> Что занятно? Было бы понятнее, если бы вы указали, что именно в лекции
> относится к обсуждаемой теме. По-моему, у Гранжера нет утверждения, что
> для прогнозирования темпа роста экономики достаточно временных рядов
> только этого одного показателя. Как раз наоборот:
Вот о роли статистики:
However, by the middle of the last millennium it be-came clear that some objects were not deterministic, they had to be described with the use of probabilities, so that Mathematics grew a substantial sub-field known as Statistics. This later became involved with the analysis of data and a number of methods have been developed for data having what may be called standard properties.
However, in some areas of application, the data that they generated were found to be not standard, and so special sub-sub-fields needed to be develo-ped. For example, Biology produced Biometrics, Psychology gave us Psycho-metrics, and Economics produced Econometrics.
Вот об экономических данных
There are many types of economic data, but the type considered by Rob Engle and myself is know as time series. Consider the measurement of unem-ployment rates which is an important measure of the health of the economy. Figures are gathered by a government agency and each month a new number is announced. Next month there will be another value, and so forth. String these value together in a simple graph and you get a time series. Rather than show a diagram, I would rather you use internal visualization (I think that you learn more that way). Suppose that you have a loosely strung string of pearls which you throw down, gently, onto a hard table top with the string of pearls roughly stretched out. You will have created a time series with time represented by the distance down the table, the size of the variable as the distance from the bottom edge of the table to a point, and the set of pearls giving the points in the series. As the placement of one pearl will im-pact where the next one lies, because they are linked together, this series will appear to be rather smooth, and will not have big fluctuations in value...
Ещё об особенностях экономических данных
Many of these series are rather smooth, moving with local trends or with long swings, but the swings are not regular. It is this relative smoothness that makes them unsuitable for analysis with standard statistical procedures, which assumes data to have a property know as stationarity. Many series in economics, particularly in finance and macroeconomics, do not have this property and can be called integrated or, sometimes incorrectly, non-stationary. However, when expressed in terms of changes or rates of returns, these derived series appear closer to being stationary. The string of pearls would be integrated as it is a smooth series.
Вот о методе анализа экономических данных
Methods to analyze a single integrated series had been proposed previous-ly by Box and Jenkins (1970) and others, but the joint analysis of pairs, or more, of such series was missing an important feature. It turns out that the difference between a pair of integrated series can be stationary, and this prop-erty is known as cointegration.
Box & Jenkins создали методологию ARMA, которая как раз описывает случайную переменную с помощью истории её реализации. Granger же занимался системами случайных переменных, поэтому, конечно, всё внимание в его лекции отведено им.
Вот об ECM
Once we know that a pair of variables has the cointegration property it fol-lows that they have a number of other interesting and useful properties. For example, they must both be cointegrated with the same hidden common fac-tor. Further, they can be considered to be generated by what is know as the error-correction model, in which the change of one of the series is ex-plained in terms of the lag of the difference between the series, possibly after scaling, and lags of the differences of each series. The other series will be rep-resented by a similar dynamic equation.
Т.е. в классе моделей ECM изменение серии объясняется через лаги изменений серии и её уровня. Правда, это касается нескольких переменных (но для одной переменной см. выше про ARMA).
Вот о роли эконометристов и о прогнозировании
The modern macro economy is large, diffuse, and difficult to define, mea-sure, and control. Economists attempt to build models that will approximate it, that will have similar major properties so that one can conduct simple ex-periments on them, such as determining the impacts of alternative policies or the long-run implications of some new institution. Economic theorists do this using constraints suggested by the theory, whereas the econometrician builds empirical models using what is hopefully relevant data and which captures the main properties of the economy in the past. All models simply assume that the model is correct and extrapolate from there, but hopefully with an indication of uncertainty around future values. Error-correction models have been a popular form of macro model in re-cent years, and cointegration is a common element. Applications have been considered using almost all major variables including investment, taxes, con-sumption, employment, interest rates, government expenditure, and so forth. It is these types of equations that central banks, the Federal Reserve Bank, and various model builders have found useful for policy simulations and other considerations.
(Выделение жирным - моё)
Вот о линейных моделях:
As a brief aside for those of you with more technical training, what I have been telling you about so far has mostly been for concepts using linear models. Everything can be generalized to the nonlinear situation and recently efforts have been pushing into using similar concepts in conditional distributions, which is a very general form. It appears that causality will play a basic role in the generalization of the error-correction model, but that is still a work-in-progress.
(выделение - моё). Т.е. линейные модели используются самым распространённым образом.
> Методика экстраполяции дает для темпов роста в период 90-х годов величину
> 2-3%. В действительности, как мы знаем, темпы "роста" были отрицательными.
Действительность - это понятие условное. Если в действительности выпал "орёл", то это не значит, что не могла выпасть "решка".
> Помешала перестройка? Да, но ведь она реально была, а экстраполяция (какие
> бы формальные математические методы ни использовала) такую возможность не
> учитывала, поэтому и дала ошибочный результат.
Нет, это ошибочное мнение. Экстраполяция верна при данном режиме. В результате перестройки произошло изменение режима под воздействием внешнего (экзогенного) фактора. Т.е. этот фактор не был частью системы. Перестройка не была единственно возможным и детерминированным вариантом. Возможны были другие варианты. Задача экстраполяции - оценить, как повела бы себя экономическая система при условии сохранения того же режима. Как пример - война. Война - это внешний фактор, случайный и имеющий весьма неприятные последствия, вносящий разрыв.
Re: Отмечу цитаты - Иванов (А. Гуревич)23.08.2007 10:05:01 (33, 3472 b)
