Distributed Lag
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Distributed Lag
In statistics and econometrics, a distributed lag model is a model for time series data in which a regression equation is used to predict current values of a dependent variable based on both the current values of an explanatory variable and the lagged (past period) values of this explanatory variable. The starting point for a distributed lag model is an assumed structure of the form :y_t = a + w_0x_t + w_1x_ + w_2x_ + ... + \text or the form :y_t = a + w_0x_t + w_1x_ + w_2x_ + ... + w_nx_ + \text, where ''y''''t'' is the value at time period ''t'' of the dependent variable ''y'', ''a'' is the intercept term to be estimated, and ''w''''i'' is called the lag weight (also to be estimated) placed on the value ''i'' periods previously of the explanatory variable ''x''. In the first equation, the dependent variable is assumed to be affected by values of the independent variable arbitrarily far in the past, so the number of lag weights is infinite and the model is called an ''infinite ...
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Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ...
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Econometrics
Econometrics is the application of Statistics, statistical methods to economic data in order to give Empirical evidence, empirical content to economic relationships.M. Hashem Pesaran (1987). "Econometrics," ''The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 [pp. 8–22]. Reprinted in J. Eatwell ''et al.'', eds. (1990). ''Econometrics: The New Palgrave''p. 1[pp. 1–34].Abstract (The New Palgrave Dictionary of Economics, 2008 revision by J. Geweke, J. Horowitz, and H. P. Pesaran). More precisely, it is "the quantitative analysis of actual economic Phenomenon, phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships". Jan Tinbergen is one of the two founding fathers of econometrics. The other, Ragnar Frisch, also coined the term in the sense in which it is used toda ...
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Time Series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series ''analysis'' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series ''forecasting' ...
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Linear Regression
In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called '' simple linear regression''; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on ...
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Dependent Variable
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (e.g. human population size) to predict future values (the dependent variable). Of the two, it is always the dependent variable whose variation is being studied, by altering inputs, also known as regressors in a statistical context. In an experiment, any variable that can be attributed a value without attributing a value to any other variable is called an in ...
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Explanatory Variable
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (e.g. human population size) to predict future values (the dependent variable). Of the two, it is always the dependent variable whose variation is being studied, by altering inputs, also known as regressors in a statistical context. In an experiment, any variable that can be attributed a value without attributing a value to any other variable is called an ind ...
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Ordinary Least Squares
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable. Geometrically, this is seen as the sum of the squared distances, parallel to the axis of the dependent variable, between each data point in the set and the corresponding point on the regression surface—the smaller the differences, the better the model fits the data. The resulting estimator can be expressed by a simple formula, especially in the case of a simple linear regression, in which there is a single regressor on the right side of the regression equation. The OLS estimator is consiste ...
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Multicollinearity
In statistics, multicollinearity (also collinearity) is a phenomenon in which one predictor variable in a multiple regression model can be linearly predicted from the others with a substantial degree of accuracy. In this situation, the coefficient estimates of the multiple regression may change erratically in response to small changes in the model or the data. Multicollinearity does not reduce the predictive power or reliability of the model as a whole, at least within the sample data set; it only affects calculations regarding individual predictors. That is, a multivariate regression model with collinear predictors can indicate how well the entire bundle of predictors predicts the outcome variable, but it may not give valid results about any individual predictor, or about which predictors are redundant with respect to others. Note that in statements of the assumptions underlying regression analyses such as ordinary least squares, the phrase "no multicollinearity" usually refer ...
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Independently And Identically Distributed
In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as ''i.i.d.'', ''iid'', or ''IID''. IID was first defined in statistics and finds application in different fields such as data mining and signal processing. Introduction In statistics, we commonly deal with random samples. A random sample can be thought of as a set of objects that are chosen randomly. Or, more formally, it’s “a sequence of independent, identically distributed (IID) random variables”. In other words, the terms ''random sample'' and ''IID'' are basically one and the same. In statistics, we usually say “random sample,” but in probability it’s more common to say “IID.” * Identically Distributed means that there are no overall trends–the distribution doesn’t fluctuate and all items in the ...
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Shirley Montag Almon
Shirley Montag Almon (February 6, 1935 – September 29, 1975) was an American economist noted for the Almon Lag. Early life and education Almon was born on February 6, 1935, in Saxonburg, Pennsylvania, the oldest of seven children of Harold and Dorothea Montag. She was educated at Goucher College, Baltimore, and then for her PhD at Harvard University (1964). A core element of her PhD was published in ''Econometrica'' (1965) and introduced the now famous technique for estimating distributed lags. Career She went on to work at the Women's Bureau, the National Bureau of Economic Research, The Federal Reserve Bank of San Francisco, the Federal Reserve Board and at both Wesley College and Harvard University. Her most noted post was her appointment to the staff of the President's Council of Economic Advisors in 1966.Blaug, Mark (1985) Great Economists Since Keynes, Harvester Selected publications * * Personal life She married Clopper Almon Jr. on June 14, 1958. She was dia ...
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Econometrica
''Econometrica'' is a peer-reviewed academic journal of economics, publishing articles in many areas of economics, especially econometrics. It is published by Wiley-Blackwell on behalf of the Econometric Society. The current editor-in-chief is Guido Imbens. History ''Econometrica'' was established in 1933. Its first editor was Ragnar Frisch, recipient of the first Nobel Memorial Prize in Economic Sciences in 1969, who served as an editor from 1933 to 1954. Although ''Econometrica'' is currently published entirely in English, the first few issues also contained scientific articles written in French. Indexing and abstracting ''Econometrica'' is abstracted and indexed in: * Scopus * EconLit * Social Science Citation Index According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 5.844, ranking it 22/557 in the category "Economics". Awards issued The Econometric Society aims to attract high-quality applied work in economics for publication in ''Eco ...
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Longitudinal Cohort Study
A prospective cohort study is a longitudinal cohort study that follows over time a group of similar individuals (cohorts) who differ with respect to certain factors under study, to determine how these factors affect rates of a certain outcome. For example, one might follow a cohort of middle-aged truck drivers who vary in terms of smoking habits, to test the hypothesis that the 20-year incidence rate of lung cancer will be highest among heavy smokers, followed by moderate smokers, and then nonsmokers. The prospective study is important for research on the etiology of diseases and disorders. The distinguishing feature of a prospective cohort study is that at the time that the investigators begin enrolling subjects and collecting baseline exposure information, none of the subjects have developed any of the outcomes of interest. After baseline information is collected, subjects in a prospective cohort study are then followed "longitudinally," i.e. over a period of time, usually for ...
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