The animation depicts the predictions for machinery orders and industrial production indexes (by year on year rate) after application of the multidimensional AR model to the following six variables. This shows that the predicted path of the recovery process in every other month from January, 1998, slowed down as time elapsed both in machinery orders and in industrial production judging from the model based on past data. It also explicitly shows the decline of the Japanese economy in this period.

[Variables used] : monetary base, interest rate on ten-year-term government bonds, wholesale price index, industrial production index, machinery orders, exchange rate (monthly data from January, 1983, to September, 1998)

[Machinery orders]
black : results;
red : prediction from January, 1998;
yellow-green : prediction from March, 1998;
blue : prediction from May, 1998;
yellow : prediction from July, 1998;
blue-green : prediction from September, 1998

[Industrial production index]
black: results;
red: prediction from January, 1998;
yellow-green: prediction from March, 1998;
blue: prediction from May, 1998;
yellow: prediction from July, 1998;
blue-green: prediction from September, 1998

## §2 The shortest route

What means of transportation should be used to go from the Institute of Statistical Mathematics (Hiroo, Shibuya-ku, Tokyo) to Narita Airport in the shortest time?

This question can be answered easily by modeling the situation as follows. We suppose a network with transit stations as the nodes as shown in the figure, and we apply an algorithm to find a shortest path from one node to another.

This is an easy example, but actually we are developing modeling techniques and algorithms for more complicated optimization problems.

## §3 Analysis of threeway deadlock

The situation of "threeway deadlock", a situation much like the game of stone, scissors, paper, in which paper beats stone, stone beats scissors, and scissors beat paper, is sometimes seen in everyday life and sports.

The statistical model makes it possible to quantitatively analyse structures such as "threeway deadlock".

The figure is based on the outcomes of all of the games in the Pacific League (a Japanese professional baseball league) in 1995.

Teams relatively hard to beat are listed in order clockwise (for example, Daiei relative to Orix) . In this case, the actual number of games won fell short of expectations. Counterclockwise teams (for example, Seibu relative to Orix) are teams relatively easy to beat.

Orix, Daiei, Lotte, and Seibu form a big quadrangle clockwise loop.

This shows that in that year there was a fourway deadlock among these four teams rather than a threeway deadlock.

## §4 Extraction of economic trend

Statistical methods attract public attention also as a way to objectively judge economic conditions.

By decomposing the gross domestic product (GDP) into trend, seasonal component, cyclical fluctuation component, and irregular component using the seasonal adjustment program developed by the Institute of Statistical Mathematics, the cyclical fluctuation component corresponds well to conventional "economic conditions".

We are actually investigating a way to judge the economic conditions quickly through the improvement of this method.

Gross domestic product data

Economic fluctuation component and economic turning point
The horizontal line represents the point of time considered to be the "turning point" in economic conditions.

## §5 Analysis and representation of geographical information

Geographical information is used in a variety of manners, from the daily weather reports to adminstrative planning for disaster prevention measures.

The Institute of Statistical Mathematics is also working on a way to analyse association effects among various variables, by representing on a map various data with geographical attributes such as the number of teachers to number of new university students by the school that they graduated from.