Weather forecastingWeather forecasting is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th century. Weather forecasts are made by collecting quantitative data about the current state of the atmosphere, land, and ocean and using meteorology to project how the atmosphere will change at a given place.
Multivariate statisticsMultivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied.
Singular spectrum analysisIn time series analysis, singular spectrum analysis (SSA) is a nonparametric spectral estimation method. It combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. Its roots lie in the classical Karhunen (1946)–Loève (1945, 1978) spectral decomposition of time series and random fields and in the Mañé (1981)–Takens (1981) embedding theorem. SSA can be an aid in the decomposition of time series into a sum of components, each having a meaningful interpretation.
Multivariate random variableIn probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value. The individual variables in a random vector are grouped together because they are all part of a single mathematical system — often they represent different properties of an individual statistical unit.
Consensus forecastUsed in a number of sciences, ranging from econometrics to meteorology, consensus forecasts are predictions of the future that are created by combining several separate forecasts which have often been created using different methodologies. Also known as combining forecasts, forecast averaging or model averaging (in econometrics and statistics) and committee machines, ensemble averaging or expert aggregation (in machine learning).
Regression analysisIn statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features'). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion.
Dependent and independent variablesDependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables 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.
Nonlinear regressionIn statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations. In nonlinear regression, a statistical model of the form, relates a vector of independent variables, , and its associated observed dependent variables, . The function is nonlinear in the components of the vector of parameters , but otherwise arbitrary.
Homoscedasticity and heteroscedasticityIn statistics, a sequence (or a vector) of random variables is homoscedastic (ˌhoʊmoʊskəˈdæstɪk) if all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance. The spellings homoskedasticity and heteroskedasticity are also frequently used.
Segmented regressionSegmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various independent variables. Segmented regression is useful when the independent variables, clustered into different groups, exhibit different relationships between the variables in these regions.
InflationIn economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduction in the purchasing power of money. The opposite of inflation is deflation, a decrease in the general price level of goods and services. The common measure of inflation is the inflation rate, the annualized percentage change in a general price index.
Forecast errorIn statistics, a forecast error is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon of interest. Since the forecast error is derived from the same scale of data, comparisons between the forecast errors of different series can only be made when the series are on the same scale. In simple cases, a forecast is compared with an outcome at a single time-point and a summary of forecast errors is constructed over a collection of such time-points.
