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Quantile Regression Averaging
Quantile Regression Averaging (QRA) is a forecast combination approach to the computation of prediction intervals. It involves applying quantile regression to the point forecasts of a small number of individual forecasting models or experts. It has been introduced in 2014 by Jakub Nowotarski and Rafał Weron and originally used for probabilistic forecasting of electricity prices and loads. Despite its simplicity it has been found to perform extremely well in practice - the top two performing teams in the ''price track'' of the Global Energy Forecasting Competition (GEFCom2014) used variants of QRA. Introduction The individual point forecasts are used as independent variables and the corresponding observed target variable as the dependent variable in a standard quantile regression setting. The Quantile Regression Averaging method yields an interval forecast of the target variable, but does not use the prediction intervals of the individual methods. One of the reasons for using poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consensus Forecast
Used in a number of sciences, ranging from econometrics to meteorology, consensus forecasts are predictions of the future that are created by combining together 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). Applications can range from forecasting the weather to predicting the annual Gross Domestic Product of a country or the number of cars a company or an individual dealer is likely to sell in a year. While forecasts are often made for future values of a time series, they can also be for one-off events such as the outcome of a presidential election or a football match. Background Forecasting plays a key role in any organisation's planning process as it provides insight into uncertainty. Through simulation, one will be able to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantile Regression
Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares estimates the conditional ''mean'' of the response variable across values of the predictor variables, quantile regression estimates the conditional ''median'' (or other '' quantiles'') of the response variable. Quantile regression is an extension of linear regression used when the conditions of linear regression are not met. Advantages and applications One advantage of quantile regression relative to ordinary least squares regression is that the quantile regression estimates are more robust against outliers in the response measurements. However, the main attraction of quantile regression goes beyond this and is advantageous when conditional quantile functions are of interest. Different measures of central tendency and statistical dispersion can be useful to obtain a more comprehensive analysis of the relationship between variables. In ecology, quantile ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prediction Interval
In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis. Prediction intervals are used in both frequentist statistics and Bayesian statistics: a prediction interval bears the same relationship to a future observation that a frequentist confidence interval or Bayesian credible interval bears to an unobservable population parameter: prediction intervals predict the distribution of individual future points, whereas confidence intervals and credible intervals of parameters predict the distribution of estimates of the true population mean or other quantity of interest that cannot be observed. Introduction For example, if one makes the parametric assumption that the underlying distribution is a normal distribution, and has a sample set , then confidence intervals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economic Forecasting
Economic forecasting is the process of making predictions about the economy. Forecasts can be carried out at a high level of aggregation—for example for GDP, inflation, unemployment or the fiscal deficit—or at a more disaggregated level, for specific sectors of the economy or even specific firms. Economic forecasting is a measure to find out the future prosperity of a pattern of investment and is the key activity in economic analysis. Many institutions engage in economic forecasting: national governments, banks and central banks, consultants and private sector entities such as think-tanks, companies and international organizations such as the International Monetary Fund, World Bank and the OECD. A broad range of forecasts are collected and compiled b"Consensus Economics" Some forecasts are produced annually, but many are updated more frequently. The economist typically considers risks (i.e., events or conditions that can cause the result to vary from their initial estimates). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forecasting
Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual results. Prediction is a similar but more general term. Forecasting might refer to specific formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods or the process of prediction and resolution itself. Usage can vary between areas of application: for example, in hydrology the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific future times, while the term "prediction" is used for more general estimates, such as the number of times floods will occur over a long period. Risk and uncertainty are central to forecasting and prediction; it is generally considered a good practice to indicate the degree of uncertainty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy Forecasting
Energy forecasting includes forecasting demand ( load) and price of electricity, fossil fuels (natural gas, oil, coal) and renewable energy sources (RES; hydro, wind, solar). Forecasting can be both expected price value and probabilistic forecasting. Background When electricity sectors were regulated, utility monopolies used short-term load forecasts to ensure the reliability of supply and long-term demand forecasts as the basis for planning and investing in new capacity. However, since the early 1990s, the process of deregulation and the introduction of competitive electricity markets have been reshaping the landscape of the traditionally monopolistic and government-controlled power sectors. In many countries worldwide, electricity is now traded under market rules using spot and derivative contracts. At the corporate level, electricity load and price forecasts have become a fundamental input to energy companies’ decision making mechanisms. The costs of over- or undercontract ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electricity Price Forecasting
Electricity price forecasting (EPF) is a branch of energy forecasting which focuses on predicting the spot and forward prices in wholesale electricity markets. Over the last 15 years electricity price forecasts have become a fundamental input to energy companies’ decision-making mechanisms at the corporate level. Since the early 1990s, the process of deregulation and the introduction of competitive electricity markets have been reshaping the landscape of the traditionally monopolistic and government-controlled power sectors. Throughout Europe, North America and Australia, electricity is now traded under market rules using spot and derivative contracts. However, electricity is a very special commodity: it is economically non-storable and power system stability requires a constant balance between production and consumption. At the same time, electricity demand depends on weather (temperature, wind speed, precipitation, etc.) and the intensity of business and everyday activities ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ensemble Averaging
In machine learning, particularly in the creation of artificial neural networks, ensemble averaging is the process of creating multiple models and combining them to produce a desired output, as opposed to creating just one model. Frequently an ensemble of models performs better than any individual model, because the various errors of the models "average out." Overview Ensemble averaging is one of the simplest types of committee machines. Along with boosting, it is one of the two major types of static committee machines.Haykin, Simon. Neural networks : a comprehensive foundation. 2nd ed. Upper Saddle River N.J.: Prentice Hall, 1999. In contrast to standard network design in which many networks are generated but only one is kept, ensemble averaging keeps the less satisfactory networks around, but with less weight.Hashem, S. "Optimal linear combinations of neural networks." Neural Networks 10, no. 4 (1997): 599–614. The theory of ensemble averaging relies on two properties o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Committee Machine
A committee machine is a type of artificial neural network using a divide and conquer strategy in which the responses of multiple neural networks (experts) are combined into a single response.HAYKIN, S. Neural Networks - A Comprehensive Foundation. Second edition. Pearson Prentice Hall: 1999. The combined response of the committee machine is supposed to be superior to those of its constituent experts. Compare with ensembles of classifiers. Types Static structures In this class of committee machines, the responses of several predictors (experts) are combined by means of a mechanism that does not involve the input signal, hence the designation static. This category includes the following methods: *Ensemble averaging In ensemble averaging, outputs of different predictors are linearly combined to produce an overall output. * Boosting In boosting, a weak algorithm is converted into one that achieves arbitrarily high accuracy. Dynamic structures In this second class of committee ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Absolute Deviations
Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical optimality criterion and a statistical optimization technique based minimizing the ''sum of absolute deviations'' (sum of absolute residuals or sum of absolute errors) or the ''L''1 norm of such values. It is analogous to the least squares technique, except that it is based on ''absolute values'' instead of squared values. It attempts to find a function which closely approximates a set of data by minimizing residuals between points generated by the function and corresponding data points. The LAD estimate also arises as the maximum likelihood estimate if the errors have a Laplace distribution. It was introduced in 1757 by Roger Joseph Boscovich. Formulation Suppose that the data set consists of the points (''x''''i'', ''y''''i'') with ''i'' = 1, 2, ..., ''n''. We want to find a function ''f'' such that f(x_i)\approx y_i. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Survey Of Professional Forecasters
The Survey of Professional Forecasters (SPF) is a quarterly survey of macroeconomic forecasts for the economy of the United States issued by the Federal Reserve Bank of Philadelphia. It is the oldest such survey in the United States. The survey includes an "anxious index" that estimates the probability of a decline in real GDP. History The survey began in 1968 and was conducted by the American Statistical Association (ASA) and the National Bureau of Economic Research (NBER). The Federal Reserve Bank of Philadelphia took over the survey in 1990. In its early days (prior to the takeover by the Federal Reserve Bank of Philadelphia) the survey was often referred to in the academic literature as the ASA-NBER survey. In May 2008, it was announced that SPF would be adding an industry classification variable for its survey respondents, so that researchers could more easily determine how people's forecasts related to the industry they were from. Variables The Survey of Professional For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
